Warping Analysis

This example demonstrates how to perform a warping analysis in sectionproperties.

Channel Section

This example will conduct a warping analysis on a 250PFC section.

First we create the cross-section geometry.

from sectionproperties.pre.library import channel_section


geom = channel_section(d=250, b=90, t_f=15, t_w=8, r=12, n_r=8)

Next we must create a finite element mesh and a Section object. Unlike geometric and plastic analyses, the warping results are mesh dependent. As a general rule of thumb, we would like all plate sections to be at least several elements thick in order to resolve the variations in the warping and shear functions.

from sectionproperties.analysis import Section


geom.create_mesh(mesh_sizes=7)
sec = Section(geometry=geom)
sec.plot_mesh(materials=False)

<Axes: title={'center': 'Finite Element Mesh'}>

We can now perform the warping analysis by calling calculate_warping_properties(), note that a geometric analysis must be performed first. We also compare the "direct" solver with the "cgs" solver for speed.

import time


sec.calculate_geometric_properties()

# direct solver
start = time.time()
sec.calculate_warping_properties(solver_type="direct")
end = time.time()
print(f"Direct Solver Time = {end - start:.4f} secs")

# cgs solver
start = time.time()
sec.calculate_warping_properties(solver_type="cgs")
end = time.time()
print(f"CGS Solver Time = {end - start:.4f} secs")

Direct Solver Time = 1.0581 secs

CGS Solver Time = 0.5944 secs

We can plot the centroids to display the geometric centroid and shear centre using plot_centroids().

sec.plot_centroids()

<Axes: title={'center': 'Centroids'}>

We can also obtain the some relevant warping properties:

• J - torsion constant

• Iw/Gamma - warping constant

• As_y - shear area for loading along the y-axis

print(f"J = {sec.get_j():.3e} mm4")
print(f"Iw = {sec.get_gamma():.3e} mm6")
print(f"As_y = {sec.get_as()[1]:.1f} mm2")

J = 2.382e+05 mm4
Iw = 3.555e+10 mm6
As_y = 1823.4 mm2

Unconnected Sections

Unlike geometric and plastic analysis, cross-sections analysed for warping must have strict connectivity. sectionproperties checks for connectivity prior to conducting a warping analysis and will throw an error if there is not full connectivity between all regions of the mesh.

from sectionproperties.pre.library import rectangular_section


# create an unconnected mesh
rect = rectangular_section(d=10, b=10)
geom = rect + rect.shift_section(x_offset=20)
geom.create_mesh(mesh_sizes=1)
sec = Section(geometry=geom)
sec.plot_mesh(materials=False)

<Axes: title={'center': 'Finite Element Mesh'}>

# geometric and plastic analyses can be conducted
sec.calculate_geometric_properties()
sec.calculate_plastic_properties()

# warping analysis will fail
sec.calculate_warping_properties()

/home/docs/checkouts/readthedocs.org/user_builds/sectionproperties/envs/latest/lib/python3.10/site-packages/sectionproperties/analysis/section.py:347: UserWarning:
The section geometry contains disjoint regions which is invalid for warping analysis.
 Please revise your geometry to ensure there is connectivity between all regions.
 Please see https://sectionproperties.rtfd.io/en/stable/user_guide/analysis.html#warping-analysis for more information.
  warnings.warn(msg)