Problem $4(2\mathrm{.}0$val$)$

Consider a $20\mathrm{.}3$ mm diameter circular shaft made of AISI $1020$ CD $($cold drawn$)$ steel and

subjected to a purely reversible cyclic torque of magnitude $203\mathrm{.}4$ N$*$m$.$ For a

$99\%$ confidence level, estimate the number of life cycles until shaft failure.

Table A$-20$ Deterministic ASTM Minimum Tensile and Yield Strengths for Some Hot$-$Rolled $($HR$)$ and

Cold$-$Drawn $($CD$)$ Steels

$[$The strengths listed are estimated ASTM minimum values $$in the size range $18$ to $32$ mm $((3)/(4)$ to $1(1)/(4)$ in$).$ These strengths are

suitable for use with the design factor defined in Sec. $1-10,$ provided the materials conform to ASTM A$6$ or A$568$

requirements or are required in the purchase specifications. Remember that a numbering system is not a specification.$]$