robustness - novembre 2014

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Progressive collapsePerformance Based Seismic DesignSteel framed structuresCatastrophic eventsCatenary effect

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Later on, the robustness of studied structures under different column-removed conditions, related to

apse

rerequperiod

must be conned within the stories above and below the onewhere the component is removed. Therefore, it is clear that thisproblem must be incorporated in the design process. In particular,on one hand, signicant uncertainties in the problem formulationand, on the other hand, the appropriate assessment of the structurerobustness should be considered. With reference to the second

licit investigationritical failure sce-ystem canf environ

conditions without noticeable effects in terms of servicelimit state.

The assessment of robustness is of increasing interest intural design. It is aimed to achieve robust structures, which possessoptimum performance under environmental oscillations. So, inaccordance with traditional design methods, the robust structuraldesign is made by solving an optimization problem. Commonly,all variable parameters are considered as random quantities, whichallow to assess structural robustness in probabilistic way. Thecorresponding optimization problem for achieving robustness

Corresponding author. Tel.: +39 081 7682438; fax: +39 081 5934792.E-mail addresses: [email protected] (A. Formisano), [email protected]

(R. Landolfo), [email protected] (F.M. Mazzolani).

Computers and Structures xxx (2014) xxxxxx

Contents lists availab

Computers an

lsethe building and (c) reducing the building sensitivity to dispropor-tionate collapse [2]. In the latter case, designers are required to cer-tify that removal of any structural building component does notproduce a total collapse. Furthermore, any resulting local damage

context of structural vulnerability with an expof the structural performance in comparison to cnarios. From the second perspective, a robust sstand either occasional or frequent changes ohttp://dx.doi.org/10.1016/j.compstruc.2014.09.0100045-7949/ 2014 Civil-Comp Ltd and Elsevier Ltd. All rights reserved.

Please cite this article in press as: Formisano A et al. Robustness assessment approaches for steel framed structures under catastrophic events. CStruct (2014), http://dx.doi.org/10.1016/j.compstruc.2014.09.010with-mentalability

struc-when the structure response is proportioned to the actions appliedto it. These actions could appear in different ways, e.g. loadsexceeding the design ones, accidental loads or damage tomembers.

A robust structure should be achieved by: (a) either preventingthe action or reducing it to an acceptable probability, (b) protecting

mance under exceptional conditions has been appraised, the sec-ond has been focused on the application of normally randomconditions. According to the rst perspective, a structure can bedeclared as robust when either collapse is not sudden or the resis-tance is not substantially lost although the deformations exceedthe serviceability level. Those developments also appear in the1. Robustness and progressive coll

Robustness is one of the main poperate without failure over a timedifferent catastrophic events (blast, impact, re and so on), has been assessed by means of two force-based analysis techniques (a literature approach and a more advanced procedure) in order to estimatetheir resistance against progressive collapse.The application of the two methods has allowed to calculate the robustness index of examined

structures, by taking into account the inuence of both the catenary effect phenomenon and differentbeam-to-column joints, with the nal aim to show their behavioural difference in terms of robustness.

2014 Civil-Comp Ltd and Elsevier Ltd. All rights reserved.

isite of a structure to[1]. It is accomplished

aspect, it should be underlined that no general denition of robust-ness exists.

In the past decades the robustness has been evaluated undertwo different points of view. Whilst in the rst the system perfor-Keywords:Robustness

First, within the methodologies used for robustness assessment under seismic loads, a deterministicmethod, framed within the Performance Based Seismic Design (PBSD), has been applied.Robustness assessment approaches for stcatastrophic events

A. Formisano , R. Landolfo, F.M. MazzolaniDepartment of Structures for Engineering and Architecture, University of Naples Federi

a r t i c l e i n f o

Article history:Accepted 29 September 2014Available online xxxx

a b s t r a c t

The current study deals wstrophic events. Two steelhave been herein analysedloads, through two investi

journal homepage: www.el framed structures under

, Piazzale Tecchio 80, 80125 Naples, Italy

he robustness assessment methods of steel framed buildings under cata-med buildings, designed according to old and new seismic Italian codes,considering the uncertainties of both the material strength and the appliedon methods.

le at ScienceDirect

d Structures

vier .com/locate /compstrucomput

generally aims at both an optimummean and a minimum varianceof the structural responses with respect to input variations. Never-theless, optimal design solutions are not often adopted in practicebecause, even if they can be considered as satisfactory from eco-nomic point of view, they are surely lacking in robustness. As awhole, the two viewpoints in understanding structural robustnessdo not contradict each other but complement one another andeven can be coupled.

When civil structures are not robust, the nal failure state isdisproportionately greater than the one initiating the collapse.So, the so called progressive collapse is attained, it being denedas the spread of an initial local failure from element to elementresulting, eventually, in the collapse of an entire structure or a dispro-portionately large part of it [3]. Thus, in structures susceptible toprogressive collapse, small events can have catastrophic conse-quences. According to this, the degree of progressivity of a col-lapse can be dened as the collapsed volume (or area) over thesame quantity directly destroyed by the event.

The concept of progressive collapse can be illustrated by thefamous failure of the Ronan Point building in London in 1968. This

case the robustness index is dened as the ratio between the directdamage and the total one and can assume different values chang-

2 A. Formisano et al. / Computers andbuilding, 22 stories high and made of precast concrete bearingwalls, suffered a gas explosion in a corner at the 18th oor whichproduced, by means of a chain reaction, the collapse of the cornerbay of the building from top to bottom (Fig. 1a).

More recently, the terrorist attacks on World Trade Centerbuildings on 2001 September 11th have represented a clear exam-ple of progressive collapse. A Boeing 767 crashed into the tower athigh speed and this caused structural damage near the impactpoint, producing also an intense re within the building (Fig. 1b).Then, as a result of the combination of impact damages and redamages, both buildings collapsed, since the weight and impactof the collapsing upper part of the towers caused a progressionof failure extending down to the ground.

Starting from these failure experiences under exceptionalactions, the interest on assessing structural robustness hasincreased in a large way in the recent years. In this framework,some efforts have been made by a large number of researchers,who have setup several code provisions (see Section 3). Neverthe-less, practice and reliable criteria either in measuring robustness ordetermining whether the robustness level of a system is acceptablehave not yet been given in detail. Therefore, based on some studiesperformed by Authors on robustness of existing buildings [4], therst step of the research within this eld is to establish a reliableFig. 1. Collapse of the Ronan Point building (a) and the World Trade Center towers(b).

Please cite this article in press as: Formisano A et al. Robustness assessment aStruct (2014), http://dx.doi.org/10.1016/j.compstruc.2014.09.010ing from zero (no robustness) to values greater than one (highrobustness, that is structural performance better than a given per-formance level).

