def WideOctagon(Dcol, Wcol, nLbar, nLbar2, DLbar, DLbar2, sTbar, units, materials):
"""
Geometric analogue of the OpenSees BuildWideOctColSection.
Parameters
----------
Dcol, Wcol : float
Short and long flat-to-flat dimensions of the wide octagon.
nLbar, nLbar2 : int
Number of outer and inner longitudinal bars.
DLbar, DLbar2 : float
Diameters of outer and inner longitudinal bars.
sTbar : float
Transverse spiral spacing. Included for signature compatibility.
It affects confinement in OpenSees, but not the plan geometry here.
units : object
Unit namespace, expected to provide units.inch.
materials : dict
Must contain "cover", "core", and "steel".
Returns
-------
CompositeSection
"""
# geometry only; transverse spacing affects confinement, not plan shape
_ = sTbar
if Dcol <= 0 or Wcol <= 0:
raise ValueError("Dcol and Wcol must be positive.")
if Wcol < Dcol:
raise ValueError("Wcol must satisfy Wcol >= Dcol.")
if int(nLbar) != nLbar or int(nLbar2) != nLbar2:
raise ValueError("nLbar and nLbar2 must be integers.")
nLbar = int(nLbar)
nLbar2 = int(nLbar2)
if nLbar % 2 != 0 or nLbar2 % 2 != 0:
raise ValueError("nLbar and nLbar2 must be even.")
cover = 2.0 * units.inch # from the OpenSees section
DTbar = 0.625 * units.inch # #5 spiral bar diameter
Rcol = Dcol / 2.0
spO = (Wcol - Dcol) / 2.0
Dcore = Dcol - 2.0 * cover
if Dcore <= 0:
raise ValueError("Cover is too large for the given Dcol.")
Rcore = Dcore / 2.0
# OpenSees bar radius:
# Dlong = Dcore - 2*DTbar - DLbar
Dlong = Dcore - 2.0 * DTbar - DLbar
if Dlong <= 0:
raise ValueError("Longitudinal bar ring radius is non-positive.")
Rlong = Dlong / 2.0
def wide_octagon_vertices(D, W):
"""
Exact outer wide-octagon implied by the OpenSees offsets.
CCW ordering.
"""
a = D / 2.0
s = (W - D) / 2.0
b = a * math.tan(math.pi / 8.0)
return [
(-s - b, a),
(-s - a, b),
(-s - a, -b),
(-s - b, -a),
( s + b, -a),
( s + a, -b),
( s + a, b),
( s + b, a),
]
def stadium_vertices(radius, half_span, n_arc=24):
"""
Polygonal approximation of the OpenSees core:
left semicircle + bottom chord + right semicircle + top chord.
CCW ordering.
"""
left_arc = np.linspace(math.pi / 2.0, 3.0 * math.pi / 2.0, n_arc, endpoint=True)
right_arc = np.linspace(3.0 * math.pi / 2.0, 5.0 * math.pi / 2.0, n_arc, endpoint=True)
pts = [(-half_span + radius * math.cos(t), radius * math.sin(t)) for t in left_arc]
pts += [( half_span + radius * math.cos(t), radius * math.sin(t)) for t in right_arc]
return pts
def arc_bars(proto, center_y, center_z, radius, nbar, start_deg, end_deg):
"""
Place bar circles along an arc.
endpoint=False matches the usual OpenSees layer circ convention:
no duplicate terminal point on a closed/full sweep.
"""
if nbar <= 0:
return []
ang = np.deg2rad(np.linspace(start_deg, end_deg, nbar, endpoint=False))
return [
proto.translate([center_y + radius * math.cos(a),
center_z + radius * math.sin(a)])
for a in ang
]
outer_vertices = wide_octagon_vertices(Dcol, Wcol)
core_vertices = stadium_vertices(Rcore, spO, n_arc=24)
cover_shape = PolygonSection(
exterior=outer_vertices,
interior=[core_vertices[::-1]], # hole orientation opposite the exterior
mesh_size=cover / 2.0,
material=materials["cover"],
group="cover",
z=0,
mesh_type="T3",
)
core_shape = PolygonSection(
exterior=core_vertices,
mesh_size=Dcore / 10.0,
material=materials["core"],
group="core",
z=1,
mesh_type="T3",
)
outer_bar = Circle(
DLbar / 2.0,
z=2,
mesh_scale=1 / 2,
divisions=8,
material=materials["steel"],
group="steel",
mesh_type="T3",
)
inner_bar = Circle(
DLbar2 / 2.0,
z=2,
mesh_scale=1 / 2,
divisions=8,
material=materials["steel"],
group="steel",
mesh_type="T3",
)
n_outer_side = nLbar // 2
n_inner_side = nLbar2 // 2
bars = []
# Match the four OpenSees layer circ commands
bars += arc_bars(outer_bar, -spO, 0.0, Rlong, n_outer_side, 45.0, 315.0)
bars += arc_bars(outer_bar, +spO, 0.0, Rlong, n_outer_side, 225.0, 495.0)
bars += arc_bars(inner_bar, -spO, 0.0, Rlong, n_inner_side, 315.0, 405.0)
bars += arc_bars(inner_bar, +spO, 0.0, Rlong, n_inner_side, 135.0, 225.0)
return ConfinedSection(cover=cover_shape,
core=core_shape, steel=bars)
