Back-analysis of the collapse of a metal truss structure

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

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

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.
2/27 FORENSIC ASPECTS

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
3/27

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
4/27
TIMELINE

SWISS CHEESE MODEL (Reason, 1997)
FORENSIC ASPECTS
5/27

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
………..
FORENSIC ASPECTS
Built-up Load-inDesign
6/27

Management &
Administration
Inadequate site
investigation
Inappropriate
ground condition
Inadequate safety
plan
………..
Inadequate
structural design
Failure to adopt
Building Codes
Inadequate loads
estimation
……..
procedure
Improper working position
Breach of regulation or code of
practice
………..
COLLAPSECOLLAPSE
FORENSIC ASPECTS
Built-up Load-inDesign
7/27

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
8/27

9/27

10/27

COLLAPSE
11/27

15/22
FINITE ELEMENT MODEL
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
12/27

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
NO HORIZONTAL LOADS
NO BRACING MEMBERS
13/27

Top of the column
Bottom of the column
Rigid or Hinged
Rigid or Hinged
IMPROPER CONSTRUCTION PROCEDURE
14/27

RIGID
HINGED
MODEL 5
Hinged
Rigid link
15/27

RIGID
HINGED
Hinged
Hinged
Beam Element
MODEL 4
16/27

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
17/27
MODEL 3

RIGID
RIGID
MODEL 0,1,2
Beam Element
Hinged Hinged
Hinged
Hinged
Hinged
Hinged
18/27 INVESTIGATION ON TECHNICAL CAUSES OF THE COLLAPSE

Model 1 Model 2
Model 0
GNL+ MNL+ Imperfection
GNL+ MNL
GNL
FINITE ELEMENT ANALYSIS RESULTS (Nonlinear)
19/27

Model 1 Model 3Model 2
Model 0
GNL+ MNL+ Imperf.+ unilat.restr.
GNL+ MNL
GNL
19/27
Model 3

Load Factor = 0
Load Factor = 2
Load Factor = 3.5
Load Factor = 4.019
INVESTIGATION ON TECHNICAL CAUSES OF THE COLLAPSE20/27
Dz = 11mm
Dz = 15mm
Load Factor = 4.019
MODEL 2
Dz = 7 mm

3/22

Model 0
Model 4
Model 5
GNL+ MNL
GNL
GNL+ MNL+ Imperf.+ Hinges
GNL+ MNL+ Imperf.+ Hinges +
no outriggers
22/27

Model 0
Model 4
Model 5
GNL+ MNL
GNL
GNL+ MNL+ Imperf.+ Hinges
GNL+ MNL+ Imperf.+ Hinges +
no outriggers
Load Factor
23% smaller
Initial
displacement
50% bigger
23/27

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

CONCLUSION
Inadequate site
investigation
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
procedure
COLLAPSECOLLAPSE
25/27

Inadequate site
investigation
Management &
Administration
Design Built-up Load-in
COLLAPSECOLLAPSE
NO HORIZONTAL LOADS
NO BRACING MEMBERS
Failure to adopt
Building Codes
procedure
COLLAPSECOLLAPSE
CONCLUSION
26/27

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

Model 1, ULF= 4.00
Model 2. ULF= 3.97
Model 3, ULF= 4.16

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
A
B
C
3/22

RIGIDHINGEDRIGID
A
A
B
B
C
C
RIGID RIGID HINGED
RIGIDHINGEDRIGID
RIGID RIGID HINGED
16m14m
A
B
C
λBuckling= 13.57
λBuckling= 8.26
λBuckling= 2.61
λ: Linear Buckling Eigenvalue
3/22

Compression Tension
Maximum Compressive Strength = 2100 Kg
Mechanical properties for the “cut-off bar”
3/22

GNL+ MNL+ Imperfection+ unilateral restraint
GNL+ MNL
GNL
Node where the Dx is measured
C2B2A2
3/22

Bending moment 1 trend of element 3001 (column C2)
3/22

Load Factor = 0
Load Factor = 2
Load Factor = 3.5
Load Factor = 4.019
INVESTIGATION ON TECHNICAL CAUSES OF THE COLLAPSE20/27

Back-analysis of the collapse of a metal truss structure

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Back-analysis of the collapse of a metal truss structure