# Two couples act on the cantilever beam

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

Image from: Hibbeler, R. C., S. C. Fan, Kai Beng. Yap, and Peter Schiavone. Statics: Mechanics for Engineers. Singapore: Pearson, 2013.

#### Solution:

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To find the resultant couple moment, we will write two separate equations to find the moment created by the 5 kN force, and the 6 kN force. To do so, we must first express each force in their x and y components.

All components of each force is shown in dashed lines.

Assuming clockwise moments are positive, we can write the following:

For the 5 kN forces:

$\circlearrowright^+ M_1=-5\left(\dfrac{3}{5}\right)(0.5+0.5)+5\left(\dfrac{4}{5}\right)(3)$

$M_1=9$ kN•m

For the 6 kN forces:

$\circlearrowright^+ M_2=6\cos30^0(0.5+0.5)-6\sin30^0(3)$

$M_2=-3.8$ kN•m

The resultant couple moment is then:

$M_c=M_1+M_1$

$M_c=9-3.8$

$M_c=5.2$ kN•m (clockwise)

$M_c=5.2$ kN•m (clockwise)