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_Ncos60° = 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 cos30⁰ = R_N  × C_P + R_B  × 1.2 sin30°

Putting value of C_P, R_N, and R_B

T = 374N                                                                      .......ANS