HomeCalculatorsMechanicalStrength of MaterialsRectangular Shear Calculator
Mechanical calculator

Rectangular Shear Calculator

Neutral-axis shear stress of one solid rectangle. The area moment comes 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
Neutral-axis shear stress 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 4714a464b018
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 rectangular beam
  • Gere and Goodno, Mechanics of Materials — Shear stress in a rectangular beam
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 = b h²/8
Shear stressτ = VQ/(I b)
iI comes from the rectangular-section engine. τ is evaluated by the transverse-shear engine. A circle is its own page.

How to use

1

Enter the shear force and the rectangle

b and h must be positive. V may be negative. The line is the neutral axis parallel to the width.

2

Read the stress

τ = VQ/(I b). For this rectangle that is 3V/(2A). The sign of V is the sign of τ.

Example calculations

Common configurations with formula and result.

ϟ

Width 2, height 6

V = 12, b = 2, h = 6

Q = 9, I = 36, τ = 12×9/(36×2)
τ = 1.5
ϟ

Reversed shear

V = −12, b = 2, h = 6

τ = −1.5
τ = −1.5

Rectangular Shear calculator specification

Version 1.0.0 · Engine tested

Calculation status

Review policy · Evidence

Definition
At the neutral axis of one solid rectangle, Q = b h²/8 and τ = VQ/(I b). I is the area moment from the rectangular-section engine. The result is also 3V/(2A).
What it calculates
Neutral-axis shear stress of one solid rectangle.
Inputs
  • V
  • b
  • h
Outputs
  • tau
  • Q
  • I
  • area
Formula
Q = b h²/8. I from the rectangular-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.
  • I comes from the rectangular-section engine. τ is evaluated by the transverse-shear engine. A circle is its own page.
Units
  • V, b, and h set the stress unit. τ has the unit of V/area.
Boundary conditions
  • missing V, b, or h → MISSING_REQUIRED_INPUT
  • b ≤ 0 or h ≤ 0 → VALUE_MUST_BE_POSITIVE
Example
V=12 b=2 h=6 → τ=1.5
Validation cases

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

  • V=12 b=2 h=6 → τ=1.5, Q=9, I=36
  • V=-12 b=2 h=6 → τ=-1.5
  • b=0 → VALUE_MUST_BE_POSITIVE
Sources
  • Hibbeler, Mechanics of Materials — Shear stress in a rectangular beam
    Supports: The largest shear stress in a solid rectangle is at the neutral axis and equals three halves of the average shear stress.
  • Gere and Goodno, Mechanics of Materials — Shear stress in a rectangular beam
    Supports: Supports the page formula: Q = b h²/8
Calculation version
1.0.0

Background

Interpretation and common distinctions.

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

Supported and not supported

Supported: Q = b h²/8, with I from the rectangular-section engine and τ from the transverse-shear engine. The sign of V is the sign of τ.

Not supported: a circle, a hollow circle, and a line that is not the neutral axis. /calc/mechanical is not open.

Agent / API notes

Capability id: mechanical.statics.rectangular_shear · tool id: rectangular-shear · pin 1.0.0.

{ "V": 12, "b": 2, "h": 6 }

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

Frequently asked questions

Key distinctions behind the calculation.

Where is the stress evaluated?

At the neutral axis, across the full width. That is the largest shear stress in a solid rectangle.

Do I enter the area moment?

No. I is the centroidal moment of this solid rectangle, b h³/12. This page forms Q = b h²/8, then τ = VQ/(I b).

Is a circle included?

No. A circle is its own page.