Lecture 6-13 - Systems SystemsofForcesandMoments Moments

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stems of Forces and Moments Systems of Forces and Moments •M o m e n t s –rotation at a point due to a force applied at some distance Sign Convention Clockwise = negative Counterclockwise = positive M P = DF
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terms of components… In terms of components… x y y x P F D F D M + = F y If line of action goes through P… D x F x D y then M P = 0
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Problem 4.24 – The tension in the cable is the same on both sides of the pulley. The sum of the moments about point A due to the 800 lb force and the forces exerted on the bar by the cable at B and C is zero. What is the tension in the cable?
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The weights W and W are suspended by the cable system shown. The cable 1 2 BC is horizontal. If the largest moment that can be resisted by the pole DP at point P is 100 lb ft, determine W 1 .
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he Moment Vector: Moment About a Point The Moment Vector: Moment About a Point …any position vector from the oint to the line of action of point to the line of action of the force. v v v v v v v The moment vector The magnitude of the moment vector If the position vector is perpendicular F D M P = θ sin F r M P v = F r M P × =
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e Moment Vector: Moment about a Point The Moment Vector: Moment about a Point Moment about point P generated by force F . Moment vector is drawn according to the rotation and right hand rule.
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oment of a Force About a Line Moment of a Force About a Line The capstan will rotate about the vertical axis (line) The capstan will not rotate The line of action of the force must be skew to the line that we want to rotate about. If the line of action of the force is parallel or intersects the line, then there will be no rotation.
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Position vector from any arbitrary point on os o eco o a yab aypo o line to any point on Line of Action F r M v v v × = P The cross product will give us the moment about a point on the line. but we want the moment about the line …but we want the moment about the line, or the component of the moment vector that is in the direction of the line.
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The dot product should give us the omponent acting in the direction of the line component acting in the direction of the line. P L M e M v = ˆ but if I want it in vector form [ ] e M M ˆ = v …but if I want it in vector form… L L
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pecial Cases… Special Cases… orce is perpendicular to plane LOA of Force Force is perpendicular to plane containing line Force is parallel to line intersects line F D M L =
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A concrete precast wall section is held by 2 cables, where one cable is not shown (behind wall). The tension in BD = 800 N Find: a) Moment about point O of the force exerted by the cable at B. b) Moment about the x-axis generated by force BD. ) ngle between cable BD and the vertical side BC c) Angle between cable BD and the vertical side BC. y B 3.5 m 4 m A x 5m O C z 3.5 m 1 m D
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ouples Couples Couples are two forces with equal agnitudes, opposite directions, and 100 N magnitudes, opposite directions, and different LOA’s 100 N
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ouples Couples What is the moment generated about point P due to the couple?
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This note was uploaded on 08/29/2010 for the course EGN 3311 taught by Professor Nohra during the Spring '08 term at University of South Florida - Tampa.

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Lecture 6-13 - Systems SystemsofForcesandMoments Moments

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