Physics 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

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Enter values to calculate.

Inputs—

Mode—

Formula—

Trust summary Engine tested · Source checked · 4/4 tests · Production surface contract 6/6 · v1.0.0

Input interpretation: Enter values to calculate.
Result: —
Model: Neutral-axis shear stress of one hollow circle.
Scope: Calculation runs locally in the browser; values are not uploaded.
Verification: Engine tested · 4/4 tests · Production surface contract 6/6 · Source checked · v1.0.0
Named expert review: Optional · Not performed
Sources: Hibbeler, Mechanics of Materials — Shear stress in a circular tube
Sources
Evidence: 2 golden · 2 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Production: Embedded snapshot: unpublished · Build schema 1.0.0 ready · Semantic contract ✓ · Attestation report not published on origin · Live production status STALE (8 capabilities; 189 remain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.

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

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.

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.

Outer 2, inner 1

V = 12, R = 2, r = 1

Q = 14/3, b = 2, τ = 112/(15π)

τ = 2.376714

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

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 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.
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: Circular shear, Hollow circular section, Transverse shear .

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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.