structural robustness: concepts and applications

www.francobontempi.org

Structural robustness:

concepts and applications

Konstantinos Gkoumas, Ph.D., P.E.

Docente: Franco Bontempi, Ph.D., P.E.

Facoltà di Ingegneria

Sapienza Università di Roma

CORSO DI COSTRUZIONI METALLICHE

1November 12 2015

http://www.francobontempi.org/

Corso di Costruzioni Metalliche – Prof. Ing. Franco Bontempi Roma, 12 Novembre 2015Konstantinos Gkoumas, PhD, PE

Word cloud


Black

Swan

Vulnerability

Cause

Damage

Index

Robustness

Collapse

resistance

Progressive

collapse

Photo Credit: Wikipedia Commons.

Member

consequence

factor

• Significant collapse cases

• LPHC events and Black Swans

• Structural robustness in qualitative terms

• Structural robustness in civil engineering

design

• Collapse types

• Structural robustness and progressive collapse

definitions

• Measures against progressive collapse

• Quantification of robustness

• Robustness and optimization

• Member consequence factor

• Assessment of simple structures

• Assessment of complex structures

• What now/next?

• References


Black

Swan

Vulnerability

Cause

Damage

Index





design

• Collapse types


definitions







• What now/next?

• References

Robustness

Collapse

resistance

Progressive

collapse


Member

consequence

factor


Ronan Point Tower Block– May 16, 1968

Description:- apartments building;

- built between 1966 and 1968;

- 64 m tall with 22 story;

- walls, floors, and staircases was precast

concrete;

- each floor was supported directly by the walls

in the lower stories, (bearing walls system).

The event:- May 16, 1968 a gas explosion blew out an

outer panel of the 18th floor,

- the loss of the bearing wall causes the

progressive collapse of the upper floors,

- the impact of the upper floors’ debris caused

the progressive collapse of the lower floors.

Cause Damage Pr. Collapse


Description:- apartments building;

- precast concrete wall and floor components

was the structural bearing system;

- ductile detailing and effective ties between

the precast components.


The event:- June 25, 1996 9 tons of

TNTeq detonated in

front of the building;

- the exterior wall was

entirely destroyed;

- collapse did not

progress beyond areas

of first damage.

Khobar Towers Bombing – June 25, 1996


Description:- office facility for the Deutsche Bank in

Manhattan;

- constructed in the early ‘70s in steel-framed

structure moment connected, 130 m tall, 40

story and 2 subterranean levels;

The event:- On September 11, 2011, the WTC towers

debris impact on a building’s façade,

- heavy damage between the 9th and the 23rd

floor, the column was lost from the 9th and

the 18th floor;

- the framing system was able to support

and redistribute the loads.

Deutsche Bank Building – September 11, 2001



Probability of progressive collapse from an abnormal event

P(F) = P(D|H) P(F|DH)P(H) x x

damage is caused in

the structure

damage spreads in

the structureoccurrence of

critical event

occurrence of broad

or global collapse

STRUCTURAL INTEGRITY (ISO/FDS 2394)

COLLAPSE RESISTANCE (Starossek&Wolff 2005)

VULNERABILITY ROBUSTNESSEXPOSURE VULNERABILITY ROBUSTNESSEXPOSURE

Faber (2006)

STRUCTURALNON STRUCTURAL

MEASURES

HAZARD

References: Ellingwood, B.R. and Dusenberry, D.O. (2005), “Building design for abnormal loads and progressive

collapse”, Comput-Aided Civ. Inf., 20(3), 194-205.


Black

Swan

Vulnerability

Cause

Damage

Index





design

• Collapse types


definitions







• What now/next?

• References

Robustness

Collapse

resistance

Progressive

collapse


Member

consequence

factor


Reference: Bontempi, F. (2005) Frameworks for structural analysis, In: Innovation in Civil and Structural

Engineering Topping, BHV ed., pp. 1-24

HPLCHigh Probability –

Low Consequences

LPHCLow Probability –

High Consequences

ComplexityNon linear issues and

interaction mechanisms

Des

ign

ap

pro

ach

:

Sto

chas

tic

Det

erm

inis

tic

QUALITATIVE RISKANALYSIS

PROBABILISTICRISK ANALYSIS

PRAGMATICANALYSIS OF

RISK SCENARIOS

Secondary

design

Primary

design

Low Probability – High Consequences Events


References: Taleb, Nassim Nicholas (April 2007). The Black Swan: The Impact of the Highly Improbable (1st ed.).

London: Penguin. p. 400. ISBN 1-84614045-5.

A Black Swan is an event with the following three attributes.

1. First, it is an outlier, as it lies outside the realm of regular expectations,

because nothing in the past can convincingly point to its possibility.

Rarity -The event is a surprise (to the observer).

