Meriam, Kraige & Bolton — Internal Forces and Moments: Problem 7_7

⚡ Mecademy AIENG정역학 · ch7  Problem Statement The upper jaw of the toggle press slides with negligible frictional resistance along the fixed vertical column. Determine the required force on the handle to produce a compression on the roller for any given value of . Problem 7/7 (a) Determination of the required force 1. Formula: The principle of virtual work states that for a system in equilibrium, the total virtual work done by all active external forces for a virtual displacement is zero: For this mechanism, we consider the virtual work done by the applied force and the reaction (compression) force . 2. Substitution: First, we establish the geometric relationship between the vertical position of the jaw and the angle . Taking pivot as the origin and the vertical direction downwards as positive: Given and : The virtual displacement of point is: The virtual work done by force (applied at a distance of from ) is: The virtual work done by the upward compression force on the downward moving jaw is: D FR Eθ F δU=δW = ∑0 F R y C θA y = C L sinθ+ AB L sinθ BC L = AB 100 mmL = BC 100 mm y = C 100sinθ+100sinθ=200sinθ C δy = C δθ = dθ dy C 200cosθδθ F250 mmA δW = F M δθ= A (F⋅250)δθ R δW= R −Rδy = C −R(200cosθδθ) 3. Calculation: Equating the total virtual work to zero: Dividing by (where ): Solving for : 4. Result: ● Final Conclusion: The required force on the handle to maintain equilibrium and produce a compression is . ✨ Final Answer Summary (a) Mecademy AI Solution · ENGProblem 7/7 δ