Meriam, Kraige & Bolton — Analysis of Structures: Problem 6_110

⚡ Mecademy AIENG정역학 · ch6  Problem Statement The coefficient of static friction between the collar of the drill-press table and the vertical column is 0.30. Will the collar and table slide down the column under the action of the drill thrust if the operator forgets to secure the clamp, or will friction be sufficient to hold it in place? Neglect the weight of the table and collar compared with the drill thrust and assume that contact occurs at the points and . Problem 6/110 (a) Analysis of sliding equilibrium 1. Formula: To determine if the collar will slide, we must find the minimum coefficient of static friction required for equilibrium and compare it to the given value . We consider the forces acting on the collar: the drill thrust , the normal reactions and at the contact points, and the friction forces and . Horizontal equilibrium: Vertical equilibrium: Moment equilibrium about the column center: Assuming impending slippage at both points (), the moment equation simplifies to: 2. Substitution: Substitute the given geometric values into the derived formula: Height between contact points Distance to drill thrust axis from column axis 3. Calculation: AB μ min μ= s 0.30P N A N B F A F B F =∑ x 0⟹N = A N = B N F =∑ y 0⟹F + A F = B P M =∑ C 0⟹N⋅h+(F − A F )⋅ B = 2 D P⋅L F = A F = B μ N s N⋅h=P⋅L⟹μ = min 2L h h=200 mm L=450 mm μ = min 2×450 mm 200 mm μ = min 900 200 4. Result: The minimum coefficient of static friction required to prevent sliding is . ● Final Conclusion: Since