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Back-analysis of the collapse of a metal truss structure
Back-analysis of the collapse of a metal truss structure
Back-analysis of the collapse of a metal truss structure
Back-analysis of the collapse of a metal truss structure
Back-analysis of the collapse of a metal truss structure
Back-analysis of the collapse of a metal truss structure
Back-analysis of the collapse of a metal truss structure
Back-analysis of the collapse of a metal truss structure
Back-analysis of the collapse of a metal truss structure
Back-analysis of the collapse of a metal truss structure
Back-analysis of the collapse of a metal truss structure
Back-analysis of the collapse of a metal truss structure
Back-analysis of the collapse of a metal truss structure
Back-analysis of the collapse of a metal truss structure
Back-analysis of the collapse of a metal truss structure
Back-analysis of the collapse of a metal truss structure
Back-analysis of the collapse of a metal truss structure
Back-analysis of the collapse of a metal truss structure
Back-analysis of the collapse of a metal truss structure
Back-analysis of the collapse of a metal truss structure
Back-analysis of the collapse of a metal truss structure
Back-analysis of the collapse of a metal truss structure
Back-analysis of the collapse of a metal truss structure
Back-analysis of the collapse of a metal truss structure
Back-analysis of the collapse of a metal truss structure
Back-analysis of the collapse of a metal truss structure
Back-analysis of the collapse of a metal truss structure
Back-analysis of the collapse of a metal truss structure
Back-analysis of the collapse of a metal truss structure
Back-analysis of the collapse of a metal truss structure
Back-analysis of the collapse of a metal truss structure
Back-analysis of the collapse of a metal truss structure
Back-analysis of the collapse of a metal truss structure
Back-analysis of the collapse of a metal truss structure
Back-analysis of the collapse of a metal truss structure
Back-analysis of the collapse of a metal truss structure
Back-analysis of the collapse of a metal truss structure
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Back-analysis of the collapse of a metal truss structure

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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 …

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.

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  • 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
  • 29. 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
  • 30. 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
  • 31. 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
  • 32. 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
  • 33. 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
  • 34. 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
  • 35. Bending moment 1 trend of element 3001 (column C2) chiara.crosti@uniroma1.it 3/22
  • 36. 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

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