The document discusses progressive collapse analysis and plastic analysis methods for structural analysis. It describes elastic and plastic analysis, the kinematic method, and incremental method for plastic analysis of structures. The incremental method involves performing elastic analysis with increasing numbers of hinges representing plastic behavior until global collapse occurs. This allows analyzing how structures behave step-by-step as plastic hinges form until full collapse.

1. STRUCTURAL ANALYSIS II
PROGRESSIVE COLLAPSE ANALYSIS
PLASTIC ANALYSIS

2. STRUCTURAL ANALYSIS II
PROGRESSIVE COLLAPSE ANALYSIS
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
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
PROGRESSIVE COLLAPSE ANALYSIS
ELASTIC ANALYSIS PLASTIC ANALYSIS
≠ RESULTS*
Part of the structure
material is working beyond
the plastic limit
The structure should be
ductile enough to have a
plastic behaviour
All the structure material is
working below the plastic
limit
The structure can be
fragile or ductile to apply
elastic analysis
SAFER CHEAPER
Superposition Principle
cannot be applied
Superposition Principle can
be applied

4. STRUCTURAL ANALYSIS II
PROGRESSIVE COLLAPSE ANALYSIS
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
PROGRESSIVE COLLAPSE ANALYSIS
KINEMATIC METHOD INCREMENTAL METHOD
= RESULTS (both plastic analysis)
It let us know how the
frames behave step by
step
It leads us to the true
failure pattern directly. We
do not have to choose
among posible different
answers
It leads directly to the final
collapse pattern
We must guess and
choose among different
possible collapse patterns
Lot of numbers because we have
to consider elastic analysis
results in the proccess
Easy maths

6. STRUCTURAL ANALYSIS II
PROGRESSIVE COLLAPSE ANALYSIS
INCREMENTAL METHOD (progressive collapse analysis)
1.- ELASTIC ANALYSIS P= 1
2.- ELASTIC ANALYSIS P=1 AND A HINGE AT THE POINT WHERE THE 1º
PLASTIC HINGE IS FORMED.
3.- …. REPEAT THE PROCCESS UNTIL THE GLOBAL COLLAPSE IS
PRODUCED
1.1. Where is the first plastic hinge formed?
1.2. Value of the load P that produces the first plastic hinge?
2.1. Where is the second plastic hinge formed?
2.2. Value of the load P that produces the second plastic hinge?
1.3. Bending moment diagram when the 1st plastic hinge is formed
2.3. Bending moment diagram when the 1st plastic hinge is formed

7. STRUCTURAL ANALYSIS II
PROGRESSIVE COLLAPSE ANALYSIS

8. STRUCTURAL ANALYSIS II
PROGRESSIVE COLLAPSE ANALYSIS
RESULT OF SAP2000 OR SLOPE DEFLECTION METHOD

9. STRUCTURAL ANALYSIS II
CLASS 9

10. STRUCTURAL ANALYSIS II
PROGRESSIVE COLLAPSE ANALYSIS
VALUE OF P WHEN THE FIRST HINGE IS FORMED
We have to choose
between these two values

11. STRUCTURAL ANALYSIS II
PROGRESSIVE COLLAPSE ANALYSIS
BENDING MOMENT DIAGRAM WHEN THE FIRST HINGE IS FORMED
THE LOWEST… WHY?

12. STRUCTURAL ANALYSIS II
PROGRESSIVE COLLAPSE ANALYSIS
BENDING MOMENT DIAGRAM WHEN THE FIRST HINGE IS FORMED

13. STRUCTURAL ANALYSIS II
PROGRESSIVE COLLAPSE ANALYSIS
TO CALCULATE WHERE THE SECOND HINGE
IS FORMED…
RESULT OF SAP2000 OR SLOPE DEFLECTION METHOD

