Mechanical calculator

Circular Shear Calculator

Neutral-axis shear stress of one solid circle. The area moment comes from the 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 solid 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 e61b32f824bb
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 beam
Gere and Goodno, Mechanics of Materials — Shear stress in a circular beam
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.

First momentQ = (2/3) r³

Shear stressτ = VQ/(I b)

iThe width at the axis is 2r. I comes from the circular-section engine. τ is evaluated by the transverse-shear engine. A hollow circle is its own page.

How to use

Enter the shear force and the radius

r must be positive. V may be negative. The line is a centroidal diameter.

Read the stress

τ = VQ/(I b). For this circle that is 4V/(3A). The sign of V is the sign of τ.

Example calculations

Common configurations with formula and result.

Radius 2

V = 12, r = 2

Q = 16/3, b = 4, τ = 4/π

τ = 1.27324

Reversed shear

V = −12, r = 2

τ = −4/π

τ = −1.27324

Circular Shear 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: At the neutral axis of one solid circle, Q = (2/3) r³ and the width is 2r. τ = VQ/(I b). I comes from the circular-section engine. The result is also 4V/(3A).
What it calculates: Neutral-axis shear stress of one solid circle.
Inputs: V
r
Outputs: tau
Q
I
b
area
Formula: Q = (2/3) r³. b = 2r. I from the 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.
The width at the axis is 2r. I comes from the circular-section engine. τ is evaluated by the transverse-shear engine. A hollow circle is its own page.
Units: V and r set the stress unit. τ has the unit of V/area.
Boundary conditions: missing V or r → MISSING_REQUIRED_INPUT
r ≤ 0 → VALUE_MUST_BE_POSITIVE
Example: V=12 r=2 → τ=4/π
Validation cases: 3 published on this page · 4/4 tests · Production surface contract 6/6 · View evidence
V=12 r=2 → τ=4/π
V=-12 r=2 → τ=-4/π
r=0 → VALUE_MUST_BE_POSITIVE
Sources: Hibbeler, Mechanics of Materials — Shear stress in a circular beam
Supports: The largest shear stress in a solid circle is at the neutral axis and equals four thirds of the average shear stress.
Gere and Goodno, Mechanics of Materials — Shear stress in a circular beam
Supports: Supports the page formula: Q = (2/3) r³
Calculation version: 1.0.0

Background

Interpretation and common distinctions.

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

Supported and not supported

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

Not supported: a hollow circle and a line that is not a centroidal diameter. /calc/mechanical is not open.

Agent / API notes

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

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

Share the link with V and r. The result is not written into the link.

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

Frequently asked questions

Key distinctions behind the calculation.

Where is the stress evaluated?

At a centroidal diameter. That is the largest shear stress in a solid circle.

Do I enter the area moment?

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

Is a hollow circle included?

No. A hollow circle is its own page.