Chapter 4 - ENGI 1400 Engineering Mechanics I – STATICS...

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Unformatted text preview: ENGI 1400 Engineering Mechanics I – STATICS Winter 2009 L. Liu, Civil and Resource Engineering Chapter 4-P1 Chapter 4 Force System Resultants ; WHAT YOU SHOULD LEARN & UNDERSTAND FROM THIS CHAPTER? ¾ How to calculate the moment of force in 2-D and 3-D 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 non-concurrent 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 (2-D) 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 4-P2 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 2-D 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 counter-clockwise 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 4-P3 For example, how to calculate the moment of the force F ? − M o = F d and the direction is counter-clockwise (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 2-D is that counter-clockwise 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 4-P4 4.2 Cross Product 1. Cross-Product 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.

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Chapter 4 - ENGI 1400 Engineering Mechanics I – STATICS...

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