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Unformatted text preview: 1 CIV100 – Mechanics Module 6: Course Review by: Jinyue Zhang 2011/10/13 1 The Big Picture Newton’s Laws SI Unit Significant Digits Scalar vs. Vector Vector Operation 2D Particle Equi. Cables + Pul eys 2D Moment 2D Body Equi. 2D Cartesian Vector, Unit Vector Vector Operation (addition. dot. cross) 3D Particle Equi. 3D Moment (about a point/line) 3D Body Equi. 3D 2D FBD 2D Supports 3D FBD 3D Supports Simple Trusses: Method of Joints Method of Sections Frames/Machines and combinations 2D Structures Internal Forces NF Æ NFD SF Æ SFD BM Æ BMD SFD BMD Rules Internal Force and Design Design against NF Tension – Yielding Compression – Yielding Design against BM 3D Structures Equivalent F/M in 2D Equivalent F/M in 3D Centroid Simple/Composite Moment of Inertia Simple/Composite Paralel-Axis Theorem Fluid Pressure Stress Blocks Centroid and Moment of Inertia 2011/10/13 2 Algebraic Method • Using Cartesian vector notation, each force is first represented as a Cartesian vector: • The vector resultant is therefore: • If scalar notation is sued, then: ) ( ) ( 3 2 1 3 2 1 ↑ + + − = → + − + = y y y Ry x x x Rx F F F F F F F F x y F 2 F 1 F 1X F 2X F 2y F 1y F 3X F 3y F 3-x-y To Remember j i F j i F j i F 3 2 1 y x y x y x F F F F F F 3 3 2 2 1 1 + − = − = + = j i j i j i j i j i F F F F 3 2 1 R ) ( ) ( ) ( ) ( 3 2 1 3 1 1 3 3 2 2 1 1 Ry Rx y y y x x x y x y x y x F F F F F F F F F F F F F F + = + − + − + = + − − + + = + + = 2011/10/13 3 Equilibrium of Coplanar Force Systems • Coplanar force system – Each force can be resolved into its i and j components – i.e. each force can be expressed in Cartesian vector notation • In order to satisfy this vector equation, both = ∑ F To Remember ∑ ∑ = + j i y x F F ∑ ∑ = = y x F F = ∑ F ∑ ∑ = + j i y x F F ∑ ∑ = = y x F F 2011/10/13 4 How to determine a Moment? • Moment is a vector – It has a magnitude • M O is the magnitude of moment M O • F is the magnitude of force F • d is the perpendicular distance from point O to the line of action of the force F – It has a direction, determined by right-hand-rule – Moment about an axis or a point ? and which plane? Fd M O = O d F x y In 2D, a curl wil simply represent a moment. The sign convention: counterclockwise is + M O 2011/10/13 5 Conditions for Equilibrium • How do we take the moment into account? – Sum to ZERO ! • New condition of equilibrium – The sum of all the external forces acting on the body is equal to ZERO ! – The sum of the moments of the external forces about a point is equal to ZERO ! To Remember ∑ ∑ = = O M F ∑ ∑ = = O M F 2 2011/10/13 6 • We know: • Expressed by algebraic notation: • Two alternatives: Equations of Equilibrium = = = ∑ ∑ ∑ C B A M M M = = = ∑ ∑ ∑ B A M M Fa = = = ∑ ∑ ∑ Mo Fy Fx To Remember = = = ∑ ∑ ∑ Mo Fy Fx ∑ ∑ = = O M F = = = ∑ ∑ ∑ B A M M Fa = = = ∑ ∑ ∑ C B A M M M 2011/10/13 7 Two-Force Members • The name says it all!The name says it all!...
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This note was uploaded on 12/10/2011 for the course CIV 100 taught by Professor Nahrvar during the Spring '08 term at University of Toronto.
- Spring '08