1. Fig. 8.4 shows the attachment of four pulleys to two different types of shafts. Pulleys B and Care connected by a hollow shaft with internal and external diameters of 50 mm and 80 mm respectively. Other pulleys are connected by solid shafts of equal diameters. The torque acting on each pulley is shown in the figure. Find (a) the maximum and the minimum shear stress induced in the hollow shaft. (b) the diameter of the solid shaft, if the maximum shear stress is not to exceed 50 MPa. T₁ - SkN-m TB = 10kN-m A 4 1.2m B Tc=20kN-m TD=5kN-m Vo D 1.0m Fig. 8.4 0.5m

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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.