Three blocks are connected by a weightless cord and rest on an inclined plane (Fig. 2(a)). The following set of simultaneous equations is derived from the free- body diagrams shown in Fig. 2(b): 100a +T + (0)R =519.72 50a -T +R=216.55 25a + (0)T – R =108.27 Without interchanging the rows and columns, solve for the acceleration a and the tensions T and R, in the two ropes by using Gauss-Seidel iteration method. Stop all calculations after three iterations. 25 kg 50 kg 100 kg 45° 692.96 x 0.25- 173.24 692.96 692.96 346,48 173 24 x 0.375 s 173.24 100 x 9.8 = 980 173.24 346.48 50 X'9,8 = 490 25 x9.8 a, acceleration 0,375 129.93

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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.