$(2$ points$)$ SS shaft eccentric mass design $01$ The carbon steel shaft shown turns at an average speed of $2700$ rpm $,$ loaded with a constant torque $T_A$ of $5\mathrm{.}33$kip$*ft$ and a reversing torque $T_D,$

oscillating between $4\mathrm{.}03$kip$*ft$ and $6\mathrm{.}63$kip$*ft.$ The shaft rotation and the applied reversing torque $T_D$ are in phase. Locations B and C are both found

to have fatigue stress concentrations of $1\mathrm{.}51$ in bending and $1\mathrm{.}32$ in torsion. The shaft shown has been found the have the following material

properties.

Find the weight of drum $BC$:$W=$

Find the radial distance to drum BC$\text{'}$s center of mass: $r_c=$

Find the midrange and alternating moment and torque at locations $B$ and $C.$

Design shafts $AB$ and $CD$ for a factor of safety of $1\mathrm{.}2$ using Goodman, Gerber, and ASME Elliptic failure criteria. Also, design for yield.

Notes:

$-$Neglect the mass of the shaft in the slender portions, but evaluate the mass of segment $BC.$

$-$Neglect the effect of torque induced by tangential$,$ centripetal acceleration of drum BC$.$

$-$Neglect $($the small changes in angular velocity for$)/($dynamic effect on$)$ centripetal force.

The carbon steel shaft shown turns at an average speed of $2700$ rpm $,$ loaded with a constant torque $T_A$ of $5\mathrm{.}33$ kip $.$ft and a reversing torque $T_D,$

oscillating between $4\mathrm{.}03$kip$*ft$ and $6\mathrm{.}63$kip$*ft.$ The shaft rotation and the applied reversing torque $T_D$ are in phase. Locations B and C are both found

to have fatigue stress concentrations of $1\mathrm{.}51$ in bending and $1\mathrm{.}32$ in torsion. The shaft shown has been found the have the following material

properties.

Find the weight of drum $BC$:$W=$

Find the radial distance to drum BC$\text{'}$s center of mass: $r_c=$

Find the midrange and alternatina moment and toraue at locations $B$ and $C.$