robustness of structures - konstruktionsteknik · robustness can be seen as an important property...

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Robustness of structures

Ivar BjörnssonDivision of Structural Engineering,

Reliability analysis in engineering application Part 2, Chalmers, 2010-12-15

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Lund University

Outline

• Introduction – building on failures• Background – failure cases• What is robustness?• Design for robustness


• Design for robustness• Methods of assessing robustness

– Example of risk based assessment• Strategies for greater robustness• Conclusions

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Introduction: Building on failure• The incentive for further developement of engineering

practices and methodologies throughout mankinds history has usually been the result of unexpected failures; i.e. learning from past mistakes.

• From each lesson learned, our confidence grows.


From each lesson learned, our confidence grows. More daring ventures perpetuate the cycle until collapse and the process starts all over again. (example: Tacoma bridge)

• Another issue is the generational gap. Old lessons learned are forgotten and knowledge is lost between generations. (example: blind fath in computer analysis)

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Introduction: Building on failure• What incentive is there otherwise?

– ”If it has worked so far, it must be right, then why try and fix it?” ... Proof by lack of counter-example.

”N l b i k b


• ”No one wants to learn by mistakes, but we cannot learn enough from successes to go beyond the state of the art” (Petroski)

• Murphy’s Law: “Anything that can go wrong, will go wrong (eventually)”

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Background – unanticipated failures

• We have a internationally proven safety system to handle uncertainties related to known types of loads and exposures as well as structural systems


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But why do failures occur rather often and what happens with built facilities under events which are not anticipated and/or difficult to quantify? Some examples are given below

The Tjörn Bridge – steel arches


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The Tjörn bridge in the morning, Jan 18, 1980


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The Tjörn bridge was far from ”robust”


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The collapse at Ronan Point in London, May 1968

Gas explosion on 18th floor caused so called progressive collapse

5 persons were killed.


p

The builiding was constructed with prefabricated concrete elements, which were not connected with each other appropriately.

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Ronan Point 1968

Lead to extensive research in Structural Engineering and the following type of requirement has been formulated in most developed countries:


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”A structure should be designed and executed in such a way that it will not be damaged … to an extent disproportionate to the original cause”(Eurocode EN1990)

11 sept. 2001


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This event has lead to renewed insight of the need for robust construction.


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Bridge for Interstate 35W –Minneapolis, USA, August 1, 2007


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Trussed steel arch with main span 140 m built 1964-67

Failure was initiated by fatigue in joint detail in the steel truss in combination with corrosion

Inspection 2005 with rating ”Structurally deficient” (corrosion, cracks, fatigue)


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13 persons were killed and about 100 were injured at the collapse which occured at rush hour

NTSB findings (Nov 2008) – undersized gusset plates.


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Question: Were the consequenses disproportionate to the original cause, i.e was the bridge robust?

The answer is a clear: NO!!!!


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Siemens arena, Danmark, Jan 2003


The failure was initited in a joint due to a gross error in structural design. No people were injured or killed (”pure luck”).

Is the extent of damage in proportion the cause?

Could the building have been designed so that the consequenses had been limited considering the fact that it is an arena where numerous people may be present?

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Skating hall in Bad Reichenhall, Germany

• collapse 2006-01-02 (built 1974/75)• 15 dead, 35 injured• ”big case” in the media

timber structure owners in panican increased publication of

collapses of timber structuresin the media

timber structures (especially glulam) and flat roofs presented as ”d b ildi ”


”dangerous buildings”

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Jyväskyle exhibition hall, FinlandExtensive collapse (2500 m2) of exhibition hall

9000 people visited the day before the failure (Feb. 2003)


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Failure initiation- manufacturing error in dowel-type joint


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Investigation of failed timber structures 2007 (LTH/SP/VTT)Failure cause(127 failure cases)

building production

overloading4%

unknown / other5% material

11%


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design53%

building production27%

Prime causes for failures, Walker, 1981

Gross human errors which could be reduced by checking and supervision

90 %


Unfavourable random effectsLoads 0%Inaccuracies in model 3%Deficiencies in materials 4%Foreseeable deterioration 3%

10 %

Only this part is handled by the general structural safety system

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General conclusion from failure investigations

The damage is predominantly caused by gross human errors related to

• Lack of knowledge (ignorance)

E i ti ( l )


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• Errors in execution (carelessness)

• Errors of intent (greed)

[Kaminetzky]

Gross errors in the building process

• Can not be reduced by higher ”safety factors” • Can be reduced with improved control systems and

education• These type of errors, however, can never be totally

eliminated


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But the consequences can be limited by design of ”robust” systems

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The total risk picture Matousek & Schneider (1976)

Reliability analysis in engineering application Part 2, Chalmers, 2010-12-15 Risk elements not considered

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How do we design structures to avoid these types of failures?

