Merge pull request #572 from Blueprints-org/571-feature-request-add-basis-for-complex-steel-shapes

Author: egarciamendez

blueprints/structural_sections/_cross_section.py

@@ -24,19 +24,25 @@ def polygon(self) -> Polygon:
         """Shapely Polygon representing the cross-section."""
 
     @property
-    @abstractmethod
     def area(self) -> MM2:
-        """Area of the cross-section [mm²]."""
+        """Area of the cross-section [mm²].
+
+        When using circular cross-sections, the area is an approximation of the area of the polygon.
+        The area is calculated using the `area` property of the Shapely Polygon.
+
+        In case you need an exact answer then you need to override this method in the derived class.
+        """
+        return self.polygon.area
 
     @property
-    @abstractmethod
     def perimeter(self) -> MM:
         """Perimeter of the cross-section [mm]."""
+        return self.polygon.length
 
     @property
-    @abstractmethod
     def centroid(self) -> Point:
         """Centroid of the cross-section [mm]."""
+        return self.polygon.centroid
 
     @property
     @abstractmethod
@@ -78,16 +84,21 @@ def plastic_section_modulus_about_y(self) -> MM3 | None:
     def plastic_section_modulus_about_z(self) -> MM3 | None:
         """Plastic section modulus about the z-axis [mm³]."""
 
-    @abstractmethod
     def geometry(self, mesh_size: MM | None = None) -> Geometry:
-        """Abstract method to be implemented by subclasses to return the geometry of the cross-section.
+        """Geometry of the cross-section.
 
         Properties
         ----------
         mesh_size : MM
             Maximum mesh element area to be used within
             the Geometry-object finite-element mesh. If not provided, a default value will be used.
         """
+        if mesh_size is None:
+            mesh_size = 2.0
+
+        geom = Geometry(geom=self.polygon)
+        geom.create_mesh(mesh_sizes=mesh_size)
+        return geom
 
     def section(self) -> Section:
         """Section object representing the cross-section."""

blueprints/structural_sections/cross_section_quarter_circular_spandrel.py

@@ -51,12 +51,15 @@ def polygon(self) -> Polygon:
         """
         left_lower = (self.x, self.y)
 
-        # Approximate the quarter circle with 50 straight lines
+        # Approximate the quarter circle with 25 straight lines.
+        # This resolution was chosen to balance performance and accuracy.
+        # Increasing the number of segments (e.g., to 50) would improve accuracy but at the cost of computational performance.
+        # Ensure this resolution meets the requirements of your specific application before using.
         quarter_circle_points = [
-            (self.x + self.radius - self.radius * math.cos(math.pi / 2 * i / 50), self.y + self.radius - self.radius * math.sin(math.pi / 2 * i / 50))
-            for i in range(51)
+            (self.x + self.radius - self.radius * math.cos(math.pi / 2 * i / 25), self.y + self.radius - self.radius * math.sin(math.pi / 2 * i / 25))
+            for i in range(26)
         ]
-        for i in range(51):
+        for i in range(26):
             if self.mirrored_horizontally:
                 quarter_circle_points[i] = (2 * left_lower[0] - quarter_circle_points[i][0], quarter_circle_points[i][1])
             if self.mirrored_vertically:

blueprints/structural_sections/cross_section_rectangle.py

@@ -3,10 +3,10 @@
 from dataclasses import dataclass
 
 from sectionproperties.pre import Geometry
-from shapely import Point, Polygon
+from shapely import Polygon
 
 from blueprints.structural_sections._cross_section import CrossSection
-from blueprints.type_alias import MM, MM2, MM3, MM4
+from blueprints.type_alias import MM, MM3, MM4
 
 
 @dataclass(frozen=True)
@@ -67,42 +67,6 @@ def polygon(self) -> Polygon:
             ]
         )
 
-    @property
-    def area(self) -> MM2:
-        """
-        Calculate the area of the rectangular cross-section.
-
-        Returns
-        -------
-        MM2
-            The area of the rectangle.
-        """
-        return self.width * self.height
-
-    @property
-    def perimeter(self) -> MM:
-        """
-        Calculate the perimeter of the rectangular cross-section.
-
-        Returns
-        -------
-        MM
-            The perimeter of the rectangle.
-        """
-        return 2 * (self.width + self.height)
-
-    @property
-    def centroid(self) -> Point:
-        """
-        Get the centroid of the rectangular cross-section.
-
-        Returns
-        -------
-        Point
-            The centroid of the rectangle.
-        """
-        return Point(self.x, self.y)
-
     @property
     def moment_of_inertia_about_y(self) -> MM4:
         """

blueprints/structural_sections/steel/steel_cross_sections/_steel_cross_section.py

