Frame Analysis

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

A frame analysis calculates only the cross-section properties required for a frame analysis:

• Cross-section area

• Second moments of area about the centroidal axis

• Torsion constant

• Principal axis angle

As a result, it is significantly more efficient than conducting both geometric and warping analyses, which is ususally required to obtain the above results.

This example will analyse a 12-sided polygonal hollow section and compare the time taken for a typical warping analysis with that taken for a frame analysis.

Create Geometry and Section

from sectionproperties.analysis import Section
from sectionproperties.pre.library import polygon_hollow_section


geom = polygon_hollow_section(d=600, t=12, n_sides=12, r_in=20, n_r=8)
geom.create_mesh(mesh_sizes=20)
sec = Section(geometry=geom)
sec.plot_mesh(materials=False)

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

Geometric and Warping Analysis

First we can time how long it takes to perform a geometric and warping analysis.

import time


start = time.time()
sec.calculate_geometric_properties()
sec.calculate_warping_properties()
end = time.time()
gw_time = end - start

We can print the time taken and the torsion constant to compare results.

print(f"Geometric/Warping Time = {gw_time:.4f} secs")
print(f"J = {sec.get_j():.3e} mm4")

Geometric/Warping Time = 4.0141 secs
J = 1.769e+09 mm4

Frame Analysis

Now we can time how long it takes to perform a frame analysis.

start = time.time()
sec.calculate_frame_properties()
end = time.time()
f_time = end - start

Again, we can print the time taken and the torsion constant.

print(f"Frame Time = {f_time:.4f} secs")
print(f"J = {sec.get_j():.3e} mm4")

Frame Time = 1.4310 secs
J = 1.769e+09 mm4

By not calculating shear functions, shear & warping integrals etc. required for a full warping analysis, significant time is saved if the user only wants frame properties.