Section 4.6 Couple Moment COUPLE B F ? A -F I' B ? A Figure: 04_026 Copyright @2013 Pearson Education, publishing as Prentice Hall • Couple A couple is defined as two anti-parallel forces that have the same magnitude and are separated by a perpendicular distance. The resultant force of a couple is zero. A couple causes rotation.
Section 4.6 Couple Moment COUPLE MOMENT (page 2) · Couple moment The couple moment M, is the sum of the moments of the two forces that form the couple: That is, MO =T! È Mo = [! F + f ! (" F) = (Ip ! I )" F where + = ip ! TA · Free vector The couple moment depends on the position vector i directed from A to B and not on the position of the arbitrary point O. The subscript O on M, will therefore be omitted: M=F! È M is a free vector. It can act at any point on a body. · Direction M is perpendicular to the plane containing F and ! F with direction given by the right-hand rule (see Figure 4-27). · Magnitude M = Fd d = rsin! ! is the angle between the tail of i and the tail of F . d is the lever arm for the couple.
Section 4.6 Couple Moment COUPLE MOMENT (page 3) M 2 1 -F d F Figure: 04_027 Copyright 02013 Pearson Education, publishing as Prentice Hall · Equivalent couples M, and M2 produce the same turning if they are parallel and ?d = F2d2 · Free-body diagrams M is drawn on free-body diagrams rather than the individual couple forces È and ! F .