Question $1$

A circular cross$-$section shaft is mated to a motor rotating at $1500$ rpm $.$ The shaft is made $40$ C $8$

steel and is used to transmit power to two pulleys of diameter $300$ mm and $200$ mm $.$ The shaff

rest on two supports situated at $200$ mm from the pulleys. The angle of wrap for the pulleys is

$180$ and the tensions on the belts are indicated in the diagram below.

Calculate the torque at the pulley A and pulley $B.$

Draw a sketch for the vertical loading.

Draw a sketch for the horizontal loading.

Calculate the reaction force at $C.$

Calculate the reaction force at $D.$

Calculate the vertical bending moments and show in a sketch.

Calculate the horizontal bending moments and show in a sketch.

Calculate the resultant bending moments and show in a sketch.

Caiculate the equivalent torque and equivalent bending moment.

Calculate the required shaft radius in shear and bending.

Question $2$

A machine in the workshop has a spindle that rotates at $41\mathrm{.}887902ra\frac{d}{sec}$ when the input power

is $2$ kW $.$ The spindle is made from $45$ C $8$ carbon steel with a modulus of rigidity of $84k\frac{N}{m}{m}^2$ and

the maximum allowable angle of twist is $0\mathrm{.}25$ per meter length.

Determine the torque in the spindle.

Determine the radius of the spindle.

Determine the factor of safety$($FOS$)$ if the maximum allowable shear stress for the shaft is

$5$ MPa $.$

Is the shaft diameter suitable for the spindle if the maximum allowable shear stress for the

shaft is $10$ MPa $.$