2. Progressive collapse mitigation options

The progressive collapse design strategies have been classied,according to the recent literature sources [6,7], into the followingthree approaches:

(a) Specic local resistance and non-structural protective mea-sures (event control).

(b) Alternate load path.(c) Prescriptive design rules.

Approaches (a) and (b) are referred to as direct, since they arebased on analytical computations for specic load cases, whileapproach (c) is referred to as indirect, since it consists in applyingdesign rules to increase the overall robustness of a structure, with-out performing an analytical computation for a specic load case.

In the specic local resistance approach, key vertical load bear-ing elements are designed to resist anticipated threats, such asblast, loads or re.

The alternate load path approach consists in designing thestructure so that stresses can be redistributed after the loss of avertical bearing element.

The prescriptive design rules approach includes best practicerules, such as continuous reinforcement, minimum joint resistanceand ductility, redundant structural systems and so on. The tie forceprovisions adopted by the current codes are also included in thisapproach aiming at insuring a sufcient tying between horizontaland vertical building components, so that the structure may sus-methodology for evaluating the performance of structures sub-jected to exceptional actions.

So, in the present paper, starting from a general review of a con-ference paper written by Authors [5], two methods for assessingthe robustness of structures under exceptional earthquakes andaccidental loads (blast, impact and so on) have been implemented.

First of all, within the deterministic methodologies used forrobustness assessment under seismic loads, a method framedwithin the Performance Based Seismic Design has been conceived.In this case the robustness under exceptional earthquakes consid-ered in the new technical Italian code has been evaluated by usingan energetic approach. The method, based on the determination ofdirect and indirect damages suffered by structures under extremeearthquakes, has allowed to evaluate the structural robustness bycomparing the structure capacity curve with the demand spectrumrelated to an exceptional seismic event. In this case the vulnerabil-ity evaluation has been intended as the relationship betweenstructural integrity and robustness, in the sense that the robust-ness reserve of the structure has to be exploited in order to pre-serve its structural integrity. As a consequence, the directdamage deriving from the load application should be preventedand the indirect one should be really limited in order to avoidthe global structural collapse.

Later on, the robustness under different column-removed con-ditions, related to various catastrophic events, has been assessedby means of a new non-linear analysis method based on a LoadHistory Dependent (LHD) procedure able to take into account boththe catenary effect and the behaviour of connections. Also in this

Structures xxx (2014) xxxxxxtain the loss of a column through catenary (i.e. membrane) effects.The notional member removal provisions are applied with con-

ventional design checks and, therefore, they ignore the benecial

pproaches for steel framed structures under catastrophic events. Comput

proportionate) collapse, which is related to the structural robust-ness improvement under extreme accidental and natural events.

combination, involving dead, live and wind loads, is specied,along with a dynamic amplication factor of two, for static analy-

andNowadays, different international codes (EN 1991-1-7 [10],United States Department of Defense [8], the United States GeneralServices Administration [9] and UK Building Regulations [11]) haveprovided different denitions for the terms robustness and pro-gressive collapse, providing at the same time defensive measuresfor the construction protection.

As an example, according to EN 1991-1-7, the robustness isintended as the ability of a structure to withstand events like re,explosions, impacts or the consequence of human error, without beingdamaged to an extent disproportionate to the original cause.

On the other hand, different meaning for progressive collapseare used. In general terms, when one or several structural memberssuddenly fail due to either accident or attack and, subsequently,every load redistribution causes in sequence the failure of otherstructural elements, then the complete failure of the building orof a major part of it occurs and the progressive collapse is attained.In this framework, all the above codes specify the extent of damageconsidered as acceptable, by limiting the oor area where collapseis tolerated after the initial local failure.

More in detail, the United States General Services Administra-tion (GSA) released in June 2003 their guidelines for progressivecollapse mitigation to be applied for all USA federal buildings.The document provides a ow-chart methodology to determinewhether constructions require detailed verications against pro-gressive collapse. If the progressive collapse risk deserves to beconsidered, the document proposes the alternate load path designstrategy when a local initial failure happens. The document allowseffects of the catenary action nonlinear phenomenon. Conse-quently, this can lead to the prediction of an unrealistically largedamage area exceeding the prescribed limits. Also, a substantialamount of local damage due to notional member removal isallowed, but no guidance on debris resulting from such a damageon other building areas, which could potentially lead to the struc-ture progressive collapse, is given.

A further signicant shortcoming of the notional memberremoval provisions is the assumption of a static structuralresponse rather than a highly dynamic phenomenon. In this con-text, sudden column loss represents a more appropriate designscenario, also considered by two most recent USA guidelines[8,9] for progressive collapse mitigation, which includes thedynamic effect of the event. Although such a scenario has not thesame dynamic effect with respect to the column damage resultingfrom impact or blast, it is able to assess the inuence of the columnfailure over a short time on the structure response.

In this paper, after some literature methodologies are applied toquantify the robustness of some steel framed structures, a detailedbut simplied new procedure for their progressive collapse assess-ment is proposed considering sudden column loss as a design sce-nario. This modus operandi offers a quantitative approach forconsidering important issues in this eld, such as ductility, redun-dancy and energy absorption of structures. The simplicity of theproposed method is such that it can be directly applied in thedesign practice, so to transform the problem of structural robust-ness from general to quantiable.

3. Code provisions

The tragic failure of structures under exceptional actionsoccurred in the past years has pushed the scientic communityto nd the way to reduce the occurrence of the progressive (or dis-

A. Formisano et al. / Computersfor sophisticated nonlinear static and/or dynamic procedures, butdescribes in detail only a static linear procedure for progressivecollapse mitigation. The combination between dead and live loads,

Please cite this article in press as: Formisano A et al. Robustness assessment aStruct (2014), http://dx.doi.org/10.1016/j.compstruc.2014.09.010ses. The DoD step-by step procedure for linear static analysis issimilar to the GSA one in terms of general philosophy. The maindifferences lie in the choice of the material behaviour used in thesimulations, as well as in the fact that the non-linear proceduresare detailed in the DoD guidelines only.

The U.K. building regulations required that buildings bedesigned to resist disproportionate failure by tying together struc-tural elements, adding redundant members and providing suf-cient strength to resist abnormal loads. These requirements leadto more robust structures, that is strong and ductile constructionscapable to redistribute loads. In particular, these specications areintended to ensure that the structure may withstand a column lossthrough catenary effects. The load combination between dead, liveand wind loads is specied, as well as the area of tolerated damage.However, both no computational procedure to estimate the dam-age extension and no dynamic amplication factor are specied.If the damage amount exceeds the acceptance criterion, the partic-ular key element is designed to resist an additional static pressureof 34 kN/m2.

