4.3 : Resultant Moment: Scalar Formulation

When multiple forces act on an object in two-dimensional space, the concept of the net moment can be used to understand the tendency of these forces to induce rotational motion about a fixed point. The scalar formulation of the resultant moment is a helpful tool in analyzing the equilibrium of structures subjected to multiple forces.

To determine the resultant moment, the moments caused by all the forces in a system in the x-y plane are considered. Positive moments are typically counterclockwise since they are directed along the positive z-axis, while negative moments are clockwise. Each moment is given a sign based on its directional sense. To calculate the resultant moment due to all the forces, an algebraic sum of the products of each force and its respective perpendicular distance with respect to a given point A is taken.

Sign conventions for moments are used in the calculation. After substituting the values of all the forces and their perpendicular distances in the above equation, if the numerical result of this equation is a positive scalar, the resultant moment will be counterclockwise. Conversely, the resultant moment will be clockwise if the result is negative.