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Structural robustness: issues, numerical modelling and future trends

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  • 1. CORSO DI PROGETTAZIONE STRUTTURALE ANTINCENDIOStructural robustness:issues, numerical modellingand future trendsKonstantinos Gkoumas, Ph.D., P.E.Franco Bontempi, Ph.D., P.E.Facoltà di IngegneriaSapienza Università di Romawww.francobontempi.orgOctober 29 2014 1
  • 2. CauseRobustnessVulnerabilityBlackSwanCollapseresistanceDamageIndexProgressivecollapseMemberconsequencefactorPhoto Credit: Wikipedia Commons.• Significant collapse cases• LPHC events and Black Swans• Structural robustness in qualitative terms• Structural robustness in civil engineeringCorso di Progettazione Strutturale antincendio Roma, 29 Ottobre 2014Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.design• Collapse types• Structural robustness and progressive collapsedefinitions• 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
  • 3. Word cloudCorso di Progettazione Strutturale antincendio Roma, 29 Ottobre 2014Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
  • 4. CauseVulnerabilityBlackSwanDamageIndex• Significant collapse cases• LPHC events and Black Swans• Structural robustness in qualitative terms• Structural robustness in civil engineeringMemberconsequencefactorCorso di Progettazione Strutturale antincendio Roma, 29 Ottobre 2014Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.design• Collapse types• Structural robustness and progressive collapsedefinitions• Measures against progressive collapse• Quantification of robustness• Robustness and optimization• Member consequence factor• Assessment of simple structures• Assessment of complex structures• What now/next?• ReferencesRobustnessCollapseresistanceProgressivecollapsePhoto Credit: Wikipedia Commons.
  • 5. Ronan Point Tower Block– May 16, 1968Description:- apartments building;- built between 1966 and 1968;- 64 m tall with 22 story;- walls, floors, and staircases was precastconcrete;- each floor was supported directly by the wallsin the lower stories, (bearing walls system).The event:- May 16, 1968 a gas explosion blew out anouter panel of the 18th floor,- the loss of the bearing wall causes theprogressive collapse of the upper floors,- the impact of the upper floors’ debris causedthe progressive collapse of the lower floors.Cause Damage Pr. CollapseCorso di Progettazione Strutturale antincendio Roma, 29 Ottobre 2014Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
  • 6. Khobar Towers Bombing – June 25, 1996Description:- apartments building;- precast concrete wall and floor componentswas the structural bearing system;- ductile detailing and effective ties betweenthe precast components.The event:- June 25, 1996 9 tons ofTNTeq detonated infront of the building;- the exterior wall wasentirely destroyed;- collapse did notprogress beyond areasof first damage.Cause Damage Pr. CollapseCorso di Progettazione Strutturale antincendio Roma, 29 Ottobre 2014Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
  • 7. Deutsche Bank Building – September 11, 2001Description:- office facility for the Deutsche Bank inManhattan;- constructed in the early ‘70s in steel-framedstructure moment connected, 130 m tall, 40story and 2 subterranean levels;The event:- On September 11, 2011, the WTC towersdebris impact on a building’s façade,- heavy damage between the 9th and the 23rdfloor, the column was lost from the 9th andthe 18th floor;- the framing system was able to supportand redistribute the loads.Cause Damage Pr. CollapseCorso di Progettazione Strutturale antincendio Roma, 29 Ottobre 2014Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
  • 8. Probability of progressive collapse from an abnormal eventoccurrence of broador global collapseSTRUCTURAL INTEGRITY (ISO/FDS 2394)COLLAPSE RESISTANCE (Starossek&Wolff 2005)P(F) = P(H) x P(D|H) x P(F|DH)damage is caused inthe structuredamage spreads inthe structureoccurrence ofcritical eventFaber (2006)EXPOSURE VULNERABILITY ROBUSTNESSNON STRUCTURAL STRUCTURALMEASURESCorso di Progettazione Strutturale antincendio Roma, 29 Ottobre 2014Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.HAZARDReferences: Ellingwood, B.R. and Dusenberry, D.O. (2005), “Building design for abnormal loads and progressivecollapse”, Comput-Aided Civ. Inf., 20(3), 194-205.
  • 9. CauseVulnerabilityBlackSwanDamageIndex• Significant collapse cases• LPHC events and Black Swans• Structural robustness in qualitative terms• Structural robustness in civil engineeringMemberconsequencefactorCorso di Progettazione Strutturale antincendio Roma, 29 Ottobre 2014Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.design• Collapse types• Structural robustness and progressive collapsedefinitions• Measures against progressive collapse• Quantification of robustness• Robustness and optimization• Member consequence factor• Assessment of simple structures• Assessment of complex structures• What now/next?• ReferencesRobustnessCollapseresistanceProgressivecollapsePhoto Credit: Wikipedia Commons.
