Meriam, Kraige & Bolton — Internal Forces and Moments: Problem 7_14

⚡ Mecademy AIENG정역학 · ch7  Problem Statement The mechanism of Prob. 4/120 is repeated here. 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 7/14 (a) Torsional Spring Stiffness Calculation 1. Formula: We use the principle of virtual work, , which for this conservative system can be expressed as: where is the elastic potential energy of the torsional spring, and is the angular deformation. 2. Substitution: Geometry: Bar has length . Point is at its midpoint, so its height is . By symmetry, point (midpoint of ) and point on the horizontal slotted bar are at the same height: . Spring Deformation: The spring is undeformed when bars overlap vertically ( ). The interior angle at is . The twist of the spring is radians. Potential Energy: . Virtual Work of Force : . Equating and : B OBBDF θ=60 ∘ k T C C δW=0 δW = ext δV e V = e k γ 2 1 T 2 γ OBbA y = A sin θ 2 b CBDE y = E y = A sin θ 2 b θ=90 ∘ Bβ=180− ∘ 2θ γ=β−β = undeformed (π−2θ)−0=π−2θ V= e k (π− 2 1 T 2θ) 2 FδW = ext −Fδy = E − F sinθδθ = dθ d ( 2 b ) − cos θδθ 2 Fb δW ext δV = e δθ dθ dV e − cos θδθ = 2 Fb k (π− T 2θ)(−2)δθ 3. Calculation: Simplify the equilibrium equation: Substitute the given values rad: 4. Re