Viewing the Results

Printing a List of the Section Properties

A list of section properties that have been calculated by various analyses can be printed to the terminal using the display_results() method that belongs to every CrossSection object.

CrossSection.display_results(fmt='8.6e')

Prints the results that have been calculated to the terminal.

Parameters:fmt (string) – Number formatting string

The following example displays the geometric section properties for a 100D x 50W rectangle with three digits after the decimal point:

import sectionproperties.pre.sections as sections
from sectionproperties.analysis.cross_section import CrossSection

geometry = sections.RectangularSection(d=100, b=50)
mesh = geometry.create_mesh(mesh_sizes=[5])

section = CrossSection(geometry, mesh)
section.calculate_geometric_properties()

section.display_results(fmt='.3f')

Getting Specific Section Properties

Alternatively, there are a number of methods that can be called on the CrossSection object to return a specific section property:

Cross-Section Area

CrossSection.get_area()

Returns:Cross-section area Return type:float

section = CrossSection(geometry, mesh)
section.calculate_geometric_properties()
area = section.get_area()

Cross-Section Perimeter

CrossSection.get_perimeter()

Returns:Cross-section perimeter Return type:float

section = CrossSection(geometry, mesh)
section.calculate_geometric_properties()
perimeter = section.get_perimeter()

Axial Rigidity

If material properties have been specified, returns the axial rigidity of the section.

CrossSection.get_ea()

Returns:Modulus weighted area (axial rigidity) Return type:float

section = CrossSection(geometry, mesh)
section.calculate_geometric_properties()
ea = section.get_ea()

First Moments of Area

CrossSection.get_q()

Returns:First moments of area about the global axis (qx, qy) Return type:tuple(float, float)

section = CrossSection(geometry, mesh)
section.calculate_geometric_properties()
(qx, qy) = section.get_q()

Second Moments of Area

CrossSection.get_ig()

Returns:Second moments of area about the global axis (ixx_g, iyy_g, ixy_g) Return type:tuple(float, float, float)

section = CrossSection(geometry, mesh)
section.calculate_geometric_properties()
(ixx_g, iyy_g, ixy_g) = section.get_ig()

CrossSection.get_ic()

Returns:Second moments of area centroidal axis (ixx_c, iyy_c, ixy_c) Return type:tuple(float, float, float)

section = CrossSection(geometry, mesh)
section.calculate_geometric_properties()
(ixx_c, iyy_c, ixy_c) = section.get_ic()

CrossSection.get_ip()

Returns:Second moments of area about the principal axis (i11_c, i22_c) Return type:tuple(float, float)

section = CrossSection(geometry, mesh)
section.calculate_geometric_properties()
(i11_c, i22_c) = section.get_ip()

Elastic Centroid

CrossSection.get_c()

Returns:Elastic centroid (cx, cy) Return type:tuple(float, float)

section = CrossSection(geometry, mesh)
section.calculate_geometric_properties()
(cx, cy) = section.get_c()

Section Moduli

CrossSection.get_z()

Returns:Elastic section moduli about the centroidal axis with respect to the top and bottom fibres (zxx_plus, zxx_minus, zyy_plus, zyy_minus) Return type:tuple(float, float, float, float)

section = CrossSection(geometry, mesh)
section.calculate_geometric_properties()
(zxx_plus, zxx_minus, zyy_plus, zyy_minus) = section.get_z()

CrossSection.get_zp()

Returns:Elastic section moduli about the principal axis with respect to the top and bottom fibres (z11_plus, z11_minus, z22_plus, z22_minus) Return type:tuple(float, float, float, float)

section = CrossSection(geometry, mesh)
section.calculate_geometric_properties()
(z11_plus, z11_minus, z22_plus, z22_minus) = section.get_zp()

Radii of Gyration

CrossSection.get_rc()

Returns:Radii of gyration about the centroidal axis (rx, ry) Return type:tuple(float, float)

section = CrossSection(geometry, mesh)
section.calculate_geometric_properties()
(rx, ry) = section.get_rc()

CrossSection.get_rp()

Returns:Radii of gyration about the principal axis (r11, r22) Return type:tuple(float, float)

section = CrossSection(geometry, mesh)
section.calculate_geometric_properties()
(r11, r22) = section.get_rp()

Principal Axis Angle

CrossSection.get_phi()

Returns:Principal bending axis angle Return type:float

section = CrossSection(geometry, mesh)
section.calculate_geometric_properties()
phi = section.get_phi()

Torsion Constant

CrossSection.get_j()

Returns:St. Venant torsion constant Return type:float

section = CrossSection(geometry, mesh)
section.calculate_geometric_properties()
section.calculate_warping_properties()
j = section.get_j()

Shear Centre

CrossSection.get_sc()

Returns:Centroidal axis shear centre (elasticity approach) (x_se, y_se) Return type:tuple(float, float)

section = CrossSection(geometry, mesh)
section.calculate_geometric_properties()
section.calculate_warping_properties()
(x_se, y_se) = section.get_sc()

CrossSection.get_sc_p()

Returns:Principal axis shear centre (elasticity approach) (x11_se, y22_se) Return type:tuple(float, float)

section = CrossSection(geometry, mesh)
section.calculate_geometric_properties()
section.calculate_warping_properties()
(x11_se, y22_se) = section.get_sc_p()

Trefftz’s Shear Centre

CrossSection.get_sc_t()

Returns:Centroidal axis shear centre (Trefftz’s approach) (x_st, y_st) Return type:tuple(float, float)

section = CrossSection(geometry, mesh)
section.calculate_geometric_properties()
section.calculate_warping_properties()
(x_st, y_st) = section.get_sc_t()

Warping Constant

CrossSection.get_gamma()

Returns:Warping constant Return type:float

section = CrossSection(geometry, mesh)
section.calculate_geometric_properties()
section.calculate_warping_properties()
gamma = section.get_gamma()

Shear Area

CrossSection.get_As()

Returns:Shear area for loading about the centroidal axis (A_sx, A_sy) Return type:tuple(float, float)

section = CrossSection(geometry, mesh)
section.calculate_geometric_properties()
section.calculate_warping_properties()
(A_sx, A_sy) = section.get_As()

CrossSection.get_As_p()

