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

[email protected]@uniroma1.it –– [email protected]@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

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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.

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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

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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

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TIM

ELI

NE

SWISS CHEESE MODEL (Reason, 1997)

FORENSIC ASPECTS

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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

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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

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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

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10/27

COLLAPSE


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11/27

15/22

FINITE ELEMENT MODEL


ton

A

B

C

1 2

16

m

21

.8 m

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

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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

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Top of the column

Bottom of the column

Rigid or Hinged

Rigid or Hinged

IMPROPER CONSTRUCTION PROCEDURE


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RIGID

HINGED

MODEL 5

Hinged

Rigid link

15/27



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RIGID

HINGED

Hinged

Hinged

Beam Element

MODEL 4

16/27



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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


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MODEL 3

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RIGID

RIGID

MODEL 0,1,2

Beam Element

Hinged Hinged

Hinged

HingedHinged

Hinged

18/27 INVESTIGATION ON TECHNICAL CAUSES OF THE COLLAPSE



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Model 1 Model 2

Model 0

GNL+ MNL+ Imperfection

GNL+ MNL

GNL

FINITE ELEMENT ANALYSIS RESULTS (Nonlinear)

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Model 1 Model 3Model 2

Model 0

GNL+ MNL+ Imperf.+ unilat.restr.


GNL+ MNL

GNL


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Model 3

Load Factor = 0

Load Factor = 2

Load Factor = 3.5

Load Factor = 4.019

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INVESTIGATION ON TECHNICAL CAUSES OF THE COLLAPSE20/27

Dz = 11mm

Dz = 15mm

Load Factor = 4.019

MODEL 2

Dz = 7 mm


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Model 0

Model 4

Model 5



GNL+ MNL

GNL

GNL+ MNL+ Imperf.+ Hinges

GNL+ MNL+ Imperf.+ Hinges +

no outriggers


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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

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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 &

AdministrationDesign Built-up Load-in

COLLAPSECOLLAPSE

123

4

5

67

8

NO HORIZONTAL LOADS

NO BRACING MEMBERS

Failure to adopt

Building Codes


procedure

COLLAPSECOLLAPSE

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25/27

Inadequate site

investigation


Management &

AdministrationDesign Built-up Load-in

COLLAPSECOLLAPSE

NO HORIZONTAL LOADS

NO BRACING MEMBERS

Failure to adopt

Building Codes


procedure

COLLAPSECOLLAPSE

CONCLUSION

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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) – [email protected]

Stro N

GERwww.stronger2012.com

Model 1, ULF= 4.00

Model 2. ULF= 3.97

Model 3, ULF= 4.16

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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

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RIGIDHINGEDRIGID

A

A

B

B

C

C

RIGID RIGID HINGED

RIGIDHINGEDRIGID

RIGID RIGID HINGED

16 m

14 m


A

B

C

λBuckling= 13.57

λBuckling= 8.26

λBuckling= 2.61

λ: Linear Buckling Eigenvalue

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Compression Tension

Maximum Compressive Strength = 2100 Kg

Mechanical properties for the “cut-off bar”


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GNL+ MNL+ Imperfection+ unilateral restraint


GNL+ MNL

GNL

Node where the Dx is measured

C2B2A2

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Bending moment 1 trend of element 3001 (column C2)

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Load Factor = 0

Load Factor = 2

Load Factor = 3.5

Load Factor = 4.019

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INVESTIGATION ON TECHNICAL CAUSES OF THE COLLAPSE20/27