  • 10. Low Probability – High Consequences EventsHPLCHigh Probability –Low ConsequencesLPHCLow Probability –High ConsequencesComplexityNon linear issues andinteraction mechanismsReference: Bontempi, F. (2005) Frameworks for structural analysis, In: Innovation in Civil and StructuralEngineering Topping, BHV ed., pp. 1-24Corso di Progettazione Strutturale antincendio Roma, 29 Ottobre 2014Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.Design approach:Stochastic DeterministicQUALITATIVE RISKANALYSISPROBABILISTICRISK ANALYSISPRAGMATICANALYSIS OFRISK SCENARIOSSecondarydesignPrimarydesign
  • 11. Black SwansA 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 concoctexplanations for its occurrence after the fact, making it explainable andpredictable.Retrospective (though not prospective) predictability - After the firstrecorded instance of the event, it is rationalized by hindsight, as if it couldhave been expected; that is, the relevant data were available butunaccounted for in risk mitigation programs. The same is true for thepersonal perception by individuals.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.Corso di Progettazione Strutturale antincendio Roma, 29 Ottobre 2014Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
  • 12. Black SwansStrengths of Black Swan Theory – Benefits• Increased awareness of uncertainty in decision making• New way to deal with risks and uncertaintyLimitations of Black Swan Theory – Disadvantages• Black Swan is rather extreme• Theory is not yet mainstreamAssumptions of Black Swan Theory• Black Swans cannot be predicted because they are rare• Overestimation of knowledge/Underestimation of randomnessand uncertainty• Overestimation of skills/underestimation of luck in lifeReferences: Taleb, Nassim Nicholas (April 2007). The Black Swan: The Impact of the Highly Improbable (1st ed.).London: Penguin. p. 400. ISBN 1-84614045-5.Corso di Progettazione Strutturale antincendio Roma, 29 Ottobre 2014Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
  • 13. CauseVulnerabilityBlackSwanDamageIndex• Significant collapse cases• LPHC events and Black Swans• Structural robustness in qualitative terms• Structural robustness in civil engineeringMemberconsequencefactorCorso di Progettazione Strutturale antincendio Roma, 29 Ottobre 2014Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.design• Collapse types• Structural robustness and progressive collapsedefinitions• Measures against progressive collapse• Quantification of robustness• Robustness and optimization• Member consequence factor• Assessment of simple structures• Assessment of complex structures• What now/next?• ReferencesRobustnessCollapseresistanceProgressivecollapsePhoto Credit: Wikipedia Commons.
  • 14. Structural RobustnessQUALITYDAMAGE or ERRORNOMINALPERFORMANCEREQUIRED PERFORMANCENOMINAL SITUATIONCorso di Progettazione Strutturale antincendio Roma, 29 Ottobre 2014Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
  • 15. 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).Corso di Progettazione Strutturale antincendio Roma, 29 Ottobre 2014Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
  • 16. Structural RobustnessQualitative definitions of structural robustness[EN 1991-1-7: 2006 ]: ability of a structure to withstand actions dueto fires, explosions, impacts or consequencesof human errors, without suffering damagesdisproportionate to the triggering causes[SEI 2007,Beton Kalender 2008]: insensitivity of the structure to local failureDP DPstructure BdP (performance)structure AdamagedintegerCorso di Progettazione Strutturale antincendio Roma, 29 Ottobre 2014Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.PsSTRUCTURE B:PsROBUSTNESS CURVESintegerSTRUCTURE ADPdamagedmore performant, less resistant(damage level)more performant, less robust less performant, more robustA B
  • 17. CauseVulnerabilityBlackSwanDamageIndex• Significant collapse cases• LPHC events and Black Swans• Structural robustness in qualitative terms• Structural robustness in civil engineeringMemberconsequencefactorCorso di Progettazione Strutturale antincendio Roma, 29 Ottobre 2014Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.design• Collapse types• Structural robustness and progressive collapsedefinitions• Measures against progressive collapse• Quantification of robustness• Robustness and optimization• Member consequence factor• Assessment of simple structures• Assessment of complex structures• What now/next?• ReferencesRobustnessCollapseresistanceProgressivecollapsePhoto Credit: Wikipedia Commons.
  • 18. Common ULS & SLSVerification FormatStructural robustness in design1st level:Material Point2nd level:ElementSectionStructural RobustnessAssessment3rd level:StructuralElement4th level:StructuralSystemCorso di Progettazione Strutturale antincendio Roma, 29 Ottobre 2014Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
  • 19. Structural robustness in designSTRUCTURAL DESIGNPRIMARY SECONDARY TERTIARYReferences:Nafday, AM. (2011) Consequence-based structuraldesign approach for black swan events. StructuralSafety, 33(1): 108-114.Corso di Progettazione Strutturale antincendio Roma, 29 Ottobre 2014Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.LOADSDEAD XLIVE XSNOW XEARTHQUAKE XFIRE X XEXPLOSIONS X X“BLACK SWAN” XMember-basedstructural designConsequence-basedstructural designBlack Swan event:- unpredictable,- large impact on community,- easy to predict after its occurrence.
  • 20. Structural robustness in designUncertainty in the likelihood thatthe harmful consequences of aparticular event will be realizedUncertainty in the consequencesrelated to the specific eventCorso di Progettazione Strutturale antincendio Roma, 29 Ottobre 2014Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.PrimarydesignSecondarydesignTertiarydesign
  • 21. CauseVulnerabilityBlackSwanDamageIndex• Significant collapse cases• LPHC events and Black Swans• Structural robustness in qualitative terms• Structural robustness in civil engineeringMemberconsequencefactorCorso di Progettazione Strutturale antincendio Roma, 29 Ottobre 2014Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.design• Collapse types• Structural robustness and progressive collapsedefinitions• Measures against progressive collapse• Quantification of robustness• Robustness and optimization• Member consequence factor• Assessment of simple structures• Assessment of complex structures• What now/next?• ReferencesRobustnessCollapseresistanceProgressivecollapsePhoto Credit: Wikipedia Commons.
