COE2001 Review

Vector Mechanics for Engineers: Statics

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Summer 2005 COE 2001 Statics 1 COE2001 Review Material Basic equilibrium equations are from Physics I Reinforce fundamental understanding of force & moments Techniques for applying to mechanical problems Applications Rigid body problems Trusses Multi-force members : axial, shear forces & bending moments Machines Problems with friction (more complex equilibrium conditions) Calculation of centroids 1D (wires), 2D (areas) and 3D (volumes) Distributed forces and their resultants
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Summer 2005 COE 2001 Statics 2 Particle Equilibrium F 1 F 2 F 3 ˆ ˆ 0 ( x y z F F i F j F = = + + r 1 1 2 2 3 3 D equation D equations D equations = = = Finite Body Equilibrium F 1 F 2 F 3 M 1 0 0 ( ) F M at any point,all points = = r r 2 2 3 3 D equations D equations = = where 0 0 sin OA A OA A A M r F M r F F d θ = = = r r r r r r r r OA F A O A d θ • F A can act anywhere along “line of action” +θ rotates r OA into F A and & O OA O A M r M F r r r r
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Summer 2005 COE 2001 Statics 3 Moments 1. Moment of a force about a line (e.g., a hinge) is the projection of M on to the line. 1. Only the component of F perpendicular to contributes to the moment. 2. M due to F is equal to M due to all components of F . 1. To compute M @ Q given M @ P and F i use: 1. Couple : moment developed by equal and opposite forces separated by d; direction is perpendicular to both F and d. Since Σ F i =0 we see that Σ M Q =0+ M P so a couple produces a moment that is constant ˆ u l ˆ ˆ ˆ ˆ ( ) (( ) ) M M u u r F u u = = l l l l l r r r r ( ) A B A B A B M r F F r F r F M M = + = + = + l r r r r r r r r r r Q QP i P M r F M = + r r r r Equipollent Systems Two force & moment systems are equipollent (“equal power”) if they have the same resultant at any point.
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