Finally, the Eurocode 1 part 1.7 provides a classication ofbuildings into four classes, based on the collapse consequences.For the lowest class, no progressive collapse requirements shouldbe met. For the second class, only horizontal tie force requirementsare specied. For the two remaining classes, not only tie require-ments should be met, but the structure also needs to be designedfor the loss of a vertical load bearing element, with damage notexceeding a specied region. If the damage is too extensive, thevertical load bearing element is considered as a key element andshould be designed to withstand an additional pressure of 34 kN/m2. Also in this case no computational procedure is specied forthe alternate load path analysis.

4. Robustness assessment methodologies

4.1. Under seismic actions

The most effective probabilistic method for robustness assess-ment is based on the work developed by the Joint Committee onStructural Safety [12], represented by the event tree shown inFig. 2.

First, modeling of exposures (EX) is done, they having the capac-ity to damage structural parts [13]. They include extreme values ofdesign loads, deterioration processes and also human errors duringthe whole structure life. When exposures occur, the structural sys-tem components can be either undamaged Dor damaged (D)according to several damage states which can lead to the failureas well as a dynamic amplication factor of two, is specied forstatic analyses in order to account for dynamic inertial effectsdue to the failure of one ground oor column. The GSA static linearguidelines are among the most complete provisions, since theyinstruct the designer in all steps of the design process.

Only the United States Department of Defense (DoD) guidelines,whose last version was delivered in 2005, provide details about thenonlinear procedures for progressive collapse prevention to beapplied. Buildings are classied according to the required protec-tion level. When a very low or low level of protection is required,the structure safety is ensured through horizontal and vertical ties,while for higher protection levels an alternate path approach isadditionally prescribed. A step-by-step procedure is provided forlinear static and non-linear static and dynamic analyses. The load

Structures xxx (2014) xxxxxx 3(F) or not F. Consequences are classied as either direct CDiror indirect CInd. The rst ones are represented from damage tostructural system parts. The second ones are due to either loss or


wheredesign

the m(Ddir,u)(Dtot),

(3) The SPC is such that Ddir,u > Dtot, which means Ir > 1 andIsi > 1; in this case Dtot = Ddir,d and at the intersection of thenominal PDC with the SPC dA/dD > 0, hence:Z Dtot0

RdD Z Ddir;d0

RdD 9

andfailure of the system functionality and can be attributed to lack ofrobustness. Consequences are generally represented by inconve-nience to system users, injuries, fatalities and/or monetary costs.In order to make a comparison among these effects, they can becombined into a scalar measure of consequences, often called util-ity (or disutility in case of negative consequences).

With the event tree dened in Fig. 2, it is possible to computethe system risk due to each possible event scenario. This is doneby multiplying the consequence of each scenario by its probabilityof occurrence and then integrating over all of the random variablesin the event tree. The risk corresponding to each branch is:

RDir Zx

ZyCDirP FjD y

P D yjEXBD x P EXBD x dydx 1

RInd Zx

ZyCIndP FjD y P D yjEXBD x P EXBD x dydx 2

A system is considered to be robust if indirect risks do not con-tribute signicantly to the total risk. Consequently, the followingindex of robustness Ir is proposed, it measuring the fraction of totalrisk resulting from direct consequences:

Ir RDirRDir RInd 3

The index can assume values between zero and one dependingupon the risk source. If the system is completely robust and thereare no risks related to indirect consequences, then Ir = 1. At theother extreme, if all risks are due to indirect consequences, thenIr = 0.

Based on Eq. (3), a deterministic procedure to dene the struc-ture robustness is needed aiming at evaluating how much thisreserve should be exploited in order to preserve the structuralintegrity [1416].

With reference to an ideal action system A, producing a globaldamage pattern D on the structure represented by means of theso called Structural Performance Curve (SPC) (resistance R dam-

EX

D

D

F

F

0

CDir

CDir+CInd

Fig. 2. Robustness quantication through an event tree.

4 A. Formisano et al. / Computersage D curve), the robustness index Ir can be dened. It is calculatedas the ratio between the maximum direct energy which can beabsorbed by the structural system, that is associated with directdamage, and the total energy, associated to both direct and indirectdamages (Fig. 3), absorbed by the structure as a consequence ofbeing exposed to a given action. Therefore, the following relation-ship is given:

Ir R Ddir;u0 RdDR Dtot0 RdD

4

For the purposes of practical calculations, Eq. (4) can be alsocomputed in approximate way as:

Ir R Ddir;u0 RdDR Dtot0 RdD

cDdir;uDtot

RuRd

5

Please cite this article in press as: Formisano A et al. Robustness assessment aStruct (2014), http://dx.doi.org/10.1016/j.compstruc.2014.09.010dened as Isi = Ddir,u/Dtot. Hence:

Ir cDdir;uDtotRuRd

cIsi RuRd 6

For a given PDC, three situations can occur:

(1) The SPC is below the PDC, which means Ir < 1 and Isi < 1; inthis case Dtot = Ddir,u + Dind, hence:

Z Dtot0

RdD Z Ddir;u0

RdDZ DtotDdir;u

RdD 7

(2) The SPC meets the PDC so as Ddir,u = Dtot, which means Ir = -Isi = 1; in this case at the intersection of the nominal PDCwith the SPC dA/dD = 0, hence:Z Dtot0

RdD Z Ddir;u0

RdD 8The counexpto und

If tdesign(RBD)out accorrestypica

4.2. Un

Whness cintendfailure

pproacaximum direct damage that the structure can withstandto the actual damage undergone due to the loading eventthen a structural integrity index can be conventionally(PDC), respectively (Fig. 3), and c, ranging in most cases from 1.1 to1.3, is a coefcient depending on the shape of the SPC.

If one observes that the ratio Ddir,u/Dtot represents the ratio ofRu and Rd are the structural ultimate resistance and theresistance for a given nominal curve of performance demandFig. 3. Denition of direct and indirect damaged.Structures xxx (2014) xxxxxxndition Ir > 1 allows for possible changes of the PDC due toected or accidental actions to be tolerated with a lower riskergo indirect damage.he commonly accepted performance levels for constructionare assumed, an ideal concept of Robustness-Based Designcan be dened, in which the structural design is carriedcording to predetermined levels of robustness, each of themponding to a value of the robustness index Ir. As a result, al multi-level performance matrix can be setup (Table 1).

der column-removed conditions

en a column is removed from a framed structure, its robust-an be assessed in terms of progressive collapse resistance,ed as the maximum loading capacity to be sustained before. In fact, when a building column failed in a sudden way due

hes for steel framed structures under catastrophic events. Comput

cityLS

jectiv

nterm

andto an accidental load, an instantaneous vertical loading equal to theone supported by the collapsed column is transferred to theremaining building part.

