Meriam, Kraige & Bolton — Equilibrium of Rigid Bodies: Problem 4_100

⚡ Mecademy AIENG정역학 · ch4  Problem Statement In the special position shown for the log hoist, booms and are at right angles to one another and is perpendicular to . If the hoist is handling a log weighing , compute the forces supported by the pins at and in this one position due to the weight of the log. Problem 4/100 (a) Force supported by the pin at D ● Calculation Process 1. Present Final Formula: We analyze the equilibrium of member by taking moments about pin . The cylinder is a two-force member, so the force at pin is equal to the magnitude of the force in cylinder . where is the angle between cylinder and boom . Using local coordinates at with along and along : - Pin is at since and . - Pin is at since . - The distance from to the line of action of is . 2. Substitute Values: 3. Partial Operations: AFEG AFAB4800 lb AD EG FCDD CD M = ∑ F 0=(FC⋅sinφ)⋅F − CD (FG⋅cos45)⋅ ∘ W φCDEG (u,v)FuAFvEGD(−12,0) OF=24 ′ OD=12 ′ C(0,4)FC=4 ′ FCDh= = (u −u )+(v −v) 21 2 21 2 ∣u v −v u ∣ 1212 = (−12−0)+(0−4) 22 ∣(−12)(4)−(0)(0)∣ 160 48 ⋅ 160 48 F = CD 10⋅ ⋅ ( 2 1 )4800 ⋅ 4 10 48 F = CD 2 48000 ⋅ 10 12 F = CD 2 48000 4. Final Calculation: ● Final Conclusion: The force supported by the pin at is . (b) Force supported by the pin at A ● Calculation Process 1. Present Final Formula: We analyze the equilibrium of the entire assembly (booms , and cylinder ) by taking moments about the main base pivot . The force at pin is the axial force in cylinder . Since , the moment arm of about is the dis