Ex 6

Statics – Exercise No. 6 5.9 Locate the centroid of the plane area shown. Answer: x = y = 202mm

5.33 Knowing that the figure shown is formed of a thin homogenous wire, determine the length l of the portion CE of the wire for which the center of gravity of the figure is located at point C, when (a) θ = 15°, (b) θ = 60°. Answer: (a) l = 1.427r, (b) l = 2.113r.

5.43 & *5.53 Determine by direct integration the centroid of the area shown. Answer: x = 1.607 a, y = 0.332h . π Answer: x = L π , y = a 8

5.78 Determine the reactions at the beam supports for the given loading condition. Answer: A = 21.45kN , B = 5.55kN .

5.93 The quick acting gate AB is 525mm wide and is held in its closed position by a vertical cable and by a hinges located along its top edge B. for a depth of water d = 1.8m, determine the minimum tension required in cable AC to prevent the gate from opening. Answer: T = 4180N. 5.118 Three brass plates are brazed to a steel pipe to form the flagpole base shown. Knowing that the pipe has a wall thickness of 6mm and that each plate is 5mm thick, determine the location of the center of gravity of the base (Density: brass = 8470 kg/m3; steel = 7850 kg/m3.) Answer: y = 85.2mm

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All the questions are taken from Ferdinand P. Beer and E. Russell Johnston Jr. “Vector Mechanics for Engineers, Statics” Second SI Metric Edition, McGraw-Hill Book Company.