Different analysis types, namely linear static, non linear staticand non linear dynamic, are usually performed to evaluate the pro-gressive collapse resistance of framed buildings [17].

First of all, a step-by-step Linear Static (LS) procedure accordingto the US General Service Administration (GSA) and the Depart-ment of Defense (DoD) guidelines can be considered. In the GSAprocedure, a step-by-step scheme of inserting moment-releasehinges is used to simulate the inelastic structural behaviour. Inparticular, beam sections attaining a bending moment larger thantheir yielding one are replaced with hinges to simulate a structuralbehaviour in the plastic range. In this analysis, the vertical loadsapplied to the structure are gradually increased up to achieve alocal exural failure mechanism resulting in the building progres-sive collapse. Catenary effect is neglected and only exural failuremode is considered. The loaddisplacement response from LS anal-yses is obtained by putting on the abscissa axis the displacement ofthe column removed point and on the ordinate the correspondingapplied load. Generally, the buildings have an approximate linearbehaviour up to the attainment of the progressive collapse resis-tance. So, the loaddisplacement curves are very similar to theresponse of an elastic-perfectly plastic model. As a consequence,this procedure should be used for elastic analysis only.

Instead, a displacement control procedure is utilised to carryout Non Linear Static (NLS) analyses. First dead loads and a per-centage of live loads are applied to the building and, consequently,a vertical pushover analysis is executed. Particularly, a vertical dis-placement is gradually applied to the column-removed point up tothe maximum building resistance attainment. Generally, this anal-ysis type provides a progressive collapse strength lower than theone obtained with linear static procedures. Besides, the responsecurve reached from the non linear static analysis starts to deviatein a signicant way from the static linear one when the structureis considerably pushed into the inelastic eld.

However, it is clear that the building behaviour under excep-

Table 1Performance matrix accounting for robustness levels.

Nominal design capaPERFORMANCE LEVEL FO OFrequent event Occasional event Rare event Very rare or catastrophic event

Maximum ob

I

A. Formisano et al. / Computerstional actions deriving from a column collapse is a dynamic prob-lem rather than a static one. Therefore, under this circumstance, itis more appropriate to perform Non Linear Dynamic (NLD) analy-ses aiming at assessing the real progressive collapse resistance ofbuildings. Nevertheless, this analysis typology, which generallyprovides a lower collapse resistance than static analyses one, istime-consuming and result to be too difcult to be carried outfor practical design applications. As a consequence, instead to per-form NLD analyses, an alternative method has been proposed in lit-erature in order to estimate precisely the building collapseresistance under the described exceptional situation [18]. This isillustrated in Fig. 4, where considering that the area below thenon linear static loaddisplacement curve represents the energystored by the column-removed building under gravity loads, acapacity curve can be accomplished by dividing the accumulatedenergy by its corresponding displacements.

Please cite this article in press as: Formisano A et al. Robustness assessment aStruct (2014), http://dx.doi.org/10.1016/j.compstruc.2014.09.010It was demonstrated that this capacity curve is able to approxi-mate very well the non linear dynamic behaviour of buildingswhen a column collapses. Based on the energy conservation prin-ciple, FCC (DCC) in Fig. 4 represents the equivalent dynamic loadingunder the displacement demand DCC. Accordingly, when the build-ing is deprived of a column, the column-removed point attain amaximum displacement such that both the hatched areas ofFig. 4 are equal.

So, even if the precision of non linear dynamic results is unques-tionable, generally more simple analyses, that is static ones, areused. In these cases, in order to take into account the dynamiceffect due to the removal of a column, the vertical loadings areincreased by means of a Dynamic Amplication Factor (DAF),which is dened as the ratio between the dynamic displacementresponse (Ddy) of an elastic SDOF system and its static displace-ment response (Dst) under the same applied load F (Fig. 4). In thesame gure it is apparent that the DAF can be expressed also asthe ratio between the static force and the dynamic one under anequal displacement.

The GSA guidelines suggest to use a DAF equal to two for con-sidering the behavioural difference between static non linear anal-yses and dynamic non linear ones. However, if the load originallysupported by the lost column and transferred to the remaining partof the structure provokes an inelastic response, the DAF mayassume values different than two and depending on the displace-ment demand. This is investigated in the present paper with refer-ence to the frame structures of Section 5.

The necessity to have a more general methodology for robust-ness assessment of steel structures under each type of exceptionalactions has led towards the implementation of a new non-linearanalysis approach able to take into account both the catenary effectand the behaviour of connections. The adopted procedure is con-ceptually similar to the one given by the U.S. Department ofDefense, which is a non-linear procedure framed in the categoryof alternative load path approaches.

Themain difference between the proposed approach and theU.S.one is that in the former the computationalwork does not start with

Robustness capacityR1 R2 CP

e

ediate objectiveMinimum objective

Structures xxx (2014) xxxxxx 5the original FEM model of the structure with a vertical elementremoved, but with the numerical structural model subjected tothe design load combination. Therefore, the structure congurationbefore column removal is taken into account by evaluating the pres-ence of vertical loads. Later on, in order to simulate the column loss,its stiffness is reduced to zero and, simultaneously, aiming at con-sidering the dynamic inertia effects, in the zones near to theremoved elements, loads are amplied with an appropriate DAF.In addition, the progressive variation of both the removed elementand loads allows to assess in accurate way the force redistributioninto structural elements. Such amethod, called LoadHistoryDepen-dent (LHD) procedure [19], is based on a 3D structure model withboth rigid oor diaphragms and beams and columnsmodeled as lin-ear elements. Since large displacement analyses (i.e. considering thecatenary effect phenomenon) are performed, geometric non-linear-ity have been considered in the FEM model.


robustness assessment method has been applied.

6. Analysis results

6.1. Under seismic actions

The robustness assessment under earthquakes has been per-formed by means of pushover analyses on the 2D FEM models ofthe examined structures, implemented through the SAP2000 nonlinear analysis program [27]. For each of the nine analyses, twodifferent lateral load distributions have been considered, namelyconstant and inverted triangular type, so leading in total to sev-enty-two pushover curves (18 for each frame). Major details onthe performed analyses are available in [28,29].

The gotten curves have been transformed into the Acceleration-Displacement Response Spectra (ADRS) plane in order to becompared with the demand spectrum given by the consideredexceptional earthquake.

Therefore, according to Eq. (4) and Fig. 3, the robustness indexhas been determined for each examined structure, leading to the

andFor beams and columns concentrated plasticity hinges, asdened in the FEMA 356 [20], have been adopted. For the deni-tion of the robustness index, the same U.S. code also species threedifferent performance levels as a function of the yielding rotationhy: Immediate Occupancy (0.25 hy), Life Safety (2hy) and NearCollapse (3hy).

