Torsion

What this module covers

• Derive the torsion relationship T/J = τ/r = Gθ/L from geometry and compatibility
• Calculate the polar second moment of area for solid and hollow shafts
• Find the angle of twist and understand torsional rigidity GJ
• Analyse thin-walled closed sections using shear flow
• Explain why circular-shaft theory must not be applied to open sections

Lessons

1. 11.1

   Deriving the torsion formula

   From the geometry of twisting to T/J = τ/r = Gθ/L.

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2. 11.2

   Thin-walled and open sections

   Shear flow in closed boxes, and why an open section is hopeless in torsion.

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3. 11.3

   Torque diagrams and plastic torsion

   The fourth internal action, drawn like the others — and what a shaft does after it yields.

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4. 11.4

   Non-circular sections, warping and the cost of a slit

   Why circular-shaft theory fails everywhere else, and how much a single cut costs.

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