By making them more ”robust”


By making them more robust

But what is meant by robustness?

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What is robustness?Robustness (rōbŭstnǝs)Latin rōbustus, from rōbur meaning strength

Scientific interpretationi hi h ” t ” i ff t d b h d / t


- manner in which a ”system” is affected by hazardous/extremeor varying procedures or circumstances

How is this applied in engineering?As yet there is no consensus as to a universallyaccepted interpretation of robustness!

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What is robustness? Some definitions

• Insensitivity of system to local failureStarossek 2009; Structural Engineering Institute of the ASCE (draft April 2010)

• The property of a system to survive unforeseen of abnormal circumstances

Knoll & Faber 2009 (SED11 - Design for Robustness)

• The ability of a structure to withstand events like fire


• 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

EN1991-1-7

• Ratio of direct risk and total risks (equal to direct risk + indirect risk) for all relevant exposures and damage states for the constituents of a system

JCSS 2008 (Risk assessment in engineering)

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Example of robustness requirements(after Sexsmith, 2005)

• The structural system shall – sustain anticipated loads even after limited damage– survive unanticipated loads with limited

consequences (the consequences shall not be disproportionate in relation to the triggering event)


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p p gg g )– give warning of imminent failure

• Critical elements are isolated or protected from exposure • Key elements, whose failure has large consequences,

are designed for higher safety. • Subsystems are isolated from each other so that failure

in one subsystem does not affect other subsystems.

Robustness can be seen as an important property for a built facility

It will provide an intrinsic resistance against extreme and unknown events


But how can we design for robustness?

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How to design robust structures?

• Standard recipes or formulas to achieve this do not exist • Advanced engineering task demanding experience, skill

and competence. • Risk analysis is an important tool.

C t i t d d th d il bl f b ildi ith


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• Certain standard methods are available for buildings with simple layout, but these are not applicable for complicated buildings, bridges etc.

• A system approach is necessary (investigation of single components is not sufficient)

Inadequacy of current design methods

• Component based design– System response to local damage lacking

• Unforeseen or improbable actions neglected– Empirical data is unavailable; hard to quantify

G h i d i d t ti


– Gross human error in design and construction not acounted for

• Specified acceptable failure probability required– Hard to adjust with regard to robustness

Current design approaches should be complemented by additional methods with focus on robustness

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Designing for robustness;some conisderations

• What are the sources of risk? (Hazards)– Identifiable abnormal circumstances

• Vehicle impact, explosion, etc.– Unforeseen circumstances

• Terror attacks, gross human error, etc.


, g ,• What are the consequences of system

failure/malfunction?– Human, economic, environmental, etc.

• Are the consequences disproportionate to the originating cause?– Robustness indicator?

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Robustness assessmentGeneral framework for robustness assessment of engineered systems


[Maes et. al 2006]

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Concept used for buildings with regular layout


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Failure circumstances

• Collapse probability


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Failure circumstancesInternal flaws, etc.• Deviations from analytical model to actual

structure must be taken into account• Possibility of gross human error during all stages

of the bridge systems lifespan


of the bridge systems lifespan– Error during design (inadequate resistance, etc.)– Error during construction (poor building procedures…)– Error during operation (inadequate inspection, etc.)

There exists no probability law to account for human error!!

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Failure circumstances

External causes• Overloading• Accidents• Fatigue/deterioration


• Fatigue/deterioration• Malevolence (purposeful destruction)• Natural events (environmental loads)

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Consequences of failureTwo types of consequences considered• Direct consequences

– Consequence related to damage of individual constituent elements

• Indirect consequencesC i t d ith l f t


– Consequences associated with loss of system functionalities

• It is important to note that the realisation of these consequences depend greatly on system definition and bounds. It is thus very important to precisely define the system, its bounds and the performance objectives!

