Seismic vulnerability of existing RC buildings - Dipartimento di ...

A Mamma, Papà e Titti

ACKNOWLEDGEMENTSI chose to deal with structural engineering wishing to give my personal contribution to thedevelopment and the protection of what man builds, becoming a place to live and a sign of hispassage.After my graduation, I had the opportunity to attend a PhD programme in Seismic Risk. It wasthe most special work I could ever do: when you make research, everything you do is aimed atleaving a sign, changing things and making them advance.During these years, I have been making research on seismic vulnerability of existing RCbuildings. When I was in L’Aquila, in April 2009, I saw with my own eyes the pain and sorrowthat an earthquake can leave behind, and I understood that I was making the right thing puttingmy energy and time into this field.I first have to express my gratitude to Gerardo Mario Verderame, the man who guided meduring these years. He not only taught me everything I know about structural engineering. Healso taught me what research is, and how paying attention to everything and working hard canmake the difference in this work. Above all, he always respected my character, which is muchmore tough than it may appear, and he always let me free to follow my inclinations.I express my thanks to Professor Gaetano Manfredi for the opportunity he gave me to be part ofthe Department of Structural Engineering of the University of Naples Federico II.I would like to thank Matjaž Dolšek and Daniel Celarec for the opportunity they gave me towork together during my stay at the University of Ljubljana. They helped me in extending myresearch on RC structures; the first results of this cooperation are included in this thesis.Special thanks to Marilena Esposito and Filippo Sansiviero; they often provided a great supportto my research activities.I would like to thank Giovanni De Carlo for his fundamental contribution to the review ofbeam-column joint models and, more generally, to the experimental and numerical research onthe behaviour of RC elements reported in this thesis. About two years ago we took differentways. It was too early. I will always remember with great pleasure the many long, enjoyable andstimulating discussions we had, which deeply influenced my vision of structural engineering.During these years, I often put work at the first place, leaving too little time to the mostimportant people in my life. Despite this, they still stand close to me. Salvatore and Angela, Igive you not only my gratitude, but also my apologies.My deepest gratitude goes to the love of who was closest to me, giving me times full ofhappiness and making me a different man. This is much more important to me than anythingthat could ever be written down on paper.Naples, December 2010

IndexIndexIntroduction 1Chapter IAssessing seismic vulnerability of reinforced concrete buildings1.1 INTRODUCTION 51.2 EMPIRICAL METHODS 81.2.1. Damage Probability Matrices 8Whitman et al., 1973 8Braga et al., 1982 9Di Pasquale et al., 2005 9Dolce et al., 2003 9EMS-98 scale (Grünthal, 1998) 10Giovinazzi and Lagomarsino, 2004 131.2.2. Continuous vulnerability curves 13Orsini, 1999 13Sabetta et al., 1998 13Rota et al., 2008 131.2.3. Vulnerability Index method 14Benedetti and Petrini, 1984 14i

Index1.2.4. Screening methods 15JBDPA, 1990 15Hassan and Sozen, 1997 16Yakut, 2004 16Ozdemir et al., 2005 161.3 ANALYTICAL METHODS 17Singhal and Kiremidjian, 1996 17Masi, 2003 20Rossetto and Elnashai, 2005 21Cosenza et al., 2005 21Iervolino et al., 2007 23HAZUS (FEMA, 2001) 24Giovinazzi, 2005 30Grant et al., 2006 31Ordaz et al., 2000 32Calvi, 1999 32DBELA (Pinho et al., 2002) 34SP-BELA (Borzi et al., 2008) 36VC (Dolce and Moroni, 2005) 381.4 HYBRID METHODS 40Kappos et al., 1995 40Singhal and Kiremidjian, 1998 401.5 EXPERT JUDGEMENT-BASED METHODS 41ATC, 1985 41REFERENCES 42ii

