Meriam, Kraige & Bolton — Analysis of Structures: Problem 6_10

⚡ Mecademy AIENG정역학 · ch6  Problem Statement The uniform 7-m pole has a mass of 100 kg and is supported as shown. Calculate the force P required to move the pole if the coefficient of static friction for each contact location is 0.40. Problem 6/10 (a) Calculation of the required force P 1. Formula: First, determine the geometry and the weight of the pole. The weight acts at the midpoint of the uniform 7-m pole. Let be the angle the pole makes with the horizontal. From the given dimensions, the contact point is 3 m high and the base is 4 m horizontally from the wall: The distance from to contact point along the pole is . The weight acts at the center of gravity , which is from point along the pole. Summing moments about point at the instant motion is impending: where is the normal force at (perpendicular to the pole). Establish equilibrium equations for forces. Assuming the force pushes the pole to the left, point moves left and point moves up the pole: where and are the friction forces at the verge of slipping. 2. Substitution: Substitute the known values: , , , , and . W W=m⋅g θ AB tanθ= ⟹ 4 3 θ=36.87,sinθ= ∘ 0.6,cosθ=0.8 BAL = AB = 3+4 22 5 m WG3.5 mB B M = ∑ B W(3.5cosθ)−N (5)= A 0 N A A PB A F = ∑ y N − B W+N cosθ− A F sinθ= A 0 F = ∑ x F + B N sinθ+ A F cosθ− A P=0 F = A μ N sA F = B μ N sB m=100 kgg= 9.81 m/s 2 μ= s 0.40sinθ=0.6cosθ=0.8 W=100×9.81=981 N From the moment equation: The friction force at : Substitute into the vertical force equation to find : The friction