A steel 0.75-in diameter shaft (G= 12,000 ksi) is subjected to the following torques in lb-ft: TA = 10; TB = 30;  TC = 70;  TD = 50. The directions of the applied torques are indicated in the figure The bearings shown allow the shaft to turn freely. The length of each segment is equal to 38 in. (a) Plot a torque diagram showing the internal torque in segments (1), (2) and (3) of the shaft. Show the FBD of each segment using a double-headed arrow to represent each torgue. Determine (b) the maximum shear stress magnitude in the shaft. (c) the rotation angle of pulley C with respect to pulley A.

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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.