IndexChapter IISeismic behaviour of existing reinforced concrete buildings2.1 GENERAL REMARKS 492.2 MEMBERS CONTROLLED BY FLEXURAL AND AXIAL LOADS 532.2.1. Code provisions for the assessment of ultimate deformationcapacity 532.2.1.1. EC8 part 3.3 – empirical approach 552.2.1.2. EC8 part 3.3 – mechanical approach 612.2.1.3. ASCE/SEI 41 approach 662.2.1.4. Critical review 712.2.2. A proposal for a new correction coefficient applied to the EC8capacity formulation for RC columns with smooth bars 742.2.2.1. Deformation capacity of RC columns with smooth bars 752.2.2.2. Calibration of correction factor 762.2.2.3. Discussion of results 812.2.3. Bond behaviour of smooth bars: experimental and analyticalinvestigation 842.2.4. The influence of transverse reinforcement anchorage detail onconfined concrete behaviour 892.2.5. Numerical modelling of RC members with smooth bars 922.3 MEMBERS CONTROLLED BY SHEAR 962.4 BEAM-COLUMN JOINTS 1022.5 STRUCTURAL PERFORMANCE OF RC BUILDINGS AFTER THE6TH APRIL 2009 L’AQUILA EARTHQUAKE, ITALY 1082.5.1. Reinforced concrete buildings in L’Aquila 1082.5.2. Overview of past seismic code provisions 1112.5.3. Spectral considerations 1152.5.4. Field survey of structural damage 118iii

IndexREFERENCES 127Chapter IIIInfluence of infills on seismic behaviour of reinforced concretebuildings3.1 INTRODUCTION 1373.2 BEHAVIOUR OF RC FRAMES WITH MASONRY INFILLS 1383.2.1. Influence of openings 1443.2.2. Brittle failure in RC members due to local interaction with infills 1453.2.3. Out-of-plane behaviour 1483.2.4. Models for the analysis of infilled RC frames 1483.3 EXPERIMENTAL BEHAVIOUR OF INFILLED RC STRUCTURES 1593.4 ANALYTICAL INVESTIGATION OF ELASTIC PERIODOF INFILLED RC MRF BUILDINGS 1763.4.1. The period of RC buildings 1763.4.1.1 Empirical estimate of period of RC MRF buildings 1773.4.1.2 Empirical estimate of period of RC SW buildings 1783.4.1.3 Empirical estimate of period of infilled RC buildings 1793.4.1.4 Numerical estimate of period of infilled RC buildings 1813.4.2. Modelling of infill stiffness 1823.4.3. Numerical estimate of period of infilled RC MRF buildings 1863.4.3.1 Building population 1863.4.3.2 Evaluation of period 1893.4.4. Analysis of results 1903.4.4.1. Uncracked infills 191iv

Index3.4.4.2. Cracked infills 2003.4.5. Comparison with literature formulas 203REFERENCES 208Chapter IVNumerical investigation of seismic capacity of reinforcedconcrete buildings with infills4.1 INTRODUCTION 2174.2 NUMERICAL INVESTIGATION OF SEISMIC BEHAVIOUR OFINFILLED RC BUILDINGS:STATE OF THE ART 2184.3 SEISMIC CAPACITY ASSESSMENT OF A FOUR-STOREY GLDBUILDING WITH DIFFERENT INFILL CONFIGURATIONS 2284.3.1. Case study structure: numerical modelling and analysismethodology 2284.3.2. Sensitivity analysis 2364.3.2.1. Uniformly Infilled frame 2394.3.2.2. Pilotis frame 2544.3.2.3. Bare frame 2654.3.3. Comparison between different infill configurations 2744.3.3.1. Comparison between different infill configurations:IN2 curves 2744.3.3.2. Comparison between different infill configurations:fragility curves 2794.3.4. Comparison with simplified models based on Shear-Typeassumption 2894.3.4.1. Uniformly infilled frame 290v

Index4.3.4.2. Pilotis frame 2944.3.4.3. Bare frame 2974.3.4.4. Summary of remarks 303REFERENCES 304Chapter VSimplified approach to the seismic vulnerability assessment ofexisting reinforced concrete buildings: the case study of Avellino5.1 INTRODUCTION 3095.2 A SIMPLIFIED PROCEDURE FOR THE ASSESSMENTOF SEISMIC VULNERABILITY OF RC BUILDINGS 3105.2.1. Definition of input data 3105.2.2. Simulated design procedure 3125.2.3. Characterization of nonlinear response 3155.2.4. Calculation of pushover curve 3185.2.5. Seismic assessment 3215.2.6. Evaluation of fragility curves 3225.2.7. Calculation of failure probability 3255.2.8. Example applications 3265.3 URBAN SCALE VULNERABILITY ASSESSMENT:THE CASE STUDY OF AVELLINO 3385.3.1. Data collection and field survey results 3385.3.1.1. Survey form 3385.3.1.2. Analysis of building stock data 3475.3.2. Seismic vulnerability assessment of RC building stock 356vi

Index5.3.2.1. Input data of the seismic vulnerability assessmentprocedure 3565.3.2.2. Analysis of results 3635.4 FUTURE RESEARCH 378REFERENCES 379vii

