Plastic Moment Calculator
Fully plastic moment from a yield stress and a plastic modulus. One centroidal axis. Runs locally.
Trust summary Engine tested · Source checked · 5/5 tests · Production surface contract 6/6 · v1.0.0
- Input interpretation
- Enter values to calculate.
- Result
- —
- Model
- Fully plastic moment on one centroidal axis from a yield stress and a plastic modulus.
- Scope
- Calculation runs locally in the browser; values are not uploaded.
- Verification
- Engine tested · 5/5 tests · Production surface contract 6/6 · Source checked · v1.0.0
- Named expert review
- Optional · Not performed
- Sources
- Hibbeler, Mechanics of Materials
- Evidence
- 2 golden · 3 boundary · Production surface contract 6/6 · Artifact integrity PASS
- Production
- Embedded snapshot: unpublished · Build schema 1.0.0 ready · Semantic contract ✓ · Attestation report not published on origin · Live production status STALE (8 capabilities; 189 remain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
Formulas
Core equations used by this calculator.
How to use
Enter the yield stress and the plastic modulus
σ_y must be positive. Z must be positive. Both use the same force and length units.
Read the moment
Mp = σ_y Z. The moment has the unit of stress times length cubed.
Example calculations
Common configurations with formula and result.
Rectangle Zx with σy = 250
σ_y = 250, Z = 18
Solid circle of radius 2
σ_y = 250, Z = 32/3
Plastic Moment calculator specification
Version 1.0.0 · Engine tested
- Engine tested 5/5 tests · Production surface contract 6/6
- Named expert review Not performed
- Calculation version 1.0.0
- Definition
- On one centroidal axis, the fully plastic moment is Mp = σ_y Z. Z is the plastic modulus. σ_y is the yield stress in the same force and length units.
- What it calculates
- Fully plastic moment on one centroidal axis from a yield stress and a plastic modulus.
- Inputs
- sigma_y
- Z
- Outputs
- Mp
- sigma_y
- Z
- Formula
Mp = σ_y Z.- Assumptions
- Calculation runs locally in the browser; values are not uploaded.
- Keep units consistent with the labels on each field.
- Bring Z from a plastic-modulus page. This page does not rebuild a rectangle, a circle, or a hollow circle.
- Units
- σ_y and Z set the moment unit. Mp has the unit of σ_y × Z.
- Boundary conditions
- missing σ_y or Z → MISSING_REQUIRED_INPUT
- σ_y ≤ 0 or Z ≤ 0 → VALUE_MUST_BE_POSITIVE
- Example
- sigma_y=250 Z=18 → Mp=4500
- Validation cases
3 published on this page · 5/5 tests · Production surface contract 6/6 · View evidence
- sigma_y=250 Z=18 → Mp=4500
- sigma_y=250 Z=32/3 → Mp=8000/3
- sigma_y=0 Z=18 → VALUE_MUST_BE_POSITIVE
- Sources
- Hibbeler, Mechanics of Materials — Plastic deformation — plastic momentSupports: The fully plastic moment on a centroidal axis is the yield stress times the plastic modulus of that axis.
- Hibbeler, Mechanics of Materials — Plastic deformation — plastic moment
- Calculation version
- 1.0.0
Background
Interpretation and common distinctions.
Find the fully plastic moment on one centroidal axis.
Supported and not supported
Supported: Mp = σ_y Z. Z is typed in. Aliases are Fy, yield_stress, yield, Zx, and plastic_modulus.
Not supported: rebuilding a rectangle, a circle, or a hollow circle, and transverse shear. /calc/mechanical is not open.
Agent / API notes
Capability id: mechanical.statics.plastic_moment · tool id: plastic-moment · pin 1.0.0.
{ "sigma_y": 250, "Z": 18 }
Share the link with sigma_y and Z. The result is not written into the link.
Related tools
Other calculators in this family: Rectangular plastic modulus, Circular plastic modulus, Hollow circular plastic modulus .
Frequently asked questions
Key distinctions behind the calculation.
Does this rebuild the section?
No. Width, height, and radii stay on the plastic-modulus pages. Bring Z here.
Which axis is this?
One centroidal axis. For a rectangle, pass Zx or Zy from the rectangular plastic-modulus page.
Is this transverse shear?
No. Transverse shear is its own page.