plastic_collapse
Compute exact plastic-hinge collapse moment and load for a solid rectangular beam without a solver, and check margins to yield and fully plastic limits.
Instructions
Exact plastic-hinge collapse of a solid rectangular beam (NO solver) — the
closed-form twin the perfectly-plastic CalculiX solve
(fem_set_nonlinear_material) is gated against. The beam bends about the
width_mm axis (depth = height_mm). σ_y from yield_mpa or a Materials-DB
material. Elastic modulus S = b·h²/6, plastic modulus Z = b·h²/4, shape
factor Z/S = 1.5; yield moment M_y = σ_y·S, fully-plastic moment M_p = σ_y·Z.
support maps the collapse moment to a point load: 'cantilever' (M = P·L) or
'simply_supported' (central, M = P·L/4). With load_n the applied moment and
its margins to M_y / M_p (and the regime: elastic / partially_plastic /
collapsed) are returned. A perfectly-plastic FEM solve caps the surface stress
at σ_y and loses equilibrium at M_p; linear theory climbs past both — that
contrast is the gate. Escalate to fem_set_nonlinear_material for
non-rectangular sections or partial-plasticity fields.
Returns {support, S_elastic_mm3, Z_plastic_mm3, shape_factor, yield_mpa, yield_moment_nmm, plastic_moment_nmm, yield_load_n, collapse_load_n, applied_moment_nmm, margin_to_yield, margin_to_collapse, regime, fidelity, band_pct, valid_range_ok, warnings, escalate_to}.
Input Schema
| Name | Required | Description | Default |
|---|---|---|---|
| load_n | No | ||
| support | No | cantilever | |
| material | No | ||
| width_mm | Yes | ||
| height_mm | Yes | ||
| length_mm | Yes | ||
| yield_mpa | No |