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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

TableJSON Schema
NameRequiredDescriptionDefault
load_nNo
supportNocantilever
materialNo
width_mmYes
height_mmYes
length_mmYes
yield_mpaNo

Schema Changelog

Changes observed during successful MCP inspections.

  1. First observed

TDQS

A4.9/5.0
Behavior5/5

Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?

With no annotations provided, the description carries the full burden and does so well: it discloses that no solver is invoked, the exact closed-form quantities computed (S, Z, shape factor, M_y, M_p), how `support` maps moment to load, and the returned regime/fidelity/band_pct/warnings/escalate_to behavior. It even explains the physical contrast (perfectly-plastic FEM loses equilibrium at M_p while linear theory climbs past it).

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Conciseness4/5

Is the description appropriately sized, front-loaded, and free of redundancy?

Purpose and the NO-solver constraint are front-loaded, and the return-key listing at the end is efficient. It is dense and formula-heavy with some redundancy across clauses, but nearly every sentence carries information an agent needs, so little is wasted.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Completeness5/5

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

For a 7-parameter analytical tool with no annotations and no output schema, the description enumerates the returned fields inline (S_elastic_mm3 through escalate_to), names the governing assumptions (rectangular section, perfectly plastic), and pins down the escalation path. Nothing an agent needs to call it correctly is missing.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Parameters5/5

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

Schema description coverage is 0%, so the description must compensate, and it does: it defines the bending axis (`width_mm`) vs depth (`height_mm`), the two alternative yield inputs (`yield_mpa` vs Materials-DB `material`), the `support` enum values and their moment formulas ('cantilever' M=P·L, 'simply_supported' M=P·L/4), and the role of `load_n`. Only `length_mm` is left implicit via L in the formulas.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Purpose5/5

Does the description clearly state what the tool does and how it differs from similar tools?

States a specific verb+resource: closed-form plastic-hinge collapse of a solid rectangular beam, explicitly flagged as NO solver. It also differentiates itself from the sibling FEM path by naming `fem_set_nonlinear_material` as the thing it is gated against, so an agent can distinguish the analytical tool from the FEM tool without opening either schema.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Usage Guidelines5/5

Does the description explain when to use this tool, when not to, or what alternatives exist?

Explicitly gives the escalation condition: use `fem_set_nonlinear_material` for non-rectangular sections or partial-plasticity fields. It also frames the tool's role (the closed-form twin the perfectly-plastic FEM solve is validated against), which tells the agent when this tool is the right one rather than the FEM path.

Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.

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