A steel shaft in the form of a solid body circular rod or a circular tube can be manufactured. The shaft is required to bear 1200 N.m of torsional torque. Anti-shear stress for shaft material 40 MPa, largest permissible unit torsion angle in the rod 0.75 ^ 0 As / m and steel's shear modulus is G = 78 GPa; a) Find the required diameter d0 for a solid circular shaft. b) Find the required outer diameter d2 for a ring-section shaft whose thickness is one tenth of the outer diameter. c) Find the diameter ratio (d2 / d0 ratio) and the weight ratio for ring cross section and solid section shafts. please solve carefully and in detail thank you

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Combined Loading

Any functioning component, such as machine parts, structural members, pressure vessels, and so on, are all under the influence of more than one force. When anybody is under the influence of more than one force such as shear forces, bending moments, axial forces, torsion, and so on, then such body is said to be under combined loading. A very practical example of combined loading is the crankshaft of an internal combustion engine (IC engine). The crankshaft of the IC engine is under high rpm, which is caused due to the torsional forces. Due to the presence of piston, counterbalances, and internal imbalances, the crankshaft experiences lateral forces and due to the rise in temperature, the crankshaft undergoes thermal expansion, which pulls the crankshaft along the axial direction and lateral direction. The presence of unbalanced loads along the periphery of the crankshaft also induces a bending moment.