If P = 0 in the figure, replace the two remaining couples with a single equivalent couple, specifying its magnitude and the direction of its axis.
The net equivalent couple vector shown in the triangular co-ordinates and its direction.
Answer to Problem 3.76P
The net equivalent couple vector is
Explanation of Solution
Write the equation of moment of first couple about an arbitrary axis.
Here, the first couple vector formed due to the force
Substitute
Write the equation of moment of second couple about an arbitrary axis.
Here, the second couple vector formed due to the force
The vector line drawn from
Here, the distance between the points
Substitute
The distance of the line drawn from
The resultant magnitude of the each force is,
Here, moment of couple formed by the force at the points
Substitute
Write the vector form for the moment of second couple
Write the equation of net moment of couple about an arbitrary axis.
Substitute equation (II) and (V) in equation (VI).
The magnitude of the net moment of couple is,
Conclusion:
Write the equation for the unit vector of the couple.
Here, the unit vector is represented as
Substitute
The resultant couple formed along the x direction.
The resultant couple formed along the y direction.
The resultant couple formed along the z direction.
Therefore, the net equivalent couple vector is
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Chapter 3 Solutions
VECTOR MECH. FOR EGR: STATS & DYNAM (LL
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- International Edition---engineering Mechanics: St...Mechanical EngineeringISBN:9781305501607Author:Andrew Pytel And Jaan KiusalaasPublisher:CENGAGE L