Physics 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

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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 solid rectangle.
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 rectangular beam
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Production: Embedded snapshot: unpublished · Build schema 1.0.0 ready · Semantic contract ✓ · Attestation report not published on origin · Live production status STALE (8 capabilities; 189 remain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 = 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

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

Q = 9, I = 36, τ = 12×9/(36×2)

τ = 1.5

Reversed shear

V = −12, b = 2, h = 6

τ = −1.5

Rectangular 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 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.
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.

Other calculators in this family: Transverse shear, Rectangular section, Rectangular plastic modulus .

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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.