Meriam, Kraige & Bolton — Equilibrium of Rigid Bodies: Problem 4_12

⚡ Mecademy AIENG정역학 · ch4  Problem Statement A drawbridge is being raised by a cable . The four joint loadings shown result from the weight of the roadway. Determine the forces in members , and . Problem 4/12 (a) Tension in cable 1. Formula: Where is the hinge support. The clockwise moments from the vertical loads must be balanced by the counter-clockwise moment from the cable tension . 2. Substitution: Clockwise moment of loads: Counter-clockwise moment of cable tension : 3. Calculation: Moment arm of : 4. Result: ● Final Conclusion: The tension in cable is . (b) Forces in members and EI EF,DE,DF,CDFG EI M = ∑ A 0 A T M = weights (4×10+4×20+2×30)cos20 ∘ T M = T T(30sin50+ ∘ 8cos50) ∘ M = weights (40+80+60)×0.9397=180×0.9397= 169.14 kip⋅ft Td = T 30sin50+ ∘ 8cos50= ∘ 22.981+5.142= 28.123 ft 28.123T=169.14⇒T=6.0143 kips T=6.01 kips EI6.01 kips EFDE 1. Formula: Apply equilibrium equations at joint . Let axes be parallel and perpendicular to the bridge chord. 2. Substitution: At joint , cable pulls at from . 3. Calculation: (Compression) (Tension) 4. Result: ● Final Conclusion: Member is in compression with a force of , and member is in tension with a force of . (c) Forces in members and 1. Formula: Apply equilibrium equations at joint . Angle of diagonal : . 2. Substitution: (Note: Tension assumed for unknowns, compression handled by sign. is the x-component pushing joint away from .) 3. Calculation: (Compression) At joint , tension pulls left ( ). load component is left (). C