Shear Stress Calculator | StrokeForge Engineering

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Cross-Section Type

Shear force V

Design value (factored)

Material

γ_M0

EN 1993-1-1 §6.1

Width b

Height h

τ_max = 3V / (2·b·h)

Diameter d

τ_max = 4V / (3·A)

Outer ∅ D

Inner ∅ d

τ_max = 2V / A at NA

Flange width b_f

Flange thickness t_f

Web height h_w

Between flanges (clear)

Web thickness t_w

τ_max in web at NA

Results

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Enter values

Cross-section area A

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Moment of inertia I

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Average shear τ_avg = V/A

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Max shear τ_max

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Shape factor α = τ_max/τ_avg

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Design resistance τ_Rd

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Utilisation η

—

Reserve capacity

—

Inner diameter ≥ outer diameter — invalid section.

Utilisation > 80% — consider larger web thickness or section.

I-profile: τ_max in web at neutral axis. Flange carries very little shear.

Cross-Section & τ Distribution

Formulas — Shear Stress Distribution

General formula

Shear stress at height y from NA:

τ(y) = V · S(y) / (I · t(y))

where S(y) = first moment of area above y, t(y) = width at y.

Design resistance:

τ_Rd = f_y / (√3 · γM0)

Section formulas

Rectangle: τ_max = 3V/(2A) — α = 1.5
Solid circle: τ_max = 4V/(3A) — α = 4/3
Hollow circle: τ_max = 2V/A — α = 2.0
I-profile (web): τ_max = V·S_max/(I·t_w)

Distribution shape

Rectangle: parabolic — max at NA, zero at top/bottom
Circle: parabolic — max at NA, zero at extremes
Hollow circle: parabolic — max at NA
I-profile: nearly uniform in web, small jump at flange junction

Shear in I-profiles

Most shear (≈ 90–95%) is carried by the web. Flanges carry very little. The shear diagram shows a nearly rectangular distribution in the web with small steps at flange–web junctions.

τ_web,NA = V · S_max / (I · t_w)