Returns:Shear area for loading about the principal bending axis (A_s11, A_s22) Return type:tuple(float, float)

section = CrossSection(geometry, mesh)
section.calculate_geometric_properties()
section.calculate_warping_properties()
(A_s11, A_s22) = section.get_As_p()

Monosymmetry Constants

CrossSection.get_beta()

Returns:Monosymmetry constant for bending about both global axes (beta_x_plus, beta_x_minus, beta_y_plus, beta_y_minus). The plus value relates to the top flange in compression and the minus value relates to the bottom flange in compression. Return type:tuple(float, float, float, float)

section = CrossSection(geometry, mesh)
section.calculate_geometric_properties()
section.calculate_warping_properties()
(beta_x_plus, beta_x_minus, beta_y_plus, beta_y_minus) = section.get_beta()

CrossSection.get_beta_p()

Returns:Monosymmetry constant for bending about both principal axes (beta_11_plus, beta_11_minus, beta_22_plus, beta_22_minus). The plus value relates to the top flange in compression and the minus value relates to the bottom flange in compression. Return type:tuple(float, float, float, float)

section = CrossSection(geometry, mesh)
section.calculate_geometric_properties()
section.calculate_warping_properties()
(beta_11_plus, beta_11_minus, beta_22_plus, beta_22_minus) = section.get_beta_p()

Plastic Centroid

CrossSection.get_pc()

Returns:Centroidal axis plastic centroid (x_pc, y_pc) Return type:tuple(float, float)

section = CrossSection(geometry, mesh)
section.calculate_geometric_properties()
section.calculate_plastic_properties()
(x_pc, y_pc) = section.get_pc()

CrossSection.get_pc_p()

Returns:Principal bending axis plastic centroid (x11_pc, y22_pc) Return type:tuple(float, float)

section = CrossSection(geometry, mesh)
section.calculate_geometric_properties()
section.calculate_plastic_properties()
(x11_pc, y22_pc) = section.get_pc_p()

Plastic Section Moduli

CrossSection.get_s()

Returns:Plastic section moduli about the centroidal axis (sxx, syy) Return type:tuple(float, float)

If material properties have been specified, returns the plastic moment \(M_p = f_y S\).

section = CrossSection(geometry, mesh)
section.calculate_geometric_properties()
section.calculate_plastic_properties()
(sxx, syy) = section.get_s()

CrossSection.get_sp()

Returns:Plastic section moduli about the principal bending axis (s11, s22) Return type:tuple(float, float)

If material properties have been specified, returns the plastic moment \(M_p = f_y S\).

section = CrossSection(geometry, mesh)
section.calculate_geometric_properties()
section.calculate_plastic_properties()
(s11, s22) = section.get_sp()

Shape Factors

CrossSection.get_sf()

Returns:Centroidal axis shape factors with respect to the top and bottom fibres (sf_xx_plus, sf_xx_minus, sf_yy_plus, sf_yy_minus) Return type:tuple(float, float, float, float)

section = CrossSection(geometry, mesh)
section.calculate_geometric_properties()
section.calculate_plastic_properties()
(sf_xx_plus, sf_xx_minus, sf_yy_plus, sf_yy_minus) = section.get_sf()

CrossSection.get_sf_p()

Returns:Principal bending axis shape factors with respect to the top and bottom fibres (sf_11_plus, sf_11_minus, sf_22_plus, sf_22_minus) Return type:tuple(float, float, float, float)

section = CrossSection(geometry, mesh)
section.calculate_geometric_properties()
section.calculate_plastic_properties()
(sf_11_plus, sf_11_minus, sf_22_plus, sf_22_minus) = section.get_sf_p()

Section Property Centroids Plots

A plot of the centroids (elastic, plastic and shear centre) can be produced with the finite element mesh in the background:

CrossSection.plot_centroids(pause=True)

Plots the elastic centroid, the shear centre, the plastic centroids and the principal axis, if they have been calculated, on top of the finite element mesh.

Parameters:pause (bool) – If set to true, the figure pauses the script until the window is closed. If set to false, the script continues immediately after the window is rendered. Returns:Matplotlib figure and axes objects (fig, ax) Return type:(matplotlib.figure.Figure, matplotlib.axes)

The following example analyses a 200 PFC section and displays a plot of the centroids:

import sectionproperties.pre.sections as sections
from sectionproperties.analysis.cross_section import CrossSection

geometry = sections.PfcSection(d=200, b=75, t_f=12, t_w=6, r=12, n_r=8)
mesh = geometry.create_mesh(mesh_sizes=[2.5])

section = CrossSection(geometry, mesh)
section.calculate_geometric_properties()
section.calculate_warping_properties()
section.calculate_plastic_properties()

section.plot_centroids()

Plot of the centroids generated by the above example.

The following example analyses a 150x90x12 UA section and displays a plot of the centroids:

import sectionproperties.pre.sections as sections
from sectionproperties.analysis.cross_section import CrossSection

geometry = sections.AngleSection(d=150, b=90, t=12, r_r=10, r_t=5, n_r=8)
mesh = geometry.create_mesh(mesh_sizes=[2.5])

section = CrossSection(geometry, mesh)
section.calculate_geometric_properties()
section.calculate_warping_properties()
section.calculate_plastic_properties()

section.plot_centroids()

Plot of the centroids generated by the above example.

Plotting Cross-Section Stresses

There are a number of methods that can be called from a StressResult object to plot the various cross-section stresses. These methods take the following form:

StressResult.plot_(stress/vector)_(action)_(stresstype)

where:

• stress denotes a contour plot and vector denotes a vector plot.
• action denotes the type of action causing the stress e.g. mxx for bending moment about the x-axis. Note that the action is omitted for stresses caused by the application of all actions.
• stresstype denotes the type of stress that is being plotted e.g. zx for the x-component of shear stress.

The examples shown in the methods below are performed on a 150x90x12 UA (unequal angle) section. The CrossSection object is created below:

import sectionproperties.pre.sections as sections
from sectionproperties.analysis.cross_section import CrossSection

geometry = sections.AngleSection(d=150, b=90, t=12, r_r=10, r_t=5, n_r=8)
mesh = geometry.create_mesh(mesh_sizes=[2.5])
section = CrossSection(geometry, mesh)

Primary Stress Plots

Axial Stress (\(\sigma_{zz,N}\))

StressPost.plot_stress_n_zz(pause=True)

Produces a contour plot of the normal stress \(\sigma_{zz,N}\) resulting from the axial load \(N\).

