The rigid Lshaped member ABC is supported by a ballandsocket

The rigid L-shaped member ABC is supported by a ball-and-socket joint at A and by three cables. If a 1.8-kN load is applied at F, determine the tension in each cable.

Solution

Let Tc, Tb and Te be the tensions in the cables supported at C,B and E

Tc and Tb have components along the y-axis where as Te s only in x-z plane and has no component in y direction.

Component of Tc along y-axis

Tc*240/400 = 0.6Tc (CD = 400)

BD =580

component of Tb along y-axis = Tb*240/580 = 0.41Tb

Taking moment of all the forces about AB.

Load at F and component of Tc, 0.75Tc are the only forces that produce moments abouts AB all others become 0.

1.8N *210 = 0.75Tc*420

Tc = 1.8*210/(0.75*420) = 1.2 N

Taking moments about x-axis

(0.6Tc + 0.41Tb)*240 = 1.8*240

Tb = 2.63 N

component of Tb in x-z plane

Tbxz = Tb*520/580 = 2.36 N

component of Tc in x-zplane

Tcxz = Tc*320/400 = 0.96 N

equating moments of all forces in x-z plane about y-axis through A.

distance of Te and Tbxz from A is 254.5

distance of Tcxz from A = 420

Te*254.5 = Tbxz*254.5 +Tcxz*420

Te = (2.36*254.5+0.96*420)/254.5 = 3.95 N