Problem 4-d Rod AC is supported by a pin and

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Equilibrium of Rigid Bodies

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Problem 4-d Rod AC is supported by a pin and bracket at A and rests against a peg at B. Neglecting the effect of friction, determine (a) the reactions at A and B when a = 8 in., (b) the distance a for which the reaction at A is horizontal and the corresponding magnitudes of the reactions at A and B. A B C a 20 in 10 in 60 lb

Problem 4-d A B C a 20 in 10 in 60 lb Solving Problems on Your Own Rod AC is supported by a pin and bracket at A and rests against a peg at B. Neglecting the effect of friction, determine (a) the reactions at A and B when a = 8 in., (b) the distance a for which the reaction at A is horizontal and the corresponding magnitudes of the reactions at A and B. 1. Draw a free-body diagram of the body. This diagram shows the body and all the forces acting on it.

Problem 4-d A B C a 20 in 10 in 60 lb Solving Problems on Your Own Rod AC is supported by a pin and bracket at A and rests against a peg at B. Neglecting the effect of friction, determine (a) the reactions at A and B when a = 8 in., (b) the distance a for which the reaction at A is horizontal and the corresponding magnitudes of the reactions at A and B. 2. For a three-force body, solution can be obtained by constructing a force triangle. The resultants of the three forces must be concurrent or parallel. To solve a problem involving a three-force body with concurrent forces, draw the free-body diagram showing that the three forces pass through the same point. Complete the solution by using a force triangle.

tan a = a = 26.57o Problem 4-d Solution A (a) a = 8 in a C a 20 in 10 in 60 lb (a) a = 8 in Draw a free-body diagram of the body. C 10 in 60 lb A g a 8 in 12 in B 2 1 G D F E tan a = a = 26.57o 1 2

AE = EB = (8) = 4 in. EF = BG = 10 _ 4 = 6 in DG = BG = (6) = 3 in. C 10 in 60 lb A g a 8 in 12 in B 2 1 G D F E Problem 4-d Solution Construct a force triangle. 3 - FORCE BODY Reaction at A passes through D where B and 60-lb load intersect AE = EB = (8) = 4 in. EF = BG = 10 _ 4 = 6 in DG = BG = (6) = 3 in. FD = FG _ DG = 8 _ 3 = 5 in. Tan g = = ; g = 26.57o 1 2 FD AF 5 10

10 in Problem 4-d Solution A FORCE TRIANGLE g E F A a = 26.57o 8 in D 30 lb A G 60 lb a B B 12 in B 2 30 lb a = 26.57o 1 C 60 lb 10 in A = B = = 67.08 lb A = 67.1 lb 26.6o B = 67.1 lb 26.6o sin 26.57o 30 lb

a Problem 4-d Solution A (b) For A horizontal a C a 20 in 10 in 60 lb (b) For A horizontal Draw a free-body diagram of the body. 10 in A F a A a a G a B B 2 a = 26.57o 1 C 60 lb

a D ABF : BF = AF cos a D BFG : FG = BF sin a a = FG = AF cos a sin a Problem 4-d Solution A Construct a force triangle. F a A a a G a B D ABF : BF = AF cos a D BFG : FG = BF sin a a = FG = AF cos a sin a a = (10 in.) cos 26.57o sin 26.57o a = 4.00 in. B 2 a = 26.57o 1 C 60 lb

10 in Problem 4-d Solution A FORCE TRIANGLE F a A a a G a B 60 lb A B a = 26.57o B 2 a = 26.57o 1 C 60 lb tan a 60 lb A = = 120 lb A = 120.0 lb B = = 134.16 lb B = 134.2 lb 26.6o sin a 60 lb