Parameters:pause (bool) – If set to true, the figure pauses the script until the window is closed. If set to false, the script continues immediately after the window is rendered. Returns:Matplotlib figure and axes objects (fig, ax) Return type:(matplotlib.figure.Figure, matplotlib.axes)

The following example plots the normal stress within a 150x90x12 UA section resulting from an axial force of 10 kN:

import sectionproperties.pre.sections as sections
from sectionproperties.analysis.cross_section import CrossSection

geometry = sections.AngleSection(d=150, b=90, t=12, r_r=10, r_t=5, n_r=8)
mesh = geometry.create_mesh(mesh_sizes=[2.5])
section = CrossSection(geometry, mesh)

section.calculate_geometric_properties()
section.calculate_warping_properties()
stress_post = section.calculate_stress(N=10e3)

stress_post.plot_stress_n_zz()

Contour plot of the axial stress.

Bending Stress (\(\sigma_{zz,Mxx}\))

StressPost.plot_stress_mxx_zz(pause=True)

Produces a contour plot of the normal stress \(\sigma_{zz,Mxx}\) resulting from the bending moment \(M_{xx}\).

Parameters:pause (bool) – If set to true, the figure pauses the script until the window is closed. If set to false, the script continues immediately after the window is rendered. Returns:Matplotlib figure and axes objects (fig, ax) Return type:(matplotlib.figure.Figure, matplotlib.axes)

The following example plots the normal stress within a 150x90x12 UA section resulting from a bending moment about the x-axis of 5 kN.m:

import sectionproperties.pre.sections as sections
from sectionproperties.analysis.cross_section import CrossSection

geometry = sections.AngleSection(d=150, b=90, t=12, r_r=10, r_t=5, n_r=8)
mesh = geometry.create_mesh(mesh_sizes=[2.5])
section = CrossSection(geometry, mesh)

section.calculate_geometric_properties()
section.calculate_warping_properties()
stress_post = section.calculate_stress(Mxx=5e6)

stress_post.plot_stress_mxx_zz()

Contour plot of the bending stress.

Bending Stress (\(\sigma_{zz,Myy}\))

StressPost.plot_stress_myy_zz(pause=True)

Produces a contour plot of the normal stress \(\sigma_{zz,Myy}\) resulting from the bending moment \(M_{yy}\).

Parameters:pause (bool) – If set to true, the figure pauses the script until the window is closed. If set to false, the script continues immediately after the window is rendered. Returns:Matplotlib figure and axes objects (fig, ax) Return type:(matplotlib.figure.Figure, matplotlib.axes)

The following example plots the normal stress within a 150x90x12 UA section resulting from a bending moment about the y-axis of 2 kN.m:

import sectionproperties.pre.sections as sections
from sectionproperties.analysis.cross_section import CrossSection

geometry = sections.AngleSection(d=150, b=90, t=12, r_r=10, r_t=5, n_r=8)
mesh = geometry.create_mesh(mesh_sizes=[2.5])
section = CrossSection(geometry, mesh)

section.calculate_geometric_properties()
section.calculate_warping_properties()
stress_post = section.calculate_stress(Myy=2e6)

stress_post.plot_stress_myy_zz()

Contour plot of the bending stress.

Bending Stress (\(\sigma_{zz,M11}\))

StressPost.plot_stress_m11_zz(pause=True)

Produces a contour plot of the normal stress \(\sigma_{zz,M11}\) resulting from the bending moment \(M_{11}\).

Parameters:pause (bool) – If set to true, the figure pauses the script until the window is closed. If set to false, the script continues immediately after the window is rendered. Returns:Matplotlib figure and axes objects (fig, ax) Return type:(matplotlib.figure.Figure, matplotlib.axes)

The following example plots the normal stress within a 150x90x12 UA section resulting from a bending moment about the 11-axis of 5 kN.m:

import sectionproperties.pre.sections as sections
from sectionproperties.analysis.cross_section import CrossSection

geometry = sections.AngleSection(d=150, b=90, t=12, r_r=10, r_t=5, n_r=8)
mesh = geometry.create_mesh(mesh_sizes=[2.5])
section = CrossSection(geometry, mesh)

section.calculate_geometric_properties()
section.calculate_warping_properties()
stress_post = section.calculate_stress(M11=5e6)

stress_post.plot_stress_m11_zz()

Contour plot of the bending stress.

Bending Stress (\(\sigma_{zz,M22}\))

StressPost.plot_stress_m22_zz(pause=True)

Produces a contour plot of the normal stress \(\sigma_{zz,M22}\) resulting from the bending moment \(M_{22}\).

Parameters:pause (bool) – If set to true, the figure pauses the script until the window is closed. If set to false, the script continues immediately after the window is rendered. Returns:Matplotlib figure and axes objects (fig, ax) Return type:(matplotlib.figure.Figure, matplotlib.axes)

The following example plots the normal stress within a 150x90x12 UA section resulting from a bending moment about the 22-axis of 2 kN.m:

import sectionproperties.pre.sections as sections
from sectionproperties.analysis.cross_section import CrossSection

geometry = sections.AngleSection(d=150, b=90, t=12, r_r=10, r_t=5, n_r=8)
mesh = geometry.create_mesh(mesh_sizes=[2.5])
section = CrossSection(geometry, mesh)

section.calculate_geometric_properties()
section.calculate_warping_properties()
stress_post = section.calculate_stress(M22=5e6)

stress_post.plot_stress_m22_zz()

Contour plot of the bending stress.

Bending Stress (\(\sigma_{zz,\Sigma M}\))

StressPost.plot_stress_m_zz(pause=True)

Produces a contour plot of the normal stress \(\sigma_{zz,\Sigma M}\) resulting from all bending moments \(M_{xx} + M_{yy} + M_{11} + M_{22}\).

