Meriam, Kraige & Bolton — Analysis of Structures: Problem 6_111

⚡ Mecademy AIENG정역학 · ch6  Problem Statement Show that the body whose shape is that of an equilateral triangle cannot bind in the vertical slot if the coefficient of static friction . The clearances on both sides are small, and the coefficient of static friction is the same at all contact points. Problem 6/111 (a) Analysis of Binding Conditions 1. Formula: For a body to "bind" (or jam) in a slot of width , the coefficient of static friction must be large enough to maintain equilibrium under the forces and moments generated by its geometry. For a body with contact points on opposite walls separated by a vertical distance , a common condition for binding is . More accurately, for a three-point contact system like the one shown (one vertex on the left wall, two on the right), the body binds if it can resist an axial force through friction-induced normal forces. This occurs when the required coefficient of friction to satisfy the moment equilibrium is less than or equal to the available coefficient . 2. Substitution: Consider the equilateral triangle of side positioned in a slot of width . In the most "spread out" orientation shown in the diagram, vertex is on the left wall, and vertices and are on the right wall. The horizontal distance from vertex to the line is the height of the triangle, . For a fit with small clearances, the width of the slot must equal the triangle's width in its orientation. In the shown orientation, , which implies . 3. Calculation: The vertical distance