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Consequences of failureType Direct IndirectHuman • Fatalities or injuries as a direct

result of the originating event• Fatalities or injuries as a result of follow

up events• Psychological damage

Economic • Replacement/repair of structure• Replacement/repair of contents

• Replacement/repair of structure• Replacement/repair of contents• Loss of functionality (e.g. user costs)


• Clean up costs• Rescue costs• Effect on share prices/market value• Investigation/compensation• Loss of reputation

Environmental • CO2 Emissions• Energy use• Toxic releases• Environmental studies/repairs

• CO2 Emissions• Energy use• Toxic releases• Environmental studies/repairs

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Measures of robustnessBases for

quantification

Structural behaviour

Probabilistic Deterministic

Structural attributes

System stiffness

Starossek & Haberland (2008) have collected and reviewed various methods developed for the quantifying robustness of engineered systems.


Failure probability

Risk

Load capacity

Extent of damage

Energy

System topology

One of these methods will be briefly discussed:

Robustness measure based on risk assessments.

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Risk based robustness concept


Exposure may lead to direct consequences as well as indirect consequences

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[Baker et. al 2006]

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( ) ( ) ( )∑∑ ⋅⋅=i j

iBDiBDjjDirDir EXPEXDPDCR ..|

( ) ( ) ( ) ( )∑∑ ⋅⋅⋅=i j

iBDiBDjjIndInd EXPEXDPDFPFCR ..||

Risk based definition of robustness index for a system

Robustness index:

Irob = Direct risk

Direct risk + Indirect risk


•Assumes values between 0 and 1

•Relative risk only

•Depends on probability of primary damage occurence

•Depends on probability of secondary effects

•Depends on consequences

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Can be expanded to include decision analysis theory


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Example by Baker et. al 2008• Parallel system with n elements

• Perfectly brittle or perfectly ductile elements

• Each carries equal portion of original load

• Applied load has a Weibull distribution (environmental load - annual maximum)


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• Resistance lognormally distributed (uncorrelated component resistances)

• Load redistribution after element failure

• Consequence of system failure set equal to 100 times the consequence of single element failure

Some resultsEffect of load variability & no. of elements


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Perfectly ductile Perfectly brittle

Increasing correlation has same effect as decreasing the no. of elements

Some resultsEffect of indirect consequences


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Perfectly ductile load CoV = 0.3

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Robust design strategies• Prevent ”local failure” (defined hazards: direct design)

– Control local resistance (often not feasable)– Protective measures

• Assume ”local failure” (undefined hazards: direct design)

Alt ti l d th


– Alternative load paths– Isolation by segmentation

• Prescriptive design rules (indirect design)– e.g. tying members, ensuring ductility, enabling catenary

action• Reducing indirect risks (consequences)

– Reducing the potential consequences of systems failure; e.g. evacuation systems, alarms, etc.

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Example: prescriptive rules for design of joint in prefabricated concrete system. Joints between

elements shall be able to tranfer 20 kN/m in tension as well as shear

Rules implemented as a result of the Ronan

F5 tas med friktion här


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the Ronan Point collapse

Fogyta med friktion F4F2

F1

Alternative load paths - principles

• Vierendeel action• Catenary action• Arch action


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• Suspension

Alternative load transfer illustrated by structural system where one base column is removed. Dynamic effects must be acounted for.


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Vierendeel action –forces are transferred through moment stiff

connections in the system


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”Catenary” action (large deformations)

Forces are tranfereed by tension in initially horisontel elements under large deformations


g

Structural elements and joints must be able to tranfer tensile forces.

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Alternative load path in concrete slab


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Can also be realised at the edge of the slab


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Suspension in upper part of structural system

•Small deformations


•Small deformations

•Often difficult to achieve

•High requirements for connections

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Arch action can be utilised in vertical panels

Can be verified with simple ”strut & tie” models


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The Öresund bridge: If one of the main cables on the high bridge is hit by a truck, the bridge is designed to still be stable although the cable will be broken. Example of alternative load paths.


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Isolation of subsystems (Segmentation)Parts of the system is sacrified to save the rest


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Confederation bridge (Canada) Controlled collapse

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Isolation of subsystems - examples

Weak section


Siemens arena DK- two main girders collapsed but the rest of the building was not affected

Charles de Gaulle Airport – Paris

20 m long part kollapsed – the rest was stable

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Conclusions

• Extreme and unforeseen events occur (often with low probability)• The concequences can be reduced by design of robust structural

systems• The concept of robustness is however not clearly defined• Known as well as unknown hazards need to be considered• Strategies for design of robust systems:


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Strategies for design of robust systems:> prevent initial damage (only for known hazard) > alternative load paths after local damage > sacrifice subsystem to preserve the rest of the system> prescriptive methods (only special cases)

Thanks for your attention!


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robustness of structures - konstruktionsteknik · robustness can be seen as an important property...

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