Mechanical calculator

Rectangular Plastic Modulus Calculator

Plastic moduli and shape factor of a solid rectangle. Elastic Sx and Sy come from the rectangular-section engine. Runs locally.

Instant result

Result

—

Enter values to calculate.

Inputs—

Mode—

Formula—

Trust summary CVP VERIFIED · production STALE · CVP protocol 1.0.0-proposed · Engineering assurance

Input interpretation: Enter values to calculate.
Result: —
Assurance: Engineering
Declared partition coverage: PASS · 2/2 declared partitions (domain, invalid-domain) · Matrix
Known limitations: Physics L1 gap capability
Core CVP does not include live graph, viewport, or pointer interaction.
Model: Plastic moduli and shape factors of one solid rectangle.
Scope: Calculation runs locally in the browser; values are not uploaded.
Verification: Engine tested · Source checked · v1.0.0 · CVP VERIFIED · production STALE · CVP protocol 1.0.0-proposed · Engineering assurance· View Manifest · CVP overview · Specification
Versions: Calculation 1.0.0 · CVP protocol 1.0.0-proposed
CVP identity: 0/0 property · digest 69d284b87665
Legacy regression: 4/4 tests · Production surface contract 6/6
Trust layers: Verification VERIFIED · Production STALE · overall VERIFIED_STALE
CVP status: STALE · Capability production binding: STALE · Site report: STALE · Evidence changed after the last successful production attestation. Re-attestation required.
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.
Supplemental domain review: Not performed
Named expert review: Not performed
CVP suite: 1/1 golden · 2/2 CVP boundary · 2/2 invalid · 1/1 cross-interface · 6/6 CVP contract · Manifest
Sources: Hibbeler, Mechanics of Materials — Plastic deformation — rectangular section
Gere and Goodno, Mechanics of Materials — Plastic deformation — rectangular section
Sources
Evidence: 2 legacy golden · 2 legacy boundary · legacy regression suite · 1/1 oracle-backed golden · 2/2 invalid · Artifact integrity PASS
Semantic contract: PASS

Full verification

Manifest identity, reference classes, interfaces, suite, and production records.

Formulas

Core equations used by this calculator.

Plastic modulusZx = b h²/4

Shape factorfx = Zx/Sx = 3/2

ib is parallel to x and h is parallel to y. Sx and Sy are not recomputed here. A circle is its own page.

How to use

Enter the width and the height

b and h are positive. They set the length unit.

Read the plastic moduli

Zx and Zy are about the centroidal axes. fx and fy are both 3/2.

Example calculations

Common configurations with formula and result.

Width 2, height 6

b = 2, h = 6

Zx = 18, Zy = 6, Sx = 12, fx = 3/2

Zx = 18, Zy = 6, fx = 1.5

Square of side 2

b = 2, h = 2

Zx = Zy = 2, Sx = Sy = 4/3, fx = 3/2

Zx = 2, fx = 1.5

Rectangular Plastic Modulus calculator specification

Version 1.0.0 · Engine tested

Calculation status

Engine tested 4/4 tests · Production surface contract 6/6
Named expert review Not performed
Calculation version 1.0.0

Review policy · Evidence

Definition: For a solid rectangle, Zx = b h²/4 and Zy = h b²/4. The elastic moduli come from the rectangular-section engine. The shape factor Z/S is 3/2.
What it calculates: Plastic moduli and shape factors of one solid rectangle.
Inputs: b
h
Outputs: Zx
Zy
Sx
Sy
fx
fy
area
Formula: Zx = b h²/4, Zy = h b²/4, fx = fy = 3/2
Assumptions: Calculation runs locally in the browser; values are not uploaded.
Keep units consistent with the labels on each field.
b is parallel to x and h is parallel to y. Sx and Sy are not recomputed here. A circle is its own page.
Units: b and h set the length unit. Z and S are that unit cubed. The shape factor is dimensionless.
Boundary conditions: missing b or h → MISSING_REQUIRED_INPUT
b ≤ 0 or h ≤ 0 → VALUE_MUST_BE_POSITIVE
Example: b=2 h=6 → Zx=18, Zy=6, Sx=12, Sy=4, fx=fy=3/2
Validation cases: 3 published on this page · 4/4 tests · Production surface contract 6/6 · View evidence
b=2 h=6 → Zx=18, Zy=6, Sx=12, Sy=4, fx=1.5
b=2 h=2 → Zx=Zy=2, fx=1.5
b=0 → VALUE_MUST_BE_POSITIVE
Sources: Hibbeler, Mechanics of Materials — Plastic deformation — rectangular section
Supports: The plastic modulus of a rectangle about the axis through mid-depth is b h²/4, and the shape factor is 3/2.
Gere and Goodno, Mechanics of Materials — Plastic deformation — rectangular section
Supports: Supports the page formula: Zx = b h²/4
Calculation version: 1.0.0

Background

Interpretation and common distinctions.

Find the plastic moduli and shape factor of a solid rectangle.

Supported and not supported

Supported: one solid rectangle. Zx = b h²/4 and Zy = h b²/4. Sx and Sy come from the rectangular-section engine. fx and fy are 3/2.

Not supported: a circle, elastic bending stress, and the plastic moment. /calc/mechanical is not open.

Agent / API notes

Capability id: mechanical.statics.rectangular_plastic_modulus · tool id: rectangular-plastic-modulus · pin 1.0.0.

{ "b": 2, "h": 6 }

Share the link with b and h. The result is not written into the link.

Other calculators in this family: Bending Stress Calculator, Circular Plastic Modulus Calculator, Circular Shear Calculator, Hollow Circular Plastic Modulus Calculator, Hollow Circular Shear Calculator, Plastic Moment Calculator, Rectangular Shear Calculator, Transverse Shear Calculator . Explore all Strength of Materials.

Frequently asked questions

Key distinctions behind the calculation.

Is the shape factor always 3/2?

For a solid rectangle, Z/S is 3/2 about either centroidal axis. A circle is a different page.

Does this return the yield moment?

No. It returns Z and the shape factor. The plastic moment is its own page.

Where do Sx and Sy come from?

From the rectangular-section engine. This page does not keep a second copy of b h²/6.