Meriam, Kraige & Bolton — Equilibrium of Rigid Bodies: Problem 4_120

⚡ Mecademy AIENG정역학 · ch4  Problem Statement The torsional spring at is undeformed when bars and are both in the vertical position and overlap. If a force is required to position the bars at a steady orientation , determine the torsional spring stiffness . The slot at is smooth, and the weight of the bars is negligible. In this configuration, the pin at is positioned at the midpoint of the slotted bar. Problem 4/120 (a) Analysis of the System Geometry and Spring Rotation 1. Formula: The relative rotation of the torsional spring is the change in the interior angle between members and . At any angle , the interior angle is . 2. Substitution: Undeformed state: . Loaded state: . 3. Calculation: Change in angle: . Spring Moment: . 4. Result: ● Final Conclusion: The torsional spring at is deformed by radians in the equilibrium configuration. (b) Equilibrium Analysis of Bar ACE 1. Formula: Apply the moment equilibrium equation about point for the horizontal bar . . 2. Substitution: BOBBD Fθ= 60 ∘ k T C C Δβ OBBDθ β=180− ∘ 2θ θ = 0 90⟹ ∘ β = 0 180− ∘ 2(90)= ∘ 0 ∘ θ=60⟹ ∘ β=180− ∘ 2(60)= ∘ 60 ∘ Δβ=β−β = 0 60− ∘ 0= ∘ 60= ∘ rad 3 π M = s k Δβ= T k T ( 3 π ) M = s 3 k π T Bπ/3 A ACEM =∑ A 0 Force acts at , at a distance from . Normal force from the slot acts at , at a distance from . Since bar is at an angle to the horizontal, the normal force is at an angle of with the vertical. The vertical component is ? No, the normal is perpendicular to the slope, so it makes with the horizontal an