A beam is loaded and supported as shown. (a) Use the double-integration method to determine the reactions at supports A and C. Reaction forces are positive upwards and couples are positive counter-clockwise unless otherwise stated. (b) Draw the shear-force and bending-moment diagrams for the beam. Assume w = 18 kN/m, L = 12.2 m and El = 5.0 x 104 kN-m² is constant for the beam. Answer: (a) Ay = i Cy- i Mc = i (b) Vmax Mmax" II IM MI W -4/2 B L/2 kN kN kN-m kN kN-m

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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.