Public evidence

mechanical.statics.bending_stress

Machine-checked verification for calculation version 1.0.0 · tier engine_tested

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Verification

6/6 calculation tests · Production surface contract 6/6

Golden tests 3 / 3
Boundary tests 3 / 3
Property tests 0 / 0
Production surface contract 6 / 6
Engine tested Yes
Source checked Yes
Artifact integrity PASS
Production attestation Embedded snapshot: unpublished · Build schema 1.0.0 ready · Semantic contract ✓ · Attestation report not published on origin · Live production status STALE (8 capabilities; 189 remain CURRENT) @ 2026-09-23T21:48:15.717Z
Semantic contract PASS
Evidence attested at 2026-09-23T02:27:54.588Z
Last production check 2026-09-23T02:27:54.588Z
Public / cache —
Origin —
Supplemental domain review Not performed
Named expert review Not performed

release artifacts aligned PASS
schema output required declared PASS
schema valid input executes PASS
engine success output validates schema PASS
schema rejects incomplete input PASS
rest success payload validates schema PASS

Fingerprint sha256:291713ddc89c6c7e4540c5dc87110f09eb98615ed09f6e1faa213efe80e4eb08

Input schema sha256:a9646269e346733a5a8bba184308a67f76135bdcae9bacf0e293bfe0757da00f · Output schema sha256:63e782554c686f896cea624f8f251f12f5d68f8495a8c44ad2cd25e55a4dcd75 · Build-time SHA-256 digests prove published artifacts agree with each other (release_integrity.scope=workspace). Production attestation GETs canonical URLs twice (public/cached view and origin), including Capability HTML, via npm run attest:production --write (published at /.well-known/calculatorx-production-attestation.json) and fails if the public Capability page advertises a different calculation_version. This is artifact consistency, not an independent immutable release log.

Build & scope

Engine identity and declared limitations.

Tool: bending-stress
Engine: bending-stress
Engine build: 2026-09-23
Evidence core: 2026-09-23T14:32:49.903Z
Rendered: 2026-09-23T21:48:01.334Z
Last reviewed: —

Limitations

One centroidal axis
σ = M/S
S = Ix/c when S is omitted
Not a rectangle built from b and h
Not transverse shear, deflection, or a plastic modulus

Sources

Standards and references supporting this tool specification. Methods are listed separately — they are algorithms, not bibliographic sources.

Hibbeler, Mechanics of Materials — Bending — flexure formula
Supports: The elastic bending stress at a fiber is the moment divided by the elastic section modulus at that fiber.

Published checks

Golden, boundary, and property cases included in this evidence build.

ID	Kind	Status	Detail
`golden-direct`	golden	pass	Expected sigma=3 · M=12 · S=4 · model=bending_stress · Actual model=bending_stress · M=12 · S=4 · sigma=3 · solver=elastic flexure · convention=σ = M/S on one centroidal axis. Positive M gives the stress sign at the fiber used to form S. S may be entered, or formed as Ix/c by the section-modulus engine. A rectangle built from b and h is the rectangular-section page. The plastic modulus of a rectangle is its own page.
`golden-ix`	golden	pass	Expected sigma=2 · S=12 · Ix=36 · c=3 · Actual model=bending_stress · M=24 · S=12 · Ix=36 · c=3 · sigma=2 · solver=section modulus · convention=σ = M/S on one centroidal axis. Positive M gives the stress sign at the fiber used to form S. S may be entered, or formed as Ix/c by the section-modulus engine. A rectangle built from b and h is the rectangular-section page. The plastic modulus of a rectangle is its own page.
`golden-sign`	golden	pass	Expected sigma=-3 · S=4 · Actual model=bending_stress · M=-12 · S=4 · sigma=-3 · solver=elastic flexure · convention=σ = M/S on one centroidal axis. Positive M gives the stress sign at the fiber used to form S. S may be entered, or formed as Ix/c by the section-modulus engine. A rectangle built from b and h is the rectangular-section page. The plastic modulus of a rectangle is its own page.
`boundary-modulus`	boundary	pass	Expected VALUE_MUST_BE_POSITIVE · Actual VALUE_MUST_BE_POSITIVE
`boundary-moment`	boundary	pass	Expected VALUE_MUST_BE_POSITIVE · Actual VALUE_MUST_BE_POSITIVE
`boundary-missing`	boundary	pass	Expected MISSING_REQUIRED_INPUT · Actual MISSING_REQUIRED_INPUT