Q2 A steel shaft of different diameter carries a pulley and a motor as shown in Figure Q2. The weights of the pulley and the motor are 4 kg and 40 kg, respectively with a similar radius of gyration 0.5 m. If the shear modulus of shaft is given as G = 5 x 10° N/mm: nd¹ G 321 Torsional stiffness equation is k = (a) Identify the equivalent torsional stiffness of the steel shaft between the pulley and the motor. (b) Solve the natural frequency of the system. (c) Determine the responses of the pulley, 0₁ and the motor, 0₂ in terms of the unknown amplitudes of A11 and A12, and phase angles of $1 and $2. 0.1 m Ø = 0.05 m 0₁ Pulley 0.1 m Ø = 0.04 m Figure Q2 0.1 m Ø= 0.035 m 0₂ Motor

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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.