2. Second, it carries an extreme 'impact'.

Extreme “impact” - the event has a major effect.

3. Third, in spite of its outlier status, human nature makes us concoct

explanations for its occurrence after the fact, making it explainable and

predictable.

Retrospective (though not prospective) predictability - After the first

recorded instance of the event, it is rationalized by hindsight, as if it could

have been expected; that is, the relevant data were available but

unaccounted for in risk mitigation programs. The same is true for the

personal perception by individuals.

Black Swans


References: Taleb, Nassim Nicholas (April 2007). The Black Swan: The Impact of the Highly Improbable (1st ed.).

London: Penguin. p. 400. ISBN 1-84614045-5.

Strengths of Black Swan Theory – Benefits

• Increased awareness of uncertainty in decision making

• New way to deal with risks and uncertainty

Limitations of Black Swan Theory – Disadvantages

• Black Swan is rather extreme

• Theory is not yet mainstream

Assumptions of Black Swan Theory

• Black Swans cannot be predicted because they are rare

• Overestimation of knowledge/Underestimation of randomness

and uncertainty

• Overestimation of skills/underestimation of luck in life

Black Swans


Black

Swan

Vulnerability

Cause

Damage

Index





design

• Collapse types


definitions







• What now/next?

• References

Robustness

Collapse

resistance

Progressive

collapse


Member

consequence

factor


QUALITY

DAMAGE or ERROR

REQUIRED PERFORMANCE

NOMINAL

PERFORMANCE

NOMINAL SITUATION

Structural Robustness


• Capacity of a construction to exhibit regulardecrease of its structural quality as a consequenceof negative causes.

• It implies:

a) some smoothness of the decrease ofstructural performance due to negativeevents (intensive feature);

b) some limited spatial spread of therupture (extensive feature).



Qualitative definitions of structural robustness

[EN 1991-1-7: 2006 ]: ability of a structure to withstand actions due

to fires, explosions, impacts or consequences

of human errors, without suffering damages

disproportionate to the triggering causes

[SEI 2007,

Beton Kalender 2008]: insensitivity of the structure to local failure

structure B

d

P

s

STRUCTURE B:

P

s

ROBUSTNESS CURVES

P (performance)

structure A

STRUCTURE A

damaged

integer

DP

damaged

more performant, less resistant

integer

(damage level)

DPDP

more performant, less robust less performant, more robust


A B


Black

Swan

Vulnerability

Cause

Damage

Index





design

• Collapse types


definitions







• What now/next?

• References

Robustness

Collapse

resistance

Progressive

collapse


Member

consequence

factor


Com

mo

n U

LS

& S

LS

Ver

ific

ati

on

Fo

rma

t


Assessment

1st level:

Material Point

2nd level:

Element

Section

3rd level:

Structural

Element

4th level:

Structural

System

Structural robustness in design


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.

References:

Nafday, AM. (2011) Consequence-based structural

design approach for black swan events. Structural

Safety, 33(1): 108-114.



Uncertainty in the likelihood that

the harmful consequences of a

particular event will be realized

Uncertainty in the consequences

related to the specific event

Primary

designSecondary

design

Tertiary

design



Black

Swan

Vulnerability

Cause

Damage

Index





design

• Collapse types


definitions







• What now/next?

• References

Robustness

Collapse

resistance

Progressive

collapse


Member

consequence

factor


STRUCTURE

& LOADS

Collapse

Mechanism

NO SWAY

“IMPLOSION”

OF THE

STRUCTURE

“EXPLOSION”

OF THE

STRUCTURE

is a process in which

objects are destroyed by

collapsing on themselves

is a process

NOT CONFINED

SWAY

Bad VS Good collapse


Initial load-bearing element failure that

triggers the rigid fall of a part of the

structure onto another and leads to a

sequential impacts on the rest of the

structure, that collapses on itself.

Characteristic feature is the force

redistribution into alternative paths,

impulsive loading due to sudden element

failure and force concentration in elements

to fail next.

Zipper Domino

Section Instability Mixed

Pancake

Initial cross-section cut and stress

concentration that cause the rupture of

further cross-sectional parts (fast fracture)

and failure progression throughout the

entire section.

Initial element rigid overturning and

falling over another element, that, by

means of transformation of potential into

kinetic energy, trigger the overturning of

the following element.

The destabilization of some load-carrying

elements in compression due to an initial

failure of stabilizing elements can trigger a

failure progression throughout the

structure.

Some collapses are less amenable to

generalization because the relative

importance of the contributing basic

categories of collapse can vary and

combine in progression of failures.

