CE 201 - Statics Lecture 13

MOMENT OF A COUPLE What is couple? Two forces Parallel Have same magnitude Have opposite directions Separated by a perpendicular distance (d) F -F d F -F r A B rA rB O

M = rA  (-F) + rB  F = ( rB - rA )  F The moment of a couple forces is called Couple Moment and is equal to the sum of the moments of both forces determined about a point. M = rA  (-F) + rB  F = ( rB - rA )  F By triangle law of vector addition, rA + r = rB ; or r = rB - rA So, M = r  F This shows that the moment of a couple depends upon the position vector between the two forces and does not depend upon position vectors between the forces and the point (O) that you want to find the moment about. That is why the couple moment is called the Free Vector.

Scalar Formulation The moment of a couple is: M = Fd Where F is the magnitude of one of the forces and d is the perpendicular distance between the two forces. The direction of the moment can be determined by the right-hand rule. The moment is perpendicular to the plane containing the two forces. F -F d M

Vector Formulation The moment of a couple can be expressed by the vector cross product M = r  F