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

#### Solution:

Show me the final answer↓

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

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

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=9-3.8

M_c=5.2 kN•m (clockwise)

#### Final Answer:

M_c=5.2 kN•m (clockwise)