Consider the shaft and keyway shown in the figure below. The shaft has a diameter equal to d= 48 mm and is subjected to a torsional load, varying from -320 Nm to 1,380 Nm, in an approximately cyclic fashion. As a first step, calculate the maximum and minimum torsional stresses (in MPa) of the shaft, using the following equation: 16T πd3 where T is the torsional load and d is the shaft diameter. T= What is the summation of maximum and minimum stresses in MPa? (Hint: you need to find the value of Tmax +Tmin, and round-off your answer to 4 decimal places). d/4 Your Answer: d d/8

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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.