Question $1$

A shaft is used to transmit power using a gear and pulley. The gear has a diameter of $25$ cm and drives a mating gear with an upward vertical tangential force $(F_t=8500N).$ The pressure$/$involute angle for the gear is $19\mathrm{.}44.$ A belt drive with a pulley diameter of $61$ cm and weight of $1300$ N $,$ supplies power to the shaft. The tight side tension of the belt drive is $T_1=6000N$ and the belt ratio for the system is$,e^{}=3\mathrm{.}529.$ The shaft is supported on bearings at $B$ and $D.$

Calculate the normal$/$radial force and the tension on the slack side.

Draw a free body diagram and calculate the vertical reaction forces at B and D$.$

Draw a free body diagram and calculate the horizontal reaction forces at B and D$.$

Calculate the vertical bending moments and show in a sketch.

$(4)$

Calculate the horizontal bending moments and show in a sketch.

$(4)$

Calculate the resultant bending momersis and show in a sketch.

$(2)$

Calculate the torque on the pulley and gear.

$(2)$

${}_b=100\frac{N}{m}{m}^2$ and $=90\frac{N}{m}{m}^2$

Question $2$

A solid shaft in a machine causes premature bearing failure due to the weight of the shaft. It is decided that the solid shaft should be replaced with a hollow shaft. The hollow shaft has the same outside diameter as the solid shaft $($d$)$ and a maximum allowable shear stress $20\%$ greater that the solid shaft. The hollow shaft and solid shaft have the same material density $(F=1000k\frac{g}{m^3})$ and length.

Calculate the inside diameter $(d_i)$ of the hollow shaft.

Determine the percentage weight saving when using the hollow shaft.

$[6]$

Question $3$

A solid steel shaft with diameter $)=(30mm$ has a modulus of rigidity of $G=0\mathrm{.}8{10}^5\frac{N}{m}{m}^2.$ If the shaft is subject to a torque $(T_{\text{o}\text{r}\text{q}\text{u}\text{e}}=0\mathrm{.}5{10}^{6}N*mm),$ determine:

Angular twist over one meter $(1$ m $)$ length of the shaft.

The maximum shear stress in the shaft.

The shear stress at a point $10$ mm from the axis of rotation of the shaft.

$(2)$

$[6]$