$5\mathrm{.}4$ Longitudinal Strains in Beams

Introductory Problems

$5\mathrm{.}4-1$ A steel wire with a diameter of $d=1\mathrm{.}6mm$

is bent around a cylindrical drum with a radius of

$R=0\mathrm{.}9m($see figure$).$

$($a$)$ Determine the maximum normal strain ${}_{\text{m}\text{a}\text{x}}.$

$($b$)$ What is the minimum acceptable radius of

the drum if the maximum normal strain must

remain below yield? Assume $E=210$GPa and

${}_Y=690$MPa.

$($c$)$ If $R=0\mathrm{.}9m,$ what is the maximum acceptable

diameter of the wire if the maximum normal

strain must remain below yield?