Parameters:pause (bool) – If set to true, the figure pauses the script until the window is closed. If set to false, the script continues immediately after the window is rendered. Returns:Matplotlib figure and axes objects (fig, ax) Return type:(matplotlib.figure.Figure, matplotlib.axes)

The following example plots the normal stress within a 150x90x12 UA section resulting from a bending moment about the x-axis of 5 kN.m, a bending moment about the y-axis of 2 kN.m and a bending moment of 3 kN.m about the 11-axis:

import sectionproperties.pre.sections as sections
from sectionproperties.analysis.cross_section import CrossSection

geometry = sections.AngleSection(d=150, b=90, t=12, r_r=10, r_t=5, n_r=8)
mesh = geometry.create_mesh(mesh_sizes=[2.5])
section = CrossSection(geometry, mesh)

section.calculate_geometric_properties()
section.calculate_warping_properties()
stress_post = section.calculate_stress(Mxx=5e6, Myy=2e6, M11=3e6)

stress_post.plot_stress_m_zz()

Contour plot of the bending stress.

Torsion Stress (\(\sigma_{zx,Mzz}\))

StressPost.plot_stress_mzz_zx(pause=True)

Produces a contour plot of the x-component of the shear stress \(\sigma_{zx,Mzz}\) resulting from the torsion moment \(M_{zz}\).

Parameters:pause (bool) – If set to true, the figure pauses the script until the window is closed. If set to false, the script continues immediately after the window is rendered. Returns:Matplotlib figure and axes objects (fig, ax) Return type:(matplotlib.figure.Figure, matplotlib.axes)

The following example plots the x-component of the shear stress within a 150x90x12 UA section resulting from a torsion moment of 1 kN.m:

import sectionproperties.pre.sections as sections
from sectionproperties.analysis.cross_section import CrossSection

geometry = sections.AngleSection(d=150, b=90, t=12, r_r=10, r_t=5, n_r=8)
mesh = geometry.create_mesh(mesh_sizes=[2.5])
section = CrossSection(geometry, mesh)

section.calculate_geometric_properties()
section.calculate_warping_properties()
stress_post = section.calculate_stress(Mzz=1e6)

stress_post.plot_stress_mzz_zx()

Contour plot of the shear stress.

Torsion Stress (\(\sigma_{zy,Mzz}\))

StressPost.plot_stress_mzz_zy(pause=True)

Produces a contour plot of the y-component of the shear stress \(\sigma_{zy,Mzz}\) resulting from the torsion moment \(M_{zz}\).

Parameters:pause (bool) – If set to true, the figure pauses the script until the window is closed. If set to false, the script continues immediately after the window is rendered. Returns:Matplotlib figure and axes objects (fig, ax) Return type:(matplotlib.figure.Figure, matplotlib.axes)

The following example plots the y-component of the shear stress within a 150x90x12 UA section resulting from a torsion moment of 1 kN.m:

import sectionproperties.pre.sections as sections
from sectionproperties.analysis.cross_section import CrossSection

geometry = sections.AngleSection(d=150, b=90, t=12, r_r=10, r_t=5, n_r=8)
mesh = geometry.create_mesh(mesh_sizes=[2.5])
section = CrossSection(geometry, mesh)

section.calculate_geometric_properties()
section.calculate_warping_properties()
stress_post = section.calculate_stress(Mzz=1e6)

stress_post.plot_stress_mzz_zy()

Contour plot of the shear stress.

Torsion Stress (\(\sigma_{zxy,Mzz}\))

StressPost.plot_stress_mzz_zxy(pause=True)

Produces a contour plot of the resultant shear stress \(\sigma_{zxy,Mzz}\) resulting from the torsion moment \(M_{zz}\).

Parameters:pause (bool) – If set to true, the figure pauses the script until the window is closed. If set to false, the script continues immediately after the window is rendered. Returns:Matplotlib figure and axes objects (fig, ax) Return type:(matplotlib.figure.Figure, matplotlib.axes)

The following example plots a contour of the resultant shear stress within a 150x90x12 UA section resulting from a torsion moment of 1 kN.m:

import sectionproperties.pre.sections as sections
from sectionproperties.analysis.cross_section import CrossSection

geometry = sections.AngleSection(d=150, b=90, t=12, r_r=10, r_t=5, n_r=8)
mesh = geometry.create_mesh(mesh_sizes=[2.5])
section = CrossSection(geometry, mesh)

section.calculate_geometric_properties()
section.calculate_warping_properties()
stress_post = section.calculate_stress(Mzz=1e6)

stress_post.plot_stress_mzz_zxy()

Contour plot of the shear stress.

StressPost.plot_vector_mzz_zxy(pause=True)

Produces a vector plot of the resultant shear stress \(\sigma_{zxy,Mzz}\) resulting from the torsion moment \(M_{zz}\).

Parameters:pause (bool) – If set to true, the figure pauses the script until the window is closed. If set to false, the script continues immediately after the window is rendered. Returns:Matplotlib figure and axes objects (fig, ax) Return type:(matplotlib.figure.Figure, matplotlib.axes)

The following example generates a vector plot of the shear stress within a 150x90x12 UA section resulting from a torsion moment of 1 kN.m:

import sectionproperties.pre.sections as sections
from sectionproperties.analysis.cross_section import CrossSection

geometry = sections.AngleSection(d=150, b=90, t=12, r_r=10, r_t=5, n_r=8)
mesh = geometry.create_mesh(mesh_sizes=[2.5])
section = CrossSection(geometry, mesh)

section.calculate_geometric_properties()
section.calculate_warping_properties()
stress_post = section.calculate_stress(Mzz=1e6)

stress_post.plot_vector_mzz_zxy()

Vector plot of the shear stress.

Shear Stress (\(\sigma_{zx,Vx}\))

StressPost.plot_stress_vx_zx(pause=True)

Produces a contour plot of the x-component of the shear stress \(\sigma_{zx,Vx}\) resulting from the shear force \(V_{x}\).

Parameters:pause (bool) – If set to true, the figure pauses the script until the window is closed. If set to false, the script continues immediately after the window is rendered. Returns:Matplotlib figure and axes objects (fig, ax) Return type:(matplotlib.figure.Figure, matplotlib.axes)

The following example plots the x-component of the shear stress within a 150x90x12 UA section resulting from a shear force in the x-direction of 15 kN:

import sectionproperties.pre.sections as sections
from sectionproperties.analysis.cross_section import CrossSection

geometry = sections.AngleSection(d=150, b=90, t=12, r_r=10, r_t=5, n_r=8)
mesh = geometry.create_mesh(mesh_sizes=[2.5])
section = CrossSection(geometry, mesh)

section.calculate_geometric_properties()
section.calculate_warping_properties()
stress_post = section.calculate_stress(Vx=15e3)

stress_post.plot_stress_vx_zx()

Contour plot of the shear stress.

