HomeCalculatorsMechanicalStrength of MaterialsTransverse Shear Calculator
Mechanical calculator

Transverse Shear Calculator

Shear stress at one line from the shear force, the first moment, the area moment, and the width. Runs locally.

Instant result
Result
—

Enter values to calculate.

Inputs—
Mode—
Formula—
Trust summary CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance · τ = VQ/(I b) (Jourawski); + O3 mpmath tabulated τ.
Input interpretation
Enter values to calculate.
Result
—
Verified scope
τ = VQ/(I b) (Jourawski); + O3 mpmath tabulated τ.
Assurance
Engineering
Declared partition coverage
PASS · 5/5 declared partitions (unit, alias, signed, awkward, invalid-domain) · Matrix
Deferred
Not a rectangle from b·h, not a circle, and not beam deflection.
Numerical scope
O2: tau vs a separate-module identity (≤2 ULP). Not a rectangle from b·h, not a circle, and not beam deflection. ≤2 ULP vs O3 applies only to the published tabulated transverse-shear vectors.
Known limitations
  • Core CVP does not include live graph, viewport, or pointer interaction.
Model
Shear stress at one line from V, Q, I, and the width at that line.
Scope
Calculation runs locally in the browser; values are not uploaded.
Verification
Engine tested · Source checked · v1.0.0 · CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance · τ = VQ/(I b) (Jourawski); + O3 mpmath tabulated τ.· View Manifest · CVP overview · Specification
Versions
Calculation 1.0.0 · CVP protocol 1.0.0-proposed · Evidence 2026-09-27.o2-o3
Verification revision
2026-09-27.o2-o3 · 1/1 property · digest d05ea939323d
Legacy regression
5/5 tests · Production surface contract 6/6
Trust layers
Verification VERIFIED · Production CURRENT · Overall CVP state: VERIFIED under CVP 1.0.0-proposed
Reference
O1 model · O3 expected_values · O3 numerical_behavior · O2 expected_values · O2 numerical_behavior
Interfaces
PASS · UI (SSR) / REST / MCP — ui-ssr is query-result HTML, not a live browser session. Error-path engine·REST·MCP 1/1 (status, code, calculation_version). SSR compared on URL-canonical requested calculations; empty query is idle (not an error) and JSON-typed object/array inputs are REST/MCP-only.
Supplemental domain review
Not performed
Named expert review
Not performed
CVP suite
4/4 golden · 3/3 CVP boundary · 5/5 invalid · 1/1 property · 1/1 metamorphic · 8/8 O3 · 2/2 cross-interface · 6/6 CVP contract · Manifest
Sources
  • Hibbeler, Mechanics of Materials — Transverse shear — shear formula
  • Gere and Goodno, Mechanics of Materials — Transverse shear — shear formula
Sources
Evidence
2 legacy golden · 3 legacy boundary · legacy regression suite · 4/4 oracle-backed golden · 5/5 invalid · Artifact integrity PASS
This calculator CURRENT · Public schema 1.0.0 matches · Semantic contract ✓ · Production attested · Public/cache ✓ · Origin ✓
Semantic contract
PASS
Full verification

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

Formulas

Core equations used by this calculator.

Jourawskiτ = VQ/(I b)
iEnter Q, I, and b. This page does not rebuild a rectangle from width and height.

How to use

1

Enter the force and the section numbers

V may be negative. Q, I, and b must be positive. They share one set of force and length units.

2

Read the stress

τ = VQ/(I b). The sign of V is the sign of the stress.

Example calculations

Common configurations with formula and result.

ϟ

Neutral axis of a 2 by 6 rectangle

V = 12, Q = 9, I = 36, b = 2, in one consistent unit system. τ then has the unit of VQ/(I b).

τ = 12×9/(36×2)
τ = 1.5
ϟ

Reversed shear

V = −12, Q = 9, I = 36, b = 2

τ = −12×9/(36×2)
τ = −1.5

Transverse Shear calculator specification

Version 1.0.0 · Engine tested

Calculation status

Review policy · Evidence

Definition
At one line across a section, the shear stress is τ = VQ/(I b). V is the shear force. Q is the first moment of the area beyond that line. I is the area moment of the whole section about the neutral axis. b is the width at the line.
What it calculates
Shear stress at one line from V, Q, I, and the width at that line.
Inputs
  • V
  • Q
  • I
  • b
Outputs
  • tau
  • V
  • Q
  • I
  • b
Formula
τ = VQ/(I b).
Assumptions
  • Calculation runs locally in the browser; values are not uploaded.
  • Keep units consistent with the labels on each field.
  • Enter Q, I, and b. This page does not rebuild a rectangle from width and height.
Units
  • V, Q, I, and b set the stress unit. τ has the unit of VQ/(I b).
Boundary conditions
  • missing V, Q, I, or b → MISSING_REQUIRED_INPUT
  • Q ≤ 0, I ≤ 0, or b ≤ 0 → VALUE_MUST_BE_POSITIVE
Example
V=12 Q=9 I=36 b=2 → τ=1.5
Validation cases

3 published on this page · 5/5 tests · Production surface contract 6/6 · View evidence

  • V=12 Q=9 I=36 b=2 → τ=1.5
  • V=-12 Q=9 I=36 b=2 → τ=-1.5
  • Q=0 → VALUE_MUST_BE_POSITIVE
Sources
  • Hibbeler, Mechanics of Materials — Transverse shear — shear formula
    Supports: The shear stress at a line is the shear force times the first moment of the area beyond that line, divided by the area moment and the width at the line.
  • Gere and Goodno, Mechanics of Materials — Transverse shear — shear formula
    Supports: Supports the page formula: τ = VQ/(I b)
Calculation version
1.0.0

Background

Interpretation and common distinctions.

Find the shear stress at one line across a section.

Supported and not supported

Supported: τ = VQ/(I b). The sign of V is the sign of τ. Aliases are shear, first_moment, statical_moment, Ix, t, and thickness.

Not supported: building Q from a rectangle's width and height. /calc/mechanical is not open.

Agent / API notes

Capability id: mechanical.statics.transverse_shear · tool id: transverse-shear · pin 1.0.0.

{ "V": 12, "Q": 9, "I": 36, "b": 2 }

Share the link with V, Q, I, and b. 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, Hollow Circular Shear Calculator, Plastic Moment Calculator, Rectangular Plastic Modulus Calculator, Rectangular 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. › → Hollow Circular Shear Calculator Neutral-axis shear stress of one hollow circle. The area moment 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. ›

Frequently asked questions

Key distinctions behind the calculation.

Does this build Q from a rectangle?

No. Width and height stay on the rectangular-section page. Bring Q, I, and the width at the line.

What does the sign of V mean?

The sign of V is the sign of τ. Q, I, and b stay positive.

Is a rectangle's neutral-axis shear included?

Not on this page. A rectangle built from width and height is its own page.