The used load combination is the one contemplated in the newItalian seismic code [21].

In order to take into account the dynamic nature of appliedloads, a DAF is obtained through the following relationship [22]:

DAF 1:08 0:76hpahy 0:83 10

where hpa is the allowed plastic rotation. Such a factor, whichdepends on the selected performance level, assumes values of1.35 and 1.28 when Life Safety Limit State and Near Collapse oneare considered, respectively.

Fully and partially restoring connections in terms of strengthand stiffness are considered in the numerical FEM models to con-nect beams and columns. These design variables have allowed toestimate the connection inuence on the inspected structuresrobustness.

The robustness index Ir, ranging from 0 to 1, is calculated as theratio between the direct damage and the total one, intended assum of direct and indirect damages. The direct damage is theacceptable structure damage with reference to a given perfor-mance level. The acceptable damage, which is an ideal damage, isa function of the allowed plastic rotation of both beams andconnections:

Ddir Xni1

hai fai 11

where hai is the allowed plastic rotation of the i-th plastic hinge, faiis the allowed plastic rotation of the i-th connection, n = 2 nb nfis the ideal number of plastic hinges activated by the catenary effectin the 3D structural scheme with nb = number of beams connectedto the removed column and nf = number of oor above the one withthe column removed.

The total damage is the real damage occurred in the structure, itbeing dened as follows:

Dtot XnToti1

hi fi 12

where hi is the allowed plastic rotation of the i-th plastic hinge, fi isthe allowed plastic rotation of the i-th connection and nTot is thereal number of activated plastic hinges.

The robustness index Ir is therefore equal to:

Ir DdirDtot Pn

i1hai faiPnToti1hi fi

13

When the indirect damage is zero, the structure is robust with ref-erence to a prexed performance level and Ir = 1. Instead, it assumesvalues tending to zero when total damage is greater than the directone, that is when the structure has low robustness. Finally, it ispossible to found robustness index greater than one, that is thestructural performance is better than that of a given performancelevel.

5. The investigated structures

Considering the exceptional nature of last Italian seismic events

6 A. Formisano et al. / Computers[23,24], two different types of steel framed structures have beenanalysed aiming at evaluating their robustness under outstandingearthquake actions having a return period of 2475 years and a

Please cite this article in press as: Formisano A et al. Robustness assessment aStruct (2014), http://dx.doi.org/10.1016/j.compstruc.2014.09.010probability to be exceeded of 2% during their service life [21].These structures have been located in the historical centre ofNaples on a soil type B. They are composed of three frames madeof S275JR steel proles, spaced 5 m each other, subjected to a per-manent and variable loads of 5.15 kN m2 and 2 kN m2, respec-tively. The rst structure (type A) is a plane frame with a single5 m bay on two levels with inter-story height of 3.5 m. The secondplane frame (type B) has three levels (H = 3.50 m at 1st oor andH = 3.00 m at 2nd and 3rd oors) with three 5 m wide bays. Bothstructures have been designed according to the old (M.D. 96)[25] and the new (M.D. 08) [21] Italian seismic codes (see Figs. 5and 6, where the used proles are indicated) [26].

For these structures, the randomness of both materials (coef-cient of variation COV of 357%) and vertical loads (coefcientof variation COV of 102030%) have been considered at the lightof a semi-probabilistic approach to be used for the robustness anal-ysis of new structures. Therefore, the combination of the aboveCOVs lead to nine analysis, which have been performed on eachof the four examined structures.

Finally, different beam-to-column connection types, namelyrigid and full strength, semi-rigid and partial strength and semi-rigid and full strength, have been considered only when the new

st

F

F

Fdy

dy st cc

kst

kdy

Static non linear response

Dynamic non linear response

Fcc (cc)

Fig. 4. Static non linear response curve vs. dynamic non linear one and explanationof the DAF.

Structures xxx (2014) xxxxxxmean values of Table 2.The achieved results have shown that frames designed accord-

ing to old prescriptions are not robust, since they have a soft-story


analysis types of the rst evaluation method described in theSection 4.2.

Two and six threat-independent column-removed conditionshave been considered for the two level structure and the threelevel one, respectively. In the 2-story building, the rst and the sec-ond level columns of the central frame have been removed sepa-rately from the structure. On the other hand, in the 3-storybuilding, the columns of the 1st, 2nd and 3rd level belonging tothe external and internal alignments of vertical elements havebeen removed one by one from the central frame.

So, for each of the examined 2-story framed structure, also con-sidering the randomness of both materials and loads, 18 3 anal-

of the 2-story building designed according to old and new seismic

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A. Formisano et al. / Computers and Structures xxx (2014) xxxxxx 7mechanism (both at the 2nd story) under lateral forces. On theother hand, frames designed according to M.D. 08 are extremelyrobust, they showing a global collapse mechanism. However, it isapparent that the new code provides results too on the safe sidein designing new steel structures. In addition, by considering thestructure characteristic curves, intended as the ones having theprobability of being minored of 5%, six different target displace-ments can be identied as a function of both the yielding Sdy andthe ultimate Sdu spectral displacements of the same curves. Suchtargets are called as Fully Operational (FO = 1/3 Sdy), Operational(O = 2/3 Sdy), Life Safety (LS = Sdy), Robustness 1 (R1 = 1/3 Sdu +2/3 Sdy), Robustness 2 (R2 = 2/3 Sdu + 1/3 Sdy) and Collapse Preven-tion (CP = Sdu = maximum acceleration). For the sake of example,the characteristic pushover curve of the two-story frame designedaccording to M.D. 08, together with the above targets, is reportedin Fig. 7.

Therefore, by considering ve different seismic demand spectra,represented by the four earthquakes given in M.D. 08 (DLS, OLS,LLS, CLS) plus the exceptional one having the probability to beexceeded of 2% (ExLS), associated to the above target displace-ments, a robustness matrix can be built for each frame. For the sakeof representation, such matrixes are reported for the 2-story frameonly (Tables 3 and 4).

First of all, it appears that the old Italian code (M. D. 96) pro-vides a very low level of robustness, whose indices are almostalways below one. Also, in case of an exceptional earthquake, thestructure designed according to M.D. 08 has a robustness indexfrom 7 to 11 times greater than the one designed according toM.D. 96 (Table 5).

Fig. 5. 2-Story frame designed according to M.D. 96 (a) and M.D. 08 (b) Italiancodes.6.2. Under column-removed conditions

Firstly, the robustness of analysed structures has been assessedin terms of progressive collapse resistance by using the three

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Please cite this article in press as: Formisano A et al. Robustness assessment aStruct (2014), http://dx.doi.org/10.1016/j.compstruc.2014.09.010codes, respectively, when the 1st story column and the 2nd storyone are separately removed from the central frame, are reported.

