aisc

Classes

ElasticSection

ElasticSection(user_name: str = 'Unnamed', *, E: float, A: float, Iz: float, Iy: Optional[float] = None, G: Optional[float] = None, J: Optional[float] = None)

Bases: Section

Linear-elastic section defined by explicit geometric and material constants.

This section represents a linear beam-column cross-section. Unlike most other Femora sections, it does not reference a Material object; instead, it takes material moduli (E, G) and geometric properties (A, I, J) directly as constructor arguments.

Tcl form

2D: section Elastic <tag> <E> <A> <Iz>
3D: section Elastic <tag> <E> <A> <Iz> <Iy> <G> <J>

Note

This section is strictly linear. For nonlinear behavior, use FiberSection or UniaxialSection.
When using this section in a 3D model, you must provide all six parameters (E, A, Iz, Iy, G, J). OpenSees usually expects either 3 or 6 values for the Elastic section command.

Tip

Use this section for preliminary modeling or when physical section dimensions are unknown but aggregate properties (like equivalent stiffness) are available.

Example

from femora.core.model import Model
import femora.components.section.beam  # noqa: F401

model = Model()
sec_2d = model.section.beam.elastic(
    user_name="Beam2D",
    E=29000.0,
    A=10.0,
    Iz=150.0,
)
sec_3d = model.section.beam.elastic(
    user_name="Column3D",
    E=29000.0,
    A=26.5,
    Iz=999.0,
    Iy=150.0,
    G=11200.0,
    J=2.5,
)
print(sec_3d.tag)

Create an ElasticSection with validated geometric properties.

Parameters:

Name	Type	Description	Default
`user_name`	`str`	User-specified name for the section.	`'Unnamed'`
`E`	`float`	Young's modulus.	required
`A`	`float`	Cross-sectional area.	required
`Iz`	`float`	Second moment of area about the local z-axis.	required
`Iy`	`Optional[float]`	Optional second moment of area about the local y-axis (for 3D).	`None`
`G`	`Optional[float]`	Optional shear modulus (for 3D).	`None`
`J`	`Optional[float]`	Optional torsional constant (for 3D).	`None`

Raises:

Type	Description
`ValueError`	If parameters are not numeric or if essential values (E, A, Iz) are non-positive.

Methods:

to_tcl

to_tcl() -> str

Render the section as an OpenSees Tcl command.

Returns:

Name	Type	Description
`str`	`str`	Tcl command string for this section.

Raises:

Type	Description
`ValueError`	If this section has not been added to a manager.

get_materials

get_materials() -> list[Material]

Return materials used by this section.

Returns:

Type	Description
`list[Material]`	An empty list as ElasticSection does not use Material objects.

get_area

get_area() -> float

Return the cross-sectional area.

Returns:

Type	Description
`float`	Area value.

get_Iz

get_Iz() -> float

Return the second moment of area about the local z-axis.

Returns:

Type	Description
`float`	Iz value.

get_Iy

get_Iy() -> float

Return the second moment of area about the local y-axis.

Returns:

Type	Description
`float`	Iy value, or 0.0 if not defined.

get_J

get_J() -> float

Return the torsional constant.

Returns:

Type	Description
`float`	J value, or 0.0 if not defined.

FiberSection

FiberSection(user_name: str = 'Unnamed', GJ: Optional[float] = None, components: Optional[List[Union[FiberElement, PatchBase, LayerBase]]] = None)

Bases: Section

General cross-section discretized into a collection of fibers.

The Fiber section is the most general section type in Femora. It allows modeling arbitrary geometries by defining individual fibers, patches (grids), or layers (lines/arcs) of uniaxial materials. The section response is obtained by integrating the response of each fiber over the area.

