Meriam, Kraige & Bolton — Analysis of Structures: Problem 6_37

⚡ Mecademy AIENG정역학 · ch6  Problem Statement The movable left-hand jaw of the bar clamp can be slid along the frame to increase the capacity of the clamp. To prevent slipping of the jaw on the frame when the clamp is under load, the dimension x must exceed a certain minimum value. For given values of a and b and a static friction coefficient , specify this design minimum value of x to prevent slipping of the jaw. Problem 6/37 (a) Minimum value of x to prevent slipping 1. Formula: We consider the equilibrium of the movable jaw. Let be the horizontal clamping force applied by the object on the jaw. This force acts at a vertical distance from the top of the bar. Due to the moment created by , the jaw tilts and makes contact with the bar at two diagonal corners of its sleeve. Let the center of the sleeve be the origin . The bar has thickness and the sleeve has length . The contact points are at top-right and bottom-left . The force acts to the left at a vertical height from the centerline. Sum of horizontal forces: Sum of vertical forces: Sum of moments about the center of the sleeve: 2. Substitution: Assuming impending slip, the friction forces are . Substituting these into the equilibrium equations: From horizontal equilibrium: The friction moments in the moment equation cancel: The simplified moment equation becomes: μ s F x F (0,0)b a(a/2,b/2) (−a/2,−b/2) Fy=x+b/2 F =∑ x f + 1 f − 2 F=0 F =∑ y N − 2 N = 1 0⟹N = 1 N = 2 N M =∑ O F(x+b/2)− N (a/2)− 1 N (a/2)− 2 f (b/2)+ 1 f (b