Shear Stress (\(\sigma_{zy,Vx}\))

StressPost.plot_stress_vx_zy(pause=True)

Produces a contour plot of the y-component of the shear stress \(\sigma_{zy,Vx}\) resulting from the shear force \(V_{x}\).

Parameters:pause (bool) – If set to true, the figure pauses the script until the window is closed. If set to false, the script continues immediately after the window is rendered. Returns:Matplotlib figure and axes objects (fig, ax) Return type:(matplotlib.figure.Figure, matplotlib.axes)

The following example plots the y-component of the shear stress within a 150x90x12 UA section resulting from a shear force in the x-direction of 15 kN:

import sectionproperties.pre.sections as sections
from sectionproperties.analysis.cross_section import CrossSection

geometry = sections.AngleSection(d=150, b=90, t=12, r_r=10, r_t=5, n_r=8)
mesh = geometry.create_mesh(mesh_sizes=[2.5])
section = CrossSection(geometry, mesh)

section.calculate_geometric_properties()
section.calculate_warping_properties()
stress_post = section.calculate_stress(Vx=15e3)

stress_post.plot_stress_vx_zy()

Contour plot of the shear stress.

Shear Stress (\(\sigma_{zxy,Vx}\))

StressPost.plot_stress_vx_zxy(pause=True)

Produces a contour plot of the resultant shear stress \(\sigma_{zxy,Vx}\) resulting from the shear force \(V_{x}\).

Parameters:pause (bool) – If set to true, the figure pauses the script until the window is closed. If set to false, the script continues immediately after the window is rendered. Returns:Matplotlib figure and axes objects (fig, ax) Return type:(matplotlib.figure.Figure, matplotlib.axes)

The following example plots a contour of the resultant shear stress within a 150x90x12 UA section resulting from a shear force in the x-direction of 15 kN:

import sectionproperties.pre.sections as sections
from sectionproperties.analysis.cross_section import CrossSection

geometry = sections.AngleSection(d=150, b=90, t=12, r_r=10, r_t=5, n_r=8)
mesh = geometry.create_mesh(mesh_sizes=[2.5])
section = CrossSection(geometry, mesh)

section.calculate_geometric_properties()
section.calculate_warping_properties()
stress_post = section.calculate_stress(Vx=15e3)

stress_post.plot_stress_vx_zxy()

Contour plot of the shear stress.

StressPost.plot_vector_vx_zxy(pause=True)

Produces a vector plot of the resultant shear stress \(\sigma_{zxy,Vx}\) resulting from the shear force \(V_{x}\).

Parameters:pause (bool) – If set to true, the figure pauses the script until the window is closed. If set to false, the script continues immediately after the window is rendered. Returns:Matplotlib figure and axes objects (fig, ax) Return type:(matplotlib.figure.Figure, matplotlib.axes)

The following example generates a vector plot of the shear stress within a 150x90x12 UA section resulting from a shear force in the x-direction of 15 kN:

import sectionproperties.pre.sections as sections
from sectionproperties.analysis.cross_section import CrossSection

geometry = sections.AngleSection(d=150, b=90, t=12, r_r=10, r_t=5, n_r=8)
mesh = geometry.create_mesh(mesh_sizes=[2.5])
section = CrossSection(geometry, mesh)

section.calculate_geometric_properties()
section.calculate_warping_properties()
stress_post = section.calculate_stress(Vx=15e3)

stress_post.plot_vector_vx_zxy()

Vector plot of the shear stress.

Shear Stress (\(\sigma_{zx,Vy}\))

StressPost.plot_stress_vy_zx(pause=True)

Produces a contour plot of the x-component of the shear stress \(\sigma_{zx,Vy}\) resulting from the shear force \(V_{y}\).

Parameters:pause (bool) – If set to true, the figure pauses the script until the window is closed. If set to false, the script continues immediately after the window is rendered. Returns:Matplotlib figure and axes objects (fig, ax) Return type:(matplotlib.figure.Figure, matplotlib.axes)

The following example plots the x-component of the shear stress within a 150x90x12 UA section resulting from a shear force in the y-direction of 30 kN:

import sectionproperties.pre.sections as sections
from sectionproperties.analysis.cross_section import CrossSection

geometry = sections.AngleSection(d=150, b=90, t=12, r_r=10, r_t=5, n_r=8)
mesh = geometry.create_mesh(mesh_sizes=[2.5])
section = CrossSection(geometry, mesh)

section.calculate_geometric_properties()
section.calculate_warping_properties()
stress_post = section.calculate_stress(Vy=30e3)

stress_post.plot_stress_vy_zx()

Contour plot of the shear stress.

Shear Stress (\(\sigma_{zy,Vy}\))

StressPost.plot_stress_vy_zy(pause=True)

Produces a contour plot of the y-component of the shear stress \(\sigma_{zy,Vy}\) resulting from the shear force \(V_{y}\).

Parameters:pause (bool) – If set to true, the figure pauses the script until the window is closed. If set to false, the script continues immediately after the window is rendered. Returns:Matplotlib figure and axes objects (fig, ax) Return type:(matplotlib.figure.Figure, matplotlib.axes)

The following example plots the y-component of the shear stress within a 150x90x12 UA section resulting from a shear force in the y-direction of 30 kN:

import sectionproperties.pre.sections as sections
from sectionproperties.analysis.cross_section import CrossSection

geometry = sections.AngleSection(d=150, b=90, t=12, r_r=10, r_t=5, n_r=8)
mesh = geometry.create_mesh(mesh_sizes=[2.5])
section = CrossSection(geometry, mesh)

section.calculate_geometric_properties()
section.calculate_warping_properties()
stress_post = section.calculate_stress(Vy=30e3)

stress_post.plot_stress_vy_zy()

Contour plot of the shear stress.

