CIV-27

Shear stress VQ/It

τ = V Q / (I t). Jourawski's complementary shear in a beam.

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ShearJourawski

Governing equation

\tau=\dfrac{VQ}{It}

where

V: Shear (kN)
Q: First moment Q (cm^3)
I: Second moment (cm^4)
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-27 — Shear stress VQ/It) is the form associated with Jourawski. Working symbols: $V$ , $Q$ , $I$ , $t$ $\rightarrow$ $\tau$ . Q is the first moment of the area beyond the fibre. t is the width at that fibre.

Purpose

Purpose: compute

\tau

from

V

Q

I

t

in Structural & civil via

\tau=\dfrac{VQ}{It}

τ = V Q / (I t). Jourawski's complementary shear in a beam. 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 = 12000.000\,\mathrm{cm^4}

t = 10.000\,\mathrm{mm}

, the governing relation

\tau=\dfrac{VQ}{It}

yields

\tau = 26.67\,\mathrm{MPa}

. A beam, a shear, a parabolic τ on a rectangle. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Shear V80 kNFirst moment Q Q400 cm^3Second moment I12000 cm^4Thickness t10 mm

Outputs

Shear stress \tau26.67 MPa

Reading speed

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Narration of this film

A beam, a shear, a parabolic τ on a rectangle.

Q is the first moment of the area beyond the fibre. t is the width at that fibre.

Reading speed

Watch on YouTube