- DOMINO + PANCAKE

(e.g. A.P.Murrah Building, Building

during Izmit Earquake)

- ZIPPER + INSTABILITY

(e.g. cable-stayed bridges)

Reference: Betoncalendar, 2008 (adapted from “Structural integrity: robustness assessment and progressive collapse

susceptibility”, Luisa Giuliani, PhD Thesis, Sapienza University of Rome, Dipartimento di Ingegneria Strutturale e Geotecnica)

Collapse types


Initial load-bearing element failure that

triggers the rigid fall of a part of the

structure onto another and leads to a

sequential impacts on the rest of the

structure, that collapses on itself.

Characteristic feature is the force

redistribution into alternative paths,

impulsive loading due to sudden element

failure and force concentration in elements

to fail next.

Zipper Domino

Section Instability Mixed

Pancake

Initial cross-section cut and stress

concentration that cause the rupture of

further cross-sectional parts (fast fracture)

and failure progression throughout the

entire section.

Initial element rigid overturning and

falling over another element, that, by

means of transformation of potential into

kinetic energy, trigger the overturning of

the following element.

The destabilization of some load-carrying

elements in compression due to an initial

failure of stabilizing elements can trigger a

failure progression throughout the

structure.

Some collapses are less amenable to

generalization because the relative

importance of the contributing basic

categories of collapse can vary and

combine in progression of failures.

- DOMINO + PANCAKE

(e.g. A.P.Murrah Building, Building

during Izmit Earquake)

- ZIPPER + INSTABILITY

(e.g. cable-stayed bridges)

Reference: Betoncalendar, 2008 (adapted from “Structural integrity: robustness assessment and progressive collapse

susceptibility”, Luisa Giuliani, PhD Thesis, Sapienza University of Rome, Dipartimento di Ingegneria Strutturale e Geotecnica)

Collapse types

Islamabad Earthquake 2005

Münsterland, 2005

Viaduct after earthquakeIzmit Earthquake

1999

Tanker S.S. Schenectady, 1941


The Boeing B-17 Flying Fortress collided with another aircraft during World War II and, although

sustaining large amount of structural damage, landed safely, due to the high redundancy of the

fuselage connections.

Design Strategy #1: Continuity (robust behavior-redundancy)


On July 1945 a B-25 bomber crashed into the Empire State Building, The impact of the plane

created a 5.5x6 m hole in the side of the tower. This crash caused extensive damage to the

masonry exterior and the interior steel structure of the building.

The 278 m building was rocked by the impact but resist the impact in consequence of the

intrinsic redundancy of its framed system.

Plane crash on the Empire State Building, 1945

Design Strategy #1: Continuity (robust behavior-redundancy)


Design Strategy #2: Segmentation (Compartmentalization)

A service-induced damage led to explosive decompression and loss of large portion of fuselage

skin when small fatigue crack suddenly linked together. The subsequent fracture was eventually

arrested by fuselage frame structure and the craft landed safely.

Aloha Boeing 737, April 1988

(compartmentalization by strengthening)


Design Strategy #2: Segmentation (Compartmentalization)

The partial collapse, started in the roof and due design and execution errors, stoped at the two joints

which separated the collapsing section from the adjacent structures.

A higher continuity could have unlikely sustained the forces during collapse, since the construction

deficiencies affected also adjacent sections.


Black

Swan

Vulnerability

Cause

Damage

Index





design

• Collapse types


definitions







• What now/next?

• References

Robustness

Collapse

resistance

Progressive

collapse


Member

consequence

factor


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.“, Invited Lecture, Structural Engineering, Mechanics and Computation (SEMC) 3, 1747-1752.

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

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:

(ASCE 7-05 2005): "Minimum design loads for buildings and other structures." American Society of Civil Engineers

(ASCE).

(GSA 2003): "Progressive collapse analysis and design guidelines for new federal office buildings and major

modernization projects." General Services Administration (GSA).

(UFC 4-010-01 2003): "DoD minimum antiterrorism standards for buildings." Department of Defense (DoD).

Progressive Collapse

Definitions:

1-"Progressive collapse is defined as the spread of an initial local failure

from element to element resulting, eventually, in the collapse of an entire

structure or a disproportionate large part of it." (ASCE 7-05 2005)

2- "A progressive collapse is a situation where local failure of a primary

structural component leads to the collapse of adjoining members which, in

turn, leads to additional collapse. Hence, the total collapse is

disproportionate to the original cause." (GSA 2003)

3-"Progressive collapse: a chain reaction failure of building members to an

extent disproportionate to the original localized damage." (UFC 4-010-01

2003)


References:

Arup (2011), Review of international research on structural robustness and disproportionate collapse, London,

Department for Communities and Local Government.

Starossek, U. and Haberland, M. (2010), “Disproportionate Collapse: Terminology and Procedures”, J. Perf. Constr.

Fac., 24(6), 519-528.

Observations:

− A progressive collapse is one which develops in a progressive manner akin to the collapse

of a row of dominos.

