A Mohr's circle for a plane state of stress is drawn with its centre on the axis at…

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 Strain and stress in a deformed solid

Problem

A Mohr's circle for a plane state of stress is drawn with its centre on the

\sigma

axis at

25\ \mathrm{MPa}

and radius

50\ \mathrm{MPa}

. The point marked for the face whose outward normal is along

x

lies on the circle at

(\sigma,\tau)=(55,40)\ \mathrm{MPa}

, where the plotted shear stress is

\sigma_{xy}

and angles are positive anticlockwise. ((a)) Read off

\sigma_{xx}

\sigma_{yy}

and

\tau_{xy}

. ((b)) Read off the two principal stresses. ((c)) Find the angle, measured in the body, from the

x

-face normal to the principal direction carrying the larger principal stress.

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