Tcl form

section Fiber <tag> [-GJ <gj>] { <fiber/patch/layer commands> }

Note

Geometric properties (Area, Iy, Iz, J) are computed automatically by discretizing all components into individual fibers and summing their contributions.
OpenSees does not prevent overlapping fibers; if two fibers occupy the same space, their contributions are summed, effectively doubling the stiffness and strength at that location.
The GJ parameter provides a linear torsional stiffness that is independent of the fibers.

Tip

Use the plot() method frequently during model development to verify that your fibers and patches are correctly positioned.
For large models, be mindful of the total fiber count. While more fibers increase accuracy, they also increase computation time.
If your section only needs flexure in one plane, consider WFSection2d for simplicity.

Example

from femora.core.model import Model
import femora.components.section.fiber  # noqa: F401

model = Model()
concr = model.material.uniaxial.elastic(user_name="Concrete", E=3600.0)
steel = model.material.uniaxial.steel01(
    user_name="Steel",
    Fy=60.0,
    E0=29000.0,
    b=0.01,
)
sec = model.section.fiber.section(user_name="RC_Beam", GJ=1000.0)
sec.add_rectangular_patch(
    material=concr,
    num_subdiv_y=10,
    num_subdiv_z=10,
    y1=-5,
    z1=-5,
    y2=5,
    z2=5,
)
sec.add_fiber(y_loc=-4.5, z_loc=-4.5, area=0.44, material=steel)
print(sec.tag)

Create a FiberSection with optional initial components.

Parameters:

Name	Type	Description	Default
`user_name`	`str`	Unique identifier for the section.	`'Unnamed'`
`GJ`	`Optional[float]`	Optional linear torsional stiffness constant. If provided, this stiffness is added to the section's torsional response.	`None`
`components`	`Optional[List[Union[FiberElement, PatchBase, LayerBase]]]`	Optional list of pre-created fiber elements, patches, or layers to populate the section.	`None`

Raises:

Type	Description
`ValueError`	If GJ is not numeric or is non-positive.

Methods:

add_fiber

add_fiber(y_loc: float, z_loc: float, area: float, material: Union[int, str, Material]) -> None

Add an individual fiber at a specific (y, z) location.

Parameters:

Name	Type	Description	Default
`y_loc`	`float`	Local y-coordinate of the fiber center.	required
`z_loc`	`float`	Local z-coordinate of the fiber center.	required
`area`	`float`	Cross-sectional area of the fiber.	required
`material`	`Union[int, str, Material]`	Uniaxial material reference for the fiber.	required

add_rectangular_patch

add_rectangular_patch(material: Union[int, str, Material], num_subdiv_y: int, num_subdiv_z: int, y1: float, z1: float, y2: float, z2: float) -> None

Add a rectangular patch discretized into a grid of fibers.

Parameters:

Name	Type	Description	Default
`material`	`Union[int, str, Material]`	Uniaxial material reference for all fibers in the patch.	required
`num_subdiv_y`	`int`	Number of fibers along the local y-axis.	required
`num_subdiv_z`	`int`	Number of fibers along the local z-axis.	required
`y1`	`float`	Minimum local y-coordinate of the rectangle.	required
`z1`	`float`	Minimum local z-coordinate of the rectangle.	required
`y2`	`float`	Maximum local y-coordinate of the rectangle.	required
`z2`	`float`	Maximum local z-coordinate of the rectangle.	required

add_quadrilateral_patch

add_quadrilateral_patch(material: Union[int, str, Material], num_subdiv_ij: int, num_subdiv_jk: int, vertices: list) -> None

Add a four-sided patch discretized into fibers.

Parameters:

Name	Type	Description	Default
`material`	`Union[int, str, Material]`	Uniaxial material reference.	required
`num_subdiv_ij`	`int`	Subdivisions along the first direction (edge 1-2).	required
`num_subdiv_jk`	`int`	Subdivisions along the second direction (edge 2-3).	required
`vertices`	`list`	Exactly 4 (y, z) vertex pairs defining the boundary.	required

add_circular_patch

add_circular_patch(material: Union[int, str, Material], num_subdiv_circ: int, num_subdiv_rad: int, y_center: float, z_center: float, int_rad: float, ext_rad: float, start_ang: float = 0.0, end_ang: float = 360.0) -> None

Add a circular or arc-shaped patch.