  • 22. STRUCTURE& LOADSBad VS Good collapseCollapseMechanismNO SWAY“IMPLOSION”OF THESTRUCTUREis a process in whichobjects are destroyed bycollapsing on themselves“EXPLOSION”OF THESTRUCTUREis a processNOT CONFINEDSWAYCorso di Progettazione Strutturale antincendio Roma, 29 Ottobre 2014Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
  • 23. PancakeInitial load-bearing element failure thattriggers the rigid fall of a part of thestructure onto another and leads to asequential impacts on the rest of thestructure, that collapses on itself.Collapse typesZipper DominoCharacteristic feature is the forceredistribution into alternative paths,impulsive loading due to sudden elementfailure and force concentration in elementsto fail next.Initial element rigid overturning andfalling over another element, that, bymeans of transformation of potential intokinetic energy, trigger the overturning ofthe following element.Section Instability MixedInitial cross-section cut and stressconcentration that cause the rupture offurther cross-sectional parts (fast fracture)and failure progression throughout theentire section.The destabilization of some load-carryingelements in compression due to an initialfailure of stabilizing elements can trigger afailure progression throughout thestructure.Some collapses are less amenable togeneralization because the relativeimportance of the contributing basiccategories of collapse can vary andcombine in progression of failures.- DOMINO + PANCAKE(e.g. A.P.Murrah Building, Buildingduring Izmit Earquake)- ZIPPER + INSTABILITY(e.g. cable-stayed bridges)Reference: Betoncalendar, 2008 (adapted from “Structural integrity: robustness assessment and progressive collapsesusceptibility”, Luisa Giuliani, PhD Thesis, Sapienza University of Rome, Dipartimento di Ingegneria Strutturale e Geotecnica)Corso di Progettazione Strutturale antincendio Roma, 29 Ottobre 2014Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
  • 24. PancakeInitial load-bearing element failure thattriggers the rigid fall of a part of thestructure onto another and leads to asequential impacts on the rest of thestructure, that collapses on itself.Collapse typesZipper DominoCharacteristic feature is the forceredistribution into alternative paths,impulsive loading due to sudden elementfailure and force concentration in elementsto fail next.Initial element rigid overturning andfalling over another element, that, bymeans of transformation of potential intokinetic energy, trigger the overturning ofthe following element.Islamabad Earthquake 2005Münsterland, 2005Section Instability MixedInitial cross-section cut and stressconcentration that cause the rupture offurther cross-sectional parts (fast fracture)and failure progression throughout theentire section.The destabilization of some load-carryingelements in compression due to an initialfailure of stabilizing elements can trigger afailure progression throughout thestructure.Izmit Earthquake1999Some collapses are less amenable togeneralization because the relativeimportance of the contributing basiccategories of collapse can vary andcombine in progression of failures.- DOMINO + PANCAKE(e.g. A.P.Murrah Building, Buildingduring Izmit Earquake)- ZIPPER + INSTABILITY(e.g. cable-stayed bridges)Viaduct after earthquakeTanker S.S. Schenectady, 1941Reference: Betoncalendar, 2008 (adapted from “Structural integrity: robustness assessment and progressive collapsesusceptibility”, Luisa Giuliani, PhD Thesis, Sapienza University of Rome, Dipartimento di Ingegneria Strutturale e Geotecnica)Corso di Progettazione Strutturale antincendio Roma, 29 Ottobre 2014Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
  • 25. Design Strategy #1: Continuity (robust behavior-redundancy)The Boeing B-17 Flying Fortress collided with another aircraft during World War II and, althoughsustaining large amount of structural damage, landed safely, due to the high redundancy of thefuselage connections.Corso di Progettazione Strutturale antincendio Roma, 29 Ottobre 2014Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
  • 26. Design Strategy #1: Continuity (robust behavior-redundancy)Plane crash on the EmpireState Building, 1945On July 1945 a B-25 bomber crashed into the Empire State Building, The impact of the planecreated a 5.5x6 m hole in the side of the tower. This crash caused extensive damage to themasonry 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 theintrinsic redundancy of its framed system.Corso di Progettazione Strutturale antincendio Roma, 29 Ottobre 2014Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
  • 27. Design Strategy #2: Segmentation (Compartmentalization)Aloha Boeing 737, April 1988(compartmentalization by strengthening)A service-induced damage led to explosive decompression and loss of large portion of fuselageskin when small fatigue crack suddenly linked together. The subsequent fracture was eventuallyarrested by fuselage frame structure and the craft landed safely.Corso di Progettazione Strutturale antincendio Roma, 29 Ottobre 2014Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
  • 28. Design Strategy #2: Segmentation (Compartmentalization)The partial collapse, started in the roof and due design and execution errors, stoped at the two jointswhich separated the collapsing section from the adjacent structures.A higher continuity could have unlikely sustained the forces during collapse, since the constructiondeficiencies affected also adjacent sections.Corso di Progettazione Strutturale antincendio Roma, 29 Ottobre 2014Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
  • 29. CauseVulnerabilityBlackSwanDamageIndex• Significant collapse cases• LPHC events and Black Swans• Structural robustness in qualitative terms• Structural robustness in civil engineeringMemberconsequencefactorCorso di Progettazione Strutturale antincendio Roma, 29 Ottobre 2014Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.design• Collapse types• Structural robustness and progressive collapsedefinitions• Measures against progressive collapse• Quantification of robustness• Robustness and optimization• Member consequence factor• Assessment of simple structures• Assessment of complex structures• What now/next?• ReferencesRobustnessCollapseresistanceProgressivecollapsePhoto Credit: Wikipedia Commons.
  • 30. Structural RobustnessDefinitions:1- "The ability of a structure to withstand events like fire, explosions,impact or the consequences of human error without being damaged to anextent disproportionate to the original cause." (EN 1991-1-7 2006)2- "The robustness of a structure, intended as its ability not to sufferdisproportionate damages as a result of limited initial failure, is anintrinsic 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." ComitéEuropean de Normalization (CEN).(Bontempi F, Giuliani L, Gkoumas K, 2007): "Handling the exceptions: robustness assessment of a complex structuralsystem.“, Invited Lecture, Structural Engineering, Mechanics and Computation (SEMC) 3, 1747-1752.(Starossek U, 2009): “Progressive collapse of structures.” London: Thomas Telford Publishing, 2009.Corso di Progettazione Strutturale antincendio Roma, 29 Ottobre 2014Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
  • 31. Progressive CollapseDefinitions:1-"Progressive collapse is defined as the spread of an initial local failurefrom element to element resulting, eventually, in the collapse of an entirestructure or a disproportionate large part of it." (ASCE 7-05 2005)2- "A progressive collapse is a situation where local failure of a primarystructural component leads to the collapse of adjoining members which, inturn, leads to additional collapse. Hence, the total collapse isdisproportionate to the original cause." (GSA 2003)3-"Progressive collapse: a chain reaction failure of building members to anextent disproportionate to the original localized damage." (UFC 4-010-012003)Corso di Progettazione Strutturale antincendio Roma, 29 Ottobre 2014Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.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 majormodernization projects." General Services Administration (GSA).(UFC 4-010-01 2003): "DoD minimum antiterrorism standards for buildings." Department of Defense (DoD).
