The compound shaft shown in the figure consists of two steel [G = 80 GPa] pipe segments. The shaft is subjected to external torques TB and To which act in the directions shown. Segment (1) has an outside diameter of 216 mm and a wall thickness of 9 mm. Segment (2) has an outside diameter of 142 mm and a wall thickness of 15 mm. The torque is known to have a magnitude of Tc = 21 kN.m. The shear strain in segment (1) is measured as 500 µrad. Determine the magnitude of external torque TB. (1) TB Tc X

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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.