Meriam, Kraige & Bolton — Analysis of Structures: Problem 6_113

⚡ Mecademy AIENG정역학 · ch6  Problem Statement A uniform slender bar of mass and length pivots about a horizontal axis through point . Because of static friction, the bearing can exert a moment of up to on the bar. Determine the largest value of for which equilibrium of the bar is possible in the absence of the rightward horizontal force . Then determine the magnitude of the force which must be applied at the lower end to move the bar from this deflected position. Such bearing friction is sometimes referred to as “stiction”. Problem 6/113 (a) Largest value of for equilibrium when 1. Formula: For the bar to be in equilibrium with no external force , the moment created by its weight about the pivot must be balanced by the bearing's friction moment. The maximum angle occurs when the weight moment equals the maximum static friction moment : 2. Substitution: Substitute the given values , , , and : 3. Calculation: Calculate the weight moment coefficient: Set up the equation for : Solve for : Calculate the angle: 4. Result: m=3 kgL=0.8 m O 0.4 N⋅mθ P P θP=0 P O θ max M f,max m g sin θ = ( 2 L ) max M f,max m=3 kgg= 9.81 m/s 2 L= 0.8 mM = f,max 0.4 N⋅m (3)(9.81) sin θ = ( 2 0.8 ) max 0.4 3×9.81×0.4=11.772 N⋅m sinθ max 11.772sinθ = max 0.4 sinθ max sinθ = max ≈ 11.772 0.4 0.033979 θ = max arcsin(0.033979)≈1.9472 ∘ θ = max 1.947 ∘ ● Final Conclusion: The largest value of the angle for which equilibrium is possible without an external force is . (b) Force required to move the bar from th