A steel channel section

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 Torsion and bending of rods and beams

Problem

A steel channel section, open at the top like a U, consists of a base plate

80\,\mathrm{mm}

wide and

8\,\mathrm{mm}

thick with two upright webs, each

8\,\mathrm{mm}

thick and

50\,\mathrm{mm}

tall, standing along its two outer edges, giving a total depth of

58\,\mathrm{mm}

. It is bent about a horizontal axis with zero net axial force. Someone argues: "Bending just stretches one side and compresses the other symmetrically about the middle of the shape, so the neutral axis is at mid-depth,

29\,\mathrm{mm}

above the bottom." ((a)) Find the true position of the neutral axis, measured from the bottom face of the base plate. ((b)) Say what is wrong with the quoted argument.

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