Meriam, Kraige & Bolton — Equilibrium of Rigid Bodies: Problem 4_65

⚡ Mecademy AIENG정역학 · ch4  Problem Statement For what value of the clockwise couple will the horizontal component of the pin reaction at be zero? If a couple of that same magnitude were applied in a counterclockwise direction, what would be the value of ? Problem 4/65 (a) Determination of the clockwise couple for 1. Formula: First, analyze member to find the vertical reaction . Sum moments about joint : Then, analyze the entire frame by summing moments about point : 2. Substitution: For member (length ), with a load at its midpoint: For the whole frame, with as the origin , point is at where and . The load is at : 3. Calculation: Solve for : (upward) Substitute and set in the moment equation: MA x AM A x MA = x 0 ABA y B M = ∑ B 0 C M = ∑ C 0 ABL=3+ ′ 3= ′ 6 ′ 150 lb A (6)− y 150(3)=0 C(0,0)A(−8,3.464) 8=6+4cos(60) ∘ 3.464=4sin(60) ∘ (−5,3.464) M = ∑ C −A (8)− y A (3.464)+ x 150(5)−M=0 A y 6A = y 450⇒A = y 75 lb A = y 75A = x 0 −75(8)−0(3.464)+750−M=0 −600+750−M=0 150−M=0 M=150 lb⋅ft 4. Result: ● Final Conclusion: The value of the clockwise couple for which the horizontal reaction is zero is . (b) Determination of for a counterclockwise couple 1. Formula: Use the established global equilibrium equation for the moment about , changing the sign of the couple term from clockwise () to counterclockwise ( ): 2. Substitution: Substitute and : 3. Calculation: 4. Result: ● Final Conclusion: If a couple of the same magnitude () is applied counterclockwise, the value of the horizontal