− A disproportionate collapse is one which is judged (by some measure defined by the

observer) to be disproportionate to the initial cause. This is merely a judgement made on

observations of the consequences of the damage which results from the initiating events.

− A collapse may be progressive in nature but not necessarily disproportionate in its extents,

for example if arrested after it progresses through a number of structural bays. Vice versa, a

collapse may be disproportionate but not necessarily progressive if, for example, the

collapse is limited in its extents to a single structural bay but the structural bays are large.

− The terms of disproportionate collapse and progressive collapse are often used

interchangeably because disproportionate collapse often occurs in a progressive manner

and progressive collapse can be disproportionate.

Progressive Collapse VS Disproportionate Collapse


Robustness and collapse resistance in a dependability framework

Sgambi, L., Gkoumas, K. and Bontempi, F. (2012), “Genetic

algorithms for the dependability assurance in the design of a long-

span suspension bridge”, Comput-Aided Civ. Inf., 27(9), 655-675.


Black

Swan

Vulnerability

Cause

Damage

Index





design

• Collapse types


definitions







• What now/next?

• References

Robustness

Collapse

resistance

Progressive

collapse


Member

consequence

factor


The currently available design strategies and methods to

prevent disproportionate collapse are as follows:

− Prevent local failure of key elements (direct design)

− Specific local resistance

− Non-structural protective measures

− Presume local failure (direct design)

− Alternative load paths

− Isolation by segmentation

− Prescriptive design rules (indirect design)

Reference:

Starossek, U. 2008. Collapse resistance and robustness of bridges. IABMAS’08: 4th International Conference on

Bridge Maintenance, Safety, and Management Seoul, Korea, July 13-17, 2008

Measures against disproportionate collapse


Reference:

Giuliani, L., 2012. Structural safety in case of extreme actions. International Journal of Lifecycle Performance Engineering

IJLCPE Special Issue on: "Performance and Robustness of Complex Structural Systems", Guest Editor Franco Bontempi, ISSN

(Online): 2043-8656 - ISSN (Print): 2043-8648.

Design strategies against progressive collapse


Black

Swan

Vulnerability

Cause

Damage

Index





design

• Collapse types


definitions







• What now/next?

• References

Robustness

Collapse

resistance

Progressive

collapse


Member

consequence

factor


RISK-BASED[Faber, 2005]

R

Iinddir

dirrob

R

R

direct risk

indirect riskDAMAGE-BASED

n

1i'

i

i

)K(tr

)K(tr.Deg.Stiff

ithelement stiffness matrix

(integer state)damagedelements

ithelement stiffnessmatrix (damaged state)

[Yan&Chang, 2006] [Biondini &Frangopol, 2008]

1

0

energy between intact

and damaged system

(backward pseudo-loads)

energy between intact

and damaged system

(forward pseudo-loads)

Indirect

Risk

Direct

Risk

Indirect

Risk

Direct

Risk

Reference:

Olmati, P., Brando, F., Gkoumas, K. “Robustness assessment of a Steel Truss Bridge”, ASCE/SEI Structures Congress,

Pittsburgh, Pennsylvania, May 2-4, 2013.

B

A Withstand actions, events

Withstand damages

Structural Robustness assessment

TOPOLOGY-BASEDOther:


[Baker et al. 2008]

R

Iinddir

dirrob

R

R

direct risk

indirect risk

Reference:

Baker J.W., Schubert M., Faber M.H., (2008). On the Assessment of Robustness, Journal of Structural Safety, Volume

30, Issue 3, pp. 253-267, DOI:10.1016/j.strusafe.2006.11.004

“A robust system is considered to be one where indirect

risks do not contribute significantly to the total system

risk”

Rdir˃˃Rind

Rdir: related to initial damage

Rind: related to additional damage

EXBD: Exposure before damageഥD : Damage

D : No Damage

F : Probability of system failure

Cdir : Direct consequences

Cind: Indirect consequences

Risk Based Structural Robustness assessment


𝑅𝑑𝑢𝑛𝑑𝑎𝑚𝑎𝑔𝑒𝑑

− 𝐸𝑑𝑢𝑛𝑑𝑎𝑚𝑎𝑔𝑒𝑑

≥ 0member-based design

𝑅 − 𝐸 ≥ 0limit state design

Resistance (probabilistic) Solicitation (probabilistic)

Resistance (design values) Solicitation (design values)

(1 − 𝐶𝑓𝑆𝑐𝑒𝑛𝑎𝑟𝑖𝑜)𝑅𝑑

𝑢𝑛𝑑𝑎𝑚𝑎𝑔𝑒𝑑−𝐸𝑑

𝑢𝑛𝑑𝑎𝑚𝑎𝑔𝑒𝑑≥ 0

Member consequence factor based design

0 ≤ 𝐶𝑓 ≤ 1

• Cf quantifies the influence that a loss of a structural element has on the load carrying capacity.