  • 32. Progressive Collapse VS Disproportionate CollapseObservations:− A progressive collapse is one which develops in a progressive manner akin to the collapseof a row of dominos.− A disproportionate collapse is one which is judged (by some measure defined by theobserver) to be disproportionate to the initial cause. This is merely a judgement made onobservations 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, acollapse may be disproportionate but not necessarily progressive if, for example, thecollapse 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 usedinterchangeably because disproportionate collapse often occurs in a progressive mannerand progressive collapse can be disproportionate.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.Corso di Progettazione Strutturale antincendio Roma, 29 Ottobre 2014Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
  • 33. Robustness and collapse resistance in a dependability frameworkSgambi, L., Gkoumas, K. and Bontempi, F. (2012), “Geneticalgorithms for the dependability assurance in the design of a long-spansuspension bridge”, Comput-Aided Civ. Inf., 27(9), 655-675.Corso di Progettazione Strutturale antincendio Roma, 29 Ottobre 2014Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
  • 34. CauseVulnerabilityBlackSwanDamageIndex• Significant collapse cases• LPHC events and Black Swans• Structural robustness in qualitative terms• Structural robustness in civil engineeringMemberconsequencefactorCorso di Progettazione Strutturale antincendio Roma, 29 Ottobre 2014Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.design• Collapse types• Structural robustness and progressive collapsedefinitions• Measures against progressive collapse• Quantification of robustness• Robustness and optimization• Member consequence factor• Assessment of simple structures• Assessment of complex structures• What now/next?• ReferencesRobustnessCollapseresistanceProgressivecollapsePhoto Credit: Wikipedia Commons.
  • 35. Measures against disproportionate collapseThe currently available design strategies and methods toprevent 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 onBridge Maintenance, Safety, and Management Seoul, Korea, July 13-17, 2008Corso di Progettazione Strutturale antincendio Roma, 29 Ottobre 2014Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
  • 36. Design strategies against progressive collapseReference:Giuliani, L., 2012. Structural safety in case of extreme actions. International Journal of Lifecycle Performance EngineeringIJLCPE Special Issue on: "Performance and Robustness of Complex Structural Systems", Guest Editor Franco Bontempi, ISSN(Online): 2043-8656 - ISSN (Print): 2043-8648.Corso di Progettazione Strutturale antincendio Roma, 29 Ottobre 2014Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
  • 37. CauseVulnerabilityBlackSwanDamageIndex• Significant collapse cases• LPHC events and Black Swans• Structural robustness in qualitative terms• Structural robustness in civil engineeringMemberconsequencefactorCorso di Progettazione Strutturale antincendio Roma, 29 Ottobre 2014Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.design• Collapse types• Structural robustness and progressive collapsedefinitions• Measures against progressive collapse• Quantification of robustness• Robustness and optimization• Member consequence factor• Assessment of simple structures• Assessment of complex structures• What now/next?• ReferencesRobustnessCollapseresistanceProgressivecollapsePhoto Credit: Wikipedia Commons.
  • 38. RISK-BASEDStructural Robustness assessment[Faber, 2005]A Withstand actions, eventsRdirect riskdirRIdir indrob RDAMAGE-BASED indirect risk[Yan&Chang, 2006] [Biondini &ithelement stiffness matrix(integer state)ni 1tr(K )i'itr(K )damagedelementsStiff .Deg.ithelement stiffnessmatrix (damaged state)Frangopol, 2008] energy between intactand damaged system(backward pseudo-loads)01  energy between intactand damaged system(forward pseudo-loads) IndirectRisk DirectRiskReference:Olmati, P., Brando, F., Gkoumas, K. “Robustness assessment of a Steel Truss Bridge”, ASCE/SEI Structures Congress,Pittsburgh, Pennsylvania, May 2-4, 2013.Corso di Progettazione Strutturale antincendio Roma, 29 Ottobre 2014Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.BWithstand damagesOther: TOPOLOGY-BASED ENERGY-BASED
  • 39. Risk Based Structural Robustness assessmentEXBD: Exposure before damageD : DamageD : No DamageF : Probability of system failureCdir : Direct consequencesCind: Indirect consequences[Baker et al. 2008]dirR“A robust system is considered to be one where indirectrisks do not contribute significantly to the total systemrisk”Rdir˃˃RindRdir: associati con il danni inizialiRind: associati con danni successiviCorso di Progettazione Strutturale antincendio Roma, 29 Ottobre 2014Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.Idir indrob RRdirect riskindirect riskReference:Baker J.W., Schubert M., Faber M.H., (2008). On the Assessment of Robustness, Journal of Structural Safety, Volume30, Issue 3, pp. 253-267, DOI:10.1016/j.strusafe.2006.11.004
  • 40. Member consequence factor and robustness assessmentlimit state design 푅 − 퐸 ≥ 0 11  MR Rdγ γ R γ γ E 0 k ME E kResistance (probabilistic) Solicitation (probabilistic)푢푛푑푎푚푎푔푒푑 − 퐸푑푅푑푢푛푑푎푚푎푔푒푑 ≥ 0member-based designResistance (design values) Solicitation (design values)Member consequence factor based design푢푛푑푎푚푎푔푒푑−퐸푑푆푐푒푛푎푟푖표)푅푑f MR        (1 − 퐶푓푢푛푑푎푚푎푔푒푑 ≥ 00 ≤ 퐶푓 ≤ 11Rd1(1 C )*( R ) E 0 k ME Ed k• 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 thenominal 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.Corso di Progettazione Strutturale antincendio Roma, 29 Ottobre 2014Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
  • 41. Member consequence factor and robustness assessment• The structure is subjected to a set of damage scenarios and the consequence of thedamages is evaluated by the member consequence factor (퐶푆푐푒푛푎푟푖표푓) that forconvenience 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 퐶푓푆푐푒푛푎푟푖표 , intended as theeffective coefficient that affects directly the resistance.• 퐶푓푆푐푒푛푎푟푖표is evaluated by the maximum percentage difference of the structural stiffnessmatrix eigenvalues of the damaged and undamaged configurations of the structure.푆푐푒푛푎푟푖표 = 푚푎푥퐶푓푢푛 − 휆푖푑휆푖푎푚푢푛 100휆푖푖=1−푁푢푛and 휆푖푑Corso di Progettazione Strutturale antincendio Roma, 29 Ottobre 2014Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.where, 휆푖푎푚are respectively the i-th eigenvalue of the structural stiffnessmatrix in the undamaged and damaged configuration, and N is the total number of theeigenvalues.
