Meriam, Kraige & Bolton — Analysis of Structures: Problem 6_109

⚡ Mecademy AIENG정역학 · ch6  Problem Statement The toggle-wedge is an effective device to close the gap between two planks during construction of a wooden boat. For the combination shown, if a force of 300 lb is required to move the wedge, determine the friction force acting on the upper end of the toggle. The coefficients of static and kinetic friction for all pairs of mating surfaces are taken to be 0.40. Problem 6/109 (a) Analysis and Friction Force at A 1. Formula: First, we model the toggle as a weightless two-force member. For a weightless member supported at two points by contact surfaces, equilibrium requires the resultant forces at each end to be equal, opposite, and collinear with the axis of the member. Thus, the resultant force at the upper end and at the lower end must act along the toggle's axis, which is inclined at to the vertical. The components of the force exerted by the toggle on the wedge are: Equilibrium equations for the wedge (on the verge of moving to the left): 2. Substitution: Substitute the known values lb, , and : 3. Calculation: Show intermediate calculations: P FA AB R A AR B B θ=15 ∘ R B R = Bx R sinθ B R = By R cosθ B F = ∑ y 0⇒N − 1 R = By 0⇒N = 1 R cosθ B F = ∑ x 0⇒−P+F + 1 R = Bx 0⇒P=μ N + s1 R sinθ B P=300μ = s 0.40θ=15 ∘ 300=0.40(R cos15)+ B ∘ R sin15 B ∘ cos15≈ ∘ 0.9659 sin15≈ ∘ 0.2588 300=R (0.40× B 0.9659+0.2588) Now, calculate the friction force at the upper end . Since must be equal and opposite to , its horizontal component (the fric