graded$).$ Used methods MUST be those

Exercise $1(40\%)$ : The steel round$-$shaft of the figure $($diameter $d=20mm,$ Young's Modulus $=E=200$GPa $)$ is

subjected to the TWO EXTERNAL torques as shown in the figure. Supports at ends A and $B$ are rigid. Find the

Reaction$-$Torques at both ends A and B$.$ You must $($in this order$)$:

$($i$)$ for the whole geometry and loads, sketch a COMPLETE, NEAT Free$-$Body$-$Diagram $($FBD$),$ and write the

corresponding equilibrium equation;

$($ii$)$ For each of the portions through the length, you must determine the internal torque by doing:

$($a$)$ Sketching a FBD for EACH portion and EACH internal torque,

$($b$)$ writing a complete equilibrium equation FOR EACH of $($a$)$ and find the internal torque in each,

$($iii$)$ Determine the sign for each of the internal torques found in previous $($ii$)$ FOR THE PURPOSE of following:

$($iv$)$ Write a complete NEAT compatibility equation from the results of $($ii$)$ and $($iii$)$

$($v$)$ Solve for reaction$-$torque values $($ANSWERS$)$ from the equations of $($i$)$ and $($iv$),$ and

$($vi$)$ Find the maximum shear stress in the shaft.

ANSWERS:

Torque at $A=$

Torque at $B=$

Maximum Shear Stress $=$