A 5mlong bar AB is supported by a ballinsocket support at A

A 5m-long bar AB is supported by a ball-in-socket support at A, the cable CD and a smooth floor at B. A force F = -10 i (N) is applied at G. Here, D is at the midpoint of the bar AB, G is the midpoint of AD, and C is the midpoint of OE. Here, the line BE is parallel to x-axis. Determine the tension in cable CD and the reactions at A and B.

Solution

Using static reslution in i,j,k or x,y,z directions

Length OB= 4

Length OE = 2*sqrt (3)

By similar triangles Ht of D above horiz = 1.5

AG=GD = 1.25

length CD = SQRT(13)/2

Resolving Horizontally

Fcd * 2/sqrt(13) -10 +Ax =0 (a)

Resolve`vertically Fcd*1.5/sqrt(13) +Ay +Fb=0 (b)

Horiz moments at D: Ax*2.5 -10*1.25 =0 => Ax =5 (c)

from (a) Fcd = 9.014

Taking vertical moments about A: Fb *5 = Fcd*1.5/sqrt(13)*2*2.5/5 => Fb =3.76

Resolving in y direction Ay=0