Question

Two couples act on the cantilever beam. If F = 6 kN, determine the resultant couple moment.

                               

Answer 1

Solution

(a)

By resolving the 6 -kN and 5 kN couples into their x and y components , Fig . a, the couple moments (M_c)₁ and (M_c)₂ produced by the 6- kN and 5 - kN couples, respectively , are given by

+(M_c)₁  =6 sin 30^ (3)-6 cos 30^ (0.5+0.5)=3.804 kN* m

+(M_c)₂ =g( 3 5 )(0.5+0.5)-5 ( 4 5 )(3)=-9kN* m

Thus, the resultant couple moment can be determined from

(M_c)_R =(M_c)₁ +(M_c)₂ =3.804-9=-5.196 kN* m=5.20 kN* m ( clockwise)

(b)

By resolving the 6- kN and 5- kN couples into their x and y components , Fig. a , and summing the moments of these force components about point A, we can write

+(M_c)_R=5(3/5)(0.5)+594/5)(3)-6cos30°(0.5)-6sin30°(3)+6sin30°(6)

             -6cos30°(0.5)+5(3/5)(0.5)-5(4/5)(6)

          =-5.196kN*m=5.20kN*m (clockwise)

               

ans. (M_c)_R=5.20kN*m