Olmati et al

P. Olmati, F. Brando, K. Gkoumas francobontempi.org/persone

Robustness assessment of a steel truss bridge

P. Olmati & K. GkoumasSapienza University of Rome

[email protected]

[email protected]

F. BrandoThornton Tomasetti, New York

[email protected]

Progressive Collapse and Structural Robustness: An International Perspective

Clay J. Naito, Ph.D., P.E., Associate Professor and Associate ChairKonstantinos Gkoumas, Ph.D., P.E., Associate Researcher

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Introduction1

Consequence factor2

Application3

Conclusions4

Outline


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1

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Introduction1

Consequence factor2

Application3

Conclusions4

Outline


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Structural Robustness

Structural

requirements

Mechanical

properties

Service

properties

Durability

properties

Dependability

Load bearing capacity

Stability

Ductility

Stiffness

Efficient use

Comfort

Appearance

Not degradation of both

mechanical and service

properties

Reliability

Robustness

Maintainability

Prompt response

Introduction


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Structural

requirements

Mechanical

properties

Service

properties

Durability

properties

Dependability

Load bearing capacity

Stability

Ductility

Stiffness

Efficient use

Comfort

Appearance

Not degradation of both

mechanical and service

properties

Reliability

Robustness

Maintainability

Prompt response

Introduction


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6


Definitions:

1- "The ability of a structure to withstand events like fire, explosions, impact

or the consequences of human error without being damaged to an extent

disproportionate to the original cause." (EN 1991-1-7 2006)

2- "The robustness of a structure, intended as its ability not to suffer

disproportionate damages as a result of limited initial failure, is an intrinsic

requirement, inherent to the structural system organization." (Bontempi

F, Giuliani L, Gkoumas K, 2007)

3- “Robustness is defined as insensitivity to local failure." (Starossek

U, 2009)

References:

(EN 1991-1-7 2006): "Eurocode 1 – Actions on structures, Part 1-7: General actions – accidental actions."

Comité European de Normalization (CEN).

(Bontempi F, Giuliani L, Gkoumas K, 2007): "Handling the exceptions: robustness assessment of a complex

structural system." Structural Engineering, Mechanics and Computation (SEMC) 3, 1747-1752.

(Starossek U, 2009): “Progressive collapse of structures.” London: Thomas Telford Publishing, 2009.

Introduction


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Definitions:






requirement, inherent to the structural system organization." (Bontempi F,

Giuliani L, Gkoumas K, 2007)

3- “Robustness is defined as insensitivity to local failure." (Starossek U,

2009)

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References:






Introduction


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2

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References:






8


Definitions:






requirement, inherent to the structural system organization." (Bontempi

F, Giuliani L, Gkoumas K, 2007)

3- “Robustness is defined as insensitivity to local failure." (Starossek

U, 2009)

B

A Withstand actions

Withstand damages

Progressive Collapse and Structural Robustness

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Interstate 90 Grand River bridge, Ohio – October, 1996

Cause Damage Pr. Collapse

Introduction9


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Features:- Deck Warren Truss type bridge built in

1960, 869 feet (265 m) in length and 150 feet

(46 m) in height.

The event:- On May 24, 1996, a gusset plate failed on the

eastbound span.

- The bridge was closed later that day and the

traffic diverted.

- The cause originally was attributed to an

overloaded semi-trailer truck.

I-35W Bridge, MN – August 1st, 2007

Introduction10


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Postcollapse overhead photos of the bridge, view looking east

North

Downtown

North Downtown

D-1

Cause Damage Pr. Collapse

Features:- Continuous Steel Deck Truss Bridge over four

piers

- State of the art bridge when built in 1964.

- High Strength steel which allowed for thin

gusset plates.

- Truss members consisted of welded box built

up section with perforations.

- Geared roller bearings.

The event:- At 6:06 pm on August 1st, 2007, the bridge

suddenly collapsed,

- 13 people died and more than 150 were injured.

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Introduction


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Structural

Robustness

Progressive

Collapse

System structural failure System structural property

Factors that affect the Structural Robustness:

1- Redundancy (Geometry – Construction Details)

2- Ductility (Material)

3- Contingency Scenario (Degradation, Existing Damage States)

12


Assessment Methods:

A relevant issue related to the structural robustness evaluation, is the choice

of appropriate synthetic parameters describing for example the sensitivity of a

damaged structure in suffering a disproportionate collapse.

In literature there are differences in the approaches and indexes towards the

structural robustness quantification.

Introduction

Approach Indexes

- property of the structure or

property of the structure and

the environment

- static or dynamic

- linear or non-linear

- deterministic or probabilistic

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STRUCTURAL DESIGN

PRIMARY SECONDARY TERTIARY

LO

AD

S

DEAD X

LIVE X

SNOW X

EARTHQUAKE X

FIRE X X

EXPLOSIONS X X

“BLACK SWAN” X

Member-basedstructural design

Consequence-basedstructural design

Black Swan event:

- unpredictable,

- large impact on community,

- easy to predict after its occurrence.

13 Introduction

References:

Nafday, AM. (2011) Consequence-based

structural design approach for black swan events.

Structural Safety, 33(1): 108-114.