Shear Stress (\(\sigma_{zxy,Vy}\))

StressPost.plot_stress_vy_zxy(pause=True)

Produces a contour plot of the resultant shear stress \(\sigma_{zxy,Vy}\) resulting from the shear force \(V_{y}\).

Parameters:pause (bool) – If set to true, the figure pauses the script until the window is closed. If set to false, the script continues immediately after the window is rendered. Returns:Matplotlib figure and axes objects (fig, ax) Return type:(matplotlib.figure.Figure, matplotlib.axes)

The following example plots a contour of the resultant shear stress within a 150x90x12 UA section resulting from a shear force in the y-direction of 30 kN:

import sectionproperties.pre.sections as sections
from sectionproperties.analysis.cross_section import CrossSection

geometry = sections.AngleSection(d=150, b=90, t=12, r_r=10, r_t=5, n_r=8)
mesh = geometry.create_mesh(mesh_sizes=[2.5])
section = CrossSection(geometry, mesh)

section.calculate_geometric_properties()
section.calculate_warping_properties()
stress_post = section.calculate_stress(Vy=30e3)

stress_post.plot_stress_vy_zxy()

Contour plot of the shear stress.

StressPost.plot_vector_vy_zxy(pause=True)

Produces a vector plot of the resultant shear stress \(\sigma_{zxy,Vy}\) resulting from the shear force \(V_{y}\).

Parameters:pause (bool) – If set to true, the figure pauses the script until the window is closed. If set to false, the script continues immediately after the window is rendered. Returns:Matplotlib figure and axes objects (fig, ax) Return type:(matplotlib.figure.Figure, matplotlib.axes)

The following example generates a vector plot of the shear stress within a 150x90x12 UA section resulting from a shear force in the y-direction of 30 kN:

import sectionproperties.pre.sections as sections
from sectionproperties.analysis.cross_section import CrossSection

geometry = sections.AngleSection(d=150, b=90, t=12, r_r=10, r_t=5, n_r=8)
mesh = geometry.create_mesh(mesh_sizes=[2.5])
section = CrossSection(geometry, mesh)

section.calculate_geometric_properties()
section.calculate_warping_properties()
stress_post = section.calculate_stress(Vy=30e3)

stress_post.plot_vector_vy_zxy()

Vector plot of the shear stress.

Shear Stress (\(\sigma_{zx,\Sigma V}\))

StressPost.plot_stress_v_zx(pause=True)

Produces a contour plot of the x-component of the shear stress \(\sigma_{zx,\Sigma V}\) resulting from the sum of the applied shear forces \(V_{x} + V_{y}\).

Parameters:pause (bool) – If set to true, the figure pauses the script until the window is closed. If set to false, the script continues immediately after the window is rendered. Returns:Matplotlib figure and axes objects (fig, ax) Return type:(matplotlib.figure.Figure, matplotlib.axes)

The following example plots the x-component of the shear stress within a 150x90x12 UA section resulting from a shear force of 15 kN in the x-direction and 30 kN in the y-direction:

import sectionproperties.pre.sections as sections
from sectionproperties.analysis.cross_section import CrossSection

geometry = sections.AngleSection(d=150, b=90, t=12, r_r=10, r_t=5, n_r=8)
mesh = geometry.create_mesh(mesh_sizes=[2.5])
section = CrossSection(geometry, mesh)

section.calculate_geometric_properties()
section.calculate_warping_properties()
stress_post = section.calculate_stress(Vx=15e3, Vy=30e3)

stress_post.plot_stress_v_zx()

Contour plot of the shear stress.

Shear Stress (\(\sigma_{zy,\Sigma V}\))

StressPost.plot_stress_v_zy(pause=True)

Produces a contour plot of the y-component of the shear stress \(\sigma_{zy,\Sigma V}\) resulting from the sum of the applied shear forces \(V_{x} + V_{y}\).

Parameters:pause (bool) – If set to true, the figure pauses the script until the window is closed. If set to false, the script continues immediately after the window is rendered. Returns:Matplotlib figure and axes objects (fig, ax) Return type:(matplotlib.figure.Figure, matplotlib.axes)

The following example plots the y-component of the shear stress within a 150x90x12 UA section resulting from a shear force of 15 kN in the x-direction and 30 kN in the y-direction:

import sectionproperties.pre.sections as sections
from sectionproperties.analysis.cross_section import CrossSection

geometry = sections.AngleSection(d=150, b=90, t=12, r_r=10, r_t=5, n_r=8)
mesh = geometry.create_mesh(mesh_sizes=[2.5])
section = CrossSection(geometry, mesh)

section.calculate_geometric_properties()
section.calculate_warping_properties()
stress_post = section.calculate_stress(Vx=15e3, Vy=30e3)

stress_post.plot_stress_v_zy()

Contour plot of the shear stress.

Shear Stress (\(\sigma_{zxy,\Sigma V}\))

StressPost.plot_stress_v_zxy(pause=True)

Produces a contour plot of the resultant shear stress \(\sigma_{zxy,\Sigma V}\) resulting from the sum of the applied shear forces \(V_{x} + V_{y}\).

Parameters:pause (bool) – If set to true, the figure pauses the script until the window is closed. If set to false, the script continues immediately after the window is rendered. Returns:Matplotlib figure and axes objects (fig, ax) Return type:(matplotlib.figure.Figure, matplotlib.axes)

The following example plots a contour of the resultant shear stress within a 150x90x12 UA section resulting from a shear force of 15 kN in the x-direction and 30 kN in the y-direction:

import sectionproperties.pre.sections as sections
from sectionproperties.analysis.cross_section import CrossSection

geometry = sections.AngleSection(d=150, b=90, t=12, r_r=10, r_t=5, n_r=8)
mesh = geometry.create_mesh(mesh_sizes=[2.5])
section = CrossSection(geometry, mesh)

section.calculate_geometric_properties()
section.calculate_warping_properties()
stress_post = section.calculate_stress(Vx=15e3, Vy=30e3)

stress_post.plot_stress_v_zxy()

Contour plot of the shear stress.

StressPost.plot_vector_v_zxy(pause=True)

Produces a vector plot of the resultant shear stress \(\sigma_{zxy,\Sigma V}\) resulting from the sum of the applied shear forces \(V_{x} + V_{y}\).

