Compute section properties for a custom section¶

Get A / I / J / shear centre / As / Z / S — plus stress fields — for a cross-section that isn't in a catalog: built-up plates, an SRC column, a holed box, an imported DXF outline. Author the flat face, mesh it at order 2, hand the FEMData to SectionProperties, and either read the numbers directly or bind the analyzer to the OpenSees bridge with ComputedSection so the emitted deck always follows the drawn geometry.

Recipe — homogeneous section¶

from apeGmsh import apeGmsh, SectionProperties
from apeGmsh.sections import SectionMaterial

g = apeGmsh(model_name="girder_section")
g.begin()

# 1. Author the flat face in the gmsh (x, y) plane. Any route works:
#    *_face builders, raw OCC loops (holes supported), load_dxf/load_step.
g.sections.W_face(bf=400.0, tf=25.0, h=1200.0, tw=12.0, label="girder")
g.sections.plot_faces()                    # optional pre-mesh sanity check

# 2. Mesh — 2-D, then SECOND ORDER (tri6/quad9). Linear elements are
#    accepted but warn on warping()/stress(): tri3/quad4 converge poorly
#    on J and shear areas.
g.mesh.sizing.set_global_size(15.0)
g.mesh.generation.generate(dim=2)
g.mesh.generation.set_order(2)
fem = g.mesh.queries.get_fem_data(dim=2)

# 3. Analyze. materials= maps PG names -> SectionMaterial; the builder's
#    label IS the auto-PG name.
steel = SectionMaterial(E=200e3, nu=0.3, fy=345.0, density=7.85e-9)  # N-mm
sec = SectionProperties(fem, materials={"girder": steel}, name="PG1200x400")

geo  = sec.geometric()     # quadrature: A, centroid, I*, phi, Z moduli
warp = sec.warping()       # FE solve: J, shear centre, Gamma, As_x/As_y
plas = sec.plastic()       # needs fy on every material: S, Mp, shape factors

geo.area, geo.Ixx_c, geo.Zxx_plus          # homogeneous -> unprefixed OK
warp.J, (warp.x_sc, warp.y_sc), warp.alpha_y
plas.Sxx, plas.sf_xx_plus

# 4. Stress recovery + plots (all matplotlib, all headless-safe).
st = sec.stress(N=-800e3, Vy=350e3, Mxx=1.9e9)
st.plot("von_mises")                       # filled tricontour
st.plot_vector(action="vy")                # (tau_zx, tau_zy) quiver
st.plot_mohrs_circle(at=(0.0, 600.0))      # beam state at the top flange
sec.plot_warping()                         # Saint-Venant omega contour
sec.plot()                                 # one-call overview figure
print(sec.summary())                       # plain-text report
# sec.viewer()                             # Qt inspector (notebooks:
                                           #   sec.viewer(blocking=False))

# 5. OpenSees handoff — the frame model references the DECLARATION;
#    properties resolve at emit time into a plain `section Elastic` line.
from apeGmsh.opensees import apeSees

p = apeSees(frame_fem)                     # your separate frame model
transf = p.geomTransf.Linear(vecxz=(0.0, 0.0, 1.0))
girder = p.section.ComputedSection(analysis=sec)   # E/G default from steel
integ  = p.beamIntegration.Lobatto(section=girder, n_ip=5)
p.element.forceBeamColumn(pg="girders", transf=transf, integration=integ)
p.tcl("frame.tcl")
# -> section Elastic $tag 200000.0 $A $Iz $Iy 76923.1 $J $alphaY $alphaZ

es = sec.to_elastic_section()              # eager escape hatch: a plain
                                           #   populated ElasticSection

