Ex 3

Statics – Exercise No. 3 3. 54 Two 80-N forces are applied as shown to the corners B and D of a rectangular plate. (a) Determine the moment of the couple formed by the two forces by resolving each force into horizontal and vertical components and adding the moments of the two resulting couples. (b) Use the result obtained to determine the perpendicular distance between lines BE and DF. Answer: (a) M = 7.33 N•m ; (b) d = 91.6 mm.

3.58 The two shafts of a speed-reducer unit are subjected to couples of magnitude M1 = 12 N•m and M2 = 5 N•m respectively. Replace the two couples by single equivalent couple, specifying its magnitude and the direction of its axis. Answer: (a) M = 13 N•m ; θx = 67.40, θx = 900 , θx = 22.60.

is applied at A to the bracket shown, which is held by screws at B and C. (a) Replace P by an equivalent force-couple system at B. (b) Find the two horizontal forces at B and C which are equivalent to the couple obtained in part a. 3.62 A 300-N vertical force P

Answer: (a) F = 300 N ; (b) MB = 54 N•m

, B = 500 N

, C = 500 N

3.77 A 3-m beam is loaded in the various ways represented in the figure. Find two loadings which are equivalent. Answer: The two equivalent loadings are (a) and (e).

3.80 By driving the truck shown over a scale, it was determined that the loads on the front and rear axles are, respectively, 18 kN and 12 kN when the truck is empty. Determine (a) the location of the center of gravity of the rtuck, (b) the weight and location of the center of gravity of the heaviest load which may be carried by the truck if the load on each axle is not to exceed 40 kN. Answer: Gt is located 200 m from front axle; (b) Heaviest load is 50 kN, located 2.8 m from front axle.

3.95 A concrete foundation mat in the shape of a regular hexagon of side 3 m supports four column loads as shown. Determine the magnitude and point of application of the resultant of the four loads. Answer: (a) R = 350 kN, X = 750 mm, Z = -185.6 mm.

3.87 Tow cables exert forces of 90 kN each on a truss of weight W = 200 kN. Find the resultant force acting on the truss and the point of intersection of its line of action with line AB. Answer: (a) R = 329 kN 61.70 6.82 m to right of A.

3.89 A blade held in a brace is used to tighten a screw at A. (a) Determine the forces exerted at B and C, knowing that these forces are equivalent to a force couple system at A consisting of R = -(25 N)i + Ryj + Rzk and MAR = -(13.5 N•m)i. (b) Find the corresponding values of Ry and Rz. (c) What is the orientation of the slot in the head of the screw for which the blade is least likely to slip when the brace is in the position shown? Answer: (a) B = 75 N, C = 37.5 N ; (b) Ry = 0 N, Rz = -37.5 N

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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.