1. PITTSBURGH, PENNSYLVANIA, MAY 2-4 2013
COLLAPSE ANALYSIS OFA
METAL TRUSS STRUCTURE
Chiara Crosti, Franco Bontempi
“Sapienza” University of Roma,
chiara.crosti@uniroma1.it, franco.bontempi@uniroma1.it

2. chiara.crosti@uniroma1.it
2/22
Radiohead’s concert, 2012
Image taken from:
http://abcnews.go.com/Entertainment/stage-collapses-
radiohead-concert
killing/story?id=16587415#.UGrriE3A9_c
Country music concert, 2011
Image taken from:
http://www.billboard.com/news/
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
FORENSIC ASPECTS

3. http://www.udine20.it/wp-content/uploads/2012/03/palco-laura-pausini.jpg
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.
chiara.crosti@uniroma1.it
3/22 FORENSIC ASPECTS

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)
chiara.crosti@uniroma1.it
4/22 FORENSIC ASPECTS

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.
Management &
Administration
Design Built-up Load-in
EVENT
Load-out Break-down
TEMPORARY DEMOUNTABLE STRUCTURES (TDM)
chiara.crosti@uniroma1.it
4/22 FORENSIC ASPECTS

6. SWISS CHEESE MODEL (Reason, 1997)
FORENSIC ASPECTS
chiara.crosti@uniroma1.it
5/22

7. Management &
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
………..
SWISS CHEESE MODEL (Reason, 1997)
FORENSIC ASPECTS
chiara.crosti@uniroma1.it
6/22
Built-up Load-inDesign

8. Management &
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
………..
COLLAPSE
SWISS CHEESE MODEL (Reason, 1997)
FORENSIC ASPECTS
chiara.crosti@uniroma1.it
6/22
Built-up Load-inDesign

9. BUILD-UP PHASES (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
secondary beams
Lifting the columns of the
roof structure and
anchoring the top of the
columns to the roof
Assembling of the hung
beams and other
components of the stage
(lighting, video, etc.)
Rigging phase Delivery of the structure
for its use
Technical-administrative
testing
COLLAPSE
INVESTIGATION ON TECHINAL CAUSES OF THE COLLAPSE
chiara.crosti@uniroma1.it
7/22

10. INVESTIGATION ON TECHINAL CAUSES OF THE COLLAPSE
chiara.crosti@uniroma1.it
8/22
BUILD-UP PHASES (CASE STUDY)

11. INVESTIGATION ON TECHINAL CAUSES OF THE COLLAPSE
chiara.crosti@uniroma1.it
8/22
BUILD-UP PHASES (CASE STUDY)

12. COLLAPSE
INVESTIGATION ON TECHINAL CAUSES OF THE COLLAPSE
chiara.crosti@uniroma1.it
8/22
BUILD-UP PHASES (CASE STUDY)

13. 15/22
FINITE ELEMENT MODEL
INVESTIGATION ON TECHINAL CAUSES OF THE COLLAPSE
chiara.crosti@uniroma1.it
9/22
ton
A
B
C
1 2
16m
21.8m
33 m
a
b
c de
f
g hi
l m
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

14. EUROCODE
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
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 COLLAPSE
chiara.crosti@uniroma1.it
NO HORIZONTAL LOADS
NO BRACING MEMBERS
10/22

15. Top of the column
Bottom of the column
Rigid or Hinged
Rigid or Hinged
IMPROPER CONSTRUCTION PROCEDURE
INVESTIGATION ON TECHINAL CAUSES OF THE COLLAPSE
chiara.crosti@uniroma1.it
11/22

16. chiara.crosti@uniroma1.it
1 kN
Rigid
Rigid
A
1 kN
Hinged
Rigid
B
1 kN
Rigid
Hinged
C
Columns going through the space roof Column not going through the space roof
1 kN
Rigid
Rigid
A
1 kN
Hinged
Rigid
B
1 kN
Rigid
Hinged
C
Node 42Node 42
INVESTIGATION ON TECHINAL CAUSES OF THE COLLAPSE
A
B
C
12/22

