Determine tension in horizontal rope:
Q: A 500N cylinder, 1 m in diameter is loaded between cross pieces AE and BD that make an angle of 60º with each other and are pinned at point C. Determine tension in horizontal rope DE assuming that the cross pieces rest on the smooth floor.
Sol.: Consider the equilibrium of the entire system.
C is the pin joint, make free body diagram of ball and rod separately.
2R_{N}cos60° = 500 ...(i)
R_{N }= 500KN
R_{A} + R_{B }= 500N ...(ii)
Because of symmetry R_{A} = R_{B} = 250N
C_{P} = 0.5 cot30° = 0.866m
By taking moment about C,
T × 1.8 cos30° - R_{N} × C_{P} - R_{B} × 1.2 sin30° = 0
T × 1.8 cos30^{0} = R_{N} × C_{P} + R_{B} × 1.2 sin30°
Putting value of C_{P}, R_{N}, and R_{B}
T = 374N .......ANS