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Unformatted text preview: 3D EQUILIBRIUM 3D EQUILIBRIUM OF A PARTICLE OF A PARTICLE LEARNING OBJECTIVES LEARNING OBJECTIVES Be able to draw a free body Be able to draw a free body diagram (FBD). diagram (FBD). Be able to apply equations of Be able to apply equations of equilibrium to solve a 3D equilibrium to solve a 3D problem problem . . PREREQUISITE PREREQUISITE KNOWLEDGE KNOWLEDGE Units of measurements Units of measurements Trigonometry concepts Trigonometry concepts Vector concepts Vector concepts Rectangular components concepts Rectangular components concepts Position vectors Position vectors 3D FORCE EQUILIBRIUM 3D FORCE EQUILIBRIUM = ⋅ + ⋅ + ⋅ = ∑ ∑ ∑ ∑ k j i z y x F F F F = ∑ x F = ∑ y F = ∑ z F FREEBODY DIAGRAM (FBD) FREEBODY DIAGRAM (FBD) Freebody diagram is a simple sketch that shows a Freebody diagram is a simple sketch that shows a particle “free” from its surroundings with all the particle “free” from its surroundings with all the forces (both known and unknown) acting on it. forces (both known and unknown) acting on it. Procedure for drawing a freebody diagram Procedure for drawing a freebody diagram 1) 1) Draw an outline showing the particle in question Draw an outline showing the particle in question isolated from its surroundings isolated from its surroundings 1) 1) Show all the active and reactive forces using arrows Show all the active and reactive forces using arrows 1) 1) Identify all known forces by labeling their Identify all known forces by labeling their magnitudes and directions. magnitudes and directions. 1) 1) Identify all unknown forces using letters Identify all unknown forces using letters FBD  EXAMPLE FBD  EXAMPLE k = 500 lb/ft EXAMPLE 1 EXAMPLE 1 100 lb Determine the force developed in each of the three cables to support the 100 lb crate. 4 f t 3 8 ft 100 lb F 1 F 2 F 3 B C D FBD SOLUTION 1 SOLUTION 1 The coordinates of Points A, B and C are: A (0,0,0); B (3,4,8); C (3,4,8) 4 f t 3 8 ft 100 lb F 1 F 2 F 3 B C D ( 29 ( 29 ( 29 k j i 8k 4j 3i F 2 2 2 2 2 2 2 2 848 . 424 . 318 . 8 4 3 F F F F += +++= Given the above coordinates, the unit vector u AB can be written as: u AB = (3 i 4 j +8 k)/(3 2 + 4 2 + 8 2 ) ½ Thus, the vector form of F 2 is SOLUTION 1  SOLUTION 1  continued continued 4 f t 3 8 ft 100 lb F 1 F 2 F 3 B C D ( 29 ( 29 ( 29 k j i 8k 4j 3i F 3 3 3 2 2 2 3 3 848 . 424 . 318 ....
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This note was uploaded on 07/26/2009 for the course CE 221 taught by Professor Buch during the Spring '08 term at Michigan State University.
 Spring '08
 Buch

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