Two couples act on the cantilever beam


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

Two couples act on the cantilever beam

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.

Two couples act on the cantilever beam

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)

 

Final Answer:

M_c=5.2 kN•m (clockwise)

 

This question can be found in Engineering Mechanics: Statics (SI edition), 13th edition, chapter 4, question 4-81.

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