Plastic analysis of frames. Progressive collapse analysis

1. STRUCTURAL ANALYSIS II
PROGRESSIVE COLLAPSE ANALYSIS

2. 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
PROGRESSIVE COLLAPSE ANALYSIS

3. 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 1st
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

4. STRUCTURAL ANALYSIS II
PROGRESSIVE COLLAPSE ANALYSIS
PROGRESSIVE COLLAPSE ANALYSIS?

5. STRUCTURAL ANALYSIS II
PROGRESSIVE COLLAPSE ANALYSIS
PROGRESSIVE COLLAPSE ANALYSIS?
PLASTIC ANALYSIS Degree of indeterminacy?

6. STRUCTURAL ANALYSIS II
PROGRESSIVE COLLAPSE ANALYSIS
Degree of indeterminacy?
1
PROGRESSIVE COLLAPSE ANALYSIS?

7. STRUCTURAL ANALYSIS II
PROGRESSIVE COLLAPSE ANALYSIS
Degree of indeterminacy? 1
Numbers of plastic hinges required
to produce the collapse?
PROGRESSIVE COLLAPSE ANALYSIS?

8. STRUCTURAL ANALYSIS II
PROGRESSIVE COLLAPSE ANALYSIS
Degree of indeterminacy?
1
Numbers of plastic hinges required
to produce the collapse? 1+1 = 2
PROGRESSIVE COLLAPSE ANALYSIS?

9. STRUCTURAL ANALYSIS II
PROGRESSIVE COLLAPSE ANALYSIS
Numbers of plastic hinges required
to produce the collapse? 1+1 = 2
TWO STEPS TO SOLVE
THE PROGRESSIVE COLLAPSE ANALYSIS

10. STRUCTURAL ANALYSIS II
PROGRESSIVE COLLAPSE ANALYSIS
PROGRESSIVE COLLAPSE ANALYSIS
1
1

11. STRUCTURAL ANALYSIS II
PROGRESSIVE COLLAPSE ANALYSIS
WHERE WILL THE FIRST PLASTIC HINGE BE FORMED?
Let-s try this
value first
because it is
the highest
We must
also check
this value
because the
support is
weaker than
the beam

12. STRUCTURAL ANALYSIS II
PROGRESSIVE COLLAPSE ANALYSIS
WHERE WILL THE FIRST PLASTIC HINGE BE FORMED?

13. STRUCTURAL ANALYSIS II
PROGRESSIVE COLLAPSE ANALYSIS
vertical displacement at DE = vDE,1 x Pu1
Displacements
and loads are
proportional

14. STRUCTURAL ANALYSIS II
PROGRESSIVE COLLAPSE ANALYSIS
PROGRESSIVE COLLAPSE ANALYSIS
2

15. STRUCTURAL ANALYSIS II
PROGRESSIVE COLLAPSE ANALYSIS
WHERE WILL THE SECOND PLASTIC HINGE BE FORMED?
Auxiliary system to compute where the second hinge is

16. STRUCTURAL ANALYSIS II
PROGRESSIVE COLLAPSE ANALYSIS
WHERE WILL THE SECOND PLASTIC HINGE BE FORMED?
Let-s try this value
because it is the
highest in both
diagrams
The second auxiliary system all alone is not enough

17. STRUCTURAL ANALYSIS II
PROGRESSIVE COLLAPSE ANALYSIS
Frame behavior
from P= 0 to P=93,2/a
Frame behavior
from P= 93,2/a to P=98,2/a

18. STRUCTURAL ANALYSIS II
PROGRESSIVE COLLAPSE ANALYSIS

19. STRUCTURAL ANALYSIS II
PROGRESSIVE COLLAPSE ANALYSIS
Mp
Mp
ALL THE OTHER BENDING MOMENTS VALUES ARE LOWER THAN Mp (or 2Mp)
PLASTIC HINGES OCCUR AT JOINT D in the beam AND AT JOINT B

20. STRUCTURAL ANALYSIS II
PROGRESSIVE COLLAPSE ANALYSIS
TO COMPUTE THE FINAL VERTICAL DISPLACEMENT AT vDE, WE NEED THE VALUE OF THE
VERTICAL DISPLACEMENT AT vDE IN THE SYSTEM WITH REAL HINGE AT D (beam)

21. STRUCTURAL ANALYSIS II
PROGRESSIVE COLLAPSE ANALYSIS
WHAT’S THE VALUE OF THE VERTICAL DISPLACEMENT IN THE MIDDLE OF SPAN DE
WHEN THE SECOND PLASTIC HINGE OCCURS?

22. STRUCTURAL ANALYSIS II
PROGRESSIVE COLLAPSE ANALYSIS
WHAT’S THE VALUE OF THE VERTICAL DISPLACEMENT IN THE MIDDLE OF SPAN DE
AT COLLAPSE?

23. STRUCTURAL ANALYSIS II
PROGRESSIVE COLLAPSE ANALYSIS
KINEMATIC METHOD
3

24. STRUCTURAL ANALYSIS II
PROGRESSIVE COLLAPSE ANALYSIS
PLASTIC ANALYSIS
KINEMATIC METHOD
WE ALREADY KNOW THAT THE TWO HINGES WILL BE AT D AND E
(affecting the supports ends)

25. STRUCTURAL ANALYSIS II
PROGRESSIVE COLLAPSE ANALYSIS
PLASTIC ANALYSIS
KINEMATIC METHOD

26. STRUCTURAL ANALYSIS II
PROGRESSIVE COLLAPSE ANALYSIS
4

27. STRUCTURAL ANALYSIS II
PROGRESSIVE COLLAPSE ANALYSIS
If the value of P that produces the collapse is P =98,2/a
THE SAFETY FACTOR WHEN P = 50 is safety factor = = 1,96/a
98,2/a
50