Meriam, Kraige & Bolton — Analysis of Structures: Problem 6_48

⚡ Mecademy AIENG정역학 · ch6  Problem Statement The 100-kg industrial door with mass center at is being positioned for repair by insertion of the wedge under corner . Horizontal movement is prevented by the small ledge at corner . If the coefficients of static friction at both the top and bottom wedge surfaces are 0.60, determine the force required to lift the door at . Problem 6/48 (a) Determination of the force to lift the door ● Calculation Process 1. Formula: First, we determine the vertical force required at corner to initiate lifting of the door by considering the moment equilibrium of the door about point . where is the weight of the door, is the total width , and is the horizontal distance from to . Next, we apply equilibrium to the wedge. For the wedge to move left and lift corner , the forces acting on it are the applied force , the normal and friction forces from the door at the top, and the normal and friction forces from the floor at the bottom. Vertical equilibrium of the wedge (top surface horizontal, bottom inclined at ): Horizontal equilibrium of the wedge: 2. Substitution: Given values: , , , , , . Calculate weight: . Total width: . Vertical force needed at : G 5 ∘ B A PB P R B B A M = ∑ A 0⟹R (L)− B W(d )= AG 0 W=mgLd + AG d GB d AG AG B P θ=5 ∘ F = ∑ y 0⟹N cosθ− 2 μ N sinθ− s2 R = B 0⟹N = 2 cosθ−μ R B F = ∑ x 0⟹P−μ R − sB N sinθ− 2 μ N cosθ= s2 0⟹P=μ s m=100 kgg= 9.81 m/s 2 d = AG 1.2 m d = GB 1 mθ=5 ∘ μ = s 0.60W=100×9.81= 981 NL=1.2+1=2.2 mB R = B 2.2 981×