  • 42. Member consequence factor and robustness assessment• The corresponding robustness index (푅푆푐푒푛푎푟푖표) is therefore defined as:푆푐푒푛푎푟푖표푅푆푐푒푛푎푟푖표=1 - 퐶푓• Values of Cf close to 100% mean that the failure of the structural member mostlikely causes a global structural collapse.• Low values of Cf do not necessarily mean that the structure survives after the failureof the structural member: this is something that must be established by additionalanalysis that considers the loss of the specific structural member.• A value of Cf close to 0% means that the structure has a good structuralrobustness.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) ina particular zone; and,2. Structures that have cable structural system (e.g., tensile structures, suspensionCorso di Progettazione Strutturale antincendio Roma, 29 Ottobre 2014Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.bridges).
  • 43. CauseVulnerabilityBlackSwanDamageIndex• Significant collapse cases• LPHC events and Black Swans• Structural robustness in qualitative terms• Structural robustness in civil engineeringMemberconsequencefactorCorso di Progettazione Strutturale antincendio Roma, 29 Ottobre 2014Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.design• Collapse types• Structural robustness and progressive collapsedefinitions• Measures against progressive collapse• Quantification of robustness• Robustness and optimization• Member consequence factor• Assessment of simple structures• Assessment of complex structures• What now/next?• ReferencesRobustnessCollapseresistanceProgressivecollapsePhoto Credit: Wikipedia Commons.
  • 44. Robustness in Optimization• The objective function for optimization may be very complexand depend on the type of the structural system, robustnessmeasures, characteristics of failure consequences andprobabilities of occurrence and intensities of various hazards.• If the total cost of robustness measures exceeds the reductionin failure consequences, then the system may be considered asrobust but uneconomic. In such a situation, probabilisticmethods of risk assessment may be effectively usedCost of robustness measures ≤ Reduction of failure consequencesReference:COST Action TU0601 Robustness of Structures STRUCTURAL ROBUSTNESS DESIGN FOR PRACTISINGENGINEERS. EUROPEAN COOPERATION IN SCIENCE AND TECHNOLOGY, Editor T. D. Gerard Canisius.Corso di Progettazione Strutturale antincendio Roma, 29 Ottobre 2014Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
  • 45. Robustness in OptimizationObjective function:Robustness term:Pfi: probability of the i-th failure modem: number of failure modesExample: Hierarchy of the failure modes (“weak beam/strong column”)...develop the less catastrophic failuremodes first....ranking the failure modes in terms ofa hierarchy in such a way that the lessharmful ones are generated at lowerloading levelsA robust structure requires the plastic moment of the column, MPc, being larger than theone of the beam, MPb; that is, Z = MPc– MPb≥ 0μc, σc, μb, σb: means and the standard deviations of the plastic moments of the columns andof the beam, respectively.To ensure robustness, the index I needs to be kept positive. The objective is, therefore, tominimize FI=-I.Reference:Casciati, S. and Faravelli, L. (2008) Building a Robustness Index. Robustness of Structures COST Action TU0601,1stWorkshop, February 4-5, ETH Zurich, Switzerland.Corso di Progettazione Strutturale antincendio Roma, 29 Ottobre 2014Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
  • 46. CauseVulnerabilityBlackSwanDamageIndex• Significant collapse cases• LPHC events and Black Swans• Structural robustness in qualitative terms• Structural robustness in civil engineeringMemberconsequencefactorCorso di Progettazione Strutturale antincendio Roma, 29 Ottobre 2014Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.design• Collapse types• Structural robustness and progressive collapsedefinitions• Measures against progressive collapse• Quantification of robustness• Robustness and optimization• Member consequence factor• Assessment of simple structures• Assessment of complex structures• What now/next?• ReferencesRobustnessCollapseresistanceProgressivecollapsePhoto Credit: Wikipedia Commons.
