BACK ANALYSIS OF THE COLLAPSE OF A METAL TRUSS STRUCTURE_Crosti, Bontempi_SEMC2013

1. CAPE TOWN, SOUTH AFRICA, 2-4 SEPTEMBER 2013
BACK ANALYSIS OF THE COLLAPSE OF ABACK ANALYSIS OF THE COLLAPSE OF A
METAL TRUSS STRUCTURE
Chiara Crosti, Franco Bontempi
““SapienzaSapienza” University of Roma,” University of Roma,
chiara.crosti@uniroma1.itchiara.crosti@uniroma1.it,, franco.bontempi@uniroma1.itfranco.bontempi@uniroma1.it

2. Radiohead’s concert, 2012
Image taken from:
http://abcnews.go.com/Entertainment/stage-collapses-
radiohead-concert
Country music concert, 2011
Image taken from:
http://www.billboard.com/news/
FORENSIC ASPECTS1/27
radiohead-concert
killing/story?id=16587415#.UGrriE3A9_c
Big valley Jamboree, 2009
Image taken from:
http://www.cbc.ca/news/canada/edmonton/story/2012/01/
20/edmonton-charges-stayed-big-valley-jamboree.html
Jovanotti’s concert, 2011
Image taken from:
http://tg24.sky.it/tg24/cronaca/photogallery/201
1/12/12/crollo_palco_concerto_jovanotti_trieste
.html
chiara.crosti@uniroma1.it

3. CASE STUDY:
AIM OF THIS WORK:
The aim of this work was not to define who made the mistake, but:
a. to investigate which kind of “error” could have compromised the safety of
this structure; and,
b. to evaluate the consequence of these “errors” in terms of global structural
response.
2/27 FORENSIC ASPECTS
http://www.udine20.it/wp-content/uploads/2012/03/palco-laura-pausini.jpg
chiara.crosti@uniroma1.it

4. A temporary structure can be defined as a structure that can be readily and completely
dismantled and removed from the site between periods of actual use.
They comprise 3 distinct elements:
1. The foundations – designed to both support the structure and hold it down (due to wind-
uplift, sliding or over-turning).
2. The superstructure – to carry all the imposed vertical (gravity) loads safely to the ground,
e.g. people, equipment.
3. The stability system – bracing and other specialist members to resist horizontal loads, e.g.
due to crowd movement and wind loads.
TEMPORARY DEMOUNTABLE STRUCTURES (TDM)
FORENSIC ASPECTS3/27
due to crowd movement and wind loads.
chiara.crosti@uniroma1.it

5. A temporary structure can be defined as a structure that can be readily and completely
dismantled and removed from the site between periods of actual use.
They comprise 3 distinct elements:
1. The foundations – designed to both support the structure and hold it down (due to wind-
uplift, sliding or over-turning).
2. The superstructure – to carry all the imposed vertical (gravity) loads safely to the ground,
e.g. people, equipment.
3. The stability system – bracing and other specialist members to resist horizontal loads, e.g.
due to crowd movement and wind loads.
TEMPORARY DEMOUNTABLE STRUCTURES (TDM)
FORENSIC ASPECTS4/27
due to crowd movement and wind loads.
chiara.crosti@uniroma1.it
TIMELINE

6. SWISS CHEESE MODEL (Reason, 1997)
FORENSIC ASPECTS5/27
chiara.crosti@uniroma1.it

7. Management &
Administration
SWISS CHEESE MODEL (Reason, 1997)
FORENSIC ASPECTS
Built-up Load-inDesign
6/27
Administration
Inadequate site
investigation
Inappropriate
ground condition
Inadequate safety
plan
………..
Inadequate
structural design
Failure to adopt
Building Codes
Inadequate loads
estimation
……..
Improper construction procedure
Improper working position
Breach of regulation or code of
practice
………..
chiara.crosti@uniroma1.it

