When a rear$-$wheel drive car accelerates around a bend at high speeds, the drive shaft is subject

to both bending and torsional loads. The accelerating torque is reasonably constant at $400N.m$

while the bending moment at a critical section varies due to cornering and is measured to be

$M_m=250$ N$.$m and $M_a=800$ N$.$m$.$ Design the shaft for infinite life using DE$-$Goodman and

DE$-$Soderberg criteria assuming the shaft is uniform cross$-$section. The reliability in estimating

the endurance limit should be at least $99\%$ and a safety factor of $4\mathrm{.}5$ should be used in the

design. The shaft is forged from $1080$ steel of ultimate strength $620$ MPa and yield strength

$380$ MPa $.$ Use the iterative shaft design procedure and show all the steps in your supporting

work. Your answers should be rounded$-$up to the nearest $\frac{1}{{10}^{th}}mm.$

DE$-$Goodman criterion, $d=$

DE$-$Soderberg criterion, $d=$