  • 47. Structural Robustness assessment - overviewStiffness matrixKun λiEigenvaluesunKdam λidamConsequence factori 1 N( )  scenario if 100unidamiunC max Rscenario= 100 - C scenariofRobustness index Corso di Progettazione Strutturale antincendio Roma, 29 Ottobre 2014Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
  • 48. Single damage – analytic calculationy Kun =x( )  R1 = 100 − CfbCorso di Progettazione Strutturale antincendio Roma, 29 Ottobre 2014Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.kakb10 00 10Cf11 = 0% Cf21 = 30%R1 = 70%1aN: total eigenvalues numberi: single eigenvalue numbera and b: elementsi 1 Nunidamiunscenario if 100C max Kdam =10 00 7Scenario 1
  • 49. Cumulative damage – numerical assessment• Single bay frame structure with a diagonal beam brace, composed in total of 5Corso di Progettazione Strutturale antincendio Roma, 29 Ottobre 2014Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.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 thedamage is cumulative: this means that the each scenario includes the damage from theprevious one.DSj = Σi=(1-j) di
  • 50. Cumulative damage – numerical assessment• star-shaped structure – 8 members - pipe cross section - 20 centimeters outsidediameter - 20 millimeters thickness - S235 steel.• members 1, 3, 5, and 7 are 0.5 meters long and members 2, 4, 6, and 8 are 0.7meters long.All the members are connected to each other by a fixed type connection. Also the boundaryconditions are of the fixed type and the structure is plane.DSj = Σi=(1-j) diCorso di Progettazione Strutturale antincendio Roma, 29 Ottobre 2014Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
  • 51. CauseVulnerabilityBlackSwanDamageIndex• Significant collapse cases• LPHC events and Black Swans• Structural robustness in qualitative terms• Structural robustness in civil engineeringMemberconsequencefactorCorso di Progettazione Strutturale antincendio Roma, 29 Ottobre 2014Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.design• Collapse types• Structural robustness and progressive collapsedefinitions• Measures against progressive collapse• Quantification of robustness• Robustness and optimization• Member consequence factor• Assessment of simple structures• Assessment of complex structures• What now/next?• ReferencesRobustnessCollapseresistanceProgressivecollapsePhoto Credit: Wikipedia Commons.
  • 52. I-35 West Bridge, Minneapolis, MN• Built 1967• 3 spans, 1067 feet long• 1977 – new wearing surface• 1998 – curbs and railings replacedCorso di Progettazione Strutturale antincendio Roma, 29 Ottobre 2014Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
  • 53. Corso di Progettazione Strutturale antincendio Roma, 29 Ottobre 2014Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.NorthDowntownI-35 West Bridge, Minneapolis, MNPhoto from aircraft flying overhead.• At 6:05 pm on August 1st 2007 Bridge Collapsed• 13 People killed & approximately 145 Injured
  • 54. I-35 West Bridge, Minneapolis, MNI-35 W bridgeNTSB 2007Corso di Progettazione Strutturale antincendio Roma, 29 Ottobre 2014Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
  • 55. I-35 West Bridge, Minneapolis, MN – damage scenariosUndamagedDamagedscenarioCorso di Progettazione Strutturale antincendio Roma, 29 Ottobre 2014Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
  • 56. I-35 West Bridge, Minneapolis, MN – damage scenariosCorso di Progettazione Strutturale antincendio Roma, 29 Ottobre 2014Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.3D2D
  • 57. I-35 West Bridge, Minneapolis, MN – single damaged1d3 d2d4d5d71001008080606040402020d3 d4 d5 d6 d7 d1 d2 d3 d4 d5 d6 d7Damage scenario Damage scenarioCorso di Progettazione Strutturale antincendio Roma, 29 Ottobre 2014Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.d6375942 4535 3823634158 5565 627701 2 3 4 5 6 7Robustness %ScenarioCf max Robustness42 4535 382358 5565 62773 4 5 6 7ScenarioCf max Robustness83 87 885360866417 13 124740143601 2 3 4 5 6 7Robustness %ScenarioCf max RobustnessDSj = di
  • 58. I-35 West Bridge, Minneapolis, MN/ enhanced– single damaged1d3 d2d4d5d7d610080604020d3 d4 d5 d6 d7 d1 d2 d3 d4 d5 d6 d7Damage scenario Damage scenarioCorso di Progettazione Strutturale antincendio Roma, 29 Ottobre 2014Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.42 4535 382358 5565 62773 4 5 6 7ScenarioCf max Robustness83 87 885360866417 13 124740143601 2 3 4 5 6 7Robustness %ScenarioCf max RobustnessDSj = di
  • 59. CauseVulnerabilityBlackSwanDamageIndex• Significant collapse cases• LPHC events and Black Swans• Structural robustness in qualitative terms• Structural robustness in civil engineeringMemberconsequencefactorCorso di Progettazione Strutturale antincendio Roma, 29 Ottobre 2014Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.design• Collapse types• Structural robustness and progressivecollapse 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?• ReferencesRobustnessCollapseresistanceProgressivecollapsePhoto Credit: Wikipedia Commons.
  • 60. (disaster) resilienceDefinition (not univocal):A resilient community is defined as the one having the ability to absorb disasterimpacts and rapidly return to normal socioeconomic activity.NEHRP (National Earthquake Hazards Reduction Program), 2010. “Comments on the Meaning of Resilience”. NEHRP Technicalreport. Available at http://www.nehrp.gov/pdf/ACEHRCommentsJan2010.pdfMCEER framework for resilience evaluation:Disaster strikesInitial losses Recovery time, depending on:• Resourcefulness• RapidityMCEER (Multidisciplinary Center for Earthquake Engineering Research), (2006). “MCEER’s Resilience Framework”. Available athttp://mceer.buffalo.edu/research/resilience/Resilience_10-24-06.pdfCorso di Progettazione Strutturale antincendio Roma, 29 Ottobre 2014Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.SystemicRobustness
  • 61. (disaster) resilienceDefinition (not univocal):A resilient community is defined as the one having the ability to absorb disasterimpacts and rapidly return to normal socioeconomic activity.NEHRP (National Earthquake Hazards Reduction Program), 2010. “Comments on the Meaning of Resilience”. NEHRP Technicalreport. Available at http://www.nehrp.gov/pdf/ACEHRCommentsJan2010.pdfMCEER framework for resilience evaluation:Resilience is inversely proportional to the area A.(dQ/dt)L0TR(dQ/dt)0AMCEER (Multidisciplinary Center for Earthquake Engineering Research), (2006). “MCEER’s Resilience Framework”. Available athttp://mceer.buffalo.edu/research/resilience/Resilience_10-24-06.pdfCorso di Progettazione Strutturale antincendio Roma, 29 Ottobre 2014Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
  • 62. “anti-fragility”People/systems/organizations/things/ideas can be described in oneof three ways:- fragile- resilient, or- antifragile"Some things benefit from shocks; they thrive and grow whenexposed to volatility, randomness, disorder, and stressors and loveadventure, risk, and uncertainty. Yet, in spite of the ubiquity of thephenomenon, there is no word for the exact opposite of fragile.Let us call it anti-fragile. Anti-fragility is beyond resilience orrobustness. The resilient resists shocks and stays the same; theanti-fragile gets better".References: Taleb, Nassim Nicholas (November 2012). Antifragile: Things That Gain from Disorder(1st ed.). London:Penguin. p. 519. ISBN 1-400-06782-0.Corso di Progettazione Strutturale antincendio Roma, 29 Ottobre 2014Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
  • 63. Things that are fragilebreak or suffer fromchaos and randomness.The resilient, orrobust, don’t care ifcircumstances becomevolatile or disruptive(up to a point).Things that are anti-fragileReferences: Taleb, Nassim Nicholas (November 2012). Antifragile: Things That Gain from Disorder(1st ed.). London:Penguin. p. 519. ISBN 1-400-06782-0 .Corso di Progettazione Strutturale antincendio Roma, 29 Ottobre 2014Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.---------“anti-fragility”Beyond “Sissy” Resilience: On Becoming Antifragile. Available online athttp://www.artofmanliness.com/2013/12/03/beyond-sissy-resilience-on-becoming-antifragile/grow andstrengthen fromvolatility and stress (toa point).
