A rectangular steel bar of width and depth is bent about its horizontal axis

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 Dislocations and the onset of plastic flow

Problem

A rectangular steel bar of width

b = 25\,\mathrm{mm}

and depth

h = 50\,\mathrm{mm}

is bent about its horizontal axis. The steel is elastic-perfectly plastic with tensile yield stress

\sigma_Y = 300\,\mathrm{MPa}

. ((a)) Find the bending moment

M_Y

at which the outer fibres first reach yield. ((b)) Find the fully plastic moment

M_p

, at which the yield front has moved right through the cross-section. ((c)) State the shape factor

M_p/M_Y

and compare it with the value quoted for a solid rectangle.

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