In the same picture, modied LS analyses accounting for thecatenary effect have been also plotted. From the analysis resultsit is apparent that the modied LS curves are able to assess the realbuilding behaviour in terms of stored energy, since the area underthese curves is equal to the one enclosed under the NLD curves. So,a simplied way to evaluate the building behaviour under dynamicconditions due to the column loss has been found.

From Figs. 8 and 9, the robustness index of structures can beachieved for each NLD curve by making the ratio between the pro-gressive collapse strength and the strength corresponding to theapplied loads. If this index is larger than one, then the structureis robust; contrary, the structure is not able to sustain exceptionalactions.

The analysis results have shown that: 1) examined structures,except the one with COVm = 7% and COVl = 10%, are not robust; 2)the robustness index of the building designed according to thenew code is larger than 10% than that of buildings satisfying theold seismic provisions; 3) the robustness index of tested structuresis slightly larger when the failure of the upper column occurs.

From the same Figs. 8 and 9, the following DAFs can be dened:

DAF1 Fmax;LSFmax;NLD

14

DAF2 Fmax;NLSFmax;NLD

15

In Figs. 10 and 11 the variation of DAFs with the displacementdemand is plotted for the 2-story buildings (COVm = 7% andCOVl = 10%).

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(b)ysis type (LS, NLS and NLD), that is a total of 54 analyses, have beenperformed. Instead, for each of the 3-story framed structures, byxing a COVm = 7%, only load COVs have been changed and, there-fore, 6 3 analysis types (18 analyses in total) have been carriedout. As a result, a total number of 144 analyses has been executed.

For the sake of example, in Figs. 8 and 9 the behavioural curves.D. 96 (a) and M.D. 08 (b) Italian codes.


From the above gures it is apparent that: (1) DAF1 values arelarger than DAF2 ones, with difference more marked when the 1ststory column is removed; (2) in both cases DAF1 assumes a meanvalue of about 2.10 in the elastic eld and is within the range[1.251.90] in the plastic one; (3) in both cases DAF2 assumes amean value of about 2.03 in the elastic eld and is within the range[1.221.80] in the plastic one.

From these results it is apparent that: (1) the GSA provisions arenot on the safe side when elastic analyses are performed, since

In Figs. 14 and 15 the robustness indices of the structure type A(with rigid and full strength connections), designed respectivelywith the new code and the old one, are reported when the removedcolumn position changes.

The same comparisons for the two structures type A have beenperformed also considering the presence of semi-rigid and partialstrength connections (Figs. 16 and 17) and semi-rigid and fullstrength connections (Figs. 18 and 19).

On the other hand, for structures type B with connection typevariation, the robustness indices corresponding to different columnremovals are reported in Figs. 2023, where the symbols FR (resis-tance and stiffness full restoring), PR (stiffness partial restoring),PRR (resistance partial restoring) and CRR (resistance completerestoring) are used.

From achieved results, it is apparent that:

Table 2Mean robustness indices of the study frames.

Frame M.D. 96 M.D. 08

2-Story 0.34 4.213-Story 0.40 3.55

Table 3Robustness matrix of the 2-story frame designed according to M. D. 96.

FO O LS R1 R2 CP

OLS 0.46DLS 0.21 1.14LLS 0.02 0.11 0.27CLS 0.07 0.17 0.21ExLS 0.11 0.14 0.16 0.19

Table 4Robustness matrix of the 2-story frame designed according to M.D. 08.

FO O LS R1 R2 CP

OLS 3.01DLS 1.47 9.17LLS 0.16 0.97 2.48

8 A. Formisano et al. / Computers and Structures xxx (2014) xxxxxxDAF1 is larger than DAF2; (2) the dynamic amplication in theinelastic eld depends on the maximum allowable plasticdisplacement.

With reference to the 3-story structures, the results have shownthat the robustness index of the structure designed with M.D. 08 is10% larger than that of the old code structure. Differently from theprevious case, the structures are always robust except when thecolumn is removed from the 3rd story. In addition, loss of internalcolumns provides robustness index lower than the cases wherecolumns are removed from external alignments. In this case, DAFshave been calculated at the ultimate condition, that is withreference to the strength corresponding to the maximum allowabledisplacement (Fig. 12).

From the above results it is evident that, when upper columnsare removed, lower values of DAF are achieved. In all cases, adecreasing behaviour of DAF with the increasing structure heightis noticed. As for the previous case, DAF1 values are larger thanDAF2 ones. Finally, DAF1 values are decreasing when number ofoors increases, with values comprised between 1.13 and 1.31for M.D. 08 and 1.36 and 1.66 for M.D. 96. Contrary, DAF2 is almostconstant when the number of oor is increased, with mean valuesof 1.07 and 1.04 for M. D. 08 and M.D. 96, respectively.

Secondly, the new robustness evaluation method has beenapplied to 3D FEM models of two investigated structures (Fig. 13).

For both of them all possible scenarios of column removinghave been considered in order to understand which are the worstconditions.

Robustness indices of examined structures have been calculatedconsidering the Life Safety Limit State as the performance level.The results achieved for the two structures are reported as followsunder form of histograms.Fig. 7. Characteristic pushover curve of the 2-s

Please cite this article in press as: Formisano A et al. Robustness assessment aStruct (2014), http://dx.doi.org/10.1016/j.compstruc.2014.09.010Table 5Robustness index ratios between the 2-story frame designed according to M.D. 08 andthe one designed according to M. D. 96.

FO O LS R1 R2 CP

OLS 6.54DLS 7.00 8.04LLS 8.00 8.82 9.18CLS 8.14 8.59 10.48ExLS 7.27 8.57 10.19 11.00

CLS 0.57 1.46 2.20ExLS 0.80 1.20 1.63 2.09tory frame designed according to M.D. 08.


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A. Formisano et al. / Computers(1) Structures designed with the old code, due to beams withhigh exural stiffness, have robustness indices greater thanthose of NTC 08 frames.

(2) The connection type is an inuent design parameter. In fact,full strength and rigid connections allow to achieve high robust-ness levels, whereas semi-rigid ones exhibit less performance,showing a better behaviour when they are of a full strength type.

(3) About the worst scenarios of column removal, bad situationsare those connected to the loss of internal columns, immedi-ately followed by the loss of the corner column.

(4) The hazard scenario increases as the structure level numberamplies. This is in agreement with the provisions of the U.S.Department of Defense [22], which foresees as obligatoryscenario the removal of the top story column.

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Fig. 10. DAF vs. displacement demand for the 2-story structure designed accordingto M.D. 96.