• Cf provides to the single structural member an additional load carrying capacity, in function of the

nominal design (not extreme) loads that can be used for contrasting unexpected and extreme loads.

• Essentially, if Cf tends to 1, the member is more likely to be important to the structural system;

instead if Cf tends to 0, the member is more likely to be unimportant to the structural system.

Member consequence factor and robustness assessment

0EγγRγγ kEMEk

1

Rd

1

MR

0E)R(*)C1( kEdMEk

1

Rd

1

MRf


• The structure is subjected to a set of damage scenarios and the consequence of the

damages is evaluated by the member consequence factor (𝐶𝑓𝑆𝑐𝑒𝑛𝑎𝑟𝑖𝑜) that for

convenience can be easily expressed in percentage.

• For damage scenario is intended the failure of one or more structural elements.

• Robustness can be expressed as the complement to 100 of 𝐶𝑓𝑆𝑐𝑒𝑛𝑎𝑟𝑖𝑜, intended as the

effective coefficient that affects directly the resistance.

• 𝐶𝑓𝑆𝑐𝑒𝑛𝑎𝑟𝑖𝑜is evaluated by the maximum percentage difference of the structural stiffness

matrix eigenvalues of the damaged and undamaged configurations of the structure.

𝐶𝑓𝑆𝑐𝑒𝑛𝑎𝑟𝑖𝑜 = 𝑚𝑎𝑥

𝜆𝑖𝑢𝑛 − 𝜆𝑖

𝑑𝑎𝑚

𝜆𝑖𝑢𝑛 100

𝑖=1−𝑁

where, 𝜆𝑖𝑢𝑛and 𝜆𝑖

𝑑𝑎𝑚are respectively the i-th eigenvalue of the structural stiffness

matrix in the undamaged and damaged configuration, and N is the total number of the

eigenvalues.



• The corresponding robustness index (𝑅𝑆𝑐𝑒𝑛𝑎𝑟𝑖𝑜) is therefore defined as:

𝑅𝑆𝑐𝑒𝑛𝑎𝑟𝑖𝑜=1 - 𝐶𝑓𝑆𝑐𝑒𝑛𝑎𝑟𝑖𝑜

• Values of Cf close to 100% mean that the failure of the structural member most

likely causes a global structural collapse.

• Low values of Cf do not necessarily mean that the structure survives after the failure

of the structural member: this is something that must be established by additional

analysis that considers the loss of the specific structural member.

• A value of Cf close to 0% means that the structure has a good structural

robustness.

The proposed method for computing the consequence factors, for different reasons,

should not be used for:

1. Structures that have high concentrated masses (especially non-structural masses) in

a particular zone; and,

2. Structures that have cable structural system (e.g., tensile structures, suspension

bridges).



Black

Swan

Vulnerability

Cause

Damage

Index





design

• Collapse types


definitions







• What now/next?

• References

Robustness

Collapse

resistance

Progressive

collapse


Member

consequence

factor


Cost of robustness measures ≤ Reduction of failure consequences

• The objective function for optimization may be very complex

and depend on the type of the structural system, robustness

measures, characteristics of failure consequences and

probabilities of occurrence and intensities of various hazards.

• If the total cost of robustness measures exceeds the reduction

in failure consequences, then the system may be considered as

robust but uneconomic. In such a situation, probabilistic

methods of risk assessment may be effectively used

Reference:

COST Action TU0601 Robustness of Structures STRUCTURAL ROBUSTNESS DESIGN FOR PRACTISING

ENGINEERS. EUROPEAN COOPERATION IN SCIENCE AND TECHNOLOGY, Editor T. D. Gerard Canisius.

Robustness and Optimization


Reference:

Casciati, S. and Faravelli, L. (2008) Building a Robustness Index. Robustness of Structures COST Action TU0601,

1st Workshop, February 4-5, ETH Zurich, Switzerland.

Robustness and Optimization

Example: Hierarchy of the failure modes (“weak beam/strong column”)

...develop the less catastrophic failure

modes first.

...ranking the failure modes in terms of

a hierarchy in such a way that the less

harmful ones are generated at lower

loading levels

Objective function:

Robustness term:Pfi: probability of the i-th failure mode

m: number of failure modes

A robust structure requires the plastic moment of the column, MPc, being larger than the

one of the beam, MPb; that is, Z = MPc– MPb≥ 0

µc, σc, µb, σb: means and the standard deviations of the plastic moments of the columns and

of the beam, respectively.

To ensure robustness, the index I needs to be kept positive. The objective is, therefore, to

minimize FI=-I.


Black

Swan

Vulnerability

Cause

Damage

Index





design

• Collapse types


definitions







• What now/next?

