Problem Statement:

A solid round bar with diameter $D=1in,$ has a grove of depth $e=0\mathrm{.}1in,$ with radius $r=0\mathrm{.}1in,$ as shown in the Figure. The bar is made of cold drawn steel with $S_{UT}=68k.$ The bar is only subjected to reversing torque $T=1\mathrm{.}5$ klfb$-$in$.$ You must carry at least $4$ significant digits for everything. Estimate $f$ using equations, not Fig. $6-18.$ Knock down $S_{UT}$ for torsion, but only AFTER calculating $S_e^{\text{'}}$ and $f$; only then calculate $a,b,$ and life $N$ with the lower $S_{UT}.$ Use Eqs. $6-34$ and $6-35$b for notch sensitivity in terms of uncorrected $S_{UT}$ and $r,$ not Fig. $6-21.$ Assume $N_t={10}^3,N_e={10}^6.$

Calculate the reduction factor $f$ from equations, not from chart.

Calculate the component endurance limit $S_e$ adjusted for modifying factors.

Calculate the component intercept $a$ of the high$-$cycle fatigue line.

Calculate the component slope $b$ of the high$-$cycle fatigue line.

Calculate the fatigue stress concentration $K_{fs}$ adjusted for notch sensitivity$.$

Calculate the number of cycles $N$ to failure.