Answer Happy

Q3. a) A solid circular shaft will be 2 m long, and its diameter is to be determined. It is made of steel with a shear modulus of 75 GPa. When the shaft is subjected to a torque of 100 Nm, the maximum shear stress is to remain below 10 MPa and the angle of twist is to remain below 3 degrees. i What is the minimum diameter of the shaft which meets the above requirements? [12] ii. Where is the minimum shear stress in the shaft and what is its value? [2] a b) Another shaft is a compound circular shaft formed by two circular shafts which are rigidly attached along their cross-sections at B, as shown in figure Q3(b). The first section of the shaft, from A to B, is a solid cylinder which has a length of 50 cm and a diameter of 3cm. The second section of the shaft, from B to C. is a hollow cylinder with a length of 100 cm, an outer diameter of 3cm and an internal diameter of 2cm. This whole shaft is subjected to a torque of 200 Nm. The material in both sections of the shaft has a shear modulus of 85 GPa. i. Determine the total angle of twist in degrees in the shaft from A to C. [9] If instead the entire 150 cm shaft length was hollow with the same internal and external diameters as the section from B to C, would the total angle of twist increase or decrease? Briefly justify your answer. 121 ii. B 200 Nm 3 cm Not to scale 2 cm T 50 cm 100 cm