• References

Robustness

Collapse

resistance

Progressive

collapse


Member

consequence

factor


Stiffness matrix

Kun λiun

Eigenvalues

Kdam λidam

Consequence factor

Robustness indexRscenario= 100 - Cfscenario

N1i

un

i

dam

i

un

iscenario

f 100)(

maxC

Structural Robustness assessment - overview


ka

kb

x

y Kun =10 00 10

Cf11 = 0% Cf2

1 = 30%

R1 = 70%

R1 = 100 − Cf1

N: total eigenvalues number

i: single eigenvalue number

a and b: elements

a

b

N1i

un

i

dam

i

un

iscenario

f 100)(

maxC

Kdam =10 00 7

Scenario 1

Single damage – analytic calculation


• Single bay frame structure with a diagonal beam brace, composed in total of 5

members

• IPE 300, S235 steel, one meter length, pinned boundary conditions.

The evaluated scenarios consist in the removal of elements 1, 2 and 3 sequentially, so the

damage is cumulative: this means that the each scenario includes the damage from the

previous one.

Cumulative damage – numerical assessment

DSj = Σi=(1-j) di


Cumulative damage – numerical assessment

• star-shaped structure – 8 members - pipe cross section - 20 centimeters outside

diameter - 20 millimeters thickness - S235 steel.

• members 1, 3, 5, and 7 are 0.5 meters long and members 2, 4, 6, and 8 are 0.7

meters long.All the members are connected to each other by a fixed type connection. Also the boundary

conditions are of the fixed type and the structure is plane.

DSj = Σi=(1-j) di


Black

Swan

Vulnerability

Cause

Damage

Index





design

• Collapse types


definitions







• What now/next?

• References

Robustness

Collapse

resistance

Progressive

collapse


Member

consequence

factor


I-35 West Bridge, Minneapolis, MN

COLLAPSE OF THE BRIDGE ON I 35-W MINNESOTA, AUGUST 1ST 2007

The I-35W Mississippi River Bridge (officially known as Bridge 9340) was an eight-lane, deck

truss bridge, designed by the engineering consulting firm of Sverdrup & Parcel and Associates.

The design plans were approved by the Minnesota Department of Transportation (Mn DOT) on

1965 and opened to traffic on 1967.

http://www.dot.state.mn.us/i35wbridge/ntsb/finalreport.pdf





• The deck truss comprised in two parallel Warren

trusses (east and west) with verticals.

• The east and west main trusses were spaced 22 m

and were connected by 27 transverse welded floor

trusses spaced 11.6 m on centers and by two floor

beams at the north and south ends.

• Steel gusset plates were used on all the 112

connections of the two main trusses. All nodes had

two gusset plates on either side of the connection.




After this tragedy, the Federal Highway Administration (FHWA) focused its attention on all the 465 steel

deck truss bridges present in the National Bridge Inventory [NTSB, 2008].

“The term “fracture critical” indicates that if one main component of a bridge fails, the entire

structure could collapse. Therefore, a fracture critical bridge is a steel structure that is designed

with little or no load path redundancy. Load path redundancy is a characteristic of the design

that allows the bridge to redistribute load to other structural members on the bridge if any one

member loses capacity. “



National Transportation Safety Board, NTSB,

2008

“Collapse of I-35 W Highway Bridge,

Minneapolis, Minnesota, August 1, 2007”

Accident Report, NTSB/HAR 08/03 PB 2008-

916213, Washington D.C. 20594..



The primary cause of the collapse was the under-sized gusset plates, with a

thickness of 0.5 inches (13 mm);

U10-W

[*] National Transportation Safety Board, “Collapse of I-35 W Highway Bridge, Minneapolis, Minnesota, August 1,

2007” Accident Report, NTSB/HAR 08/03 PB 2008-916213, Washington D.C. 20594. 2008.



FINITE ELEMENT MODEL FOR OUTSIDE WEST GUSSET PLATE AT U10W

[*] National Transportation Safety Board, “Collapse of I-35 W Highway Bridge, Minneapolis, Minnesota, August 1, 2007”

Accident Report, NTSB/HAR 08/03 PB 2008-916213, Washington D.C. 20594. 2008.