Parameters:

Name	Type	Description	Default
`material`	`Union[int, str, Material]`	Uniaxial material reference.	required
`num_subdiv_circ`	`int`	Circumferential subdivisions.	required
`num_subdiv_rad`	`int`	Radial subdivisions.	required
`y_center`	`float`	Y-coordinate of the circle center.	required
`z_center`	`float`	Z-coordinate of the circle center.	required
`int_rad`	`float`	Inner radius (0 for solid circle).	required
`ext_rad`	`float`	Outer radius.	required
`start_ang`	`float`	Starting angle in degrees.	`0.0`
`end_ang`	`float`	Ending angle in degrees.	`360.0`

add_straight_layer

add_straight_layer(material: Union[int, str, Material], num_fibers: int, area_per_fiber: float, y1: float, z1: float, y2: float, z2: float) -> None

Add a straight line of fibers.

Parameters:

Name	Type	Description	Default
`material`	`Union[int, str, Material]`	Uniaxial material reference.	required
`num_fibers`	`int`	Number of fibers along the line.	required
`area_per_fiber`	`float`	Cross-sectional area of each fiber.	required
`y1`	`float`	Y-coordinate of start point.	required
`z1`	`float`	Z-coordinate of start point.	required
`y2`	`float`	Y-coordinate of end point.	required
`z2`	`float`	Z-coordinate of end point.	required

add_circular_layer

add_circular_layer(material: Union[int, str, Material], num_fibers: int, area_per_fiber: float, y_center: float, z_center: float, radius: float, start_ang: float = 0.0, end_ang: Optional[float] = None) -> None

Add a circular arc of fibers.

Parameters:

Name	Type	Description	Default
`material`	`Union[int, str, Material]`	Uniaxial material reference.	required
`num_fibers`	`int`	Number of fibers along the arc.	required
`area_per_fiber`	`float`	Cross-sectional area of each fiber.	required
`y_center`	`float`	Y-coordinate of arc center.	required
`z_center`	`float`	Z-coordinate of arc center.	required
`radius`	`float`	Arc radius.	required
`start_ang`	`float`	Optional starting angle in degrees.	`0.0`
`end_ang`	`Optional[float]`	Optional ending angle in degrees.	`None`

to_tcl

to_tcl() -> str

Render the complete Fiber section command block.

Returns:

Name	Type	Description
`str`	`str`	Tcl command block including nested fiber, patch, and layer commands.

Raises:

Type	Description
`ValueError`	If this section has not been added to a manager.

get_materials

get_materials() -> List[Material]

Return all unique materials used in the section.

Returns:

Type	Description
`List[Material]`	List of unique Material objects found in any component.

get_area

get_area() -> float

Calculate the total cross-sectional area from fibers.

Returns:

Type	Description
`float`	The sum of all fiber areas.

get_Iy

get_Iy() -> float

Calculate the second moment of area about the local y-axis.

Returns:

Type	Description
`float`	The computed Iy value.

get_Iz

get_Iz() -> float

Calculate the second moment of area about the local z-axis.

Returns:

Type	Description
`float`	The computed Iz value.

get_J

get_J() -> float

Approximate the torsional constant as Iy + Iz.

Note

This is a geometric polar moment of inertia approximation. If explicit torsional stiffness is needed, use the GJ parameter in the constructor.

Returns:

Type	Description
`float`	Sum of Iy and Iz.

clear_all

clear_all() -> None

Remove all fibers, patches, and layers from the section.

plot

plot(ax: Optional[Axes] = None, figsize: Tuple[float, float] = (10, 8), show_fibers: bool = True, show_patches: bool = True, show_layers: bool = True, show_patch_outline: bool = True, show_fiber_grid: bool = True, show_layer_line: bool = True, title: Optional[str] = None, material_colors: Optional[Dict[str, str]] = None, save_path: Optional[str] = None, dpi: int = 300) -> plt.Figure

Visualize the fiber section geometry using Matplotlib.

