Physics 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 Engine tested · Source checked · 5/5 tests · Production surface contract 6/6 · v1.0.0

Input interpretation: Enter values to calculate.
Result: —
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 · 5/5 tests · Production surface contract 6/6 · Source checked · v1.0.0
Named expert review: Optional · Not performed
Sources: Hibbeler, Mechanics of Materials — Transverse shear — shear formula
Sources
Evidence: 2 golden · 3 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Production: Embedded snapshot: unpublished · Build schema 1.0.0 ready · Semantic contract ✓ · Attestation report not published on origin · Live production status STALE (8 capabilities; 189 remain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.

Jourawskiτ = VQ/(I b)

iEnter Q, I, and b. This page does not rebuild a rectangle from width and height.

How to use

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.

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.

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

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

Engine tested 5/5 tests · Production surface contract 6/6
Named expert review Not performed
Calculation version 1.0.0

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.
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: Rectangular section, Bending stress, Rectangular shear .

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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.