8. Management &
Administration
COLLAPSECOLLAPSE
SWISS CHEESE MODEL (Reason, 1997)
FORENSIC ASPECTS
Built-up Load-inDesign
7/27
Administration
Inadequate site
investigation
Inappropriate
ground condition
Inadequate safety
plan
………..
Inadequate
structural design
Failure to adopt
Building Codes
Inadequate loads
estimation
……..
Improper construction procedure
Improper working position
Breach of regulation or code of
practice
………..
chiara.crosti@uniroma1.it

9. BUILD-UP PHASE (CASE STUDY)
Positioning on the ground
of the load distribution
plates
Positioning of the bases of
the columns
Assembling on the floor of
the roof structure called
“Space Roof”
Assempled and anchored
Lifting the columns of the
roof structure and
Assembling of the hung
beams and other
INVESTIGATION ON TECHINAL CAUSES OF THE COLLAPSE8/27
Assempled and anchored
secondary beams
roof structure and
anchoring the top of the
columns to the roof
beams and other
components of the stage
(lighting, video, etc.)
Rigging phase Delivery of the structure
for its use
Technical-administrative
testing
COLLAPSE
chiara.crosti@uniroma1.it

10. INVESTIGATION ON TECHINAL CAUSES OF THE COLLAPSE
BUILD-UP PHASE (CASE STUDY)
9/27
chiara.crosti@uniroma1.it

11. INVESTIGATION ON TECHINAL CAUSES OF THE COLLAPSE
BUILD-UP PHASE (CASE STUDY)
10/27
chiara.crosti@uniroma1.it

12. COLLAPSE
INVESTIGATION ON TECHINAL CAUSES OF THE COLLAPSE
BUILD-UP PHASE (CASE STUDY)
11/27
COLLAPSE
chiara.crosti@uniroma1.it

13. 15/22
FINITE ELEMENT MODEL
INVESTIGATION ON TECHINAL CAUSES OF THE COLLAPSE
A
B
C
21.8m
33 m
a
b
c de
f
g hi
l m
12/27
ton
A
1 2
16m
a
a (ton) 8.7
b (ton) 6.5
c (ton) 8.7
d (ton) 2.3
e (ton) 2.3
f (ton) 7.75
g (ton) 4.3
h (ton) 5.6
I (ton) 5.6
l (ton) 6.7
m (ton) 6.7
MATERIAL: ALUMINIUM
EN AW-6082 T6
chiara.crosti@uniroma1.it

14. EUROCODE
φ 0.005
This structure is designed to be indoor; therefore the structural elements were
designed to carry vertical loads but may not have been designed for lateral loads. That
could be a fatal error in the design phase, in fact, following what prescribed in the
UNI ENV 1999-1-1:2007, in order to run global analyses, it is necessary to take
account of horizontal forces due to the imperfections of the elements composing the
structure.
FAILURE TO ADOPT STANDARD PROCEDURES
INVESTIGATION ON TECHINAL CAUSES OF THE COLLAPSE13/27
φ 0.005
kc 1.224745 > 1
nc 1
ks 1.224745 > 1
ns 1
φ0 0.005
N 2.25E+05 N
φN 1.13E+03 N
NO HORIZONTAL LOADS
NO BRACING MEMBERS
chiara.crosti@uniroma1.it

15. Top of the column
Rigid or Hinged
IMPROPER CONSTRUCTION PROCEDURE
INVESTIGATION ON TECHINAL CAUSES OF THE COLLAPSE14/27
Bottom of the column
Rigid or Hinged
chiara.crosti@uniroma1.it

16. INVESTIGATION ON TECHINAL CAUSES OF THE COLLAPSE
RIGID
15/27
IMPROPER CONSTRUCTION PROCEDURE
chiara.crosti@uniroma1.it
HINGED
MODEL 5
Hinged
Rigid link

17. INVESTIGATION ON TECHINAL CAUSES OF THE COLLAPSE
RIGID
Beam Element
16/27
IMPROPER CONSTRUCTION PROCEDURE
chiara.crosti@uniroma1.it
HINGED
Hinged
Hinged
MODEL 4