17. RIGIDHINGEDRIGID
A
A
B
B
C
C
RIGID RIGID HINGED
RIGIDHINGEDRIGID
RIGID RIGID HINGED
16m14m
INVESTIGATION ON TECHINAL CAUSES OF THE COLLAPSE
A
B
C
λBuckling= 13.57
λBuckling= 8.26
λBuckling= 2.61
λ: Linear Buckling Eigenvalue
chiara.crosti@uniroma1.it
13/22

18. 0
3
6
9
12
-1,0 -0,8 -0,6 -0,4 -0,2 0,0
LoadFactor(verticalloads)
Horizontal Displacement node 42 (m)
RIGID
HINGED
B C
RIGID
RIGID
A
RIGID
HINGED
B
A
B
C
ULF=11.3 ULF=7.86 ULF=1.53
INVESTIGATION ON TECHINAL CAUSES OF THE COLLAPSE
FINITE ELEMENT ANALYSIS RESULTS (Nonlinear)
chiara.crosti@uniroma1.it
14/22

19. Cut-off bar,
No tension element
Translation Stiffness
BeamRigid
link
Column
Hinge
Rigid
Unilateral
INVESTIGATION ON TECHINAL CAUSES OF THE COLLAPSE
FINITE ELEMENT ANALYSIS RESULTS (Nonlinear)
chiara.crosti@uniroma1.it
15/22

20. -2,5E+04
-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)
Displacement (m)
Compression Tension
Maximum Compressive Strength = 2100 Kg
Mechanical properties for the “cut-off bar”
chiara.crosti@uniroma1.it
16/22 INVESTIGATION ON TECHINAL CAUSES OF THE COLLAPSE

21. 0
2
4
6
8
10
12
-0,40 -0,35 -0,30 -0,25 -0,20 -0,15 -0,10 -0,05 0,00
LoadFactor(verticalloads)
Horizontal Displacement node 42 (m)
A
D
Decreasing of 63 %
123
4
5
6
7
8
INVESTIGATION ON TECHINAL CAUSES OF THE COLLAPSE
FINITE ELEMENT ANALYSIS RESULTS (Nonlinear)
chiara.crosti@uniroma1.it
17/22
Case D: Column C2

22. 123
4
5
6
7
8
Compression Tension
INVESTIGATION ON TECHINAL CAUSES OF THE COLLAPSE
FINITE ELEMENT ANALYSIS RESULTS (Nonlinear)
chiara.crosti@uniroma1.it
18/22
5
6
3
4
8
7

23. 123
4
5
6
7
8
INVESTIGATION ON TECHINAL CAUSES OF THE COLLAPSE
FINITE ELEMENT ANALYSIS RESULTS (Nonlinear)
chiara.crosti@uniroma1.it
19/22

24. INVESTIGATION ON TECHINAL CAUSES OF THE COLLAPSE
chiara.crosti@uniroma1.it
20/22

25. INVESTIGATION ON TECHINAL CAUSES OF THE COLLAPSE
chiara.crosti@uniroma1.it
21/22

26. CONCLUSION
chiara.crosti@uniroma1.it
Inadequate site
investigation
SWISS CHEESE MODEL (Reason, 1997)
Management &
Administration
Design Built-up Load-in
COLLAPSE
123
4
5
6
7
8
NO HORIZONTAL LOADS
NO BRACING MEMBERS
Failure to adopt
Building Codes
Improper construction
procedure
COLLAPSE
22/22

27. Inadequate site
investigation
SWISS CHEESE MODEL (Reason, 1997)
chiara.crosti@uniroma1.it
Management &
Administration
Design Built-up Load-in
COLLAPSE
NO HORIZONTAL LOADS
NO BRACING MEMBERS
Failure to adopt
Building Codes
Improper construction
procedure
COLLAPSE
22/22 CONCLUSION