14. STRUCTURAL ANALYSIS II
PROGRESSIVE COLLAPSE ANALYSIS
THIS DIAGRAM IS NOT ENOUGH TO KNOW IT!

15. STRUCTURAL ANALYSIS II
PROGRESSIVE COLLAPSE ANALYSIS

16. STRUCTURAL ANALYSIS II
PROGRESSIVE COLLAPSE ANALYSIS
BENDING MOMENT DIAGRAM WHEN THE SECOND HINGE IS FORMED

17. STRUCTURAL ANALYSIS II
PROGRESSIVE COLLAPSE ANALYSIS

18. STRUCTURAL ANALYSIS II
CLASS 9
RESULT OF SAP2000 OR SLOPE DEFLECTION METHOD
We place another hinge
where the second plastic
hinge is formed

19. STRUCTURAL ANALYSIS II
PROGRESSIVE COLLAPSE ANALYSIS
WE NEED THESE TWO DIAGRAMS TO KNOW
WHERE THE THIRD PLASTIC HINGE WILL OCCUR

20. STRUCTURAL ANALYSIS II
PROGRESSIVE COLLAPSE ANALYSIS
BENDING MOMENT DIAGRAM WHEN THE THIRD HINGE IS FORMED

21. STRUCTURAL ANALYSIS II
PROGRESSIVE COLLAPSE ANALYSIS
BENDING MOMENT DIAGRAM WHEN THE THIRD HINGE IS FORMED

22. STRUCTURAL ANALYSIS II
PROGRESSIVE COLLAPSE ANALYSIS
AS IT IS STATICALLY DETERMINATE, WE DO NOT NEED SAP2000 BUT WE COULD USE IT
We place a hinge where
the second plastic hinge is
formed

23. STRUCTURAL ANALYSIS II
PROGRESSIVE COLLAPSE ANALYSIS
WE NEED THESE TWO DIAGRAMS TO KNOW
WHERE THE FOURTH PLASTIC HINGE WILL OCCUR

24. STRUCTURAL ANALYSIS II
PROGRESSIVE COLLAPSE ANALYSIS

25. STRUCTURAL ANALYSIS II
PROGRESSIVE COLLAPSE ANALYSIS

26. STRUCTURAL ANALYSIS II
PROGRESSIVE COLLAPSE ANALYSIS

27. STRUCTURAL ANALYSIS II
PROGRESSIVE COLLAPSE ANALYSIS
33,23 = - 0,00008831 m x 124,57 - 0,0002 m x 10,104 - 0,000277 m x 36,24 - 0,00572 m x 1,775

28. STRUCTURAL ANALYSIS II
PROGRESSIVE COLLAPSE ANALYSIS
PROGRESSIVE COLLAPSE ANALYSIS?

29. STRUCTURAL ANALYSIS II
CLASS 9
RESULT OF SAP2000 OR SLOPE DEFLECTION METHOD

30. STRUCTURAL ANALYSIS II
PROGRESSIVE COLLAPSE ANALYSIS
VALUE OF THE LOAD THAT PRODUCES THE FIRST PLASTIC HINGE?

31. STRUCTURAL ANALYSIS II
PROGRESSIVE COLLAPSE ANALYSIS
BENDING MOMENT DIAGRAM WHEN THE FIRST PLASTIC HINGE IS PRODUCED

32. STRUCTURAL ANALYSIS II
PROGRESSIVE COLLAPSE ANALYSIS
AS IT IS STATICALLY DETERMINATE, WE DO NOT NEED SAP2000 BUT WE COULD USE IT

33. STRUCTURAL ANALYSIS II
PROGRESSIVE COLLAPSE ANALYSIS
VALUE OF PU2? WE MUST CONSIDER TWO DIAGRAMS!!!

34. STRUCTURAL ANALYSIS II
PROGRESSIVE COLLAPSE ANALYSIS

35. STRUCTURAL ANALYSIS II
PROGRESSIVE COLLAPSE ANALYSIS

36. STRUCTURAL ANALYSIS II
PROGRESSIVE COLLAPSE ANALYSIS
PLASTIC ANALYSIS