Parameters:pause (bool) – If set to true, the figure pauses the script until the window is closed. If set to false, the script continues immediately after the window is rendered. Returns:Matplotlib figure and axes objects (fig, ax) Return type:(matplotlib.figure.Figure, matplotlib.axes)

The following example generates a vector plot of the shear stress within a 150x90x12 UA section resulting from a shear force of 15 kN in the x-direction and 30 kN in the y-direction:

import sectionproperties.pre.sections as sections
from sectionproperties.analysis.cross_section import CrossSection

geometry = sections.AngleSection(d=150, b=90, t=12, r_r=10, r_t=5, n_r=8)
mesh = geometry.create_mesh(mesh_sizes=[2.5])
section = CrossSection(geometry, mesh)

section.calculate_geometric_properties()
section.calculate_warping_properties()
stress_post = section.calculate_stress(Vx=15e3, Vy=30e3)

stress_post.plot_vector_v_zxy()

Vector plot of the shear stress.

Combined Stress Plots

Normal Stress (\(\sigma_{zz}\))

StressPost.plot_stress_zz(pause=True)

Produces a contour plot of the combined normal stress \(\sigma_{zz}\) resulting from all actions.

Parameters:pause (bool) – If set to true, the figure pauses the script until the window is closed. If set to false, the script continues immediately after the window is rendered. Returns:Matplotlib figure and axes objects (fig, ax) Return type:(matplotlib.figure.Figure, matplotlib.axes)

The following example plots the normal stress within a 150x90x12 UA section resulting from an axial force of 100 kN, a bending moment about the x-axis of 5 kN.m and a bending moment about the y-axis of 2 kN.m:

import sectionproperties.pre.sections as sections
from sectionproperties.analysis.cross_section import CrossSection

geometry = sections.AngleSection(d=150, b=90, t=12, r_r=10, r_t=5, n_r=8)
mesh = geometry.create_mesh(mesh_sizes=[2.5])
section = CrossSection(geometry, mesh)

section.calculate_geometric_properties()
section.calculate_warping_properties()
stress_post = section.calculate_stress(N=100e3, Mxx=5e6, Myy=2e6)

stress_post.plot_stress_zz()

Contour plot of the normal stress.

Shear Stress (\(\sigma_{zx}\))

StressPost.plot_stress_zx(pause=True)

Produces a contour plot of the x-component of the shear stress \(\sigma_{zx}\) resulting from all actions.

Parameters:pause (bool) – If set to true, the figure pauses the script until the window is closed. If set to false, the script continues immediately after the window is rendered. Returns:Matplotlib figure and axes objects (fig, ax) Return type:(matplotlib.figure.Figure, matplotlib.axes)

The following example plots the x-component of the shear stress within a 150x90x12 UA section resulting from a torsion moment of 1 kN.m and a shear force of 30 kN in the y-direction:

import sectionproperties.pre.sections as sections
from sectionproperties.analysis.cross_section import CrossSection

geometry = sections.AngleSection(d=150, b=90, t=12, r_r=10, r_t=5, n_r=8)
mesh = geometry.create_mesh(mesh_sizes=[2.5])
section = CrossSection(geometry, mesh)

section.calculate_geometric_properties()
section.calculate_warping_properties()
stress_post = section.calculate_stress(Mzz=1e6, Vy=30e3)

stress_post.plot_stress_zx()

Contour plot of the shear stress.

Shear Stress (\(\sigma_{zy}\))

StressPost.plot_stress_zy(pause=True)

Produces a contour plot of the y-component of the shear stress \(\sigma_{zy}\) resulting from all actions.

Parameters:pause (bool) – If set to true, the figure pauses the script until the window is closed. If set to false, the script continues immediately after the window is rendered. Returns:Matplotlib figure and axes objects (fig, ax) Return type:(matplotlib.figure.Figure, matplotlib.axes)

The following example plots the y-component of the shear stress within a 150x90x12 UA section resulting from a torsion moment of 1 kN.m and a shear force of 30 kN in the y-direction:

import sectionproperties.pre.sections as sections
from sectionproperties.analysis.cross_section import CrossSection

geometry = sections.AngleSection(d=150, b=90, t=12, r_r=10, r_t=5, n_r=8)
mesh = geometry.create_mesh(mesh_sizes=[2.5])
section = CrossSection(geometry, mesh)

section.calculate_geometric_properties()
section.calculate_warping_properties()
stress_post = section.calculate_stress(Mzz=1e6, Vy=30e3)

stress_post.plot_stress_zy()

Contour plot of the shear stress.

Shear Stress (\(\sigma_{zxy}\))

StressPost.plot_stress_zxy(pause=True)

Produces a contour plot of the resultant shear stress \(\sigma_{zxy}\) resulting from all actions.

Parameters:pause (bool) – If set to true, the figure pauses the script until the window is closed. If set to false, the script continues immediately after the window is rendered. Returns:Matplotlib figure and axes objects (fig, ax) Return type:(matplotlib.figure.Figure, matplotlib.axes)

The following example plots a contour of the resultant shear stress within a 150x90x12 UA section resulting from a torsion moment of 1 kN.m and a shear force of 30 kN in the y-direction:

import sectionproperties.pre.sections as sections
from sectionproperties.analysis.cross_section import CrossSection

geometry = sections.AngleSection(d=150, b=90, t=12, r_r=10, r_t=5, n_r=8)
mesh = geometry.create_mesh(mesh_sizes=[2.5])
section = CrossSection(geometry, mesh)

section.calculate_geometric_properties()
section.calculate_warping_properties()
stress_post = section.calculate_stress(Mzz=1e6, Vy=30e3)

stress_post.plot_stress_zxy()

Contour plot of the shear stress.

StressPost.plot_vector_zxy(pause=True)

Produces a vector plot of the resultant shear stress \(\sigma_{zxy}\) resulting from all actions.

