This paper is organized in two parts. The first one describes a case history of few collapses of metal truss structures designed to be used as entertainment structures for which the structural safety gains therefore much more importance due to the people that can be involved in the collapse. In the second part, a specific case of the collapse of an entertainment structure made by aluminum is taken under study. A back analysis of the collapse of this metal truss structure is developed and produces a flowchart that points out the possible causes that led the structure to the collapse. By means of non linear analyses by Finite Element Model (FEM) the failure sequence of this particular structure is shown and forensic investigation concerning the whole phase of the construction phase is performed, starting from the design one, through the assembling and ending with the rigging phase.

1. CAPE TOWN, SOUTH AFRICA, 2-4 SEPTEMBER 2013
BACK ANALYSIS OF THE COLLAPSE
OF A METAL TRUSS STRUCTURE
Chiara Crosti, Franco Bontempi
““SapienzaSapienza”” University of RomeUniversity of Rome
School of Civil and Industrial EngineeringSchool of Civil and Industrial Engineering
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
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
chiara.crosti@uniroma1.it
1/27

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
2/27 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)
FORENSIC ASPECTS
chiara.crosti@uniroma1.it
3/27

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 ASPECTS
chiara.crosti@uniroma1.it
4/27
TIMELINE

6. SWISS CHEESE MODEL (Reason, 1997)
FORENSIC ASPECTS
chiara.crosti@uniroma1.it
5/27

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
Built-up Load-inDesign
chiara.crosti@uniroma1.it
6/27

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
………..
COLLAPSECOLLAPSE
SWISS CHEESE MODEL (Reason, 1997)
FORENSIC ASPECTS
Built-up Load-inDesign
chiara.crosti@uniroma1.it
7/27

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
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 TECHNICAL CAUSES OF THE COLLAPSE
chiara.crosti@uniroma1.it
8/27

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

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

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

13. 15/22
FINITE ELEMENT MODEL
INVESTIGATION ON TECHNICAL CAUSES OF THE COLLAPSE
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
chiara.crosti@uniroma1.it
12/27

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 TECHNICAL CAUSES OF THE COLLAPSE
NO HORIZONTAL LOADS
NO BRACING MEMBERS
chiara.crosti@uniroma1.it
13/27

15. Top of the column
Bottom of the column
Rigid or Hinged
Rigid or Hinged
IMPROPER CONSTRUCTION PROCEDURE
INVESTIGATION ON TECHNICAL CAUSES OF THE COLLAPSE
chiara.crosti@uniroma1.it
14/27

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

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

18. INVESTIGATION ON TECHNICAL CAUSES OF THE COLLAPSE
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
RIGID
UNILATERAL
1
2
3
4
5
6
7
8
Point contact
Element
L= 0.065 m
Beam Element
Hinged
Hinged
Hinged
Hinged
Hinged
Hinged
Hinged
Hinged
Translation
Stiffness
IMPROPER CONSTRUCTION PROCEDURE
17/27
MODEL 3

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

20. INVESTIGATION ON TECHNICAL CAUSES OF THE COLLAPSE
chiara.crosti@uniroma1.it
Model 1 Model 2
Model 0
GNL+ MNL+ Imperfection
GNL+ MNL
GNL
FINITE ELEMENT ANALYSIS RESULTS (Nonlinear)
19/27

21. INVESTIGATION ON TECHNICAL CAUSES OF THE COLLAPSE
chiara.crosti@uniroma1.it
Model 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

22. Load Factor = 0
Load Factor = 2
Load Factor = 3.5
Load Factor = 4.019
chiara.crosti@uniroma1.it
INVESTIGATION ON TECHNICAL CAUSES OF THE COLLAPSE20/27
Dz = 11mm
Dz = 15mm
Load Factor = 4.019
MODEL 2
Dz = 7 mm

23. INVESTIGATION ON TECHNICAL CAUSES OF THE COLLAPSE
chiara.crosti@uniroma1.it
3/22

24. INVESTIGATION ON TECHNICAL CAUSES OF THE COLLAPSE
chiara.crosti@uniroma1.it
Model 1 Model 3Model 2
Model 0
Model 4
Model 5
GNL+ MNL+ Imperf.+ unilat.restr.
GNL+ MNL+ Imperfection
GNL+ MNL
GNL
GNL+ MNL+ Imperf.+ Hinges
GNL+ MNL+ Imperf.+ Hinges +
no outriggers
FINITE ELEMENT ANALYSIS RESULTS (Nonlinear)
22/27

25. INVESTIGATION ON TECHNICAL CAUSES OF THE COLLAPSE
chiara.crosti@uniroma1.it
Model 1 Model 3Model 2
Model 0
Model 4
Model 5
GNL+ MNL+ Imperf.+ unilat.restr.
GNL+ MNL+ Imperfection
GNL+ MNL
GNL
GNL+ MNL+ Imperf.+ Hinges
GNL+ MNL+ Imperf.+ Hinges +
no outriggers
FINITE ELEMENT ANALYSIS RESULTS (Nonlinear)
Load Factor
23% smaller
Initial
displacement
50% bigger
23/27

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

27. CONCLUSION
Inadequate site
investigation
SWISS CHEESE MODEL (Reason, 1997)
Management &
Administration
Design Built-up Load-in
COLLAPSECOLLAPSE
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
25/27

28. Inadequate site
investigation
SWISS CHEESE MODEL (Reason, 1997)
Management &
Administration
Design Built-up Load-in
COLLAPSECOLLAPSE
NO HORIZONTAL LOADS
NO BRACING MEMBERS
Failure to adopt
Building Codes
Improper construction
procedure
COLLAPSECOLLAPSE
CONCLUSION
chiara.crosti@uniroma1.it
26/27

30. StroNGER S.r.l.
Research Spin-off for Structures of the Next Generation
Energy Harvesting and Resilience
Rome – Athens – Milan – Nice Cote Azur
Sede operativa: Via Giacomo Peroni 442-444, Tecnopolo Tiburtino,
00131 Roma (ITALY) – info@stronger2012.com
Str
o N
GER
www.stronger2012.com

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

32. 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 TECHNICAL CAUSES OF THE COLLAPSE
A
B
C
chiara.crosti@uniroma1.it
3/22

33. RIGIDHINGEDRIGID
A
A
B
B
C
C
RIGID RIGID HINGED
RIGIDHINGEDRIGID
RIGID RIGID HINGED
16m14m
INVESTIGATION ON TECHNICAL CAUSES OF THE COLLAPSE
A
B
C
λBuckling= 13.57
λBuckling= 8.26
λBuckling= 2.61
λ: Linear Buckling Eigenvalue
chiara.crosti@uniroma1.it
3/22

34. Compression Tension
Maximum Compressive Strength = 2100 Kg
Mechanical properties for the “cut-off bar”
INVESTIGATION ON TECHNICAL CAUSES OF THE COLLAPSE
chiara.crosti@uniroma1.it
3/22

35. INVESTIGATION ON TECHNICAL CAUSES OF THE COLLAPSE
FINITE ELEMENT ANALYSIS RESULTS (Nonlinear)
Model 1 Model 3Model 2
GNL+ MNL+ Imperfection+ unilateral restraint
GNL+ MNL+ Imperfection
GNL+ MNL
GNL
Node where the Dx is measured
C2B2A2
chiara.crosti@uniroma1.it
3/22

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

37. Load Factor = 0
Load Factor = 2
Load Factor = 3.5
Load Factor = 4.019
chiara.crosti@uniroma1.it
INVESTIGATION ON TECHNICAL CAUSES OF THE COLLAPSE20/27