Variable Fatigue Loading $(20$ pts$).$ Combination of Loads. A bicycle crank is modeled using nonrotating shafts that are fixed at plane A$,$ while the pedal is subjected to a fluctuating load. A fillet exists on the wall with a radius of $\frac{1}{10}"$ and fatigue stress$-$concentration factors of $K_{f,\text{b}\text{e}\text{n}\text{d}\text{i}\text{n}\text{g}}=K_f,$ torsion $=1\mathrm{.}7.$ The crank is made from AISI $1020$ hotrolled steel $(S_{ut}=90k,S_y=50k).$

Note: $k_a=0\mathrm{.}569kb=0\mathrm{.}978k_c=1,k_d=k_e=k_f=1$

a$.$ At plane $A,$ calculate the factor of safety for fatigue based on infinite life using the modified Goodman fatigue failure criterion.