@@ -0,0 +1,164 @@
+"""Base class of all steel cross-sections."""
+
+from abc import ABC
+from collections.abc import Sequence
+from dataclasses import dataclass, field
+
+from shapely.geometry import Polygon
+from shapely.geometry.base import BaseGeometry
+from shapely.geometry.polygon import orient
+
+from blueprints.structural_sections._cross_section import CrossSection
+from blueprints.structural_sections.steel.steel_element import SteelElement
+from blueprints.type_alias import KG_M, M3_M, MM, MM3, MPA
+from blueprints.unit_conversion import MM3_TO_M3
+
+
+@dataclass(kw_only=True)
+class CombinedSteelCrossSection(CrossSection, ABC):
+    """Base class of all steel cross-sections.
+
+    Parameters
+    ----------
+    elements : Sequence[SteelElement], optional
+        A sequence of steel elements that make up the cross-section.
+        Default is an empty list.
+    name : str, optional
+        The name of the cross-section. Default is "Combined Steel Cross Section".
+    """
+
+    elements: Sequence[SteelElement] = field(default_factory=list)
+    name: str = "Combined Steel Cross Section"
+
+    @property
+    def polygon(self) -> Polygon:
+        """Return the polygon of the steel cross-section."""
+        # check if there are any elements
+        if not self.elements:
+            raise ValueError("No elements have been added to the cross-section.")
+
+        # return the polygon of the first element if there is only one
+        if len(self.elements) == 1:
+            return self.elements[0].cross_section.polygon
+
+        # Combine the polygons of all elements if there is multiple
+        combined_polygon: BaseGeometry = self.elements[0].cross_section.polygon
+        for element in self.elements[1:]:
+            combined_polygon = combined_polygon.union(element.cross_section.polygon)
+
+        # Ensure the result is a valid Polygon
+        if not isinstance(combined_polygon, Polygon):
+            raise TypeError("The combined geometry is not a valid Polygon.")
+
+        # Ensure consistent orientation
+        return orient(combined_polygon)
+
+    @property
+    def height(self) -> MM:
+        """Height of the cross-section [mm]."""
+        return self.polygon.bounds[3] - self.polygon.bounds[1]
+
+    @property
+    def width(self) -> MM:
+        """Width of the cross-section [mm]."""
+        return self.polygon.bounds[2] - self.polygon.bounds[0]
+
+    @property
+    def volume_per_meter(self) -> M3_M:
+        """Total volume of the reinforced cross-section per meter length [m³/m]."""
+        length = 1000  # mm
+        return self.area * length * MM3_TO_M3
+
+    @property
+    def weight_per_meter(self) -> KG_M:
+        """
+        Calculate the weight per meter of the steel element.
+
+        Returns
+        -------
+        KG_M
+            The weight per meter of the steel element.
+        """
+        return sum(element.weight_per_meter for element in self.elements)
+
+    @property
+    def moment_of_inertia_about_y(self) -> KG_M:
+        """Moment of inertia about the y-axis per meter length [mm⁴]."""
+        body_moments_of_inertia = sum(element.cross_section.moment_of_inertia_about_y for element in self.elements)
+        parallel_axis_theorem = sum(
+            element.cross_section.area * (element.cross_section.centroid.y - self.centroid.y) ** 2 for element in self.elements
+        )
+        return body_moments_of_inertia + parallel_axis_theorem
+
+    @property
+    def moment_of_inertia_about_z(self) -> KG_M:
+        """Moment of inertia about the z-axis per meter length [mm⁴]."""
+        body_moments_of_inertia = sum(element.cross_section.moment_of_inertia_about_z for element in self.elements)
+        parallel_axis_theorem = sum(
+            element.cross_section.area * (element.cross_section.centroid.x - self.centroid.x) ** 2 for element in self.elements
+        )
+        return body_moments_of_inertia + parallel_axis_theorem
+
+    @property
+    def elastic_section_modulus_about_y_positive(self) -> KG_M:
+        """Elastic section modulus about the y-axis on the positive z side [mm³]."""
+        distance_to_top = max(y for _, y in self.polygon.exterior.coords) - self.centroid.y
+        return self.moment_of_inertia_about_y / distance_to_top
+
+    @property
+    def elastic_section_modulus_about_y_negative(self) -> KG_M:
+        """Elastic section modulus about the y-axis on the negative z side [mm³]."""
+        distance_to_bottom = self.centroid.y - min(y for _, y in self.polygon.exterior.coords)
+        return self.moment_of_inertia_about_y / distance_to_bottom
+
+    @property
+    def elastic_section_modulus_about_z_positive(self) -> KG_M:
+        """Elastic section modulus about the z-axis on the positive y side [mm³]."""
+        distance_to_right = max(x for x, _ in self.polygon.exterior.coords) - self.centroid.x
+        return self.moment_of_inertia_about_z / distance_to_right
+
+    @property
+    def elastic_section_modulus_about_z_negative(self) -> KG_M:
+        """Elastic section modulus about the z-axis on the negative y side [mm³]."""
+        distance_to_left = self.centroid.x - min(x for x, _ in self.polygon.exterior.coords)
+        return self.moment_of_inertia_about_z / distance_to_left
+
+    @property
+    def plastic_section_modulus_about_y(self) -> MM3 | None:
+        """Plastic section modulus about the y-axis [mm³]."""
+        return self.section_properties().sxx
+
+    @property
+    def plastic_section_modulus_about_z(self) -> MM3 | None:
+        """Plastic section modulus about the z-axis [mm³]."""
+        return self.section_properties().syy
+
+    @property
+    def yield_strength(self) -> MPA:
+        """
+        Calculate the yield strength of the steel element.
+
+        This is the minimum yield strength of all elements in the cross-section.
+
+        Returns
+        -------
+        MPa
+            The yield strength of the steel element.
+        """
+        # let's find the minimum yield strength of all elements
+        return min(element.yield_strength for element in self.elements)
+
+    @property
+    def ultimate_strength(self) -> MPA:
+        """
+        Calculate the ultimate strength of the steel element.
+
+        This is the minimum ultimate strength of all elements in the cross-section.
+
+        Returns
+        -------
+        MPa
+            The ultimate strength of the steel element.
+        """
+        # let's find the minimum ultimate strength of all elements
+        return min(element.ultimate_strength for element in self.elements)