Geometric Analysis

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

Steel I-Beam

In this example, the geometric cross-section properties of a 200UB25.4 are obtained.

First we create the cross-section geometry.

from sectionproperties.pre.library import i_section


geom = i_section(d=203, b=133, t_f=7.8, t_w=5.8, r=8.9, n_r=8)

Next we must create a finite element mesh and a Section() object.

from sectionproperties.analysis import Section


geom.create_mesh(mesh_sizes=5)
sec = Section(geometry=geom)

We can check the mesh quality by calling the display_mesh_info() method, or by generating a plot of the mesh by using plot_mesh().

sec.display_mesh_info()

Mesh Statistics:

- 2304 nodes

- 991 elements

- 1 region

sec.plot_mesh(materials=False)

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

Note that in sectionproperties, the geometric properties are mesh independent. As a result, we can create a mesh with no area constraints by setting mesh_sizes=0.

geom.create_mesh(mesh_sizes=0)
sec = Section(geometry=geom)
sec.display_mesh_info()
sec.plot_mesh(materials=False)

Mesh Statistics:

- 622 nodes

- 235 elements

- 1 region

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

We can now perform the geometric analysis by calling calculate_geometric_properties().

sec.calculate_geometric_properties()

One easy way to view all the results that have been calculated to date, is to print them to the terminal by using display_results().

sec.display_results(fmt=".0f")

   Section Properties   
┏━━━━━━━━━━━┳━━━━━━━━━━┓
┃ Property  ┃    Value ┃
┡━━━━━━━━━━━╇━━━━━━━━━━┩
│ area      │     3232 │
│ perimeter │      911 │
│ qx        │   328027 │
│ qy        │   214915 │
│ ixx_g     │ 56839451 │
│ iyy_g     │ 17355200 │
│ ixy_g     │ 21813826 │
│ cx        │       66 │
│ cy        │      102 │
│ ixx_c     │ 23544664 │
│ iyy_c     │  3063383 │
│ ixy_c     │       -0 │
│ zxx+      │   231967 │
│ zxx-      │   231967 │
│ zyy+      │    46066 │
│ zyy-      │    46066 │
│ rx        │       85 │
│ ry        │       31 │
│ i11_c     │ 23544664 │
│ i22_c     │  3063383 │
│ phi       │        0 │
│ z11+      │   231967 │
│ z11-      │   231967 │
│ z22+      │    46066 │
│ z22-      │    46066 │
│ r11       │       85 │
│ r22       │       31 │
└───────────┴──────────┘

Unconnected Sections

sectionproperties can compute the geometric properties of unconnected sections. Note that a warping analysis cannot be undertaken on unconnected sections. This example analyses two 150PFC sections separated by 1 metre forming the flanges of a truss.

from sectionproperties.pre.library import channel_section


# create 150 pfc geometry
pfc = channel_section(d=150, b=75, t_f=9.5, t_w=6, r=10, n_r=8)
pfc.plot_geometry(legend=False)

<Axes: title={'center': 'Cross-Section Geometry'}>

We can analyse the section properties of a single PFC first, then compare the results to the combined section.

pfc.create_mesh(mesh_sizes=0)
sec_pfc = Section(geometry=pfc)
sec_pfc.calculate_geometric_properties()

Now we create the truss geometry by mirroring one PFC and offsetting the other.

# create compound geometry
geom = pfc.mirror_section(axis="y", mirror_point=(0, 0)) + pfc.shift_section(
    x_offset=1000
)
geom.create_mesh(mesh_sizes=0)
sec_truss = Section(geometry=geom)
sec_truss.plot_mesh(materials=False)
sec_truss.calculate_geometric_properties()

Let’s compare some of the calculated section properties:

area_ratio = sec_truss.get_area() / sec_pfc.get_area()
ixx_ratio = sec_truss.get_ic()[0] / sec_pfc.get_ic()[0]
iyy_ratio = sec_truss.get_ic()[1] / sec_pfc.get_ic()[1]
zyy_ratio = sec_truss.get_z()[2] / sec_pfc.get_z()[2]
ry_ratio = sec_truss.get_rc()[1] / sec_pfc.get_rc()[1]

We can format the results in a tabulated way by using the rich library.

from rich.console import Console
from rich.table import Table


# setup table
table = Table(title="Section Properties Comparison")
table.add_column("Property", justify="left", style="cyan", no_wrap=True)
table.add_column("PFC", justify="right", style="green")
table.add_column("Truss", justify="right", style="green")
table.add_column("Ratio", justify="right", style="green")

# add data to the table
table.add_row(
    "area",
    f"{sec_pfc.get_area():.0f}",
    f"{sec_truss.get_area():.0f}",
    f"{area_ratio:.2f}",
)
table.add_row(
    "ixx",
    f"{sec_pfc.get_ic()[0]:.3e}",
    f"{sec_truss.get_ic()[0]:.3e}",
    f"{ixx_ratio:.2f}",
)
table.add_row(
    "iyy",
    f"{sec_pfc.get_ic()[1]:.3e}",
    f"{sec_truss.get_ic()[1]:.3e}",
    f"{iyy_ratio:.2f}",
)
table.add_row(
    "zyy",
    f"{sec_pfc.get_z()[2]:.3e}",
    f"{sec_truss.get_z()[2]:.3e}",
    f"{zyy_ratio:.2f}",
)
table.add_row(
    "ry",
    f"{sec_pfc.get_rc()[1]:.0f}",
    f"{sec_truss.get_rc()[1]:.0f}",
    f"{ry_ratio:.2f}",
)

# print table
console = Console()
console.print(table)

        Section Properties Comparison        
┏━━━━━━━━━━┳━━━━━━━━━━━┳━━━━━━━━━━━┳━━━━━━━━┓
┃ Property ┃       PFC ┃     Truss ┃  Ratio ┃
┡━━━━━━━━━━╇━━━━━━━━━━━╇━━━━━━━━━━━╇━━━━━━━━┩
│ area     │      2255 │      4510 │   2.00 │
│ ixx      │ 8.344e+06 │ 1.669e+07 │   2.00 │
│ iyy      │ 1.286e+06 │ 1.245e+09 │ 968.42 │
│ zyy      │ 2.567e+04 │ 2.166e+06 │  84.37 │
│ ry       │        24 │       525 │  22.00 │
└──────────┴───────────┴───────────┴────────┘