Meriam, Kraige & Bolton — Rigid Bodies: Equivalent Systems of Forces: Problem 3_98

⚡ Mecademy AIENG정역학 · ch3  Problem Statement Each of the three uniform 1200-mm bars has a mass of 20 kg. The bars are welded together into the configuration shown and suspended by three vertical wires. Bars AB and BC lie in the horizontal x-y plane, and the third bar lies in a plane parallel to the x-z plane. Compute the tension in each wire. Problem 3/98 (a) Determination of tensions in the supporting wires ● Calculation Process 1. Establish Coordinate System and Identify Key Points: Let the junction point where the three bars meet be the origin . The horizontal bars lie along the and axes. According to the diagram: Attachment points of vertical wires: Point is at the end of the bar along the -axis: Point is at the junction: Point is in the middle of the bar along the -axis: Centers of mass of the three 20-kg bars: Bar 1 (along -axis): Bar 2 (along -axis): Bar 3 (in plane, from vertical): Its midpoint has coordinates , , and . External Forces: Tensions: (all in direction) Weights: (all in direction) B(0,0,0) xy Axr = A 1.2i(m) Br = B 0 Cyr = C 0.6j(m) xG = 1 (0.6,0,0)(m) yG= 2 (0,0.6,0)(m) x-z30 ∘ G 3 x = G3 0.6sin30= ∘ 0.3my = G3 0z = G3 −0.6cos30≈ ∘ −0.520m T ,T ,T ABC +z W = 1 W = 2 W = 3 mg=20×9.81=196.2N −z 2. Equilibrium of Moments about the x-axis through B: 3. Equilibrium of Moments about the y-axis through B: 4. Equilibrium of Forces in the vertical (z) direction: ● Final Conclusion: The tensions in the three vertical wires are: ✨ Final Answer Summary (a) , , Mecad