determine the moment of forcesthe side of a

Question

Determine the moment of forces:

The side of a square ABCD is 1.60 m long .Four forces equal to 6, 5, 4 and 8 N acts respectively along with the line CB, BA, DA, DB. Determine the moment of these forces w.r.t. O, the point of intersection of the diagonals of the square.

Solution

Taking moments w.r.t. O,

Resultant moment M_o = - 6 x₂ - 5 x₃ + 4 x₁ + 8 × 0

Where x₁, x₂ and x₃ are the perpendicular distances of the forces 4, 6, and 5 N, respectively from O, and force of 8 N has zero moment around O as its line of action passes out through this point.

Here,  x₁ = x₂ = x₃ = 1.6/2 = 0.8 m

∴ M _o  = - 6 (0.8) - 5 (0.8) + 4 (0.8) + 0

          = - 4.8 - 4.0 + 3.2

           = - 5.6 N-m or 5.6 N-m (clockwise)