Rectangular Shear Calculator
Neutral-axis shear stress of one solid rectangle. The area moment comes from the rectangular-section engine. Runs locally.
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
- 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
- Gere and Goodno, Mechanics of Materials
- 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
Formulas
Core equations used by this calculator.
How to use
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.
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.
Width 2, height 6
V = 12, b = 2, h = 6
Reversed shear
V = −12, b = 2, h = 6
Rectangular Shear calculator specification
Version 1.0.0 · Engine tested
- Engine tested 4/4 tests · Production surface contract 6/6
- Named expert review Not performed
- Calculation version 1.0.0
- 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 beamSupports: 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 beamSupports: Supports the page formula: Q = b h²/8
- Hibbeler, Mechanics of Materials — Shear stress in a rectangular beam
- 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.
Related tools
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 Plastic Modulus Calculator, Transverse Shear Calculator . Explore all Strength of Materials.
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.