The gusset plate showing if figure is subject to the forces

The gusset plate showing if figure is subject to the forces acting along member A, member B and member C. The forces are concurrent at point O. Determine the force, F, in member C and its proper orientation, Theta. Force at point A is 5 kN, at B 7.5kN, and the angle between B and C is theta.

Solution

apply force equlibrium ;

X axis :    - B cos ( /2 ) + C cos ( /2 ) = 0 ;

                  or C = B ;

or C = B = 7.5 k N = F ;

Y axis :

- F sin ( /2 ) - B sin ( / 2 ) + 5 = 0 ;

- 7.5 sin ( / 2 ) - 7.5 sin( / 2 ) + 5 = 0 ;

or ( / 2 ) = 19.471222 degrrees .

or = 38.942 degree .