  • 64. “anti-fragility”Fragile people/ systems/organizations are concave.As fluctuations increase (x-axis) youexperience more loss.Anti-fragile things are convex.As variability increases (x-axis),gains increase.References: Beyond “Sissy” Resilience: On Becoming Antifragile. Available online athttp://www.artofmanliness.com/2013/12/03/beyond-sissy-resilience-on-becoming-antifragile/Corso di Progettazione Strutturale antincendio Roma, 29 Ottobre 2014Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
  • 65. CauseVulnerabilityBlackSwanDamageIndex• Significant collapse cases• LPHC events and Black Swans• Structural robustness in qualitative terms• Structural robustness in civil engineeringMemberconsequencefactorCorso di Progettazione Strutturale antincendio Roma, 29 Ottobre 2014Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.design• Collapse types• Structural robustness and progressivecollapse 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?• ReferencesRobustnessCollapseresistanceProgressivecollapsePhoto Credit: Wikipedia Commons.
  • 66. ReferencesAlashker, Y., Li, H. and El-Tawil, S. (2011), “Approximations in Progressive Collapse Modeling”, J. Struct. Eng.- ASCE, 137(9), 914-924.Arup (2011), Review of international research on structural robustness and disproportionate collapse, London: Department forCommunities and Local Government.ASCE 7-05 (2005), Minimum design loads for buildings and other structures, American Society of Civil Engineers (ASCE).Biondini, F. and Frangopol, D. (2009), “Lifetime reliability-based optimization of reinforced concrete cross-sections under corrosion”,Struct. Saf., 31(6), 483-489.Biondini, F., Frangopol, D.M. and Restelli, S. (2008), “On structural robustness, redundancy and static indeterminancy”, Proceedings ofthe 2008 Structures Congress, April 24-26, 2008, Vancouver, BC, Canada.Bontempi, F. and Giuliani, L. (2008), “Nonlinear dynamic analysis for the structural robustness assessment of a complex structuralsystem”, Proceedings of the 2008 Structures Congress, April 24-26, 2008, Vancouver, BC, Canada.Bontempi, F., Giuliani, L. and Gkoumas, K. (2007), “Handling the exceptions: dependability of systems and structural robustness”, InvitedLecture, Proceedings of the 3rd International Conference on Structural Engineering, Mechanics and Computation (SEMC), Cape Town,South Africa, September 10-12.Brando, F., Testa, R.B. and Bontempi, F. (2010), “Multilevel structural analysis for robustness assessment of a steel truss bridge”, BridgeMaintenance, Safety, Management and Life-Cycle Optimization - Frangopol, Sause and Kusko (eds), Taylor & Francis Group, London,ISBN 978-0-415-87786-2.Canisius, T.D.G., Sorensen, J.D. and Baker, J.W. (2007), “Robustness of structural systems - A new focus for the Joint Committee onStructural Safety (JCSS)”, Proceedings of the 10th Int. Conf. on Applications of Statistics and Probability in Civil Engineering(ICASP10), Taylor and Francis, London.Casciati, S. and Faravelli, L. (2008) Building a Robustness Index. Robustness of Structures COST Action TU0601, 1st Workshop,February 4-5, 2008, ETH Zurich, Zurich, Switzerland.Cha, E. J. and Ellingwood, B. R. (2012), “Risk-averse decision-making for civil infrastructure exposed to low-probability, high-consequenceevents”, Reliab. Eng. Syst. Safe., 104(1), 27-35.Choi, J-h. and Chang, D-k. (2009), “Prevention of progressive collapse for building structures to member disappearance by accidentalactions”, J. Loss Prevent. Proc., 22(6), 1016-1019.COST (2011), TU0601 - Structural Robustness Design for Practising Engineers, Canisius, T.D.G. (Editor).Crosti, C. and Duthinh, D. (2012), “Simplified gusset plate model for failure prediction of truss bridges”, Bridge Maintenance, Safety,Management, Resilience and Sustainability - Proceedings of the 6th International Conference on Bridge Maintenance, Safety andManagement, IABMAS 2012, Italy, Stresa, 8-12 July 2012.Crosti, C., Duthinh, D. and Simiu, E. (2011), “Risk consistency and synergy in multihazard design”, J. Struct. Eng.- ASCE, 137(8), 844-849.Corso di Progettazione Strutturale antincendio Roma, 29 Ottobre 2014Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
