CVP verified calculation capability

Principal section modulus Calculation Capability

Elastic section modulus about the principal axes. S1 = I1/c1 and S2 = I2/c2 after the principal-moment engine. Not Sx and Sy, and not bending stress.

Mechanical · Statics Capability ID mechanical.statics.principal_section_modulus version 1.0.0 CVP VERIFIED CURRENT Engineering

Model

I1 axis

I1 axis: S1 = I1 / c1
I2 axis: S2 = I2 / c2

Inputs / Outputs

Canonical symbols for this capability. Agent schemas remain the contract.

Symbol	Quantity	Unit	Role
`parts`	Rows Ix,Iy,Ixy,A,x,y	—	input
`c1`	Distance from the centroid to the extreme fiber along the I1 axis	—	input / output
`c2`	Distance from the centroid to the extreme fiber along the I2 axis	—	input / output
`area`	—	—	output
`x`	—	bar	output
`y`	—	bar	output
`I1`	—	—	output
`I2`	—	—	output
`theta_deg`	—	—	output
`S1`	—	—	output
`S2`	—	—	output
`n`	—	—	output
`model`	—	—	output
`solver`	—	—	output

Assumptions / Validity

Declared scope for this capability. Do not use it outside this domain.

Assumptions

S1 = I1/c1 and S2 = I2/c2 along the principal axes
c1 and c2 are distances from the composite centroid to the extreme fiber
A blank distance omits that modulus
θ is the I1 axis, CCW from +x, in (−90°, 90°]
Not Sx or Sy, bending stress, plastic modulus, or beam deflection

Example

One numerical check. The calculator page holds worked steps and FAQ.

parts=4,1,0,2,0,0 c1=2 c2=1 → S1=2, S2=1, θ=0

Open this example in the calculator

Trust

CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance. Computational verification is defined by CVP. Supplemental domain review (internal) and named expert review are defined by the Review policy and do not by themselves determine CVP conformance.

CVP: CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance· View Manifest · CVP overview · Specification
Assurance: Engineering
Declared partition coverage: PASS · 2/2 declared partitions (domain, invalid-domain)
Calculation version: 1.0.0
Verification: 6/6 calculation tests · 2/2 legacy golden · 4/4 legacy boundary
Production surface contract: 6/6
Versions: Calculation 1.0.0 · CVP protocol 1.0.0-proposed
CVP identity: 0/0 property · digest ee2915a1dd5a
Reference: O1 model · O2 expected_values · O2 numerical_behavior
Interfaces: PASS · UI (SSR) / REST / MCP
ui-ssr is query-result HTML, not a live browser session.
CVP suite: 1/1 golden · 4/4 CVP boundary · 3/3 invalid · 1/1 cross-interface · 6/6 CVP contract
Supplemental domain review: Not performed
Named expert review: Not performed
Version lock: Supported (409 VERSION_MISMATCH)
Artifact consistency: Build verified · 1.0.0 (workspace artifacts agree)
Review-policy tier: Engine tested — catalog token engine_tested; supplemental; not CVP status

This calculator CURRENT · Public schema 1.0.0 matches · Semantic contract ✓ · Production attested · Public/cache ✓ · Origin ✓

Call this capability

Human page, REST, and MCP share the same engine and calculation_version. Build verified hashes workspace artifacts only. After deploy, attest:production GETs canonical URLs twice — the public/cached view an Agent actually hits, and origin — including every /capabilities/{id} HTML page. Public Capability HTML version must match catalog before production attestation passes. Live Trust rows above fetch /.well-known/calculatorx-production-attestation.json and the output schema const. Build hashes: release integrity. That proves currently published page / engine / schema / evidence / MCP agree — not that a historical version is independently immutable. Reference Calculation Standard — Production surface contract 6/6.

curl -sS -X POST 'https://www.calculatorx.com/api/v1/calc/principal-section-modulus' \
  -H 'Content-Type: application/json' \
  -d '{"inputs":{"parts":"4,1,0,2,0,0","c1":2,"c2":1},"calculation_version":"1.0.0"}'

{
  "inputs": {
    "parts": "4,1,0,2,0,0",
    "c1": 2,
    "c2": 1
  },
  "calculation_version": "1.0.0"
}

POST /api/v1/calc/principal-section-modulus. This is a POST calculate endpoint — do not GET it.

Full REST contract: REST API docs.

Tool id: principal-section-modulus
Engine: principal-section-modulus
REST: POST /api/v1/calc/principal-section-modulus
MCP: execute_calculation with capability_id: "mechanical.statics.principal_section_modulus"
Agent input schema: Canonical (MCP / Agent)
Output schema: JSON Schema (latest)
Versioned input schema: Immutable pin (1.0.0)
Versioned output schema: Immutable pin (1.0.0)

References

Human-readable sources plus CVP reference evidence classes.

Sources

Hibbeler, Engineering Mechanics: Statics — Moments of inertia
Gere and Goodno, Mechanics of Materials — Moments of inertia

Reference evidence classes: O1 model · O2 expected_values · O2 numerical_behavior

Try with an agent

Inspect, then execute. Same engine as REST and the human calculator.

curl -sS -X POST 'https://www.calculatorx.com/mcp' \
  -H 'Content-Type: application/json' \
  -H 'MCP-Protocol-Version: 2026-07-28' \
  -H 'Mcp-Method: tools/call' \
  -H 'Mcp-Name: inspect_capability' \
  -d '{"jsonrpc":"2.0","id":1,"method":"tools/call","params":{"name":"inspect_capability","arguments":{"capability_id":"mechanical.statics.principal_section_modulus"},"_meta":{"io.modelcontextprotocol/protocolVersion":"2026-07-28","io.modelcontextprotocol/clientInfo":{"name":"calculatorx-docs-example","version":"1.0.0"},"io.modelcontextprotocol/clientCapabilities":{}}}}'

curl -sS -X POST 'https://www.calculatorx.com/mcp' \
  -H 'Content-Type: application/json' \
  -H 'MCP-Protocol-Version: 2026-07-28' \
  -H 'Mcp-Method: tools/call' \
  -H 'Mcp-Name: execute_calculation' \
  -d '{"jsonrpc":"2.0","id":2,"method":"tools/call","params":{"name":"execute_calculation","arguments":{"capability_id":"mechanical.statics.principal_section_modulus","inputs":{"parts":"4,1,0,2,0,0","c1":2,"c2":1},"calculation_version":"1.0.0"},"_meta":{"io.modelcontextprotocol/protocolVersion":"2026-07-28","io.modelcontextprotocol/clientInfo":{"name":"calculatorx-docs-example","version":"1.0.0"},"io.modelcontextprotocol/clientCapabilities":{}}}}'

Pin calculation_version (1.0.0) when the result must stay reproducible.

Inspect the trust tier and required assurance level before execution. Full protocol notes: MCP docs.