Parameters:pause (bool) – If set to true, the figure pauses the script until the window is closed. If set to false, the script continues immediately after the window is rendered. Returns:Matplotlib figure and axes objects (fig, ax) Return type:(matplotlib.figure.Figure, matplotlib.axes)

The following example generates a vector plot of the shear stress within a 150x90x12 UA section resulting from a torsion moment of 1 kN.m and a shear force of 30 kN in the y-direction:

import sectionproperties.pre.sections as sections
from sectionproperties.analysis.cross_section import CrossSection

geometry = sections.AngleSection(d=150, b=90, t=12, r_r=10, r_t=5, n_r=8)
mesh = geometry.create_mesh(mesh_sizes=[2.5])
section = CrossSection(geometry, mesh)

section.calculate_geometric_properties()
section.calculate_warping_properties()
stress_post = section.calculate_stress(Mzz=1e6, Vy=30e3)

stress_post.plot_vector_zxy()

Vector plot of the shear stress.

von Mises Stress (\(\sigma_{vM}\))

StressPost.plot_stress_vm(pause=True)

Produces a contour plot of the von Mises stress \(\sigma_{vM}\) resulting from all actions.

Parameters:pause (bool) – If set to true, the figure pauses the script until the window is closed. If set to false, the script continues immediately after the window is rendered. Returns:Matplotlib figure and axes objects (fig, ax) Return type:(matplotlib.figure.Figure, matplotlib.axes)

The following example plots a contour of the von Mises stress within a 150x90x12 UA section resulting from the following actions:

• \(N = 50\) kN
• \(M_{xx} = -5\) kN.m
• \(M_{22} = 2.5\) kN.m
• \(M_{zz} = 1.5\) kN.m
• \(V_{x} = 10\) kN
• \(V_{y} = 5\) kN

import sectionproperties.pre.sections as sections
from sectionproperties.analysis.cross_section import CrossSection

geometry = sections.AngleSection(d=150, b=90, t=12, r_r=10, r_t=5, n_r=8)
mesh = geometry.create_mesh(mesh_sizes=[2.5])
section = CrossSection(geometry, mesh)

section.calculate_geometric_properties()
section.calculate_warping_properties()
stress_post = section.calculate_stress(
    N=50e3, Mxx=-5e6, M22=2.5e6, Mzz=0.5e6, Vx=10e3, Vy=5e3
)

stress_post.plot_stress_vm()

Contour plot of the von Mises stress.

Retrieving Cross-Section Stress

All cross-section stresses can be recovered using the get_stress() method that belongs to every StressPost object:

StressPost.get_stress()

Returns the stresses within each material belonging to the current StressPost object.

Returns:A list of dictionaries containing the cross-section stresses for each material. Return type:list[dict]

A dictionary is returned for each material in the cross-section, containing the following keys and values:

• ‘Material’: Material name
• ‘sig_zz_n’: Normal stress \(\sigma_{zz,N}\) resulting from the axial load \(N\)
• ‘sig_zz_mxx’: Normal stress \(\sigma_{zz,Mxx}\) resulting from the bending moment \(M_{xx}\)
• ‘sig_zz_myy’: Normal stress \(\sigma_{zz,Myy}\) resulting from the bending moment \(M_{yy}\)
• ‘sig_zz_m11’: Normal stress \(\sigma_{zz,M11}\) resulting from the bending moment \(M_{11}\)
• ‘sig_zz_m22’: Normal stress \(\sigma_{zz,M22}\) resulting from the bending moment \(M_{22}\)
• ‘sig_zz_m’: Normal stress \(\sigma_{zz,\Sigma M}\) resulting from all bending moments
• ‘sig_zx_mzz’: x-component of the shear stress \(\sigma_{zx,Mzz}\) resulting from the torsion moment
• ‘sig_zy_mzz’: y-component of the shear stress \(\sigma_{zy,Mzz}\) resulting from the torsion moment
• ‘sig_zxy_mzz’: Resultant shear stress \(\sigma_{zxy,Mzz}\) resulting from the torsion moment
• ‘sig_zx_vx’: x-component of the shear stress \(\sigma_{zx,Vx}\) resulting from the shear force \(V_{x}\)
• ‘sig_zy_vx’: y-component of the shear stress \(\sigma_{zy,Vx}\) resulting from the shear force \(V_{x}\)
• ‘sig_zxy_vx’: Resultant shear stress \(\sigma_{zxy,Vx}\) resulting from the shear force \(V_{x}\)
• ‘sig_zx_vy’: x-component of the shear stress \(\sigma_{zx,Vy}\) resulting from the shear force \(V_{y}\)
• ‘sig_zy_vy’: y-component of the shear stress \(\sigma_{zy,Vy}\) resulting from the shear force \(V_{y}\)
• ‘sig_zxy_vy’: Resultant shear stress \(\sigma_{zxy,Vy}\) resulting from the shear force \(V_{y}\)
• ‘sig_zx_v’: x-component of the shear stress \(\sigma_{zx,\Sigma V}\) resulting from all shear forces
• ‘sig_zy_v’: y-component of the shear stress \(\sigma_{zy,\Sigma V}\) resulting from all shear forces
• ‘sig_zxy_v’: Resultant shear stress \(\sigma_{zxy,\Sigma V}\) resulting from all shear forces
• ‘sig_zz’: Combined normal stress \(\sigma_{zz}\) resulting from all actions
• ‘sig_zx’: x-component of the shear stress \(\sigma_{zx}\) resulting from all actions
• ‘sig_zy’: y-component of the shear stress \(\sigma_{zy}\) resulting from all actions
• ‘sig_zxy’: Resultant shear stress \(\sigma_{zxy}\) resulting from all actions
• ‘sig_vm’: von Mises stress \(\sigma_{vM}\) resulting from all actions

The following example returns the normal stress within a 150x90x12 UA section resulting from an axial force of 10 kN:

import sectionproperties.pre.sections as sections
from sectionproperties.analysis.cross_section import CrossSection

geometry = sections.AngleSection(d=150, b=90, t=12, r_r=10, r_t=5, n_r=8)
mesh = geometry.create_mesh(mesh_sizes=[2.5])
section = CrossSection(geometry, mesh)

section.calculate_geometric_properties()
section.calculate_warping_properties()
stress_post = section.calculate_stress(N=10e3)

stresses = stress_post.get_stress()
print('Material: {0}'.format(stresses[0]['Material']))
print('Axial Stresses: {0}'.format(stresses[0]['sig_zz_n']))

$ Material: default
$ Axial Stresses: [3.6402569 3.6402569 3.6402569 ... 3.6402569 3.6402569 3.6402569]