  • 67. ReferencesDoD - Department of Defense (2009), Unified Facilities Criteria (UFC). Report No. UFC 4-023-03: Design of buildings to resistprogressive collapse. Washington DC: National Institute of Building Sciences.Ellingwood, B. (2002), “Load and resistance factor criteria for progressive collapse design”, Proceedings of Workshop on Prevention ofProgressive Collapse, National Institute of Building Sciences, Washington, D.CEllingwood, B.R. and Dusenberry, D.O. (2005), “Building design for abnormal loads and progressive collapse”, Comput-Aided Civ. Inf.,20(3), 194-205.Ellingwood, B.R., Smilowitz, R., Dusenberry, D.O., Duthinh, D. and Carino, N.J. (2007), Report No. NISTIR 7396: Best practices forreducing the potential for progressive collapse in buildings. Washington DC: National Institute of Standards and Technology (NIST)EN 1990 (2002), Eurocode - Basis of structural design.Faber, M.H. and Stewart, M.G. (2003), “Risk assessment for civil engineering facilities: critical overview and discussion”, Reliab. Eng.Syst. Safe., 80(2), 173-184.FHWA(2011), Framework for Improving Resilience of Bridge Design, Publication No IF-11-016.Galal, K. and El-Sawy, T. (2010), “Effect of retrofit strategies on mitigating progressive collapse of steel frame structures”, J. Constr. SteelRes., 66(4), 520-531.Ghosn, M. and Moses, F. (1998), NCHRP Report 406: Redundancy in Highway Bridge Superstructures, TRB, National Research Council,Washington, D.C.Giuliani, L. (2012), “Structural safety in case of extreme actions”, Special Issue on: “Performance and Robustness of Complex StructuralSystems”, Int. J. of Lifecycle Performance Engineering (IJLCPE), 1(1), 22-40.GSA - General Service Administration (2003), Progressive collapse analysis and design guidelines for new federal office buildings andmajor modernization project, Washington DC: GSA.Hoffman, S. T. and Fahnestock, L. A. (2011), “Behavior of multi-story steel buildings under dynamic column loss scenarios”, SteelCompos. Struc., 11(2), 149-168.HSE - Health and Safety Executive (2001), Reducing risks, protecting people, HSE’s decision-making process, United King: Crowncopyright.Izzuddin, B. A., Vlassis, A. G., Elghazouli, A. Y. and Nethercot, D. A. (2008a), “Progressive collapse of multi-storey buildings due tosudden column loss - Part I: Simplified assessment framework”, Eng. Struct., 30(5), 1308-1318.Izzuddin, B. A., Vlassis, A. G., Elghazouli, A. Y. and Nethercot, D. A. (2008b), “Progressive collapse of multi-storey buildings due tosudden column loss - Part II: Application”, Eng. Struct., 30(5), 1424-1438.Kim, J. and Kim, T. (2009), “Assessment of progressive collapse-resisting capacity of steel moment frames”, J. Constr. Steel Res., 65(1),169-179.Corso di Progettazione Strutturale antincendio Roma, 29 Ottobre 2014Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
  • 68. ReferencesKwasniewski, L. (2010), “Nonlinear dynamic simulations of progressive collapse for a multistory building”, Eng. Struct., 32(5), 1223-1235.Malla, R.B., Agarwal, P. and Ahmad, R. (2011), “Dynamic analysis methodology for progressive failure of truss structures consideringinelastic postbuckling cyclic member behavior”, Eng. Struct., 33(5), 1503-1513.Miyachi, K., Nakamura, S. and Manda, A. (2012), “Progressive collapse analysis of steel truss bridges and evaluation of ductility”, J.Constr. Steel Res., 78, 192-200.Nafday, A.M. (2008), “System Safety Performance Metrics for Skeletal Structures”, J. Struct. Eng.- ASCE, 134(3), 499-504.Nafday, A.M. (2011), “Consequence-based structural design approach for black swan events”, Struct. Saf., 33(1), 108-114.Olmati, P., Gkoumas, K., Brando, F., Cao, L. (2013) “Consequence-based robustness assessment of a steel truss bridge”, Steel andComposite Structures, An International Journal, 14(4), 379-395.Rezvani, F. H. and Asgarian, B. (2012), “Element loss analysis of concentrically braced frames considering structural performancecriteria”, Steel Compos. Struc., 12(3), 231-248.Saydam, D. and Frangopol, D. M. (2011), “Time-dependent performance indicators of damaged bridge superstructures”, Eng. Struct.,33(9), 2458-2471.Starossek, U. (2009), Progressive collapse of structures, London: Thomas Telford Publishing.Starossek, U. and Haberland, M. (2010), “Disproportionate Collapse: Terminology and Procedures”, J. Perf. Constr. Fac. 24(6), 519-528.Starossek, U. and Haberland, M. (2012), “Robustness of structures”, Special Issue on: “Performance and Robustness of ComplexStructural Systems”, Int. J. of Lifecycle Performance Engineering (IJLCPE), 1(1), 3-21.Taleb, Nassim Nicholas (April 2007). The Black Swan: The Impact of the Highly Improbable (1st ed.). London: Penguin. p. 400. ISBN 1-84614045-5.Yuan, W. and Tan, K. H. (2011), “Modeling of progressive collapse of a multi-storey structure using a spring-mass-damper system”,Struct. Eng. Mech., 37(1), 79-93.Taleb, Nassim Nicholas (November 2012). Antifragile: Things That Gain from Disorder(1st ed.). London: Penguin. p. 519. ISBN 1-400-06782-0Corso di Progettazione Strutturale antincendio Roma, 29 Ottobre 2014Prof.-Ing. Franco Bontempi, Ing. Konstantinos Gkoumas, Ph.D.
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