Free Body Diagram (FBD) Lecture 5 To apply equilibrium equations we must account for all known and unknown forces acting on the particle. 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. 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: Draw outlined shape - Imagine the particle isolated or cut “free” from its surroundings Show all forces and moments - Include “active forces” and “reactive forces”. Place each force and couple at the point that it is applied. Identify each force: Known forces labeled with proper magnitude and direction. Letters used for unknown quantities. Isolating boundary Add any relevant dimensions onto your picture for calculations.

Free Body Diagram (FBD) Lecture 5 Type of Forces: 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 q L/2 W L W Weight on inclined surface: W q

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

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

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

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

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

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, and the knot at C. Solution: 1 ) For the sphere: 2 ) For the Cord CE: W = 6 * 9.8 = 58.9 N FCE (force of cord CE acting on sphere) FCE (force of knot acting on cord CE) FCE (force of sphere acting on cord CE) FCB (force of cord CB acting on the knot C) 3 ) For the knot: FCD (force of spring CD acting on the knot C) FCE (force of cord CE acting on knot C)

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

Free Body Diagram (FBD) Lecture 5 Example 3: 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?