(Solved): Shaft Design under Static Loading: Consider the shaft shown below. The loads on gears B and C are a ...

Shaft Design under Static Loading: Consider the shaft shown below. The loads on gears B and C are as shown on the diagram. Gear C is mounted on diameter ${\mathrm{D}}_3$ and is flushed against the step. As a practical matter, you should ignore the thickness of gears and bearings. The following geometry information is available: $\begin{array}{l}\text{ Radius of Gear }B=75\mathrm{mm};\text{ Radius of Gear }C=50\mathrm{mm}\\ D_2/D_3=1.5\\ \text{ Fillet ratio at all steps, }r/d=0.2\end{array}$ Design the shaft by following the steps below: 1. Draw $\mathrm{FBD}$ and compute Gear $\mathrm{C}$ force ${\mathrm{F}}_{\mathrm{Cz}}$ as well as the bearing reactions at $\mathrm{A}$ and $\mathrm{D}$. Note 1: You may draw one 3D-FBD or two 2D-FBD's Note 2: You must present your calculation process in detail; show equations before substitutions. Ans. $F_{Cz}=3720\mathrm{N},R_{Ay}=1301\mathrm{N},R_{Az}=?785\mathrm{N},R_{Dy}=2449\mathrm{N},R_{Dz}=2025\mathrm{N}$ 2. Now consider the vertical plane of bending. Determine the bending moment (in the vertical plane) at sections B and C. Note: Either draw shear and moment diagrams or directly calculate internal bending moments. Ans. ${\mathrm{M}}_{\mathrm{z}B}=260\mathrm{N}.\mathrm{m},{\mathrm{M}}_{\mathrm{z}}\mathrm{C}=220\mathrm{N}.\mathrm{m}$ 3. Now consider the horizontal plane of bending. Determine the bending moment (in the horizontal plane) at sections $\mathrm{B}$ and $\mathrm{C}$. Ans. ${\mathrm{M}}_{\mathrm{yB}}=157\mathrm{N}?\mathrm{m},{\mathrm{M}}_{\mathrm{y}}\mathrm{C}=?182\mathrm{N}?\mathrm{m}$ 4. Now based on the resultant two-plane bending and transmitted torque, determine which section, B or C, is more critical? Provide a justification. Ans. Section $\mathrm{C}$ is more critical even though it has less bending moment. 5. Design shaft diameter $D_3$ for static loading under the following requirements: Material $=$ medium-carbon steel AISI 1080 (HotRolled). Desired factor of safety $=1.5$ Use Distortion Energy Theory (DET); include the effect of stress concentration factor at C. Note 1: You may ignore effect of direct (transverse) shear stress. Note 2: You must state the source for all values you collect from a table or figure. Ans. $\mathrm{d}=25\mathrm{mm}$