Meriam, Kraige & Bolton — Analysis of Structures: Problem 6_63

⚡ Mecademy AIENG정역학 · ch6  Problem Statement The vertical position of the 100-kg block is adjusted by the screw-activated wedge. Calculate the moment which must be applied to the handle of the screw to raise the block. The single- thread screw has square threads with a mean diameter of 30 mm and advances 10 mm for each complete turn. The coefficient of friction for the screw threads is 0.25, and the coefficient of friction for all mating surfaces of the block and wedge is 0.40. Neglect friction at the ball joint A. Problem 6/63 (a) Calculation of the screw moment M ● Calculation Process 1. Analyze the block equilibrium to find the normal force between the block and wedge: To raise the 100-kg block, the wedge must be moved to the right. As it moves, the block is pushed upward and against the vertical wall on its right side. The forces acting on the block are its weight , the normal force and friction force from the vertical wall, and the normal force and friction force from the wedge. From horizontal equilibrium (): From vertical equilibrium (): Substitute the expression for : Substituting and : M N 2 WN 1 F = 1 μN 1 N 2 F = 2 μN 2 F =∑ x 0 N = 1 N sin10+ 2 ∘ μN cos10= 2 ∘ N (sin10+ 2 ∘ μcos10) ∘ F =∑ y 0 N cos10− 2 ∘ μN sin10− 2 ∘ μN − 1 W=0 N 1 N (cos10− 2 ∘ μsin10)− ∘ μ[N (sin10+ 2 ∘ μcos10)]= ∘ W N [cos10(1− 2 ∘ μ)− 2 2μsin10]= ∘ W W=100×9.81=981 Nμ=0.40 N [cos10(1− 2 ∘ 0.40)− 2 2(0.40)sin10]= ∘ 981 N [0.84cos10− 2 ∘ 0.8sin10]= ∘ 981 N [0.8272− 2 0.1389]=981⟹N = 2 = 0.688