18. INVESTIGATION ON TECHINAL CAUSES OF THE COLLAPSE
RIGID
5
7
Beam Element
HingedTranslation
Stiffness
IMPROPER CONSTRUCTION PROCEDURE
17/27
chiara.crosti@uniroma1.it
Point contact element: used to model a gap between two surface,
stiffness is provided in compression but zero stiffness in tension
UNILATERAL
1
2
3
4
5
68
Point contact
Element
L= 0.065 m
Hinged
Hinged
Hinged
Hinged
Hinged
Hinged
HingedStiffness
MODEL 3

19. RIGID
Beam Element
Hinged
18/27 INVESTIGATION ON TECHINAL CAUSES OF THE COLLAPSE
IMPROPER CONSTRUCTION PROCEDURE
chiara.crosti@uniroma1.it
RIGID
MODEL 0,1,2
Hinged Hinged
Hinged
Hinged
Hinged
Hinged

20. INVESTIGATION ON TECHINAL CAUSES OF THE COLLAPSE
4.0
5.0
6.0
7.0
LoadFactor
Model 0
Model 1
Model 2
Model 1 Model 2
Model 0
GNL+ MNL+ Imperfection
GNL+ MNL
GNL
FINITE ELEMENT ANALYSIS RESULTS (Nonlinear)
19/27
chiara.crosti@uniroma1.it
0.0
1.0
2.0
3.0
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40
LoadFactor
Dx (m)

21. INVESTIGATION ON TECHINAL CAUSES OF THE COLLAPSE
4.0
5.0
6.0
7.0
LoadFactor
Model 0
Model 1
Model 2
Model 3Model 1 Model 3Model 2
Model 0
GNL+ MNL+ Imperf.+ unilat.restr.
GNL+ MNL+ Imperfection
GNL+ MNL
GNL
FINITE ELEMENT ANALYSIS RESULTS (Nonlinear)
19/27
Model 3
chiara.crosti@uniroma1.it
0.0
1.0
2.0
3.0
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40
LoadFactor
Dx (m)
Model 3

22. 4.0
5.0
6.0
7.0
LoadFactor
Model 3
Load Factor = 4.019
INVESTIGATION ON TECHINAL CAUSES OF THE COLLAPSE20/27
Dz = 11mm
Dz = 15mm
Load Factor = 4.019
MODEL 2
Dz = 7 mm
0.0
1.0
2.0
3.0
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40
LoadFactor
Dx (m)
Load Factor = 0
Load Factor = 2
Load Factor = 3.5
chiara.crosti@uniroma1.it

23. INVESTIGATION ON TECHINAL CAUSES OF THE COLLAPSE3/22
chiara.crosti@uniroma1.it

24. INVESTIGATION ON TECHINAL CAUSES OF THE COLLAPSE
4.0
5.0
6.0
7.0
LoadFactor
Model 0
Model 1
Model 2
Model 3
Model 4
Model 1 Model 3Model 2
Model 0
GNL+ MNL+ Imperf.+ unilat.restr.
GNL+ MNL+ Imperfection
GNL+ MNL
GNL
GNL+ MNL+ Imperf.+ Hinges
FINITE ELEMENT ANALYSIS RESULTS (Nonlinear)
22/27
chiara.crosti@uniroma1.it
0.0
1.0
2.0
3.0
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40
LoadFactor
Dx (m)
Model 5
Model 4
Model 5
GNL+ MNL+ Imperf.+ Hinges +
no outriggers

25. INVESTIGATION ON TECHINAL CAUSES OF THE COLLAPSE
4.0
5.0
6.0
7.0
LoadFactor
Model 0
Model 1
Model 2
Model 3
Model 4
Model 1 Model 3Model 2
Model 0
GNL+ MNL+ Imperf.+ unilat.restr.
GNL+ MNL+ Imperfection
GNL+ MNL
GNL
GNL+ MNL+ Imperf.+ Hinges
FINITE ELEMENT ANALYSIS RESULTS (Nonlinear)
23/27
chiara.crosti@uniroma1.it
0.0
1.0
2.0
3.0
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40
LoadFactor
Dx (m)
Model 5
Model 4
Model 5
GNL+ MNL+ Imperf.+ Hinges +
no outriggers
Load Factor 23%
smaller
Initial
displacement
50% bigger

