CIV-06

Jourawski shear formula

Horizontal shear τ = VQ /(I t) in a beam web.

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ShearJourawski 1856EN 1993-1-1

Governing equation

\tau = \dfrac{V Q}{I t}

where

V: Shear force (kN)
Q: First moment (cm³)
I: Second moment (cm⁴)
t: Thickness (mm)
\tau: Shear stress (MPa)

Lecture brief

Historical brief

From Euler’s 1744 elastica and Navier’s beam theory to Mohr’s circle and transformed-section RC, structural mechanics grew as a closed-form craft before finite elements. The lab keeps those governing lines for buckling, flexure, joints and influence. This sheet (CIV-06 — Jourawski shear formula) is the form associated with Jourawski 1856 · EN 1993-1-1. Working symbols: $V$ , $Q$ , $I$ , $t$ $\rightarrow$ $\tau$ . Longitudinal equilibrium of a beam fibre requires a shear flow q = VQ/I; dividing by thickness gives Jourawski's τ.

Purpose

Purpose: compute

\tau

from

V

Q

I

t

in Structural & civil via

\tau = \dfrac{V Q}{I t}

Horizontal shear τ = VQ /(I t) in a beam web. Use it when a real structural & civil question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

V = 80.000\,\mathrm{kN}

Q = 400.000\,\mathrm{cm^{3}}

I = 8000.000\,\mathrm{cm⁴}

t = 8.000\,\mathrm{mm}

, the governing relation

\tau = \dfrac{V Q}{I t}

yields

\tau = 50.000\,\mathrm{MPa}

. Elastic beam, thin web. Q is first moment of the area beyond the fibre. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Shear force V80 kNFirst moment Q400 cm³Second moment I8000 cm⁴Thickness t8 mm

Outputs

Shear stress \tau50.000 MPa

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Narration of this film

Elastic beam, thin web. Q is first moment of the area beyond the fibre.

Longitudinal equilibrium of a beam fibre requires a shear flow q = VQ/I; dividing by thickness gives Jourawski's τ.

Reading speed

Watch on YouTube