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  1. 1. T A B The Concurrent System The Free Body Diagram
  2. 2. Concept of Free Body Diagrams Particle System Rigid Body Systems Concept of Equilibrant Graphical Determination of Equilibrant Applied and Reaction Forces in Beams Types of Beam Supports Free Body diagram of Rigid Bodies
  3. 3. Free Body Diagrams • Essential step in solving Equilibrium problems •Complex Structural systems reduced into concise FORCE systems WHAT IS A FREE BODY DIAGRAM? A FBD is a simplified representation of a PARTICLE or RIGID BODY that is isolated from its surroundings and on which all applied forces and reactions are shown. All forces acting on a particle original body must be considered, and equally important any force not directly applied on the body must be excluded.
  4. 4. W A B C W BC BA Free Body Diagram
  5. 5. Draw the Free Body Diagrams
  6. 6. REAL LIFE CONCURRENT SYSTEMS Equilibrium of a Particle
  7. 7. 1. Two cables support the traffic light weighing 250 pounds. Determine the tension in the cables AB and BC. • Solution: • Resolving T1 along x and y directions: • Resolving T2 along x and y directions: • . °20 °30A B °20 °30 200lb A C B T1 T2 T1 T2 T1Y T2Y T1X T2X T3=200lb 12 21 21 21 085.1 866.0*9396.0* 30cos20cos 0 TT TT TT TTFR XXxx = = °=° =+== ∑ 2005.0342.0 20030sin20sin 0200 21 21 21 =+ =°+° =−+== ∑ TT TT TTFR yyyy 1
  8. 8. • Substituting equation 1 in the above equation, we get .342T1+.5425T2=200 .8845T1=200 T1=226lb • From equation 1 we get T2=1.085*226 T2= 245.56lb Answers: Tension in cable AB = 226lb Tension in cable BC = 245.56lb
  9. 9. W=100# A C D E B  30=θ 4 3 BA=? BC=? CD=? CE=? Problem Change
  10. 10. 400# F1 F2 300N 450N F1 X Y X X X Y Y Y  30=θ  60=θ F 3 kN 7 kN 4.5 kN 7.5 kN 2.25 kN F  60=θ  30=θ P P PP 1 2 3 4 θ θ θ  20=θ 4 3 12 5 3
  11. 11. CONCEPT OF THE EQUIBILIRIANT Resultant 1F 2F R E Equilibrant
  12. 12. ASimple Supported Beam A Cantilever Beam RIGID BODY SYSTEMS
  13. 13. A Propped Cantilever with Three Concentrated Load A Simply Supported Beam with Three concentrated Loads
  14. 14. APPLIED AND REACTION FORCES IN BEAMS In the Chapter on Force Systems, we discussed the concept of APPLIED FORCES, REACTION FORCES and INTERNAL FORCES Here we well discuss the relevance and importance of APPLIED FORCES and REACTION FORCES in the case of Beams. Before we proceed further please study the animated visuals on the next slide
  16. 16. A Beam is an example of Rigid Body. Generally loads are applied on the beams. And the beams develop reactions. We named the loads hat are applied on the beams like Dead Load, Live Load, Wind Load. Earthquake Loads as APPLIED FORCES, and the consequent reactions that are simultaneously developed as REACTION FORCES. These REACTION FORCES generally develop at the supports. We use the same color code as described earlier for clarity. The reactions develop as a direct consequence of Newton’s Third Law,. Which states that for every action there is an equal and opposite reaction. In the three examples presented, if we separate the rigid body for its supports we can see equal and opposite forces acting at the supports..
  17. 17. From the above we can describe the concept of the FREE BODY DIAGRAM of a Rigid Body as folows. It is representing the rigid body with all the Forces- the APPLIED FORCES and REACTION FORCES acting on it It is axiomatic that the Rigid Body must be in equilibrium under the action of the APPLIED FORCES and the REACTION FORCES. Hence the FREE BODY DIAGRAMS can also be called as EQUILIBRIUM DIAGRAMS, even though the former name is more popular. Finding the REACTION of beams for various types of APPLIED LOADS is a basic requirement in STATICS
  18. 18. The above diagrams, which show the complete system of applied and reactive forces acting on a body, are called free body diagrams. The whole system of applied and reactive forces acting on a body must be in a state of equilibrium. Free-body diagrams are, consequently ,often called equilibrium diagrams. Drawing equilibrium diagrams and finding reactions for loaded structural members is a common first step in a complete structural analysis
  19. 19. Roller, Hinge and Fixed Supports Hinge supports Roller Supports Fixed Supports
  20. 20. ROLLER SUPPORT Applied Force Reactive Forces The Reactive Force must always be perpendicular to the surface for a ROLLER
  21. 21. Roller Support Roller Support allows horizontal movement It allows the beam to bend
  22. 22. Rocker Support A Rocker Support is similar to the Roller Support
  23. 23. A variation of Roller Support
  24. 24. PIN or HINGE SUPPORT Applied Force Reactive Force The Reactive Force can be in any direction
  25. 25. Pin or Hinge Support Pin support does no allow any movement It allows the beam to bend
  26. 26. FIXED SUPPORT No movement No Rotation
  27. 27. Half the strength of the Bridge is lost by not allowing the Bridge to expand due to the Temperature Rise Why Roller Support is Important? 500 ft. 2.34” T= 100 degT= 40 deg
  28. 28. Why Hinge Support is Important ?
  29. 29. Why Fixed Support is Important? A Cantilever has to be fixed to support a load Hinge
  30. 30. REAL LIFE HINGES A Steel Hinge A Concrete Hinge A Neoprene Pad Hinge The shear deformation of the Neoprene pad mimics the horizontal movement of a Roller The close confinement of the steel rods will not allow moment transfer, but only Vertical & Horizontal Forces Top part Bottom part Pin The rotation of the top part about the pin allows a Hinge action
  31. 31. Question 1. What is the difference between a Rigid Body and a Particle Question 2: Explain the Difference between a Roller Support, Hinge Support and Fixed Support
  33. 33. Free Body Diagrams 1. Try to draw the free body diagram for a axle of a bicycle wheel as shown below: 2. Draw the free body diagram for a propped cantilever shown below: 3. Does a Neoprene pad bearing function like a Hinge or a Roller. 4. Attempt to draw the Free body diagram for the circled part of the building P Axle
  34. 34. 5. Draw the Free Body Diagram for the following Dam: Water