Free Body Diagram FBD Lecture 5 v To

Free Body Diagram (FBD) Lecture 5 v To apply equilibrium equations we must account for all known and unknown forces acting on the particle. v The best way to do this is to draw a free-body diagram of the particle. FBD: A diagram showing the particle under consideration and all the forces and moments acting on this particle. Ø It is a sketch that shows the particle “free” from its surroundings with all the forces acting on it. How to draw a Free Body Diagram: v Draw outlined shape - Imagine the particle isolated or cut “free” from its surroundings v Show all forces and moments - Include “active forces” and “reactive forces”. Place each force and couple at the point that it is applied. v Identify each force: § Known forces labeled with proper magnitude and direction. § Letters used for unknown quantities. v Add any relevant dimensions onto your picture for calculations. Isolating boundary 1

Free Body Diagram (FBD) Lecture 5 Type of Forces: 1. Weight and Center of Gravity: • Each particle has a specified weight. • System can be represented by a single resultant force, known as weight W of the body • Location of the force application is known as the center of gravity L/2 L L/2 W q q W 2. Weight on inclined surface: q W 2

Free Body Diagram (FBD) 3. Tension force ( T ) in cable, cord and string: 4. Reaction forces: Lecture 5 T Ø If a support prevents the translation of a body in a given direction, then a force is developed on the body in that direction. Ø If rotation is prevented, a couple moment is exerted on the body. a ) Smooth horizontal surface: b ) Smooth inclined surface: A A q 3

Free Body Diagram (FBD) Lecture 5 c ) Roller support: Inclined surfaces d ) Pin connections: q q 4

Free Body Diagram (FBD) Lecture 5 d ) Pin connections: Ax Ay e ) Fixed Beam: 5

Free Body Diagram (FBD) Lecture 5 f ) Collar connections on frictionless Rod: g ) Frictionless Sliding guide ( Pin or Roller in slot ) connections: 90 o F h ) Ball and Socket: F q q Ay Ax Az Az Ax Ay 6

Free Body Diagram (FBD) i ) Smooth Cylinder: Lecture 5 j ) Frictionless Pulley: k ) Distributed Load: 1 ) Rectangular: 2 ) Triangular: 7

Free Body Diagram (FBD) Lecture 5 Example 1: The sphere has a mass of 6 kg and is supported as shown. Draw a free-body diagram of the sphere, cord CE, CE and the knot at C. Solution: 1 ) For the sphere: 2 ) For the Cord CE: FCE (force of knot acting on cord CE) FCE (force of cord CE acting on sphere) FCE (force of sphere acting on cord CE) W = 6 * 9. 8 = 58. 9 N 3 ) For the knot: FCB (force of cord CB acting on the knot C) FCD (force of spring CD acting on the knot C) FCE (force of cord CE acting on knot C) 8

Free Body Diagram (FBD) Lecture 5 Example 2: Draw the free-body diagram of the uniform beam. The beam has a mass of 100 kg. Solution: Free-Body Diagram for the diagram of uniform beam will be shown below: 9

Free Body Diagram (FBD) Example 3: Lecture 5 Draw the FBD diagram of the ring A: Solution: Is this the FBD of A? No! this is not the free body diagram of A! W= 2. 452 KN This is the FBD of A? 10