Statics - Couples — Couples

About this lesson

This unit introduces the concept of a couple in statics, defined as a system of two forces of equal magnitude and opposite direction acting along different lines of action. It explains that the moment of a couple is the sum of the moments of its two forces about any point, and that this moment is a constant vector independent of the point chosen. The unit covers how to calculate the algebraic measure of a couple's moment (magnitude times the perpendicular distance between the forces, with sign indicating direction) and how to determine if two couples are equivalent (equal algebraic measures of moments). It also addresses the equilibrium of a rigid body under the action of two or more coplanar couples, stating that equilibrium occurs when the sum of the algebraic measures of the moments of all couples is zero. Worked examples and exercises involve finding moments of couples, determining unknown force magnitudes or directions for equilibrium, and solving problems with rods, laminae, and rectangles under various force systems. By the end, a student should be able to identify a couple, compute its moment, apply the condition for equilibrium of multiple couples, and solve problems involving equivalent couples.