sectionproperties: angled hat section

angled_hat.py

from sectionproperties.pre.geometry import Geometry
from sectionproperties.pre.pre import Material, DEFAULT_MATERIAL
from sectionproperties.pre.library.primitive_sections import rectangular_section
from math import radians, sin, cos


def angled_hat(
    dim_1: float,
    dim_2: float,
    dim_3: float,
    dim_4: float,
    dim_5: float,
    dim_6: float,
    dim_7: float = None,
    material: Material = DEFAULT_MATERIAL,
) -> Geometry:
    """
    Creates a hat section with angled walls and 
        dim_1: total height (Y)
        dim_2: brim width
        dim_3: cap width
        dim_4: web thickness
        dim_5: cap thickness
        dim_6: web angle in degrees, 0 is vertical, 90 is horizontal
        dim_7: skin thickness (to close section for torsion constant calculation)
    """
    overall_height = dim_1
    brim_width = dim_2
    cap_width = dim_3
    web_thickness = dim_4
    cap_thickness = dim_5
    web_angle_deg = dim_6
    web_angle_rad = radians(web_angle_deg)

    # TODO Better validation and throw error instead
    if web_angle_deg < 0 or web_angle_deg >= 90:
        print(f"ERROR: Web angle ({web_angle_deg}) out of bounds. Value must be in range [0,90) degrees.")
        return
    
    # define exterior points from left to right, stopping at midplane
    pt_a0_l_bot = (0, 0)
    pt_a0_l_top = (0, web_thickness)

    pt_a0_r_bot = (brim_width + web_thickness, 0)
    pt_a0_r_top = (brim_width, web_thickness)

    h2 = overall_height - cap_thickness
    h_sl = (overall_height - cap_thickness / 2 - web_thickness / 2) / cos(web_angle_rad)
    l_sl = h_sl * sin(web_angle_rad)

    l2 = brim_width + l_sl
    pt_a1_r_bot = (l2 + web_thickness, h2)
    pt_a1_r_top = (l2, overall_height)

    midplane_width = l2 + (cap_width / 2)
    pt_a2_mid_bot = (midplane_width, h2)
    pt_a2_mid_top = (midplane_width, overall_height)

    points = [
        pt_a0_l_bot,
        pt_a0_r_bot,
        pt_a1_r_bot,
        pt_a2_mid_bot,
        pt_a2_mid_top,
        pt_a1_r_top,
        pt_a0_r_top,
        pt_a0_l_top,
    ]

    facets = [(0, 1), (1, 2), (2, 3), (3, 4), (4, 5), (5, 6), (6, 7), (7, 0)]

    # Create half the shape then mirror about the midplane
    shape_L = Geometry.from_points(
        points=points,
        facets=facets,
        control_points=[(brim_width / 2, web_thickness / 2)],
        material=material
    )
    shape_R = shape_L.mirror_section(axis="y", mirror_point=(midplane_width, 0))
    angled_hat = shape_L + shape_R

    # TODO refactor into separate `angled_hat_with_skin()` constructor
    if dim_7 is not None:
        t_skin = dim_7
        bounding_box = angled_hat.calculate_extents()
        overall_width = bounding_box[1] - bounding_box[0]
        skin = rectangular_section(d=t_skin, b=overall_width).align_to(
            other=angled_hat, on="bottom"
        )
        angled_hat += skin
    else:
        print(
            "WARN: dim_7 (skin thickness) not provided. Shape is open and warping properties cannot be calculated."
        )
    return angled_hat