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Introduction1

Consequence factor2

Application3

Conclusions4

Outline


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Undamaged

Damaged

CfscenarioConsequence factor

Consequence factor

scenario


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2

3

4

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Structural Robustness assessment

Stiffness matrix

Kun λiun

Eigenvalues

Kdam λidam

Consequence factor

Consequence factor

Robustness indexRscenario= 100 - Cfscenario

N1i

un

i

dam

i

un

iscenario

f 100)(

maxC


1

2

3

4

17 Consequence factor

Structural Robustness assessment

ka

kb

x

y

N: total eigenvalues number

i: single eigenvalue number

a and b: elements

a

b

N1i

un

i

dam

i

un

iscenario

f 100)(

maxC

Scenario 1


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Introduction1

Consequence factor2

Application3

Conclusions4

Outline


I-35 West Bridge, Minneapolis, MN

• Built 1967

• 3 spans, 1067 feet long

• 1977 – new wearing surface

• 1998 – curbs and railings

replaced

19 Case Study



20 Case Study


• At 6:05 pm on

August 1st 2007

Bridge Collapsed

• 13 People killed &

approximately 145

Injured

Photo from aircraft flying overhead.


North

Downtown

North Downtown

D-1


21 Case Study


• At 6:05 pm on

August 1st 2007

Bridge Collapsed

• 13 People killed &

approximately 145

Injured

Photo from aircraft flying overhead.


North

Downtown

North Downtown

D-1

Security Camera video

22 Analysis Procedure


N

FIMForensic Investigation Modeling

Thornton Tomasetti was engaged to perform investigation into the causes the collapse by Robins, Kaplan Miller

&Ciresi, a national law firm with offices in Minneapolis, Minnesota. Firm partners recruited and oversaw a

consortium of 17 law firms that agreed to provide pro bono legal services to the survivors of the collapse.

Pier 7

Pier 6

23 Collapse Initiation Area


Failure Initiation

North of Pier 6

N

U10-E

U10-W

L9

L11

Pier 7

Pier 6

24 Collapse Initiation Area


N

U10-E

U10-W

L9

L11

L11

L9

U10

Failure Initiation

North of Pier 6

Weight

Temp. & Const.

Weight

Temp. & Const.

The upper gusset plate is half as thick as it should

be.

Construction loads increase forces by 3%

Forces due to weight of bridge and traffic

Additional forces due to temperature

(corroded bearings) and construction load

25


L11

L9

L11

L9

L11

L9

U10

• Forces due to weight of bridge and traffic

• Additional forces due to temperature


Failure Initiation

North of Pier 6

Collapse Initiation Area

NTSB Theory – U10 Gusset failed in

a “lateral shifting instability”

Gusset hinges, tears at top and buckles at bottom

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L11L9

L11

L9

L11

L9

U10

Lower chord fails in buckling




• Lower chord fails in buckling

• Gusset hinges, tears at top and buckles at bottom

Failure Initiation

North of Pier 6


Gusset plate hinging

BUCKLED

TORN

Rivet hole elongation

U

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L11

L9

U10




• Lower chord fails in buckling

• Gusset hinges, tears at top and buckles at bottom

• Rivet hole elongation

Failure Initiation

North of Pier 6


Structural Robustness assessment – Damage based method

28 Application


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Pier 7

Pier 6

L11

L9

U10

NTSB 2007

29

Single damage

d1d2d3

d4

d5d7

d6

37

59

42 4535 38

23

63

41

58 5565 62

77

0

20

40

60

80

100

1 2 3 4 5 6 7

Robust

nes

s %

ScenarioCf max Robustness

37

59

42 4535 38

23

63

41

58 5565 62

77

0

20

40

60

80

100

1 2 3 4 5 6 7

Ro

bu

stn

ess

%


83 87 88

5360

86

64

17 13 12

4740

14

36

0

20

40

60

80

100

1 2 3 4 5 6 7

Ro

bu

stn

ess

%


Damage scenario Damage scenariod1 d2 d3 d4 d5 d6 d7 d1 d2 d3 d4 d5 d6 d7

Application

DSj = di


1

2

3

4

Pier 6Pier 7

North

Pier 6

30

d1d2d3

d4

d5d7

d6

Single damage

37

59

42 4535 38

23

63

41

58 5565 62

77

0

20

40

60

80

100

1 2 3 4 5 6 7

Ro

bu

stn

ess

%


83 87 88

5360

86

64

17 13 12

4740

14

36

0

20

40

60

80

100

1 2 3 4 5 6 7

Robust

nes

s %



Application

DSj = di


1

2

3

4

Pier 6Pier 7

North

Pier 6

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Introduction1

Consequence factor2

Application3

Conclusions4

Outline


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• The consequence coefficient Cf can be used primarily as an index to

establish the critical structural members for the global structural

stability or to compare different structural design solutions from a

robustness point of view.

• The latter implementation of Cf can be helpful for the robustness

assessment of complex structures since it provides an indication on

the key structural elements.

• The method applied in this study aims at increasing the collapse

resistance of a structure, by focusing on the resistance of the single

structural members, and accounting for their importance to the global

structural behavior consequently to a generic extreme event that can

cause a local damage.


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Conclusions

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Thank you!


Conclusions

d1d2d3

d4

d5d7

37

59

42 4535 38

23

63

41

58 5565 62

77

0

20

40

60

80

100

1 2 3 4 5 6 7

Ro

bu

stn

ess

%


37

59

42 4535 38

23

63

41

58 5565 62

77

0

20

40

60

80

100

1 2 3 4 5 6 7

Robust

nes

s %


83 87 88

5360

86

64

17 13 12

4740

14

36

0

20

40

60

80

100

1 2 3 4 5 6 7

Ro

bust

nes

s %



Kun λiun

Eigenvalues

Kdam λidam

Consequence factor

Robustness index

Documents

Olmati et al