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Class 6_ae2_plastic analysis_kinematic method_ss
- 1. STRUCTURAL ANALYSIS II PLASTIC ANALYSIS. KINEMATIC METHOD PLASTIC ANALYSIS
- 2. STRUCTURAL ANALYSIS II PLASTIC ANALYSIS. KINEMATIC METHOD 1.- ELASTIC ANALYSIS OF GRIDS 1.1.- COMPATIBILITY METHOD 1.2- SLOPE DEFLECTION METHOD 2.- PLASTIC ANALYSIS OF STRUCTURES 2.1- PLASTIC ANALYSIS OF BEAMS. EQUILIBRIUM METHOD 2.2- PLASTIC ANALYSIS OF FRAMES 2.2.1- KINEMATIC METHOD 2.2.2- INCREMENTAL ANALYSIS. HINGE BY HINGE METHOD 3.- INTRODUCTION TO SECOND ORDER ANALYSIS OF STRUCTURES 2.3- PLASTIC ANALYSIS OF SLABS. FEBRUARY MARCHADNAPRIL MAY
- 3. STRUCTURAL ANALYSIS II PLASTIC ANALYSIS. KINEMATIC METHOD When the punctual load is not applied in the middle of the span… Or when we are analysing frames… We cannot apply the expressions of Plastic Moments in simple beams We apply the KIMENATIC METHOD
- 4. STRUCTURAL ANALYSIS II PLASTIC ANALYSIS. KINEMATIC METHOD KIMENATIC METHOD 1.- DRAW A POSSIBLE COLLAPSE PATTERN 2.- CALCULATE THE Mp THAT PRODUCES THAT COLLAPSE PATTERN 3.- CHECK IF THE COLLAPSE PATTERN + Mp VALUE ARE LINKED WITH A BENDING MOMENT DIAGRAM IN EQUILIBRIUM 1.1. Number of hinges required? 1.2. Points where a hinge can be formed? 1.3. Combinations? 2.1. Application of Virtual Work Principle Wext = Wint 2.2. Calculation of Mp 3.1. Equilibrium (three equilibrium equations)
- 5. STRUCTURAL ANALYSIS II PLASTIC ANALYSIS. KINEMATIC METHOD 1.- DRAW A POSSIBLE COLLAPSE PATTERN 1.1. Number of hinges required? (degree of indeterminacy + 1) 1.2. Points where a hinge can be formed? 1.3. Combinations? 1 + 1 = 2 A, B, C AB, AC, BC
- 6. STRUCTURAL ANALYSIS II PLASTIC ANALYSIS. KINEMATIC METHOD 2.- COLLAPSE PATTERN AB. VIRTUAL WORK PRINCIPLE External Work: Load · displacement Internal Work: Mp · rotation Where there is a hinge in the collapse pattern, there is a Mp in the bending moment diagram BENDING MOMENT DIAGRAM
- 7. STRUCTURAL ANALYSIS II PLASTIC ANALYSIS. KINEMATIC METHOD 2.- COLLAPSE PATTERN AB. VIRTUAL WORK PRINCIPLE External Work: Load · displacement Internal Work: Mp · rotation Where there is a hinge in the collapse pattern, there is a Mp in the bending moment diagram BENDING MOMENT DIAGRAM
- 8. STRUCTURAL ANALYSIS II PLASTIC ANALYSIS. KINEMATIC METHOD 2.- COLLAPSE PATTERN AC. VIRTUAL WORK PRINCIPLE External Work: Load x displacement Internal Work: Mp x rotationExternal Work: Load · displacement Internal Work: Mp · rotation BENDING MOMENT DIAGRAM
- 9. STRUCTURAL ANALYSIS II PLASTIC ANALYSIS. KINEMATIC METHOD 2.- COLLAPSE PATTERN AC. VIRTUAL WORK PRINCIPLE External Work: Load x displacement Internal Work: Mp x rotation External Work: Load · displacement Internal Work: Mp · rotation BENDING MOMENT DIAGRAM
- 10. STRUCTURAL ANALYSIS II PLASTIC ANALYSIS. KINEMATIC METHOD 2.- COLLAPSE PATTERN BC. VIRTUAL WORK PRINCIPLE External Work: Load x displacement Internal Work: Mp x rotationExternal Work: Load · displacement Internal Work: Mp · rotation BENDING MOMENT DIAGRAM
- 11. STRUCTURAL ANALYSIS II PLASTIC ANALYSIS. KINEMATIC METHOD 2.- COLLAPSE PATTERN BC. VIRTUAL WORK PRINCIPLE External Work: Load x displacement Internal Work: Mp x rotationExternal Work: Load · displacement Internal Work: Mp · rotation BENDING MOMENT DIAGRAM
- 12. STRUCTURAL ANALYSIS II PLASTIC ANALYSIS. KINEMATIC METHOD 2.- CHOOSE THE TRUE COLLAPSE PATTERN ¿? Mp….. The highest Pu….. The lowest So the correct collapse pattern should be AC Mp = 1,5 P Pu = 0,666 Mp
