Sectiony

A Python library for calculating section properties and performing stress analysis of structural cross-sections.

Library of Standard Shapes

Sectiony provides a library of common structural shapes that can be easily generated. These are available under sectiony.library.

Circular Hollow Section (chs)

sectiony.library.chs(d, t)

Parameters:

• d (float): Outer diameter
• t (float): Wall thickness

---

Rectangular Hollow Section (rhs)

sectiony.library.rhs(b, h, t, r)

Parameters:

• b (float): Width (x-direction)
• h (float): Height (y-direction)
• t (float): Wall thickness
• r (float): Outer corner radius

---

I Section (i)

sectiony.library.i(d, b, tf, tw, r)

Parameters:

• d (float): Depth (Height, y-direction)
• b (float): Width (Base, x-direction)
• tf (float): Flange thickness
• tw (float): Web thickness
• r (float): Root radius (fillet between web and flange)

---

U (Channel) Section (u)

sectiony.library.u(b, h, tw, tf, r)

Parameters:

• b (float): Width (x-direction)
• h (float): Height (y-direction)
• tw (float): Web thickness
• tf (float): Flange thickness
• r (float): Outside corner radius

---

Solid Rectangle (solid_rect)

sectiony.library.solid_rect(b, h)

Parameters:

• b (float): Width (x-direction)
• h (float): Height (y-direction)

---

Solid Circle (solid_circle)

sectiony.library.solid_circle(d)

Parameters:

• d (float): Outer diameter

---

Square Hollow Section (shs)

sectiony.library.shs(d, t, r=0.0)

Parameters:

• d (float): Side length
• t (float): Wall thickness
• r (float): Outer corner radius

---

Angle (angle)

sectiony.library.angle(b, h, t, r=0.0)

Parameters:

• b (float): Horizontal leg width (x-direction)
• h (float): Vertical leg height (y-direction)
• t (float): Leg thickness
• r (float): Root fillet radius

---

T-Section (t_section)

sectiony.library.t_section(b, d, tf, tw, r=0.0)

Parameters:

• b (float): Flange width
• d (float): Total depth
• tf (float): Flange thickness
• tw (float): Web thickness
• r (float): Fillet radius

---

Features

Geometry Visualization

You can visualize the cross-section geometry, including accurate rendering of curved segments. Holes are automatically clipped to only show where they intersect with solid material.

from sectiony.library import i

# Create an I-section
beam = i(d=100.0, b=50.0, tf=10.0, tw=5.0, r=5.0)

# Plot the section
beam.plot()

# Save plot to file
import matplotlib.pyplot as plt
fig, ax = plt.subplots()
beam.plot(ax=ax, show=False)
fig.savefig("beam.svg", format='svg')

Stress Analysis and Plotting

Sectiony can calculate and visualize stress distributions resulting from internal forces (Axial, Bending, Shear, Torsion).

# Apply loads to the section
# N: Axial force, Vx/Vy: Shear forces, Mz: Torsion, Mx/My: Bending moments
stress_analysis = beam.calculate_stress(
    N=1000,    # Tension
    Mx=50000,  # Bending about x-axis
    Vy=500     # Shear in y-direction
)

# Plot von Mises stress distribution
stress_analysis.plot(stress_type="von_mises", cmap="inferno")

# Available stress types:
# "sigma" (Normal), "tau" (Shear), "von_mises" (Combined)
# "sigma_axial", "sigma_bending"
# "tau_shear", "tau_torsion"
# "sigma_1", "sigma_2" (Principal stresses)

JSON Serialization

You can save and load complex section geometries using JSON. The format preserves exact curve definitions (not just discretized points) and includes schema versioning.

from sectiony import Geometry

# Save geometry
beam.geometry.to_json("my_beam.json")

# Load geometry
loaded_geom = Geometry.from_json("my_beam.json")

# Properties are preserved exactly
new_section = Section(name="Loaded", geometry=loaded_geom)
print(f"Area: {new_section.A:.2f}")  # Same as original

See Examples:

• examples/making_sections.py - Comprehensive examples of creating sections
• examples/gallery/ - Visual gallery of section types
• jsons/ - Sample JSON files for all section types

Section Properties

Sectiony automatically calculates a comprehensive set of properties for any geometry.

Symbol	Property	Description
A	Area	Total cross-sectional area.
Cx, Cy	Centroids	Geometric center of the section.
Ix, Iy	Moments of Inertia	Resistance to bending about x and y axes.
Ixy	Product of Inertia	Measure of asymmetry.
J	Torsional Constant	Resistance to twisting.
Sx, Sy	Elastic Moduli	Used for elastic stress calculation ($I/c$).
Zpl_x, Zpl_y	Plastic Moduli	Used for plastic moment capacity.
rx, ry	Radii of Gyration	Used for buckling analysis ($\sqrt{I/A}$).
SCx, SCy	Shear Center	Point where transverse loads induce no torsion.
Cw	Warping Constant	Resistance to warping.
I1, I2	Principal Second Moments	Maximum and minimum bending stiffness about principal axes.
principal_angle	Principal Axis Angle	Angle (radians) of the principal axes from the x-axis.
shape_factor_x, shape_factor_y	Shape Factors	Plastic/elastic modulus ratio ($Z_{pl}/S$).

Accessing Properties

Properties are available as attributes on the Section object:

# Print properties
print(f"Area: {beam.A:.2f}")
print(f"Ix: {beam.Ix:.2f}")
print(f"J: {beam.J:.2f}")