Parameters:

Name	Type	Description	Default
`ax`	`Optional[Axes]`	Optional Matplotlib axes. If None, a new figure is created.	`None`
`figsize`	`Tuple[float, float]`	Figure size for the new plot.	`(10, 8)`
`show_fibers`	`bool`	Whether to draw small markers at each fiber location.	`True`
`show_patches`	`bool`	Whether to draw filled polygons for patches.	`True`
`show_layers`	`bool`	Whether to draw markers/lines for layers.	`True`
`show_patch_outline`	`bool`	Whether to highlight the boundaries of patches.	`True`
`show_fiber_grid`	`bool`	Whether to draw internal grid lines for patches.	`True`
`show_layer_line`	`bool`	Whether to draw the center-line of layers.	`True`
`title`	`Optional[str]`	Optional plot title.	`None`
`material_colors`	`Optional[Dict[str, str]]`	Optional map from material names to color strings.	`None`
`save_path`	`Optional[str]`	Optional file path to save the image.	`None`
`dpi`	`int`	Resolution for the saved image.	`300`

Returns:

Type	Description
`Figure`	The Matplotlib Figure object.

plot_components `staticmethod`

plot_components(fibers: List[FiberElement], patches: List[PatchBase], layers: List[LayerBase], ax: Optional[Axes] = None, figsize: Tuple[float, float] = (10, 8), show_fibers: bool = True, show_patches: bool = True, show_layers: bool = True, show_patch_outline: bool = True, show_fiber_grid: bool = True, show_layer_line: bool = True, title: Optional[str] = None, material_colors: Optional[Dict[str, str]] = None, save_path: Optional[str] = None, dpi: int = 300) -> plt.Figure

Static utility to plot arbitrary fiber section components.

Parameters:

Name	Type	Description	Default
`fibers`	`List[FiberElement]`	Individual fiber elements to draw.	required
`patches`	`List[PatchBase]`	Patch components to draw.	required
`layers`	`List[LayerBase]`	Layer components to draw.	required
`ax`	`Optional[Axes]`	Optional Matplotlib axes. If None, a new figure is created.	`None`
`figsize`	`Tuple[float, float]`	Figure size for the new plot.	`(10, 8)`
`show_fibers`	`bool`	Whether to draw small markers at each fiber location.	`True`
`show_patches`	`bool`	Whether to draw filled polygons for patches.	`True`
`show_layers`	`bool`	Whether to draw markers or lines for layers.	`True`
`show_patch_outline`	`bool`	Whether to highlight patch boundaries.	`True`
`show_fiber_grid`	`bool`	Whether to draw internal grid lines for patches.	`True`
`show_layer_line`	`bool`	Whether to draw the center-line of layers.	`True`
`title`	`Optional[str]`	Optional plot title.	`None`
`material_colors`	`Optional[Dict[str, str]]`	Optional map from material names to color strings.	`None`
`save_path`	`Optional[str]`	Optional file path to save the image.	`None`
`dpi`	`int`	Resolution for the saved image.	`300`

Returns:

Type	Description
`Figure`	The Matplotlib Figure object.

generate_material_colors `staticmethod`

generate_material_colors(fibers: List[FiberElement], patches: List[PatchBase], layers: List[LayerBase]) -> Dict[str, str]

Generate a stable color mapping for materials in the section.

calculate_scale_factor `staticmethod`

calculate_scale_factor(fibers: List[FiberElement]) -> float

Determine a visualization scale factor based on fiber distribution.

Section

Section(section_type: str, section_name: str, user_name: str)

Bases: ABC

Abstract base class for all sections with manager-owned tagging.

