Final answer:
To ensure the resultant couple moment is zero for two couples on a frame, the distance 'd' can be found by equating the moments of the opposing couples, resulting in the formula d = M/F.
Step-by-step explanation:
The question posed relates to the concept of equilibrium in a rigid body, where a couple is created by two forces that are equal in magnitude, opposite in direction, and do not act along the same line.
In order for the resultant couple moment to be zero for two couples acting on a frame, the moments created by the couples must be equal in magnitude and opposite in direction. The distance ‘d’ can be determined by equating the moments of the two opposing couples. This results in the equation d = M/F, where M is the moment of one of the couples and F is the magnitude of one of the forces in the couple.
Considering this equation, and given that the moment caused by a couple is the product of the force and the distance between the forces, we can rearrange the equation to solve for distance ‘d’.