Recipe — composite (SRC column: steel W inside concrete)¶

Material PGs must partition the face — every 2-D element covered by exactly one materials= PG. The trap: authoring the inner shape overlapping the outer one and fragmenting maps the overlap piece to both parents' PGs (double-cover → SectionMeshError). Carve first with cut(remove_tool=False), then fragment for a conformal mesh:

g = apeGmsh(model_name="src_column_section")
g.begin()

conc  = g.sections.rect_face(b=600.0, h=600.0, label="concrete")
steel = g.sections.W_face(bf=250.0, tf=17.0, h=250.0, tw=10.0, label="steel")
g.model.boolean.cut(                       # W-shaped hole in the concrete;
    conc.entities[2], steel.entities[2],   # keep the tool so the W face
    dim=2, remove_tool=False,              # survives as its own region
)
g.parts.fragment_pair("concrete", "steel", dim=2)   # conformal shared boundary

g.mesh.sizing.set_global_size(20.0)
g.mesh.generation.generate(dim=2)
g.mesh.generation.set_order(2)
fem = g.mesh.queries.get_fem_data(dim=2)

sec = SectionProperties(
    fem,
    materials={
        "concrete": SectionMaterial(E=25e3, nu=0.2),
        "steel":    SectionMaterial(E=200e3, nu=0.3, fy=345.0),
    },
    name="SRC600",
)

geo, warp = sec.geometric(), sec.warping()
geo.EA, geo.EIxx_c, warp.GJ                # rigidity form — always valid
geo.transformed(e_ref=200e3).Ixx_c         # steel-transformed section
# geo.Ixx_c on a composite raises CompositeSectionError — there is no
#   silently-chosen reference modulus.

col = p.section.ComputedSection(analysis=sec, E=200e3, G=76.9e3)
# composite -> explicit reference E/G REQUIRED; omitting them fails loud
#   at emit naming "SRC600". The deck reproduces the analyzer's
#   rigidities exactly (EA/E, EI/E, GJ/G), whatever reference you pick.

Notes / gotchas¶

Order 2 or warnings. warping()/stress() on a tri3/quad4 mesh emit SectionAccuracyWarning — constant-strain elements converge poorly on J and shear areas. g.mesh.generation.set_order(2) is the fix, not finer linear meshing.
The naming law. Rigidity-form fields (EA, EIxx_c, GJ, GAs_y, Mp_xx) are always valid. Unprefixed accessors (Ixx_c, J, As_y, Sxx) divide by the section's single modulus and raise CompositeSectionError on composites — use transformed(e_ref=...). Reference-free ratios (rx/ry/r11/r22, alpha_x/alpha_y) are valid in every mode.
Composite authoring = cut, then fragment. Overlap + fragment double-covers the inner region in both PGs and the exact-cover gate fires. Hand-authored multi-region faces must share lines, not just points — two rectangles drawn with their own coincident edges mesh as disconnected parts.
Disconnected parts are a policy, not an accident. warping() on a disconnected mesh raises by default (usually the forgot-to-fragment bug). For intentionally separate parts (twin girders + deck strip) pass disconnected="sum" — the classical equal-twist-rate lower bound, per-part results on warp.parts. Effective deck width is authored, never inferred.
Axis contract. Analyzer results live in gmsh authoring (x, y) axes (Ixx = ∫y²dA). The lowering maps authoring x ≡ local z, authoring y ≡ local y: Ixx_c → Iz, Iyy_c → Iy, As_y/A → alphaY, As_x/A → alphaZ. Making local y land on the section's authoring-y is the geomTransf author's job — pick vecxz accordingly.
ndm= on ComputedSection selects the deck form (3 → E A Iz Iy G J alphaY alphaZ; 2 → E A Iz G alphaY). Match it to your ops.model(ndm=) envelope yourself — sections emit before the bridge ndm is visible.
Catalog comparisons: expect J low. The fillet-less plate assembly lands A/Ix/Iy within ~1–2 % of AISC tables, but J 5–15 % below catalog (J is fillet-sensitive). That's a modeling difference — don't chase it with mesh refinement.
One analyzer, one solve. Analyses are memoized; N ComputedSection references to the same analyzer trigger a single solve at emit, and the deck line is byte-identical to a hand-typed ElasticSection.

Compute section properties for a custom section¶

Recipe — homogeneous section¶

Recipe — composite (SRC column: steel W inside concrete)¶

Notes / gotchas¶

See also¶