CAPE TOWN, SOUTH AFRICA, 2-4 SEPTEMBER 2013
BACK ANALYSIS OF THE COLLAPSE OF ABACK ANALYSIS OF THE COLLAPSE OF A
METAL TRU...
Radiohead’s concert, 2012
Image taken from:
http://abcnews.go.com/Entertainment/stage-collapses-
radiohead-concert
Country...
CASE STUDY:
AIM OF THIS WORK:
The aim of this work was not to define who made the mistake, but:
a. to investigate which ki...
A temporary structure can be defined as a structure that can be readily and completely
dismantled and removed from the sit...
A temporary structure can be defined as a structure that can be readily and completely
dismantled and removed from the sit...
SWISS CHEESE MODEL (Reason, 1997)
FORENSIC ASPECTS5/27
chiara.crosti@uniroma1.it
Management &
Administration
SWISS CHEESE MODEL (Reason, 1997)
FORENSIC ASPECTS
Built-up Load-inDesign
6/27
Administration
...
Management &
Administration
COLLAPSECOLLAPSE
SWISS CHEESE MODEL (Reason, 1997)
FORENSIC ASPECTS
Built-up Load-inDesign
7/2...
BUILD-UP PHASE (CASE STUDY)
Positioning on the ground
of the load distribution
plates
Positioning of the bases of
the colu...
INVESTIGATION ON TECHINAL CAUSES OF THE COLLAPSE
BUILD-UP PHASE (CASE STUDY)
9/27
chiara.crosti@uniroma1.it
INVESTIGATION ON TECHINAL CAUSES OF THE COLLAPSE
BUILD-UP PHASE (CASE STUDY)
10/27
chiara.crosti@uniroma1.it
COLLAPSE
INVESTIGATION ON TECHINAL CAUSES OF THE COLLAPSE
BUILD-UP PHASE (CASE STUDY)
11/27
COLLAPSE
chiara.crosti@uniroma...
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...
EUROCODE
φ 0.005
This structure is designed to be indoor; therefore the structural elements were
designed to carry vertica...
Top of the column
Rigid or Hinged
IMPROPER CONSTRUCTION PROCEDURE
INVESTIGATION ON TECHINAL CAUSES OF THE COLLAPSE14/27
Bo...
INVESTIGATION ON TECHINAL CAUSES OF THE COLLAPSE
RIGID
15/27
IMPROPER CONSTRUCTION PROCEDURE
chiara.crosti@uniroma1.it
HIN...
INVESTIGATION ON TECHINAL CAUSES OF THE COLLAPSE
RIGID
Beam Element
16/27
IMPROPER CONSTRUCTION PROCEDURE
chiara.crosti@un...
INVESTIGATION ON TECHINAL CAUSES OF THE COLLAPSE
RIGID
5
7
Beam Element
HingedTranslation
Stiffness
IMPROPER CONSTRUCTION ...
RIGID
Beam Element
Hinged
18/27 INVESTIGATION ON TECHINAL CAUSES OF THE COLLAPSE
IMPROPER CONSTRUCTION PROCEDURE
chiara.cr...
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 ...
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 3...
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 ...
INVESTIGATION ON TECHINAL CAUSES OF THE COLLAPSE3/22
chiara.crosti@uniroma1.it
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 ...
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 ...
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 T...
CONCLUSION
Inadequate site
SWISS CHEESE MODEL (Reason, 1997)
Management &
Administration
Design Built-up Load-in
COLLAPSEC...
Inadequate site
SWISS CHEESE MODEL (Reason, 1997)
Management &
Administration
Design Built-up Load-in
COLLAPSECOLLAPSE
Fai...
Model 1, ULF= 4.00
Model 2. ULF= 3.97
INVESTIGATION ON TECHINAL CAUSES OF THE COLLAPSE
Model 3, ULF= 4.16
chiara.crosti@un...
1 kN
Rigid
Rigid
A
1 kN
Hinged
Columns going through the space roof Column not going through the space roof
1 kN
Rigid
Rig...
RIGIDHINGEDRIGID
A B C
RIGID RIGID HINGED
16m
INVESTIGATION ON TECHINAL CAUSES OF THE COLLAPSE
A C
λBuckling= 13.57 λBuckl...
-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)
Compres...
INVESTIGATION ON TECHINAL CAUSES OF THE COLLAPSE
FINITE ELEMENT ANALYSIS RESULTS (Nonlinear)
4.0
5.0
6.0
7.0
LoadFactor
Mo...
Bending moment 1 trend of element 3001 (column C2)
3/22
chiara.crosti@uniroma1.it
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...
BACK ANALYSIS OF THE COLLAPSE OF A METAL TRUSS STRUCTURE_SEMC2013
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BACK ANALYSIS OF THE COLLAPSE OF A METAL TRUSS STRUCTURE_SEMC2013

  1. 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. 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. 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. 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. 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. 6. SWISS CHEESE MODEL (Reason, 1997) FORENSIC ASPECTS5/27 chiara.crosti@uniroma1.it
  7. 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. 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. 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. 10. INVESTIGATION ON TECHINAL CAUSES OF THE COLLAPSE BUILD-UP PHASE (CASE STUDY) 9/27 chiara.crosti@uniroma1.it
  11. 11. INVESTIGATION ON TECHINAL CAUSES OF THE COLLAPSE BUILD-UP PHASE (CASE STUDY) 10/27 chiara.crosti@uniroma1.it
  12. 12. COLLAPSE INVESTIGATION ON TECHINAL CAUSES OF THE COLLAPSE BUILD-UP PHASE (CASE STUDY) 11/27 COLLAPSE chiara.crosti@uniroma1.it
  13. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 23. INVESTIGATION ON TECHINAL CAUSES OF THE COLLAPSE3/22 chiara.crosti@uniroma1.it
  24. 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. 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. 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. 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. 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
  29. 29. 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
  30. 30. 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
  31. 31. 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
  32. 32. -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
  33. 33. 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
  34. 34. Bending moment 1 trend of element 3001 (column C2) 3/22 chiara.crosti@uniroma1.it
  35. 35. 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

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