Meriam, Kraige & Bolton — Statics of Particles: Problem 2_60

⚡ Mecademy AIENG정역학 · ch2  Problem Statement 2/60 A lug wrench is used to tighten a square-head bolt. If 50-lb forces are applied to the wrench as shown, determine the magnitude F of the equal forces exerted on the four contact points on the 1-in. bolt head so that their external effect on the bolt is equivalent to that of the two 50-lb forces. Assume that the forces are perpendicular to the flats of the bolt head. Problem 2/60 1. Analysis of the Applied Moment (Couple) The two 50-lb forces applied at the ends of the wrench handles form a couple. The external effect of this couple is a moment. From the diagram, each force is applied at a distance of from the center of the bolt (point ). ● Calculation Process 1. Present Final Formula: The moment of a couple is , where is the magnitude of the forces and is the perpendicular distance between them. 2. Substitute Values: 3. Final Calculation: 2. Analysis of the Forces on the Bolt Head The 1-in. square-head bolt is acted upon by four equal forces , each perpendicular to a flat of the bolt head. According to "View C Detail", these four forces form two couples that act in the same rotational direction (clockwise). ● Calculation Process 14 in.C M=P⋅dP d P=50 lb d=14 in.+14 in.=28 in. M = applied 50 lb×28 in. M = applied 1400 lb⋅in. F 1. Present Final Formula: The total moment exerted on the bolt head is the sum of the moments of the two constituent couples. where is the distance across the flats (the side of the square), which is 2.