A Swiss Study 

Collapse for Impr

and Safety of Ex

Building Str

Sep

Swis

s Federal Ins

M. H. Fab

e

r

O. Kübler M. Fontana M. KnoblochInstitute of Structural En
A Swiss Study on the WTC Collapse for Improving 

Design and Safety of Extraordinary Building Structures

Contents of Presentation•

Motivation

•

Framework for risk based optimal 

extraordinary structures

•

Mapping of socio-economical conse

WTC collapse

• P

rin

cip

al s

t

u

die

s

-

vulnerability improvement by fire 

-

robustness against progressive c

•

Optimal target reliability levels for 

structures

•

Structural robustness –

new appro

•

Conclusions
A Swiss Study on the WTC Collapse for Improving 

Design and Safety of Extraordinary Building Structures

Motivation•

Most modern design codes implicit

explicitly set requirements to strucreliability

1 2 3 

R

elative cost o

f safety

me

asu

r

e

Minor consequ

ences 

of failure

Moderat

e

consequences o

f

failure 

Large (A) 

β=3.1 (p

F

≈10-3) 

β=3.

3 (pF 

≈ 5 10-4) 

N

ormal (B) 

β=3.

7 (p

F

≈10-4) 

β=4.

2 (pF 

≈ 10-5) 

S

mall (C) 

β=4.

2 (p

F

≈10-5) 

β=4.

4 (pF 

≈ 5 10-6) 

Joint Committee on Structural Safety Probab
A Swiss Study on the WTC Collapse for Improving 

Design and Safety of Extraordinary Building Structures

Motivation•

„Normal structures“ are designed accor

structural design codes

Structures

De

Design codespossibly inappropriateNew purposesUnusual designsNew materialsNew maintenanceExtreme consequences

Exceptional Structures
A Swiss Study on the WTC Collapse for Improving 

Design and Safety of Extraordinary Building Structures

Motivation•

Very little or no experience was av

consequences of failures of extraostructures prior to the collapse of t

•

Despite the tragic circumstances in

collapse of the WTC the “event” shin more detail to: -

enhance design of extraordina

the future 

-

help reduce the risk associated 

events in the future
A Swiss Study on the WTC Collapse for Improving 

Design and Safety of Extraordinary Building Structures

Framework for risk based design

Risk Based 

S

truct

u

ral Design

Structural Desig

n

Structural Relia

bilit

y Conseq

Expected Lif

e Cycle Benefit

Expected revenueExpected life cyclConstruction costExpected failure cExpected life cycl

Reasonable range

Maximum life cycle benefit withoptimal design variable

Human Econ
A Swiss Study on the WTC Collapse for Improving 

Design and Safety of Extraordinary Building Structures

Framework for risk based design

Decision variables Reconstruction strategy, 

decom

missioning, 

replacement

Structural design

Inspection & maintenance

Consequ

(revenues 

Probab

[ ]

[ ]

[

]

[

[ ] (

) [ ] (

)

[

(

)

(

)

(

(

)

(

)