Please cite this article in press as: Formisano A et al. Robustness assessment aStruct (2014), http://dx.doi.org/10.1016/j.compstruc.2014.09.01000

00

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Structures xxx (2014) xxxxxx 97. Concluding remarks

In the current paper the robustness assessment of steel framedbuildings designed according to the old and the new Italian seismiccodes has been performed.

First, after recalling the denitions of robustness and progres-sive collapse, a general overview on the methodologies usedfor evaluating the structural robustness has been given. In particu-lar, within the methods used for robustness assessment underearthquakes, a new deterministic approach, framed within thePerformance Based Design, has been applied for evaluating thecase studies performances. For these frames, the implemented

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Fig. 12. Change of DAFs with respect to the column removal at different stories.

Fig. 13. 3D FEM models of type A (a) and type B (b) structures.

Fig. 15. Robustness indices of the DM 96 structure type A with rigid and full strength connections at the rst level (a) and the second one (b).

Fig. 14. Robustness indices of the NTC 08 structure type A with rigid and full strength connections at the rst level (a) and the second one (b).

Fig. 16. Robustness indices of the NTC 08 structure type A with semi-rigid and partial strength connections at the rst level (a) and the second one (b).

10 A. Formisano et al. / Computers and Structures xxx (2014) xxxxxx

Please cite this article in press as: Formisano A et al. Robustness assessment approaches for steel framed structures under catastrophic events. ComputStruct (2014), http://dx.doi.org/10.1016/j.compstruc.2014.09.010

andA. Formisano et al. / Computersmethod has allowed to calculate the robustness indices corre-sponding to specied targets, providing multi-level performancematrices. The analyses have shown that the old Italian frames havea very low robustness level, with both indices almost always belowone and a soft-story mechanism at the second level. On the con-trary, the investigated structures, when designed according tothe new Italian seismic code, have provided high robustness indi-ces under exceptional actions, their behaviour being characterisedby a global collapse mechanism. Moreover, for the 2-storyframe subjected to an exceptional earthquake, it has beennoticed that, for CP limit state, the new seismic resistant structure

Fig. 17. Robustness indices of the DM 96 structure type A with semi-rigid and

Fig. 18. Robustness indices of the NTC 08 structure type A with semi-rigid and

Fig. 19. Robustness indices of the DM 96 structure type A with semi-rigid and

Fig. 20. Robustness indices of the structure t

Please cite this article in press as: Formisano A et al. Robustness assessment aStruct (2014), http://dx.doi.org/10.1016/j.compstruc.2014.09.010Structures xxx (2014) xxxxxx 11has a robustness index 11 times greater that of the old seismicstructure.

Second, the resistance to progressive collapse of steel framedstructures designed according to the old and the new Italian seis-mic codes has been initially assessed by using linear static, non lin-ear static and non linear dynamic analyses. The linear staticanalyses has been used when the column-removed structure issubstantially elastic. Instead, in the plastic eld, the collapse resis-tance has been well estimated from the capacity curves, which areused to simulate the structure NLD behaviour by exploitingthe energy conservation principle. Also, linear static analyses

partial strength connections at the rst level (a) and the second one (b).



ype B with removal of a corner column.


and12 A. Formisano et al. / Computersaccounting for the catenary effect have been also performed, theybeing able to assess in a simple way the real building behaviour interms of stored energy.

The analyses have shown that the robustness index of new codebuildings is averagely 10% larger than that of structures satisfyingold seismic provisions. Furthermore, the Dynamic AmplicationFactors (DAFs) accounting for the dynamic effect due to the columnremoval when static analyses are executed have been assessed.From the results it has been shown that the GSA US code provisionsare not on the safe side when elastic analyses are performed,since achieved DAFs are larger than two, and that the dynamicamplication in the inelastic eld depends on the maximumallowable plastic displacement. In particular, for the 2-storyand the 3-story structure, a mean DAF value of 1.23 and 1.16 is

Fig. 21. Robustness indices of the structure type B with

Fig. 23. Robustness indices of the structure t

Fig. 22. Robustness indices of the structure type B with

Please cite this article in press as: Formisano A et al. Robustness assessment aStruct (2014), http://dx.doi.org/10.1016/j.compstruc.2014.09.010Structures xxx (2014) xxxxxxrespectively achieved when the maximum allowable displacementis attained.

Finally, a new non linear static analysis method based on thealternative load path approach has been proposed in order to esti-mate the resistance against progressive collapse of examined struc-tures. In particular, the computational model has been started withthe whole structural model where gravity loads are applied. After-wards, both the structural stiffness is decreased for taking intoaccount the column loss and applied loads are increased through aDAF for considering the phenomenon dynamic nature. This allowsto assess in a more precise way the stress redistribution intostructural elements, so leading towards a Load History Dependentprocedure. Therefore, the structure robustness index has beendetermined as ratio between the direct damage caused by the

removal of one perimeter column on its long side.

ype B with removal of a central column.

removal of one perimeter column on its short side.


exceptional event and the total damage, equal to the sum of thedirect damage and the indirect one.

The analyses performed has allowed to evaluate the robustnessperformance of study structures, by considering the variability ofthe joint types (full strength and partial strength), as well as thepresence of geometric non linearity due to the catenary effect phe-

[6] Starossek K. Progressive collapse of structures: nomenclature and procedures.Struct Eng Int 2006;16(2):1137.

[7] United States National Institute of Standards and Technology (NIST). Bestpractices for reducing the potential for progressive collapse in buildings.Washington, D.C.: Technology Administration, U.S. Department of Commerce;2007

[8] Department of Defense (DoD). Unied Facilities Criteria (UFC): design of

A. Formisano et al. / Computers and Structures xxx (2014) xxxxxx 13 By following a PBSD approach, old Italian framed structuresshow low ductility and do not satisfy robustness requirements,whereas the new ones exhibit high robustness levels, even ifthey are not explicitly designed against exceptional actions.

Contrary, on the basis of a force-based analysis approach estab-lished on column-removed conditions, it can be afrmed thatstructures designed by the old code have better behaviour thannew ones thanks to higher stiffness beams able to offer an effec-tive catenary effect, indispensable to avoid structural collapses.Therefore, a new beam-to-column strength hierarchy criterionshould be dened for robustness analysis of new framed struc-tures. Furthermore, by analysing the inuence of the connectiontype among members, the best performance are exhibited byfull strength and rigid connections, which are recommendedfor steel moment resisting frames. Finally, it is advisable thatboth the hazard scenario increases as the structure level num-ber increases and the worst circumstance of column removalis generally represented by the internal column loss.

References

[1] Beer M, Liebscher M. Designing robust structures a non linear simulationbased approach. Comput Struct 2008;86:110222.

[2] Blockey D, Agarwal J, Pinto T, Woodman NJ. Structural vulnerability, reliabilityand risk. Prog Struct Eng Mater 2002;4:20312.