Stress contours for outside (west) gusset plate at U10W at time of bridge opening in 1967

Yield stress

of 51.5 ksi

South North



2 inches (51 mm) of concrete were added to the road surface over the years, increasing

the dead load by 20%;



1977, Renovation:

Increased Deck Thickness

1998, Renovation:

Median Barrier, Traffic Railings,

and Anti-Icing System

2007, Repair and Renovation:

Repaving






Stress contours for outside (west) gusset plate at U10W after 1977 and 1998 renovation projects

Yield stress

of 51.5 ksi

South North



The extraordinary weight of construction equipment and material resting on the bridge just

above its weakest point at the time of the collapse



[*]

U10-WNorth South

184 380 lbf (820 kN) of gravel

198 820 lbf (884 kN) of sand

195 535 lbf (870 kN) of parked construction vehicles and personnel



The extraordinary weight of construction equipment and material resting on the bridge just

above its weakest point at the time of the collapse



[*]

U10-WNorth South

Pier 6

184 380 lbf (820 kN) of gravel

198 820 lbf (884 kN) of sand

195 535 lbf (870 kN) of parked construction vehicles and personnel





Stress contours for outside (west) gusset plate at U10W on August 1, 2007

Yield stress

of 51.5 ksi

South North




Stress contours for outside (west) gusset plate at U10W on August 1, 2007

Yield stress

of 51.5 ksi

8/3112/44 BRIDGE COLLAPSE

/3125/44 BRIDGE COLLAPSE



INSPECTION REPORT FOR I-35W BRIDGE, 1983-2007


GUSSET PLATE???





BOWED GUSSET PLATE AT NODE U10



RESISTANCE OF GUSSET PLATES:

GUSSET PLATES IN TENSION

GUSSET PLATES SUBJECT TO SHEAR

GUSSET PLATES IN COMPRESSION

RESISTANCE OF FASTENERS

SHEAR RESISTANCE OF FASTENERS

PLATE BEARING RESISTANCE AT FASTENERS

http://bridges.transportation.org/Documents/FHWA-IF-09

014LoadRatingGuidanceandExamplesforGussetsFebruary2009rev3.pdf

FHWA GUIDELINES, (2009)

http://bridges.transportation.org/Documents/FHWA-IF-09-014LoadRatingGuidanceandExamplesforGussetsFebruary2009rev3.pdf


I-35 West Bridge, Collapse Initiation

Pier 7

Pier 6

Failure Initiation North of Pier 6

N

U10-E

U10-W

L9

L11


Pier 7

Pier 6

N

U10-E

U10-W

L9

L11

L11

L9

U10





Weight

Temp. & Const.

Weight

Temp. & Const.

Construction loads increase forces by 3%

Forces due to weight of bridge and traffic

Additional forces due to temperature

(corroded bearings) and construction load

L11

L9

L11

L9

L11

L9

U10

• Additional forces due to temperature



• Forces due to weight of bridge and traffic



Gusset hinges, tears at top and buckles at bottom

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





BUCKLED

TORN

Rivet hole elongation

U

L11

L9

U10



• Lower chord fails in buckling

• Gusset hinges, tears at top and buckles at

bottom



• Rivet hole elongation


I-35 W bridge


NTSB 2007


Undamaged

Damaged

scenario

I-35 West Bridge, Minneapolis, MN – damage scenarios


I-35 West Bridge, Minneapolis, MN – damage scenarios

3D

2D


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

bust

nes

s %


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

DSj = di

I-35 West Bridge, Minneapolis, MN – single damage


d1

d2d3

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

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

bust

nes

s %


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

I-35 West Bridge, Minneapolis, MN/ enhanced– single damage

DSj = di


I-35W SAINT ANTHONY FALLS BRIDGE (September 2008)

There are 323 sensors that regularly measure bridge conditions

such as deck movement, stress, and temperature


•100-year life span

•10 lanes of traffic, five in each direction—two lanes wider than the former bridge

•189 feet wide—the previous bridge was 113 feet wide

•13 foot wide right shoulders and 14 foot wide left shoulders, the previous bridge had no

shoulders

•Light Rail Transport-ready which may help accommodate future transportation needs

•Design-build project complete in 339 days.

•Designed to be aesthetically pleasing and fit in with its environment

•There are 323 sensors that regularly measure bridge conditions such as deck

movement, stress, and temperature

•The bridge is equipped with anti-icing sprayers and was constructed with high-strength

concrete.

I-35W SAINT ANTHONY FALLS BRIDGE (September 2008)


Black

Swan

Vulnerability

Cause

Damage

Index





design

• Collapse types

• Structural robustness and progressive

collapse definitions







• What now/next?

• References

Robustness

Collapse

resistance

Progressive

collapse


Member

consequence

factor


(disaster) resilience

Definition (not univocal):

A resilient community is defined as the one having the ability to absorb disaster

impacts and rapidly return to normal socioeconomic activity.

MCEER (Multidisciplinary Center for Earthquake Engineering Research), (2006). “MCEER’s Resilience Framework”. Available at

http://mceer.buffalo.edu/research/resilience/Resilience_10-24-06.pdf

NEHRP (National Earthquake Hazards Reduction Program), 2010. “Comments on the Meaning of Resilience”. NEHRP Technical

report. Available at http://www.nehrp.gov/pdf/ACEHRCommentsJan2010.pdf

MCEER framework for resilience evaluation:

Initial losses Recovery time, depending on:

• Resourcefulness

• Rapidity

Disaster strikes

Systemic

Robustness


(disaster) resilience

Definition (not univocal):

A resilient community is defined as the one having the ability to absorb disaster

impacts and rapidly return to normal socioeconomic activity.

