Sum of the Moments Due to Two Couples Determine the sum of the moments exerted on the pipe in Fig. 4.32 by the two couples.

Question

Sum of the Moments Due to Two Couples

Determine the sum of the moments exerted on the pipe in Fig. 4.32 by the two couples.

Accepted Answer

Consider the 20-N couple. The magnitude of the moment of the couple is (2 m)(20 N) = 40 N-m. The direction of the moment vector is perpendicular to the y-z plane, and the right-hand rule indicates that it points in the positive x-axis direction. The moment of the 20-N couple is 40i (N-m).

By resolving the 30-N forces into y and z components, we obtain the two couples in Fig. a. The moment of the couple formed by the y components is -(30 sin 60°)(4)j (N-m), and the moment of the couple formed by the z components is (30 cos 60°)(4)j (N-m).

The sum of the moments is

[latex]\sum{M } = 40i + (30 cos 60°) (4)j - (30 sin 60°)(4)k = 40i + 60j - 103.9k[/latex] (N-m).

Discussion

Although the method we used in this example helps you recognize the contributions of the individual couples to the sum of the moments, it is convenient only when the orientations of the forces and their points of application relative to the coordinate system are fairly simple. When that is not the case, you can determine the sum of the moments by choosing any point and calculating the sum of the moments of the forces about that point.

Question 4.12: Sum of the Moments Due to Two Couples Determine the sum of t...

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