What formula is used to calculate the maximum shear stress?

The calculator uses the transverse shear formula τ = VQ/(Ib) at the neutral axis, which simplifies to 1.5V/A for rectangles and 4V/3A for solid circles.

What units should I use for the inputs?

Input the shear force in Newtons (N) and all dimensional measurements in millimeters (mm) to obtain the shear stress output in Megapascals (MPa).

How does the calculator handle I-beams?

It calculates the exact maximum shear stress in the web at the neutral axis using the I-beam's specific moment of inertia and first moment of area.

Why is the maximum shear stress higher than the average shear stress?

Average shear stress is simply force divided by area (V/A), whereas transverse shear stress varies across the depth of the beam and peaks at the neutral axis.

Can this calculator compute shear stress at points other than the neutral axis?

No, this calculator specifically computes the maximum shear stress occurring at the neutral axis of the cross-section.

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Shear Stress Calculator

Calculate the maximum shear stress τ_max = V·Q/(I·b) at the neutral axis of a beam section. Supports rectangle (1.5V/A), solid circle (4V/3A), hollow tube, and I-beam (exact V·Q_web/(I·tw)). Also returns the average shear stress V/A for comparison.

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2 examples

Rectangle b=50, h=100 mm, V=20000 N → τ_max = 6 MPa

A = b·h = 5000 mm². τ_avg = V/A = 4 MPa. τ_max = 1.5·V/A = 6 MPa at the neutral axis.

{"result":"Rectangle b=50 mm, h=100 mm, V=20000 N. A = b·h = 5000 mm². τ_avg = V/A = 4 MPa. τ_max = 1.5·V/A = 6 MPa at the neutral axis.","metadata":{"input":{"shape":"rectangle","V":20000,"b":50,"h":100},"result":{"shape":"rectangle","shearStress":6,"shearStressUnit":"MPa","avgShear":4,"avgShearUnit":"MPa","area":5000}}}

Solid circle D=100 mm, V=20000 N → τ_max ≈ 3.3953 MPa

A = π·D²/4 = 7853.98 mm². τ_avg = V/A ≈ 2.5465 MPa. τ_max = 4·V/(3·A) ≈ 3.3953 MPa at the neutral axis.

{"result":"Solid circle D=100 mm, V=20000 N. A = π·D²/4 = 7853.9816 mm². τ_avg = V/A = 2.5465 MPa. τ_max = 4·V/(3·A) = 3.3953 MPa at the neutral axis.","metadata":{"input":{"shape":"circle","V":20000,"D":100},"result":{"shape":"circle","shearStress":3.3953,"shearStressUnit":"MPa","avgShear":2.5465,"avgShearUnit":"MPa","area":7853.9816}}}

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12 options

SettingsAdjust formats, ranges, numbers, and modes.12

Cross-Section ShapeselectOptionalShear Force V (N)numberRequiredWidth b (mm)numberOptionalSection width (horizontal). Required for Rectangle.Height h (mm)numberOptionalSection height (vertical). Required for Rectangle.Diameter D (mm)numberOptionalRequired for Solid Circle.Outer Diameter Do (mm)numberOptionalRequired for Hollow Circle.Inner Diameter Di (mm)numberOptionalRequired for Hollow Circle. Must be less than Do.Flange Width B (mm)numberOptionalRequired for I-Beam.Total Height H (mm)numberOptionalRequired for I-Beam.Web Thickness tw (mm)numberOptionalRequired for I-Beam.Flange Thickness tf (mm)numberOptionalRequired for I-Beam.Decimal PlacesnumberOptional

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Shear Stress Calculator

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Examples

1. Rectangular Timber Beam Shear Analysis

2. Solid Steel Shaft Shear Verification

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