Hint: For internal torques, we obey the same sign convention as for axially loaded members. However, when calculating the torsional shear stress, we instead consider the absolute value of the shear stress. Therefore, you should calculate positive quantities for all torsional shear stresses.

Take T$\_($A$)=400$lb$*$in$,$ T$\_($B$)=1200$lb$*$in$,$ T$\_($C$)=500$lb$*$in$.$

Take d$=0\mathrm{.}15$ in and d$\_($hole $)=0\mathrm{.}3$in$.$

Problem $3($Provided Problem$)$

Consider a solid circular shaft A$-$D with a varied diameter between the gears: d$\_($AB$),$d$\_($BC$),$ and d$\_($CD$).$ The shaft is fixed to a rigid wall at D and three external torques are applied to each gear at A$,$B$,$

and C$.$ The torques are applied in the senses shown below. a$)$ Draw the Torsion Moment diagram for the structure and find the maximum shear stress in each segment of the shaft. Then, determine which segment has the overall maximum shear stress in the shaft. Finally, plot a cross$-$sectional shear stress distribution at the section where the maximum shear stress in the shaft occurs. b$)$ Reconsider the structure shown above after creating a drill hole with diameter d$\_($hole$)$ through the entire length $($from A to D$)$ of the shaft. The shaft diameters d$\_($AB$),$ d$\_($BC$),$ and d$\_($CD$)$ remain the same, as do the maximum and minimum shear stress in each segment of the shaft. Then, determine which segment has the overall maximum shear stress in the shaft as well as which segment has the overall minimum shear stress in the shaft. Finally, plot a cross$-$sectional shear stress distribution at the section where the maximum shear stress in the shaft occurs.

Here are the questions I need answered:

$1.$ Find the internal torque in segment AB $($lb$*$in$).$

$2.$ Find the internal torque in segment BC $($lb$*$in$).$

$3.$ Find the internal torque in segment CD $($lb$*$in$).$

$4.$ For part a$,$ draw the Torsion Moment Diagram for the shaft.

$5.$ For part a$,$ find the maximum shear stress in segment AB $($psi$).$

$6.$ For part a$,$ find the maximum shear stress in segment BC $($psi$).$

$7.$ For part a$,$ find the maximum shear stress in segment CD $($psi$).$

$8.$ For part a$,$ which segment has the maximum shear stress in the entire shaft?

$9.$Plot a cross$-$sectional shear stress distribution at the section where $10.$ For part b$,$ find the maximum shear stress in the shaft occurs.

find the maximum shear stress in segment AB $($psi$).$

$11.$ For part b$,$ find the minimum shear stress in segment AB $($psi$).$

$12.$ For part b$,$ find the maximum shear stress in segment BC $($psi$).$

$13.$ For part b$,$ find the minimum shear stress in segment BC $($psi$).$

$14.$ For part b$,$ find the maximum shear stress in segment CD $($psi$).$

$15.$ For part b$,$ find the minimum shear stress in segment CD $($psi$).$

$16.$ For part b$,$ plot a cross$-$sectional shear stress distribution at the section where the maximum shear stress in the shaft occurs.