Rep

F

F

F

D

C

F

O

F

M

F

F

E

C

P

E

C

P

E

C

E

C

P

E

C

P

E

C

E LCC

P

B

P

+

+

+

=

+

+

=
A Swiss Study on the WTC Collapse for Improving 

Design and Safety of Extraordinary Building Structures

Framework for risk based design

Identifical and 

mo

d

ellin

g

of r

elevant accidental

hazards

As

s

e

s

s

ment of d

a

mage 

state

s t

o

stru

cture from

different hazard

s

Ass

e

s

s

men

perform

a

nc

da

ma

g

ed st

Assessment of th

e proba

bility of

occurence of different hazard

s

with differe

nt intensitie

s

Asse

s

s

m

e

nt of th

e pr

o

ba

bility of

differe

nt state

s of da

mage and

c

orre

sponding con

sequences 

for given hazard

s

As

s

essment of t

h

e pr

performance(

s) of t

h

together with th

e

corre

s

St

e

p 1 Step 2

Step 

Identifical and 

mo

d

ellin

g

of r

elevant accidental

hazards

As

s

e

s

s

ment of d

a

mage 

state

s t

o

stru

cture from

different hazard

s

Ass

e

s

s

men

perform

a

nc

da

ma

g

ed st

Assessment of th

e proba

bility of

occurence of different hazard

s

with differe

nt intensitie

s

Asse

s

s

m

e

nt of th

e pr

o

ba

bility of

differe

nt state

s of da

mage and

c

orre

sponding con

sequences 

for given hazard

s

As

s

essment of t

h

e pr

performance(

s) of t

h

together with th

e

corre

s

Identifical and 

mo

d

ellin

g

of r

elevant accidental

hazards

As

s

e

s

s

ment of d

a

mage 

state

s t

o

stru

cture from

different hazard

s

Ass

e

s

s

men

perform

a

nc

da

ma

g

ed st

Assessment of th

e proba

bility of

occurence of different hazard

s

with differe

nt intensitie

s

Asse

s

s

m

e

nt of th

e pr

o

ba

bility of

differe

nt state

s of da

mage and

c

orre

sponding con

sequences 

for given hazard

s

As

s

essment of t

h

e pr

performance(

s) of t

h

together with th

e

corre

s

St

e

p 1 Step 2

Step 
A Swiss Study on the WTC Collapse for Improving 

Design and Safety of Extraordinary Building Structures

Framework for risk based design

[ ]

1 1

(

)

(

) (

) (

NNN HDP

F k k

j

i j

k

E C

A

C

P

P

P

D

P

D

= =

= ∑∑∑

Identifical and modelling

of relevant accidental

hazards

Assessment of da

mag

states to structure from

different hazards

Assessment of the probability of

occurence of different hazards

with different intensities

Assessment of the probabil

different states of da

mage 

corresponding consequenc

for given hazards

St

e

p 1 Step 2

Identifical and modelling

of relevant accidental

hazards

Assessment of da

mag

states to structure from

different hazards

Assessment of the probability of

occurence of different hazards

with different intensities

Assessment of the probabil

different states of da

mage 

corresponding consequenc

for given hazards

Identifical and modelling

of relevant accidental

hazards

Assessment of da

mag

states to structure from

different hazards

Assessment of the probability of

occurence of different hazards

with different intensities

Assessment of the probabil

different states of da

mage 

corresponding consequenc

for given hazards

St

e

p 1 Step 2

Eurocode on accidentalloads
A Swiss Study on the WTC Collapse for Improving 

Design and Safety of Extraordinary Building Structures

Mapping of socio-economical con
A Swiss Study on the WTC Collapse for Improving 

Design and Safety of Extraordinary Building Structures

Mapping of socio-economical con

Cons

e

q

u

enc

e T

y

p

e Low

High

Re

s

cue & Clean-Up 1.7 1.7

Property 19.0 19.0

WT

C T

o

w

ers

4.7

Oth

er Destroyed 

B

uildings 2.0

Dam

aged Buildings 4.3

Inventor

y

5.2

Infrastructure 2.8

F

atalities 5.0

5.0

Environment & Cultural A

s

s

ets 0.1

0.1

Impact to econom

y

9.1

6

6.2

B

usi

n

esse

s

7.2

6

4.3

Infrastructure 0.7

0.7

Rents 1.2 1.2

T

otal 34.9

92.0

(in billion USD)

Scenario
A Swiss Study on the WTC Collapse for Improving 

Design and Safety of Extraordinary Building Structures

Mapping of socio-economical con

Cons

e

q

u

enc

e T

y

p

e Low

High

Re

s

cue & Clean-Up 1.7 1.7

Property 19.0 19.0

WT

C T

o

w

ers

4.7

Oth

er Destroyed 

B

uildings 2.0

Dam

aged Buildings 4.3

Inventor

y

5.2

Infrastructure 2.8

F

atalities 5.0

5.0

Environment & Cultural A

s

s

ets 0.1

0.1

Impact to econom

y

9.1

6

6.2

B

usi

n

esse

s

7.2

6

4.3

Infrastructure 0.7

0.7

Rents 1.2 1.2

T

otal 34.9

92.0

(in billion USD)

