4. [3.4-8] Two sections of steel drill pipe, joined by bolted flange plates at B, are being tested to assess the adequacy of both pipes. In the test, the pipe structure is fixed at A, a concentrated torque of 500 kN-m is applied at x = 0.5 m, and uniformly distributed torque intensity = 250 kN-m/m is applied on pipe BC. Both pipes have the same inner diameter d = 200 mm. Pipe AB has thickness = 15 mm, while pipe BC has thickness= 12 mm. Find the maximum shear stress and maximum twist of the pipe and their locations along the pipe. Assume G = 75 GPa. A 0.5 m 500 KN m →X 2 m B 250 kN. m/m -1.5 m C

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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.