9. A torsion tube is made from aluminium tube having an outside diameter of 60mm and a wall thickness of 5mm. Young's modulus for titanium is 70GPA; Poission's ratio is 0.33. Determine: (a) the maximum Torque T (acting clockwise) that can be applied to the tube if the shear stress cannot exceed 100MPA. (b) sketch the shear stress and shear strain profile for the Torque calculated in (a) using a polar co-ordinate axis system, where the z axis runs along the length of the tube, and the perpendicular circumferential axis acts in a positive clockwise direction. [Ans: (a) 2200Nm, (b) 100MPA, 83.3MPA, 3779µɛ, 3140µɛ]

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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.