A steel cylinder used to calibrate a high-pressure gauge has bore radius and outer radius

PHYSICS · Multi-part · Fermi University Physics · Fluids & Continuum Physics · Solid continuum mechanics and complex fluids · Solid continuum mechanics and complex fluids

Bending, Ringing, Breaking and Flowing, Ch Hooke's law for an isotropic solid

Problem

A steel cylinder used to calibrate a high-pressure gauge has bore radius

a = 40\,\mathrm{mm}

and outer radius

b = 80\,\mathrm{mm}

, and is pressurised internally to

p = 350\,\mathrm{MPa}

with its outer surface free of load;

\nu = 0.30

. ((a)) Find the radial stress

\sigma_{rr}

at the mid-wall radius,

r = 60\,\mathrm{mm}

. ((b)) Find the axial stress if the cylinder's ends are held so that it cannot change length (plane strain). ((c)) Find the axial stress if instead the ends are closed by caps and the cylinder is free to extend, using a force balance on one end cap far from where you look.

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