26. Model 3, ULF= 4.019 Model 4, ULF= 1.122 Model 5, ULF= 0.853Model 2, ULF= 3.946
24/27 INVESTIGATION ON TECHINAL CAUSES OF THE COLLAPSE
chiara.crosti@uniroma1.it

27. CONCLUSION
Inadequate site
SWISS CHEESE MODEL (Reason, 1997)
Management &
Administration
Design Built-up Load-in
COLLAPSECOLLAPSE
Failure to adopt Improper construction
25/27
Inadequate site
investigation
123
4
5
6
7
8
NO HORIZONTAL LOADS
NO BRACING MEMBERS
Failure to adopt
Building Codes
Improper construction
procedure
COLLAPSECOLLAPSE
chiara.crosti@uniroma1.it

28. Inadequate site
SWISS CHEESE MODEL (Reason, 1997)
Management &
Administration
Design Built-up Load-in
COLLAPSECOLLAPSE
Failure to adopt Improper construction
CONCLUSION26/27
Inadequate site
investigation
NO HORIZONTAL LOADS
NO BRACING MEMBERS
Failure to adopt
Building Codes
Improper construction
procedure
COLLAPSECOLLAPSE
chiara.crosti@uniroma1.it

30. Model 1, ULF= 4.00
Model 2. ULF= 3.97
INVESTIGATION ON TECHINAL CAUSES OF THE COLLAPSE
Model 3, ULF= 4.16
chiara.crosti@uniroma1.it

31. 1 kN
Rigid
Rigid
A
1 kN
Hinged
Columns going through the space roof Column not going through the space roof
1 kN
Rigid
Rigid
A
1 kN
Hinged
Node 42Node 42
INVESTIGATION ON TECHINAL CAUSES OF THE COLLAPSE
A
3/22
Rigid
B
1 kN
Rigid
Hinged
C
Rigid
B
1 kN
Rigid
Hinged
C
B
C
chiara.crosti@uniroma1.it

32. RIGIDHINGEDRIGID
A B C
RIGID RIGID HINGED
16m
INVESTIGATION ON TECHINAL CAUSES OF THE COLLAPSE
A C
λBuckling= 13.57 λBuckling= 2.61
3/22
A B C
RIGIDHINGEDRIGID
RIGID RIGID HINGED
14m
B
λBuckling= 8.26
λ: Linear Buckling Eigenvalue
chiara.crosti@uniroma1.it

33. -2.0E+04
-1.5E+04
-1.0E+04
-5.0E+03
0.0E+00
5.0E+03
-0.1 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 0.1
Load(N)
Compression Tension
INVESTIGATION ON TECHINAL CAUSES OF THE COLLAPSE3/22
-2.5E+04
Displacement (m)
Maximum Compressive Strength = 2100 Kg
Mechanical properties for the “cut-off bar”
chiara.crosti@uniroma1.it

34. INVESTIGATION ON TECHINAL CAUSES OF THE COLLAPSE
FINITE ELEMENT ANALYSIS RESULTS (Nonlinear)
4.0
5.0
6.0
7.0
LoadFactor
Model 0
Model 1 Model 3Model 2
Node where the Dx is measured
3/22
0.0
1.0
2.0
3.0
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40
LoadFactor
Dx (m)
Model 0
Model 1
Model 2
Model 3 GNL+ MNL+ Imperfection+ unilateral restraint
GNL+ MNL+ Imperfection
GNL+ MNL
GNL
C2B2A2
chiara.crosti@uniroma1.it

35. Bending moment 1 trend of element 3001 (column C2)
3/22
chiara.crosti@uniroma1.it

36. 4.0
5.0
6.0
7.0
LoadFactor
Model 3
Load Factor = 4.019
INVESTIGATION ON TECHINAL CAUSES OF THE COLLAPSE20/27
0.0
1.0
2.0
3.0
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40
LoadFactor
Dx (m)
Load Factor = 0
Load Factor = 2
Load Factor = 3.5
chiara.crosti@uniroma1.it