Staitics: Lecture3c


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Staitics: Lecture3c

  1. 1. Today:Trusses continued- Method of sections- Rigid trusses- FramesBook: Chapter 6.4 & 6.6
  2. 2. Two Methods to Analyze Trusses1) Method of joints2) Method of sections
  3. 3. Method of joints Determine the force in the members by calculating the equilibrium of the joints1. Draw Free Body Diagram2. Determine the reaction forces at the supports of the whole structure3. Calculate the forces in a joint with max. 2 unknowns4. Proceed to the next joint with max. 2 unknowns until all joints are analyzed
  4. 4. Method of sections Determine the force in a members by dividing the structure in two sections by cutting the members and calculating the equilibrium of one of the sections.1) Determine the section by cutting just three members (in general)2) Use the moment equilibrium equation in a clever way.
  5. 5. Determine the force in member DE. Source: R.C. Hibbeler, "Engineering Mechanics – Statics"
  6. 6. 1) Determine the force inmember DE.2) Determine the force inmember DL.
  7. 7. H Calculate the forces in members F L CE, DE, DF D N RBA Q C E G K M
  8. 8. H Calculate the forces in member F L HG D N RBA Q C E G K M
  9. 9. Rigid truss Flexible truss (mechanism) 3 members, 3 joints 4 members, 4 joints
  10. 10. 3 members, 3 joints 5 members, 4 joints 7 members, 5 joints
  11. 11. Rigid truss consisting of triangular elementsWhere s = number of members k = number of joints
  12. 12. Non-rigid trussRigid truss This is a necessary condition, but not sufficient!!
  13. 13. Rigid or non-rigid?
  14. 14. Rigid or non-rigid?
  15. 15. Rigid or non-rigid?
  16. 16. Rigid or non-rigid?
  17. 17. Rigid or non-rigid?
  18. 18. Constraints
  19. 19. Constraints
  20. 20. Constraint truss structureWhere n = difference between number of unknowns and equations r = number of constraints s = number of members k = number of joints
  21. 21. Constraint truss structure n<0 kinematically indeterminate (mechanism) n >= 0 kinematically determinate (necessary, not sufficient) n=0 statically determinate n>0 statically indeterminate
  22. 22. Statically determinate?
  23. 23. Frames
  24. 24. Calculate the reaction forcesin hinge A when the normalreaction force on the nosewheel is 24 kN. Source: R.C. Hibbeler, "Engineering Mechanics – Statics"
  25. 25. Source: R.C. Hibbeler, "Engineering Mechanics – Statics" C D B O A
  26. 26. Law of sines and cosines
  27. 27. Frame A frame is a structure where at least one of its individual members is a multi-force member.
  28. 28. Calculate the angle of the ramp in B for which the reaction force in A isA completely horizontal. B
  29. 29. Determine the orientation of the reaction force in A graphically .A B
  30. 30. Source: R.C. Hibbeler, "Engineering Mechanics – Statics" Compound-lever snips are designed to replace regular tinners’ snips when large cutting forces are required. For the gripping force of 150 N, what is the cutting force P at a distance of 30 mm along the blade from the pin at A
  31. 31. Calculate the force in member FGA E B C D F G