Meriam, Kraige & Bolton — Internal Forces and Moments: Problem 7_48

⚡ Mecademy AIENG정역학 · ch7  Problem Statement The uniform garage door shown in section has a mass and is equipped with two of the spring-loaded mechanisms shown, one on each side of the door. The arm has negligible mass, and the upper corner of the door is free to move horizontally on a roller. The unstretched length of the spring is , so that in the top position with the spring force is zero. To ensure smooth action of the door as it reaches the vertical closed position , it is desirable that the door be insensitive to movement in this position. Determine the spring stiffness required for this design. Problem 7/48 (a) Determination of Spring Stiffness 1. Formula: The principle of virtual work or potential energy analysis is used for equilibrium and stability. For the door to be "insensitive" to movement at the closed position (), it must be in a state of neutral equilibrium, which requires both the first and second derivatives of the total potential energy with respect to to be zero at that position: The total potential energy is the sum of gravitational potential energy and elastic potential energy : 2. Substitution: First, establish the geometry. Let the pivot be the origin . The track for roller is horizontal at height above , so . The bottom corner of the door is attached to arm of length , so its coordinates are . The door has a height . In the vertical closed position (), corner is at and corner is at . The vertical door height is . Given , we find: ABm OB A r−aθ=π θ=0