CIV-28

Bredt thin-wall torsion

τ = T / (2 Am t). Closed thin-wall tubes, constant shear flow.

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TorsionBredt

Governing equation

\tau=\dfrac{T}{2 A_m t}

where

T: Torque (kN·m)
A_m: Mean enclosed area (cm^2)
t: Wall 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-28 — Bredt thin-wall torsion) is the form associated with Bredt. Working symbols: $T$ , $A_m$ , $t$ $\rightarrow$ $\tau$ . Bredt's first formula. Am is the area enclosed by the midline. q = T/(2 Am) is constant.

Purpose

Purpose: compute

\tau

from

T

A_m

t

in Structural & civil via

\tau=\dfrac{T}{2 A_m t}

τ = T / (2 Am t). Closed thin-wall tubes, constant shear flow. 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

T = 40.000\,\mathrm{kN·m}

A_m = 800.000\,\mathrm{cm^2}

t = 8.000\,\mathrm{mm}

, the governing relation

\tau=\dfrac{T}{2 A_m t}

yields

\tau = 31250.00\,\mathrm{MPa}

. A hollow box, a torque, a circulating shear flow. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Torque T40 kN·mMean enclosed area A_m800 cm^2Wall thickness t8 mm

Outputs

Shear stress \tau31250.00 MPa

Reading speed

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Narration of this film

A hollow box, a torque, a circulating shear flow.

Bredt's first formula. Am is the area enclosed by the midline. q = T/(2 Am) is constant.

Reading speed

Watch on YouTube