4m solid core steel shaft with 50 mm diameter is fixed at its ends. It is subjected to a 400 N-m torque 1m from the left end and a 100 N-m torque 0.5 m from the right end (same direction). a) Determine the reactions at the ends. b) Determine the maximum shear stress in the shaft. c) If the shaft is hollow core and the maximum allowable shear stress in the shaft is 37 MPa, determine the thickness of the shaft given that the outside diameter is still 50 mm.

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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.