Meriam, Kraige & Bolton — Rigid Bodies: Equivalent Systems of Forces: Problem 3_29

⚡ Mecademy AIENG정역학 · ch3  Problem Statement A pipe is being bent by the pipe bender as shown. If the hydraulic cylinder applies a force of magnitude to the pipe at , determine the magnitude of the roller reactions at and . Problem 3/29 (a) Magnitude of the roller reactions at A and B 1. Formula: Consider the equilibrium of the pipe. Due to the symmetry of the setup, the magnitudes of the reaction forces at rollers and must be equal, so we let . From the geometry shown in the diagram, the angle of the reaction forces with the vertical is . The equilibrium equation for the vertical forces is: 2. Substitution: Substitute the given force magnitude and the angle : 3. Calculation: Solve for the reaction magnitude : Using the numerical value : 4. Result: ● Final Conclusion: The magnitudes of the roller reactions at and are identical due to symmetry and are found to be . ✨ Final Answer Summary P F=24 kNCA B AB R = A R = B R θ=15 ∘ F = ∑ y 0⟹F−R cosθ− A R cosθ= B 0 F=24 kN θ=15 ∘ 24 kN−2Rcos(15)= ∘ 0 R 2Rcos(15)= ∘ 24 kN R= kN cos(15) ∘ 12 cos(15)≈ ∘ 0.9659 R= ≈ 0.9659 12 12.4233 kN R = A R = B 12.42 kN AB R = A R = B 12.42 kN (a) Mecademy AI Solution · ENGProblem 3/29 R = A R = B 12.42 kN