MCEER (Multidisciplinary Center for Earthquake Engineering Research), (2006). “MCEER’s Resilience Framework”. Available at

http://mceer.buffalo.edu/research/resilience/Resilience_10-24-06.pdf

NEHRP (National Earthquake Hazards Reduction Program), 2010. “Comments on the Meaning of Resilience”. NEHRP Technical

report. Available at http://www.nehrp.gov/pdf/ACEHRCommentsJan2010.pdf

MCEER framework for resilience evaluation:

Resilience is inversely proportional to the area A.

(dQ/dt)L0

TR

(dQ/dt)0

A


Combined effect of discrete events and continuous deterioration

-

Aftermath of the event

-

i. historical - political - decisions (e.g. local governance) influence the initial system quality

Q0. This parameter is related to the initial system state.


-


-

ii. urban and social service planning is relevant for the pre-event system integrity and it is one

of the factors determining the trend of system quality before the event (dQ/dt) and the

amount of immediate losses (ΔQ). The first parameter is by a statistical correlation

between the political decision and the quality trend, while the second parameter can be

modeled by the system fragility.



-


-

iii. fast decisions are taken during the event or a disaster (on the basis of knowledge and

experience from similar past events - if any - and the system properness knowledge); the

decisions in this phase influence the initial slope of the recovery phase (dQR/dt), a

parameter that can be modeled by a statistical correlation between the political decision

and the quality trend.



-


-

iv. emergency plans and prioritization of recovery actions are relevant in the aftermath of the

event (recovery phase). In addition, the declaration of a state of emergency can have a

substantial short and long-term effect on the local economy. The actions in this phase

influence the shape of the recovery function fR(t).



-


-

v. urban and social service re-planning on the basis of the consequences of the occurred event

are relevant in the long run (influencing the losses and the recovery for the next discrete

event).



References: Taleb, Nassim Nicholas (November 2012). Antifragile: Things That Gain from Disorder(1st ed.). London:

Penguin. p. 519. ISBN 1-400-06782-0.

People/systems/organizations/things/ideas can be described in one

of three ways:

- fragile

- resilient, or

- antifragile

"Some things benefit from shocks; they thrive and grow when

exposed to volatility, randomness, disorder, and stressors and love

adventure, risk, and uncertainty. Yet, in spite of the ubiquity of the

phenomenon, there is no word for the exact opposite of fragile.

Let us call it anti-fragile. Anti-fragility is beyond resilience or

robustness. The resilient resists shocks and stays the same; the

anti-fragile gets better".

“anti-fragility”


References: Taleb, Nassim Nicholas (November 2012). Antifragile: Things That Gain from Disorder(1st ed.). London:

Penguin. p. 519. ISBN 1-400-06782-0 .

-----

----


References: Beyond “Sissy” Resilience: On Becoming Antifragile. Available online at

http://www.artofmanliness.com/2013/12/03/beyond-sissy-resilience-on-becoming-antifragile/

Things that are fragile

break or suffer from

chaos and randomness.

The resilient, or

robust, don’t care if

circumstances become

volatile or disruptive

(up to a point).

Things that are anti-

fragile grow and

strengthen from

volatility and stress (to

a point).




Fragile people/ systems/

organizations are concave.

As fluctuations increase (x-axis) you

experience more loss.

Anti-fragile things are convex.

As variability increases (x-axis),

gains increase.

References: Beyond “Sissy” Resilience: On Becoming Antifragile. Available online at




Robustness, then resilience, then antrifragility…

resilience

robustness

antifragility

timespacial complexity

spatialcomplexity

Ronan Point (1968)Building (5th Amendment) Regulations 1970

1960 1970 1980 1990 2000 2010

Seismic (Bruneau et al. 2003)Urban (MCEER, 2006)Ecological (Holling, 1973)

(TALEB, 2012)

Eurocodes ‘80

structural (global)+resilience (local)

+resilience (social)

+antifragility (social)

robustness: single structure (or a

series of structures)

antifragility and resilience

complex of structures in the most

wide sense, including issues well

beyond structural design.

• scale (small - big)

• context (structural – urban - social)

• multi-, trans- and inter - disciplinarity


Black

Swan

Vulnerability

Cause

Damage

Index





design

• Collapse types

• Structural robustness and progressive

collapse definitions







• What now/next?

• References

Robustness

Collapse

resistance

Progressive

collapse


Member

consequence

factor


References

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References

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