A steel tie bar in a machine frame has a square cross-section and an unstretched length of

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

Fluids and Continuum Physics, Ch Mechanical properties of materials: the Young modulus, plasticity and fracture

Problem

A steel tie bar in a machine frame has a square cross-section

20\ \mathrm{mm} \times 20\ \mathrm{mm}

and an unstretched length of

1.60\ \mathrm{m}

. It is pulled along its axis with a force of

60\ \mathrm{kN}

at each end, so the stress state is uniform uniaxial tension,

\sigma_{xx} = \sigma

with

x

along the bar and all other components of the stress tensor zero. The Young modulus of the steel is

200\ \mathrm{GPa}

and the bar stays in its linear elastic range; the bar's own weight is negligible. ((a)) Find the tensile stress

\sigma

. ((b)) Using the traction

\mathbf{t}(\mathbf{n}) = \boldsymbol{\sigma}\mathbf{n}

, find the largest shear stress acting on any plane through the bar, and say which plane carries it. ((c)) Find the extension of the bar. ((d)) Find the total elastic energy stored in the bar.

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