A rectangular bar is cut from an AISI $1018$ cold$-$drawn steel flat. The bar is $60$ mm wide by

$10$ mm thick and has a $12$ mm hole drilled through the center as depicted in Table A$-15-1.$ The

bar is concentrically loaded in push$-$pull fatigue by axial forces $F_a,$ uniformly distributed across

the width.

a$)$ Using a factor of safety $n=1\mathrm{.}8,$ estimate the largest force $F_a$ that can be applied ignoring

column action. $($assume infinite life$).$

b$)$ When the force from part $($a$)F_a$ is applied, determine the factor of safety for the bar for

$100,000$ cycles