Problem 1 The side of a tank presents a protrusion having the shape of a half sphere having radius R=0.25m and centre located at point C (see figure below). The tank is filled with air and water (specific weight y = 9806 N/m³ ) whose fre surface is at the same elevation as C. The gage pressure of the air inside the tank is n= 32 Kpa. Determine: Air a) the hydrostatic force (magnitude and line of action) that the air exerts on the quarter of the sphere. Water R b) The total hydrostatic force (magnitude and line of action) that both fluids exert on the half sphere. (the volume of a sphere of radius R can be computed as TR3).

Q: II. Find the reaction forces. A 9m 30 KN/m 25 KN/m 7m 15 KN-m 3m 5 KN 3m 3 m 9m 10 KN/m 10 KN/m 7m B

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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.