Scenario
A Swiss Study on the WTC Collapse for Improving 

Design and Safety of Extraordinary Building Structures

Mapping of socio-economical con

Cons

e

q

u

enc

e T

y

p

e Low

High

Re

s

cue & Clean-Up 1.7 1.7

Property 19.0 19.0

WT

C T

o

w

ers

4.7

Oth

er Destroyed 

B

uildings 2.0

Dam

aged Buildings 4.3

Inventor

y

5.2

Infrastructure 2.8

F

atalities 5.0

5.0

Environment & Cultural A

s

s

ets 0.1

0.1

Impact to econom

y

9.1

6

6.2

B

usi

n

esse

s

7.2

6

4.3

Infrastructure 0.7

0.7

Rents 1.2 1.2

T

otal 34.9

92.0

(in billion USD)

Scenario

low

high low high low

high 

Income losses E

conomic losses 28.0 43.0 52.3 64.3 38.8 38.8

(in billion U

S

D)

Comptroller NYC 

O

ct. 4, 2001

Comptroller NYC 

Sept. 4, 2002

New Y

ork City

Part

n

ership
A Swiss Study on the WTC Collapse for Improving 

Design and Safety of Extraordinary Building Structures

Principal studies•

Vulnerability of fire protection

Investigations were made to assesvulnerability of passive fire protectcolumnsThe analysis –

based on nonlinear 

showed that the effect of even smfire protection is significant –

and 

insensitive to the location of the dThe integrity of passive fire protecmajor issue
A Swiss Study on the WTC Collapse for Improving 

Design and Safety of Extraordinary Building Structures

Principal studies•

Robustness against progressive co

Studies were carried out to assess of two approaches to reduce the riprogressive collapse due to airplandamage and subsequent fire load:1 reduce vulnerability -

avoid story 

ensuring small damage

2 improve robustness to avoid pro

collapse due to falling stories 

Approach 1 (steel) seems superior expensive – in the order of 1-10% 
A Swiss Study on the WTC Collapse for Improving 

Design and Safety of Extraordinary Building Structures

Optimal target reliability levels

( ) ( ) 1 y G

G g z X = − f ξ α

G

+

⎡

−

α

⎤

L

⎣

⎦

g z fi y ( ) X = − f

k

y ξ α fi ( G

G

+⎡ ⎤ ⎣ ⎦

1−

α G

Lfi)

Optimal dwith fire 

A

0: requi

ensure anfailure of 

0

j = - A A/ 1

X

Dist. T

y

p

e E[X]

V

X

fy LN 1.00 5%

ξ LN 1.00 10%

G

N 1.00 10%

L

G 1.00 40%

ξfi LN 1.00 15%

Lfi

G

0.57 59%

q G 400 MJ/m

2 25%

[1]

JCSS 2001, Probabilistic Model C

ode, J

oint Committee 

Safety, online, available at: www.jcss.ethz.ch
A Swiss Study on the WTC Collapse for Improving 

Design and Safety of Extraordinary Building Structures

Optimal target reliability levels 
A Swiss Study on the WTC Collapse for Improving 

Design and Safety of Extraordinary Building Structures

Structural robustness –

new app

•

Robustness against progressive co

D

EBD

F

EAD

FF

C

IndirDirec

2 

( ) ( ) ( , ) ( , ) ( ) ( 

R

D = + P

EB

D

P

D

EB

D P EA

D

D

EB

D P F

D

EA

D

CD

P

EBD

P

( )

(

)

( , )

( , )

RID

= P EB

D P D

EBD

P

EAD

D

EBD

P

F

D

EAD

CID
A Swiss Study on the WTC Collapse for Improving 

Design and Safety of Extraordinary Building Structures

Structural robustness –

new app

•

Robustness against progressive co

D

EBD

F

EAD

FF

D 

R

D ID

R 

I

R R

= 

+ 

Index of robustness

( ) 

C a R 

R

a 

∂

∂

= −

∂

Requirement to robustness
A Swiss Study on the WTC Collapse for Improving 

Design and Safety of Extraordinary Building Structures

Conclusions•

Extraordinary building structures justify e

reliability acceptance criteria

•

There seems to be a need for scenario ba

to structural design – robustness

•

Robustness should be quantified and requ

robustness should be provided for most u

• International consens

us and homogeneity 

necessary

•

Collaboration on further developments sh