Determine the allowable value of the torque, T, which can be applied to the solid circular shaft shown in the figure below, so that there is no failure based on the maximum shear stress theory. In addition to the torque, T, the shaft which is 25 mm in diameter, is also subjected to a centric load, P, of 10 kN, and a bending moment, M, of 150 Nm. The shaft is made of a material having a yield strength of 550 MPa.

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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.