Consider a rod with a solid circular cross section undergoing a pure bending loading, where the bending moment fluctuates between $13$ kip$-$in and $45$ kip$-$in $(1$kip$=1,000lbs).$

If the Goodman diagram below applies to the rod, what is the minimum required diameter of the rod $($in inches$)$ to ensure infinite life of the rod? Give your answer to the nearest hundredth. If no feasible limit exists, put $0.$

Minimum diameter required:

$d=$ inches