Meriam, Kraige & Bolton — Statics of Particles: Problem 2_61

⚡ Mecademy AIENG정역학 · ch2  Problem Statement 2/61 The force F is applied at the end of arm ACD, which is mounted to a vertical post. Replace this single force F by an equivalent force–couple system at B. Next, redistribute this force and couple by replacing it with two forces acting in the same direction as F, one at C and the other at D, and determine the forces supported by the two hex-bolts. Use values of F = 425 N, θ = 30°, b = 1.9 m, d = 0.2 m, h = 0.8 m, and l = 2.75 m. Problem 2/61 1. Analysis of Given Data and Geometry First, we define the given parameters and set up a coordinate system. Let the origin be at the base of the post, with the positive -axis directed vertically upwards along the centerline of the post and the positive -axis directed horizontally to the right. Applied force: at an angle below the negative -axis (as shown by the arrow pointing down and left). Force vector: Coordinates of points: Point : Point : Point : Point : 2. Equivalent Force-Couple System at Point B ● Calculation Process 1. Resultant Force: The resultant force at is equal to the original force . O y x F=425 Nθ=30 ∘ x F=F(−cosθi−sinθj)=425(−cos30i− ∘ sin30j) ∘ A(−b,l)=(−1.9,2.75) m B(0,h)=(0,0.8) m C(−d,l)=(−0.2,2.75) m D(d,l)=(0.2,2.75) m RBF R=F=425(−cos30i− ∘ sin30j) ∘ R = x −425⋅0.8660=−368.1 N R = y −425⋅0.5000=−212.5 N 2. Resultant Moment about B: The moment is calculated using the position vector from to . ● Conclusion: The equivalent system at is a force and a counter-clockwise