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Moment of a Couple

Moment of a Couple. ES2501: Statics/Unit 10-1: Moment of a Couple and Moment of a Force about an Axis. Couple ----- a pair of forces with the same magnitude and opposite direction. Moments of a Couple:. Position vector from B to A

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Moment of a Couple

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  1. Moment of a Couple ES2501: Statics/Unit 10-1: Moment of a Couple and Moment of a Force about an Axis Couple ----- a pair of forces with the same magnitude and opposite direction Moments of a Couple: Position vector from B to A A --- Any point on the line of action of B --- Any point on the line of action of Moment vector of a Couple A B Distance between lines of action of the couple Magnitude of couple moment Consistent with 2D definition Sign convention O’ O Moments of a couple about ANY point is the same

  2. Example:Find moment of the couple ES2501: Statics/Unit 10-2: Moment of a Couple and Moment of a Force about an Axis P(10,7,3) Couple moment B(6,6,0) Total moment of the couple about P A(8,3,0) Moment of a couple about ANY point is the same Total moment of the couple about O:

  3. Moment of a Force about an Axis passing through a Point ES2501: Statics/Unit 10-3: Moment of a Couple and Moment of a Force about an Axis Unit vector of given axis O’ O A Moment vector of a force about a given axis Magnitude Unit vector of given axis • Component (projection) of • on the direction of given axis • -Measure of effects of a force • on rotation about the axis • Can be calculated by a triple • product, O ----- ANY point on the axis; A ----- ANY point on the line of action of the force

  4. Decomposition of Moment Vector: ES2501: Statics/Unit 10-4: Moment of a Couple and Moment of a Force about an Axis Moment vector of a force about a given axis O A Unit vector of given axis Special Cases: A O

  5. Example: Find moment of the force about the x-axis, y-axis, z-axis, and the axis of OA ES2501: Statics/Unit 10-5: Moment of a Couple and Moment of a Force about an Axis y A(4,4,3) (in ft) O x z Should be 0 since the axis passes through A

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