Problem 6.166 (a) For the frame shown and neglecting the effect of friction at the horizontal and vertical surfaces, determine the forces exerted at B.

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Problem 6.166 (a) For the frame shown and neglecting the effect of friction at the horizontal and vertical surfaces, determine the forces exerted at B and C on member BCE. 12 in 50 lb 6 in 6 in E D 4 in 2 in C 6 in A B

Solving Problems on Your Own Problem 6.166 (a) Solving Problems on Your Own 12 in 50 lb 6 in 6 in For the frame shown and neglecting the effect of friction at the horizontal and vertical surfaces, determine the forces exerted at B and C on member BCE. E D 4 in 2 in C 6 in A B For this problem we note that there are no two-force members. In solving this problem, we 1. Dismember the frame, and draw a free-body diagram for each member. 2. To simplify the solution, seek a way to write an equation involving a single unknown.

Dismember the frame, and draw a free-body diagram for each member. Problem 6.166 (a) Solution Dismember the frame, and draw a free-body diagram for each member. 50 lb Cy Cy D H D C 2 in Cx Cx 6 in A A 18 in Bx By 6 in 6 in

S MH = 0: Cx(2 in) - Cy(18 in) = 0 Cx = 9Cy Problem 6.166 (a) Solution To simplify the solution, seek a way to write an equation involving a single unknown. 50 lb Cy Cy D H D C 2 in Cx Cx 6 in A A 18 in Bx 6 in 6 in By Free-Body: Member ACD + S MH = 0: Cx(2 in) - Cy(18 in) = 0 Cx = 9Cy

S MB = 0: Cx(6 in) + Cy(6 in) - (50 lb)(12 in) = 0 To simplify the solution, seek a way to write an equation involving a single unknown. Problem 6.166 (a) Solution 50 lb Cy Cy D D H C 2 in Cx = 9Cy Cx Cx 6 in A A 18 in Bx 6 in 6 in By Free-Body: Member BCE + S MB = 0: Cx(6 in) + Cy(6 in) - (50 lb)(12 in) = 0 Substitute Cx = 9Cy: 9Cy(6 in) + Cy(6 in) - 600 = 0 Cy = + 10 lb; Cx = 9Cy = 9(10) = 90 lb

C S Fx = 0: Bx - 90 lb = 0 Bx = 90 lb S Fy = 0: By + 10 lb - 50 lb = 0 Problem 6.166 (a) Solution Free-Body: Member BCE C 50 lb 10 lb C = 90.6 lb Cy 6.3o C C Cx 90 lb + S Fx = 0: Bx - 90 lb = 0 Bx = 90 lb S Fy = 0: By + 10 lb - 50 lb = 0 By = 40 lb Bx + 6 in 6 in By B 40 lb 24.0o B = 98.5 lb B 90 lb