Meriam, Kraige & Bolton — Rigid Bodies: Equivalent Systems of Forces: Problem 3_44

⚡ Mecademy AIENG정역학 · ch3  Problem Statement A torque (moment) of is required to turn the bolt about its axis. Determine and the forces between the smooth hardened jaws of the wrench and the corners and of the hexagonal head. Assume that the wrench fits easily on the bolt so that contact is made at corners and only. Problem 3/44 (a) Determination of applied force P and contact forces at A and B 1. Formula: To turn the bolt, the moment of the force about the bolt's center must equal the required torque . For the entire wrench-bolt system: where is the moment arm of from . For the wrench in equilibrium as a three- force member (forces ): where is the horizontal distance from the center to the corners and . 2. Substitution: Given and . From geometry, the vertical distance between the jaws is . For a standard hexagonal bolt head with a face-to-face width of , the corner-to-corner diagonal distance is . If only the corners and touch the horizontal jaws, the hexagon is tilted such that the vertical separation of the corners is . The diagonal makes an angle with the horizontal where: The horizontal moment arm for the contact forces is . 24 N⋅mP AB AB PO M M = ∑ O 0⇒P⋅d=M dPO P,F ,F AB F = ∑ y 0⇒F− B F − A P=0 (assuming jaws are horizontal) M = ∑ O 0⇒(F + B F )x− A P⋅d=0 xOAB M=24 N⋅md=120 mm=0.12 m P= = 0.12 m 24 N⋅m 200 N 14 mm 14 mm D= ≈ cos30 ∘ 14 16.166 mmAB 14 mmABθ Dsinθ=14⇒sinθ= = 16.166 14 ⇒ 2 3 θ=60 ∘ x= cos60= 2 D ∘ = 4 D ≈ 4 16.166 4.0415 mm 3. Calculation: Solve for and