Assume coplanar 2D structure and forces The structure ABCDEA

Assume coplanar (2-D) structure and forces. The structure ABCDEA is acted upon by a known applied force of -40 j kN and 3 unknown reaction forces, namely, If the moment of the known applied force about the point B is equal and opposite to that of the moment of A_x about B: Calculate, using vector algebra, the magnitude of A_x.

Solution

Sumation on Horizontal force, Fh=Bx+Ax=0

i.e. Bx=-Ax....................1)

Sumation of vertical force, Fv=By-40=

By=40KN

Now take moment at point A,

Ma=Bx*5+40*(4+4)=0

Bx=-64KN

From equation 1,

Ax=-Be

Hence, Ax=64KN