[3] ASCE. Minimum design loads for buildings and other structures. AmericanSociety of Washington, D.C.; 2002.

[4] De Gregorio D, Faggiano B, Formisano A, Mazzolani FM. Air fall deposits due toexplosive eruptions: action model and robustness assessment of the Vesuvianroofs. In: Proc of the COST Action C26 nal conference Urban HabitatConstructions under Catastrophic Events, Federico M. Mazzolani, Chair,Naples. CRC Press, Taylor & Francis Group, London; 1618 September 2010.p. 50712. ISBN: 978-0-415-60685-1.

[5] Formisano A, Mazzolani FM. Progressive collapse and robustness of steel framedstructures. In: Topping BHV, editor. Proceedings of the eleventh internationalconference on computational structures technology. Stirlingshire, UK: Civil-Comp Press. Paper 13; 2012. http://dx.doi.org/10.4203/ccp.99.13.nomenon. The achieved results have shown the best behaviour ofstructures designed by the old normative code due to more robustbeams able to offer a better catenary effect, which is one of themost important parameters to resist to progressive collapse.Another fundamental robustness factor is the connection type. Infact, full strength and rigid connections allow to achieve highrobustness levels, whereas semi-rigid ones exhibit less perfor-mance, showing a better behaviour when they are of full strengthtype. In addition, indications about the worst scenarios of columnremoval have been given. Adverse situations are those connectedto the loss of internal columns, followed in order by the cornercolumn loss and the perimeter columns lack.

In conclusion, the main achieved results, to be validatedthrough further applications on real case studies, can be general-ised and summarised as follows:Please cite this article in press as: Formisano A et al. Robustness assessment aStruct (2014), http://dx.doi.org/10.1016/j.compstruc.2014.09.010structures to resist progressive collapse. Washington, D.C.; 2005.[9] United States General Services Administration (GSA). Progressive collapse

analysis and design guidelines for new federal ofce buildings and majormodernization project. Washington, DC; 2003.

[10] EN 1991-1-7. Actions on structures Part 17: General actions accidentalactions, January; 2006.

[11] British Standards (BS) 6399-1. Loading for buildings. Code of practice for deadand imposed loads, September; 1996.

[12] The Joint Committee in Structural Safety (JCSS). Probabilistic model code;2001.

[13] Faber M, Narasimhan H. Advances in the evaluation of robustness ofstructures. In: Proc of the COST C26 symposium, Malta, September; 2008.

[14] Mazzolani FM, Mandara A, Faggiano B. Structural integrity and robustnessassessment of historical buildings under exceptional situations. In: Proc of thePROTECT 07 conference, Whistler, August; 2007.

[15] Formisano A, Mazzolani FM. On the catenary effect of steel buildings. In: Procof the COST Action C26 nal conference Urban Habitat Constructions underCatastrophic Events. Federico M. Mazzolani, Chair, Naples, 1618 September2010. CRC Press, Taylor & Francis Group, London; 2010. p. 61924. ISBN: 978-0-415-60685-1.

[16] Mazzolani FM, Faggiano B, Formisano A, Mandara A, Marzo A. Performancebased approach for the evaluation of the structural integrity vs robustness ofthe historical buildings under exceptional situations. In: Faella Ciro, MazzolaniFederico M, editors. Innovative strategies for structural protection of builtheritage PRIN 2005. Italy: Polimetrica Publisher; 2009. p. 736, ISBN 978-88-7699-107-3.

[17] Tsai MH, Lin BH. Investigation of progressive collapse resistance and inelasticresponse for an earthquake-resistant RC building subjected to column failure.Eng Struct 2008;30:361928.

[18] Abruzzo J, Matta A, Panariello G. Study of mitigation strategies for progressivecollapse of a reinforced concrete commercial building. J Perform ConstrFacilities 2006;30(4):38490.

[19] Menchel K. Progressive collapse: comparison of main standards, formulationand validation of new computational procedures. Universite Libre deBruxelles, Faculte des Sciences Appliquees, Ph.D. Thesis; 2009.

[20] Federal Emergency Management Agency (FEMA) 356. Prestandard andcommentary for the seismic rehabilitation of building. Washington, D.C.; 2000.

[21] Ministerial Decree of Public Works emanated on 2008, January 14th (M.D. 08).New technical codes for constructions (in Italian). Ofcial Gazette of the ItalianRepublic n. 29 published; 2008 [04.02.08].

[22] United States Department of Defense (DoD). Unied Facilities Criteria (UFC) 4-023-03: design of structures to resist progressive collapse. Washington, D.C.;2009.

[23] Formisano A. Seismic damage assessment of school buildings after 2012 EmiliaRomagna earthquake. Ingegneria Sismica (ISSN:03931420). Special numberEarthquake in Emilia Romagna May 2012, vol. 23. p. 7286; AprilSeptember, 2012.

[24] Indirli M, Kouris LAS, Formisano A, Borg RP, Mazzolani FM. Seismic damageassessment of unreinforced masonry structures after the Abruzzo 2009earthquake: the case study of the historical centres of LAquila andCastelvecchio Subequo. Int J Arch Heritage 2013;7:53678 [ISSN: 13507524].

[25] Ministerial Decree of Public Works (M.D.). Technical codes for constructions inseismic zones (in Italian). Ofcial Gazette of the Italian Republic published onJanuary 16th; 1996.

[26] Ferraioli M, Lavino A. Performance evaluation of steel framed structures bymeans of simplied non-linear analysis methods (in Italian). In: Proc of the XXIC.T.A. Italian conference, Catania; October, 2007.

[27] Computer and Structures, Inc. (CSI). SAP 2000 Non linear, version 11. Berkeley,California, USA; 2008.

[28] Formisano A, Marzo A, Mazzolani FM. Robustness based design of new andexisting steel structures. In: Proc of the 6th int conference on the Behaviour ofSteel Structures in Seismic Areas (STESSA 09), Philadelphia; August 1620,2009.

[29] Formisano A, Mazzolani FM. Robustness assessment of steel framed structures(in Italian). In: Proc of the XXII CTA congress Lacciaio per un futurosostenibile, Padova, 2830 September 2009, ACS ACAI SERVIZI srl Milano(ed.) Tipograa Gotica (Padova); 2009. p. 55162.pproaches for steel framed structures under catastrophic events. Comput

Robustness assessment approaches for steel framed structures under catastrophic events1 Robustness and progressive collapse2 Progressive collapse mitigation options3 Code provisions4 Robustness assessment methodologies4.1 Under seismic actions4.2 Under column-removed conditions

5 The investigated structures6 Analysis results6.1 Under seismic actions6.2 Under column-removed conditions

7 Concluding remarksReferences

robustness - novembre 2014

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