A compound shaft consists of segment (1), which has a diameter of 1.25 in., and segment (2), which has a diameter of 1.75 in. The shaft is subjected to a tensile axial load P = 9 kips and torques TA = 7 kip ⋅ in. and TB = 28 kip ⋅ in., which act in the directions shown in Figure below. Determine the normal and shear stresses at (a) point H and (b) point K. For each point, show the stresses on a stress element.

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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.