Meriam, Kraige & Bolton — Internal Forces and Moments: Problem 7_2

⚡ Mecademy AIENG정역학 · ch7  Problem Statement Each of the uniform links of the frame has a mass and a length . The equilibrium position of the frame in the vertical plane is determined by the horizontal force applied to the left- hand link. Determine the equilibrium angle . Problem 7/2 (a) Calculation of the Equilibrium Angle 1. Formula: The principle of virtual work states that for a system in equilibrium, the total virtual work done by all active forces during a virtual displacement is zero: For this system, the active forces are the weights of the two links and the applied horizontal force . We can also express this using potential energy and the work of non-conservative forces : 2. Substitution: Let the right-hand pin be fixed at the origin . The position of the left-hand pin (assuming it's on a roller) is then at . The center of mass for both links is at their midpoints. The vertical height of each center of mass is . The total gravitational potential energy is . The force is applied at the midpoint of the left-hand link. Its horizontal coordinate relative to the fixed right pin is: The virtual displacement of the application point of in the direction of the force (to the right) is: mb P θ θ δU=F ⋅ ∑ i δr = i 0 PV δW nc δU=−δV+δW = nc 0 (0,0) x=−2bcosθ y = G sin θ 2 b V=2⋅ m g ( sin θ )= 2 b mgbsinθ δV= (m g bsin θ ) δθ = dθ d mgbcosθδθ PD x = D x + left pin cos θ = 2 b −2bcosθ+0.5bcosθ=−1.5bcosθ P The virtual work done by force is . 3. Calculation: Substitute the expres