Section objects do not self-register and do not assign their own tags. A :class:~femora.core.section_manager.SectionManager owns lifecycle operations, tag assignment, removal, and retagging for a local model context.

Parameters:

Name	Type	Description	Default
`section_type`	`str`	The type of section (e.g., 'section').	required
`section_name`	`str`	The specific section name for OpenSees (e.g., 'Elastic').	required
`user_name`	`str`	User-specified name for the section.	required

Attributes:

Name	Type	Description
`tag`	`Optional[int]`	Manager-assigned OpenSees tag. It remains `None` until the instance is added to a :class:`~femora.core.section_manager.SectionManager`.
`_owner`	`Optional[Any]`	Reference to the owning manager, or `None` when unmanaged.

Methods:

to_tcl `abstractmethod`

to_tcl() -> str

Convert the section to a TCL string representation for OpenSees.

Returns:

Type	Description
`str`	TCL command string for this section.

resolve_material

resolve_material(material_input: Union[int, str, 'Material', None]) -> Optional['Material']

Resolve material using the owner manager when possible.

resolve_materials_dict

resolve_materials_dict(materials_input: Dict[str, Union[int, str, 'Material']]) -> Dict[str, 'Material']

Resolve a dictionary of material references.

resolve_section

resolve_section(section_input: Union[int, str, 'Section', None]) -> Optional['Section']

Resolve another section using the owner manager when possible.

resolve_material_reference `staticmethod`

resolve_material_reference(material_input: Union[int, str, 'Material', None]) -> Optional['Material']

Resolve a material object passed directly to an unmanaged section.

get_materials

get_materials() -> List['Material']

Return materials used by this section for dependency tracking.

has_material

has_material() -> bool

Return True when this section depends on a material.

get_area

get_area() -> float

Return cross-sectional area when the section provides it.

get_Iy

get_Iy() -> float

Return second moment of area about local y when available.

get_Iz

get_Iz() -> float

Return second moment of area about local z when available.

get_J

get_J() -> float

Return torsional constant when the section provides it.

Functions:

create_section

create_section(name: str, model, material, type: str = 'Elastic', unit_system: str = 'in', user_name: str = None) -> Section

Create a Femora Section object from an AISC database name using the provided model instance.

Parameters:

Name	Type	Description	Default
`name`	`str`	AISC section name (e.g., "W14X90").	required
`model`	`Model`	Femora Model instance with a `section` manager.	required
`material`	`Material`	Femora material object.	required
`type`	`str`	'Elastic' or 'Fiber'. Defaults to "Elastic".	`'Elastic'`
`unit_system`	`str`	Target unit system for geometric properties ('in', 'ft', 'm', 'cm', 'mm'). Defaults to "in". Material properties (E, G) are NOT converted.	`'in'`
`user_name`	`str`	Custom name for the created section. If None, defaults to 'name'.	`None`

Returns:

Name	Type	Description
`Section`	`Section`	A standard Femora section object (ElasticSection or FiberSection).

Raises:

Type	Description
`ValueError`	If section name is not found in database.

aisc

aisc

Classes

ElasticSection

Methods:

to_tcl

get_materials

get_area

get_Iz

get_Iy

get_J

FiberSection

Methods:

add_fiber

add_rectangular_patch

add_quadrilateral_patch

add_circular_patch

add_straight_layer

add_circular_layer

to_tcl

get_materials

get_area

get_Iy

get_Iz

get_J

clear_all

plot

plot_components staticmethod

generate_material_colors staticmethod

calculate_scale_factor staticmethod

Section

Methods:

to_tcl abstractmethod

resolve_material

resolve_materials_dict

resolve_section

resolve_material_reference staticmethod

get_materials

has_material

get_area

get_Iy

get_Iz

get_J

Functions:

create_section

plot_components `staticmethod`

generate_material_colors `staticmethod`

calculate_scale_factor `staticmethod`

to_tcl `abstractmethod`

resolve_material_reference `staticmethod`