Lecture_9-Moment_of_a_Couple.ppt

Lecture_9-Moment_of_a_Couple.ppt - Direction of couple...

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Force System Resultants  Lecture 9-Moment of a Couple (Section 4.6)
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Learning Objectives Be able to define a couple. Be able to determine the moment of a couple. 
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Pre-requisite Knowledge Units of measurements. Trigonometry concepts. Vector concepts. Rectangular components concepts. Moment concept. Cross product and dot product.
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Definition of Couple A couple is defined as two forces in the opposite direction with the same magnitude and the two forces are separated by a constant distance F -F Moment of a couple or couple moment has a constant direction  and  magnitude  regardless  the  location  of  the  positions  of  the  forces to the referenced point Resultant force of  a couple = 0
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Moment of a Couple Scalar formulation Magnitude of couple moment: d F M = Where d is the perpendicular distance  between the couple forces
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Unformatted text preview: Direction of couple moment: Direction of couple moment follows the right-handed rule Moment of a Couple-Example (scalar formulation) Determine the magnitude and direction of the moment couple Magnitude of moment couple: in. 20 . 5 30 cos 6 = ° ⋅ = d Direction of moment couple: in. lb 130 20 . 5 25-= ⋅ = ⋅ = d F M negative y-axis (right-handed rule) Moment of a Couple Vector formulation F r M × = Where r is any position vector projecting from one couple force to another Also, ( 29 F r F r M B A × +-× = As couple moment is a free vector Example 1 Determine the couple moment in vector format if F=25 k N Example 2 Determine the distance d so that the resultant couple moment has a magnitude of 20 N-m Example 3 Determine the distance d, if the resultant couple moment is 350 N-m....
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This note was uploaded on 06/14/2009 for the course CE 221 taught by Professor Buch during the Spring '08 term at Michigan State University.

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Lecture_9-Moment_of_a_Couple.ppt - Direction of couple...

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