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Unformatted text preview: ENGI 1400 Engineering Mechanics I – STATICS Winter 2009 L. Liu, Civil and Resource Engineering Chapter 4P1 Chapter 4 Force System Resultants ; WHAT YOU SHOULD LEARN & UNDERSTAND FROM THIS CHAPTER? ¾ How to calculate the moment of force in 2D and 3D force systems ¾ How to calculate the moment of force about an axis and the moment of a couple ¾ How to determine the resultants of nonconcurrent force systems ¾ How to reduce a simple distributed loading to a resultant force having a fixed location ; READING MATERIALS IN TEXTBOOK – CHAPTER 4 (All Sections 4.1 – 4.10) ; Fundamental RINCIPLES and APPLICATION EXAMPLES – throughout the whole course 4.1. Moment of a Force – Scalar Formulation (2D) What is the net effect of the two forces on the wheel? What is the effect of the 30 N force on the lug nut? ENGI 1400 Engineering Mechanics I – STATICS Winter 2009 L. Liu, Civil and Resource Engineering Chapter 4P2 The moment of a force about a point provides a measure of the tendency for rotation (tendency of the force to cause the body to rotate about the point/axis) (called a torque, moment of a force, moment). e.g., The horizontal force F x acting perpendicular to the handle of the wrench, experience tells us:  This force tends to cause the pipe to turn (rotate) about the z axis;  The larger the force or the distance dy , the greater the turning effect (rotate the pipe or tends to rotate). For this 2D case, mathematically,  The magnitude of the moment M o is M o = F d. As shown, d is the perpendicular (shortest) distance from point O to the line of action of the force F .  The direction of M o is either clockwise or counterclockwise depending on the tendency for rotation. Î Moment is a vector quantity! ENGI 1400 Engineering Mechanics I – STATICS Winter 2009 L. Liu, Civil and Resource Engineering Chapter 4P3 For example, how to calculate the moment of the force F ? − M o = F d and the direction is counterclockwise (what is the perpendicular distance from O to the line of actions of F ); − M o can also be determined by using the two rectangular components of F as shown (the perpendicular distances from O to the lines of actions of two components, respectively): M = ( F Y a) – ( F X b). Note the different signs on the terms! The typical sign convention for a moment in 2D is that counterclockwise is considered positive . We can determine the direction of rotation by imagining the body pinned at O and deciding which way the body would rotate because of the force a b O F F x F y a b O F F x F y F a b d O ENGI 1400 Engineering Mechanics I – STATICS Winter 2009 L. Liu, Civil and Resource Engineering Chapter 4P4 4.2 Cross Product 1. CrossProduct Definition and Method  Expand our knowledge of vector algebra (i.e., cross product method of vector multiplication) in order to formulate the moment of a force using Cartesian vectors....
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This note was uploaded on 07/15/2010 for the course ENGI 1400 taught by Professor L.liu during the Winter '09 term at Dalhousie.
 Winter '09
 L.Liu

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