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
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)