Overview
Sections define the geometric properties of structural members. Each section is associated with a material and provides area, moment of inertia, and shear coefficients needed for structural analysis.
milcapy supports four types of sections:
- Rectangular: Standard rectangular cross-sections
- Circular: Circular cross-sections
- Generic: Custom sections with user-defined properties
- Shell: Thin sections for membrane/plate elements
add_rectangular_section()
Adds a rectangular cross-section to the model.
model.add_rectangular_section(
name="beam_30x50",
material_name="concrete",
base=0.30,
height=0.50
)
Parameters
Unique identifier for the section. Used when creating members.
Name of a previously defined material.
Width of the rectangular section (b).Must be greater than 0.
Height/depth of the rectangular section (h).Must be greater than 0.
Returns
Returns a RectangularSection object with computed properties:
- Area: A = b × h
- Moment of Inertia: I = (b × h³) / 12
- Shear Coefficient: k = 5/6 (Timoshenko)
Example
from milcapy import SystemModel
model = SystemModel()
# Define material first
model.add_material("concrete", 25000, 0.2, 2400)
# Add rectangular sections
model.add_rectangular_section(
name="column_40x40",
material_name="concrete",
base=0.40,
height=0.40
)
model.add_rectangular_section(
name="beam_30x60",
material_name="concrete",
base=0.30,
height=0.60
)
add_circular_section()
Adds a circular cross-section to the model.
model.add_circular_section(
name="pipe_200",
material_name="steel",
diameter=0.20
)
Parameters
Unique identifier for the section.
Name of a previously defined material.
Diameter of the circular section (d).Must be greater than 0.
Returns
Returns a CircularSection object with computed properties:
- Area: A = π × r²
- Moment of Inertia: I = (π × d⁴) / 64
- Shear Coefficient: k = 9/10 (Timoshenko)
Example
model.add_material("steel", 200000, 0.3, 7850)
# Solid circular sections
model.add_circular_section(
name="rod_25mm",
material_name="steel",
diameter=0.025 # 25mm
)
model.add_circular_section(
name="column_300",
material_name="steel",
diameter=0.30 # 300mm
)
add_generic_section()
Adds a section with custom geometric properties.
model.add_generic_section(
name="W14x22",
material_name="steel",
area=6.49e-3,
inertia=2.06e-5,
k_factor=0.54
)
Parameters
Unique identifier for the section.
Name of a previously defined material.
Cross-sectional area (A).Must be greater than 0.
Moment of inertia about the strong axis (I).Must be greater than 0.
Shear coefficient factor.The effective shear area is: A_shear = A × k_factorTypical values:
- Rectangular: 5/6 ≈ 0.833
- Circular: 9/10 = 0.9
- I-beams: 0.3 - 0.6
Returns
Returns a GenericSection with the specified properties.
Example: Steel Wide Flange Sections
model.add_material("A992_steel", 200000, 0.3, 7850)
# W14x22 section (SI units: m)
model.add_generic_section(
name="W14x22",
material_name="A992_steel",
area=4.19e-3, # m²
inertia=2.06e-5, # m⁴
k_factor=0.54
)
# W18x50 section
model.add_generic_section(
name="W18x50",
material_name="A992_steel",
area=9.48e-3,
inertia=8.88e-5,
k_factor=0.51
)
Example: Composite Section
# Custom composite or built-up section
model.add_generic_section(
name="composite_beam",
material_name="concrete",
area=0.25, # Pre-calculated area
inertia=0.0052, # Pre-calculated inertia
k_factor=0.75 # Estimated shear factor
)
add_shell_section()
Adds a shell section for membrane or plate finite elements.
model.add_shell_section(
name="wall_200mm",
material_name="concrete",
thickness=0.20
)
Parameters
Unique identifier for the section.
Name of a previously defined material.
Thickness of the shell element (t).Must be greater than 0.
Returns
Returns a ShellSection object used for 2D membrane elements (CST, Q4, Q6, Q8).
Example
model.add_material("concrete", 25000, 0.2, 2400)
# Concrete wall sections
model.add_shell_section(
name="wall_150",
material_name="concrete",
thickness=0.15
)
model.add_shell_section(
name="wall_200",
material_name="concrete",
thickness=0.20
)
model.add_shell_section(
name="slab_120",
material_name="concrete",
thickness=0.12
)
Property Modifiers
set_property_modifiers()
Apply modification factors to section properties. Useful for cracked section analysis or construction staging.
model.set_property_modifiers(
section_name="beam_30x50",
axial_area=0.8, # 80% of gross area
shear_area=1.0, # 100% of shear area
moment_inertia=0.5, # 50% of gross inertia (cracked)
weight=1.0 # 100% of weight
)
Parameters
Name of the section to modify.
Multiplier for axial area (kA).Effective area: A_eff = A × axial_area
Multiplier for shear area (kAs).Effective shear area: As_eff = As × shear_area
Multiplier for moment of inertia (kI).Effective inertia: I_eff = I × moment_inertiaCommon for cracked concrete sections (often 0.35 - 0.5).
Multiplier for self-weight (kg).Effective weight: W_eff = W × weight
Example: Cracked Section Analysis
model.add_material("concrete", 25000, 0.2, 2400)
model.add_rectangular_section("beam", "concrete", 0.3, 0.5)
# Model cracked concrete section
model.set_property_modifiers(
section_name="beam",
moment_inertia=0.35, # 35% of gross inertia (typical for cracked concrete)
weight=1.0 # Full weight still applies
)
Section Properties Summary
Each section type computes the following properties:
Rectangular Section
A = b × h
I = (b × h³) / 12
k = 5/6 (Timoshenko shear coefficient)
Circular Section
A = π × r² = π × (d/2)²
I = (π × d⁴) / 64
k = 9/10 (Timoshenko shear coefficient)
Generic Section
A = (user specified)
I = (user specified)
k = (user specified)
Shell Section
t = thickness (used in membrane stiffness calculations)
Validation
All section creation methods perform validation:
Unique Name: Section name must not already exist
Material Exists: Referenced material must be defined
Positive Dimensions: All geometric properties must be > 0
Error Examples
# These will raise ValueError
# Material doesn't exist
model.add_rectangular_section("beam", "undefined_mat", 0.3, 0.5)
# Negative dimensions
model.add_rectangular_section("beam", "concrete", -0.3, 0.5)
# Zero diameter
model.add_circular_section("column", "steel", 0)
# Duplicate name
model.add_rectangular_section("beam", "concrete", 0.3, 0.5)
model.add_rectangular_section("beam", "steel", 0.4, 0.6) # Error: name exists
Complete Example
from milcapy import SystemModel, BeamTheoriesType
model = SystemModel()
# Define materials
model.add_material("concrete", 25000, 0.2, 2400)
model.add_material("steel", 200000, 0.3, 7850)
# Define various sections
model.add_rectangular_section("column_40x40", "concrete", 0.4, 0.4)
model.add_rectangular_section("beam_30x60", "concrete", 0.3, 0.6)
model.add_circular_section("brace_100", "steel", 0.1)
model.add_shell_section("wall_200", "concrete", 0.2)
# Apply cracking to beam
model.set_property_modifiers(
section_name="beam_30x60",
moment_inertia=0.35 # Cracked section
)
# Use sections in members
model.add_node(1, 0, 0)
model.add_node(2, 5, 0)
model.add_member(1, 1, 2, "beam_30x60", BeamTheoriesType.TIMOSHENKO)
See Also
