FiberSection

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

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.

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.

clear_all

clear_all() -> None

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