A hollow steel shaft used in a construction auger has outer  diameter d2 = 7.8 in. and inner diameter d1 = 5.5 in. (see figure). The steel has shear modulus of elasticity G = 11.5 x 10^6 psi. For an applied torque of 175 k-in. , determine the following quantities: a.) Shear stess T2 at the outer surface of the shaft b.) Shear stress T1 at the inner surface c.) rate of twist Θ (degrees per unit of length)

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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.