HomeCalculatorsMechanicalStrength of MaterialsHollow Circular Shear Calculator
Mechanical calculator

Hollow Circular Shear Calculator

Neutral-axis shear stress of one hollow circle. The area moment comes from the hollow-circular-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
Neutral-axis shear stress of one hollow circle.
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 f812f26353e3
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 — Shear stress in a circular tube
  • Gere and Goodno, Mechanics of Materials — Shear stress in a circular tube
Sources
Evidence
2 legacy golden · 2 legacy boundary · legacy regression suite · 1/1 oracle-backed golden · 2/2 invalid · Artifact integrity PASS
STALE · Last attested schema matched 1.0.0 snapshot / local build · Semantic contract ✓ · Last attestation PASS · current evidence changed · re-attestation required · CVP STALE · attestation STALE — Production CURRENT withheld · Public/cache ✓ · Origin ✓
Semantic contract
PASS
Full verification

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

Formulas

Core equations used by this calculator.

First momentQ = (2/3)(R³−r³)
Widthb = 2(R−r)
Shear stressτ = VQ/(I b)
iR is the outer radius and r is the inner radius. I comes from the hollow-circular-section engine. τ is evaluated by the transverse-shear engine. A solid circle is the circular-shear page.

How to use

1

Enter the shear force and the two radii

R and r must be positive, and r must be less than R. V may be negative.

2

Read the stress

τ = VQ/(I b) at the neutral axis. The sign of V is the sign of τ.

Example calculations

Common configurations with formula and result.

ϟ

Outer 2, inner 1

V = 12, R = 2, r = 1

Q = 14/3, b = 2, τ = 112/(15π)
τ = 2.376714
ϟ

Similar section, four times the area

V = 48, R = 4, r = 2

R/r stays 2 and V scales with the area, so τ stays 112/(15π)
τ = 2.376714

Hollow Circular Shear calculator specification

Version 1.0.0 · Engine tested

Calculation status

Review policy · Evidence

Definition
At the neutral axis of one hollow circle, Q = (2/3)(R³−r³) and the width is 2(R−r). τ = VQ/(I b). I comes from the hollow-circular-section engine.
What it calculates
Neutral-axis shear stress of one hollow circle.
Inputs
  • V
  • R
  • r
Outputs
  • tau
  • Q
  • I
  • b
  • area
Formula
Q = (2/3)(R³−r³). b = 2(R−r). I from the hollow-circular-section engine. τ = VQ/(I b).
Assumptions
  • Calculation runs locally in the browser; values are not uploaded.
  • Keep units consistent with the labels on each field.
  • R is the outer radius and r is the inner radius. I comes from the hollow-circular-section engine. τ is evaluated by the transverse-shear engine. A solid circle is the circular-shear page.
Units
  • V, R, and r set the stress unit. τ has the unit of V/area.
Boundary conditions
  • missing V, R, or r → MISSING_REQUIRED_INPUT
  • R ≤ 0 or r ≤ 0 → VALUE_MUST_BE_POSITIVE
  • r ≥ R → INVALID_INPUT
Example
V=12 R=2 r=1 → τ=112/(15π)
Validation cases

3 published on this page · 4/4 tests · Production surface contract 6/6 · View evidence

  • V=12 R=2 r=1 → τ=112/(15π)
  • V=48 R=4 r=2 → τ=112/(15π)
  • r=R → INVALID_INPUT
Sources
  • Hibbeler, Mechanics of Materials — Shear stress in a circular tube
    Supports: At the neutral axis of a hollow circle, the first moment is (2/3)(R³−r³) and the width is the two wall thicknesses along the diameter.
  • Gere and Goodno, Mechanics of Materials — Shear stress in a circular tube
    Supports: Supports the page formula: Q = (2/3)(R³−r³)
Calculation version
1.0.0

Background

Interpretation and common distinctions.

Find the neutral-axis shear stress of one hollow circle.

Supported and not supported

Supported: Q = (2/3)(R³−r³) and b = 2(R−r), with I from the hollow-circular-section engine and τ from the transverse-shear engine. The sign of V is the sign of τ.

Not supported: a solid circle and beam deflection. /calc/mechanical is not open.

Agent / API notes

Capability id: mechanical.statics.hollow_circular_shear · tool id: hollow-circular-shear · pin 1.0.0.

{ "V": 12, "R": 2, "r": 1 }

Share the link with V, R, and r. 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, Plastic Moment Calculator, Rectangular Plastic Modulus Calculator, Rectangular Shear Calculator, Transverse Shear Calculator . Explore all Strength of Materials.

→ Bending Stress Calculator Elastic bending stress from a moment and a section modulus. S can also be formed from Ix and c. Runs locally. › → Circular Plastic Modulus Calculator Plastic modulus and shape factor of a solid circle. The elastic modulus comes from the circular-section engine. Runs locally. › → Circular Shear Calculator Neutral-axis shear stress of one solid circle. The area moment comes from the circular-section engine. Runs locally. › → Hollow Circular Plastic Modulus Calculator Plastic modulus of a hollow circle from the outer and inner radii. The elastic modulus comes from the hollow-circular-section engine. Runs locally. › → Plastic Moment Calculator Fully plastic moment from a yield stress and a plastic modulus. One centroidal axis. Runs locally. › → 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. › → Rectangular Shear Calculator Neutral-axis shear stress of one solid rectangle. The area moment comes from the rectangular-section engine. Runs locally. › → Transverse Shear Calculator Shear stress at one line from the shear force, the first moment, the area moment, and the width. Runs locally. ›

Frequently asked questions

Key distinctions behind the calculation.

What is b at the neutral axis?

The diameter crosses two walls. Their combined width is 2(R−r).

Do I enter the area moment?

No. I is the centroidal moment of this hollow circle, π(R⁴−r⁴)/4. This page forms Q = (2/3)(R³−r³) and b = 2(R−r), then τ = VQ/(I b).

Is the stress at the outer fiber?

No. This stress is at the neutral axis, where the width is the two wall thicknesses. Bending stress at the outer fiber uses the section modulus on the hollow-circular-section page.