- 13. STRUCTURAL ANALYSIS II PLASTIC ANALYSIS. KINEMATIC METHOD 2.- WHAT HAPPENS IF I MAKE A MISTAKE OR I FORGET A COLLAPSE PATTERN THAT IS THE CORRECT ONE? 3.- CHECK IF THE COLLAPSE PATTERN + Mp VALUE ARE LINKED WITH A BENDING MOMENT DIAGRAM IN EQUILIBRIUM THE SOLUTION IS UNIQUE AND IF THE COLLAPSE PATTERN IS THE CORRECT ONE AND IF THE Mp IS THE CORRECT ONE THE BENDING MOMENT DIAGRAM WILL BE IN EQUILIBRIUM and no moment value in the diagram will be higher than Mp
- 14. STRUCTURAL ANALYSIS II PLASTIC ANALYSIS. KINEMATIC METHOD 3.- CHECK IF THE COLLAPSE PATTERN + Mp VALUE ARE LINKED WITH A BENDING MOMENT DIAGRAM IN EQUILIBRIUM
- 15. STRUCTURAL ANALYSIS II PLASTIC ANALYSIS. KINEMATIC METHOD
- 16. STRUCTURAL ANALYSIS II PLASTIC ANALYSIS. KINEMATIC METHOD KIMENATIC METHOD 1.- DRAW A POSSIBLE COLLAPSE PATTERN 2.- CALCULATE THE Mp THAT PRODUCES THAT COLLAPSE PATTERN 3.- CHECK IF THE COLLAPSE PATTERN + Mp VALUE ARE LINKED WITH A BENDING MOMENT DIAGRAM IN EQUILIBRIUM 1.1. Number of hinges required? 1.2. Points where a hinge can be formed? 1.3. Combinations? 2.1. Application of Virtual Work Principle Wext = Wint 2.2. Calculation of Mp 3.1. Equilibrium (three equilibrium equations)
- 17. STRUCTURAL ANALYSIS II PLASTIC ANALYSIS. KINEMATIC METHOD The cantilever breaks: partial collapse
- 18. STRUCTURAL ANALYSIS II PLASTIC ANALYSIS. KINEMATIC METHOD The beam breaks: beam collapse
- 19. STRUCTURAL ANALYSIS II PLASTIC ANALYSIS. KINEMATIC METHOD The frame moves horizontally: panel collapse
- 20. STRUCTURAL ANALYSIS II PLASTIC ANALYSIS. KINEMATIC METHOD The collapse is produce by the combination of horizontal and vertical load: combined mechanism
- 21. STRUCTURAL ANALYSIS II PLASTIC ANALYSIS. KINEMATIC METHOD RULES TO DRAW A COLLAPSE PATTERN 1.- BARS CANNOT GET LONGER OR SHORTER 2.- JOINT ANGLES CAN ONLY CHANGE IF THERE IS A HINGE (plastic or real) = bars can only rotate about hinges 3.- WE ASSUME THAT PERPENDICULAR DISPLACEMENTS ARE AS CIRCUMFERENCE ARCS (small-angle theory)
- 22. STRUCTURAL ANALYSIS II PLASTIC ANALYSIS. KINEMATIC METHOD
- 23. STRUCTURAL ANALYSIS II PLASTIC ANALYSIS. KINEMATIC METHOD Wext = P · u + P/2 · v= P · 4 · γ1 + P/2 · 2 γ1 = 5 · P · γ1 Wint = Mp ·γ1 + Mp · (γ3+ γ3) = 3 Mp · γ1 u = 4 ·γ1 v = 2 ·γ3 γ1 = γ3 u = 4 ·γ3 5 · P · γ1 = 3 Mp · γ1 Mp = 5P / 3
- 24. STRUCTURAL ANALYSIS II PLASTIC ANALYSIS. KINEMATIC METHOD
- 25. STRUCTURAL ANALYSIS II PLASTIC ANALYSIS. KINEMATIC METHOD
- 26. STRUCTURAL ANALYSIS II PLASTIC ANALYSIS. KINEMATIC METHOD
- 27. STRUCTURAL ANALYSIS II PLASTIC ANALYSIS. KINEMATIC METHOD 2.- CHOOSE THE TRUE COLLAPSE PATTERN ¿? Mp….. The highest Pu….. The lowest So the correct collapse pattern should be …. THE SOLUTION IS ALWAYS UNIQUE AND WE CAN BE SURE ABOUT IT
- 28. STRUCTURAL ANALYSIS II PLASTIC ANALYSIS. KINEMATIC METHOD
- 29. STRUCTURAL ANALYSIS II PLASTIC ANALYSIS. KINEMATIC METHOD
- 30. STRUCTURAL ANALYSIS II PLASTIC ANALYSIS. KINEMATIC METHOD
- 31. STRUCTURAL ANALYSIS II PLASTIC ANALYSIS. KINEMATIC METHOD
- 32. STRUCTURAL ANALYSIS II PLASTIC ANALYSIS. KINEMATIC METHOD
- 33. STRUCTURAL ANALYSIS II PLASTIC ANALYSIS. KINEMATIC METHOD
- 34. STRUCTURAL ANALYSIS II PLASTIC ANALYSIS. KINEMATIC METHOD
- 35. STRUCTURAL ANALYSIS II PLASTIC ANALYSIS. KINEMATIC METHOD
- 36. STRUCTURAL ANALYSIS II PLASTIC ANALYSIS. KINEMATIC METHOD
- 37. STRUCTURAL ANALYSIS II PLASTIC ANALYSIS. KINEMATIC METHOD
- 38. STRUCTURAL ANALYSIS II PLASTIC ANALYSIS. KINEMATIC METHOD
- 39. STRUCTURAL ANALYSIS II PLASTIC ANALYSIS. KINEMATIC METHOD
- 40. STRUCTURAL ANALYSIS II PLASTIC ANALYSIS. KINEMATIC METHOD
- 41. STRUCTURAL ANALYSIS II KINEMATIC METHOD
- 42. STRUCTURAL ANALYSIS II PLASTIC ANALYSIS. KINEMATIC METHOD
- 43. STRUCTURAL ANALYSIS II PLASTIC ANALYSIS. KINEMATIC METHOD
- 44. STRUCTURAL ANALYSIS II PLASTIC ANALYSIS. KINEMATIC METHOD