1IntroductionThe assessment of seismic vulnerability of the existing building stock plays akey role in the development of instruments aimed at the evaluation and themitigation of seismic risk. The investigation of seismic vulnerability of existingReinforced Concrete (RC) buildings is of fundamental importance since thisbuilding typology represents a large part of the existing building stock in manyareas subjected to high seismic risk; moreover, the seismic behaviour of thesebuildings is often affected by deficiencies due to the absence of compliancewith the modern earthquake engineering design principles or, even, to theabsence of a seismic design.In this thesis, the seismic vulnerability of existing RC buildings isinvestigated from different points of view.First, an overview of literature methods is carried out, illustrating mainempirical and analytical approaches to large scale vulnerability assessment(Chapter I).Hence, in Chapter II the seismic behaviour of existing RC buildings isinvestigated through experimental and numerical activities focused on thedeformation capacity of substandard RC members, with emphasis on memberswith smooth bars. To this aim, code and literature formulations for theevaluation of deformation capacity of RC members are illustrated anddiscussed; then, based on experimental data, a new proposal for the assessmentof deformation capacity of columns with smooth bars is presented. Then, bondbetween steel and concrete for this kind of reinforcement is investigatedthrough an experimental study and the formulation of an analytical model basedon the obtained data. The influence of the absence of proper transversereinforcement details is experimentally investigated, too. Finally, the so-called

Type assumption. The proposed method employs few data – such as number ofstoreys, global dimensions and type of design – to define the structural modelby means of a simulated design procedure. Nonlinear static response of thestructural model, including infill elements, is characterized, and pushoveranalysis is carried out in closed-form. Fragility curves and corresponding failureprobability at different Limit States are calculated, once seismic hazard hasbeen defined. Finally, the proposed method is applied to the Avellino city(southern Italy), employing data about building stock from a field survey,including structural typology, global building dimensions and age ofconstruction. Obtained results show the influence of main characteristics, suchas the number of storeys and type of design, on the seismic vulnerability of thebuilding stock.3

6 Chapter I – Assessing seismic vulnerability of reinforced concrete buildingsLoss models provide the expected losses at a given site of interest and in agiven time window by convolving the seismic hazard, the vulnerability of thestructures and infrastructures composing the built environment and the exposedvalue (accounting for costs of repair or replacement of structures, contentslosses and interruption of activities due to the loss of functionality).In this framework, structural vulnerability is given by methodologies whichprovide the probability of a given level of damage as a function of a parameterrepresenting the seismic intensity (e.g., macroseismic intensity, Peak GroundAcceleration (PGA)). A method for the assessment of seismic vulnerability of abuilding stock has to represent the best compromise between reliability andreasonable demand of computational effort, depending on the availability ofdata (that is, the availability of time and money necessary to gather them) andon the required level of detail.A fundamental distinction has to be made between empirical and analyticalvulnerability methods: in empirical methods the assessment of expecteddamage for a given building typology is based on the observation of damagesuffered during past seismic events; in analytical methods the relationshipbetween seismic intensity and expected damage is provided by a model withdirect physical meaning.Reliability and significance of observed data allow empirical methods togive a realistic indication about expected damage, provided they are applied toa building stock with similar characteristic compared with the one used for theirconstruction. However, different disadvantages come from the use of empiricalmethods. These methods do not allow to account for the vibrationcharacteristics of the buildings. They do not explicitly model the differentsources of uncertainty, thus not allowing to remove the uncertainty in theseismic demand from the vulnerability assessment. A macroseismic measure isoften used to define the seismic intensity, but macroseismic intensity is, in turn,obtained from observed damage, thus seismic intensity and damage are notindependent (Crowley et al., 2009). The collection of data about buildingdamage after a seismic event, required for the derivation of any empirical

Chapter I – Assessing seismic vulnerability of reinforced concrete buildings 7relationship between seismic intensity and expected damage, is affected bydifferent shortcomings such as a not homogeneous availability of data, resultingin a higher statistical reliability for the low damage/ground motion rangecompared with the high damage/ground motion range, or the errors due toinadequate compilation of the post-earthquake assessment forms (Colombi etal., 2008). Also, empirical methods do not allow to model the influence ofretrofit solutions on vulnerability, given by the improvement in structuralresponse.On the contrary, the use of an algorithm to evaluate the structuralvulnerability allows to take into account directly and transparently, in a detailedway, the various characteristics of building stock, and also to explicitly accountfor the uncertainties involved in the assessment procedure. An analyticalapproach allows to include in the vulnerability assessment structurescharacterized by different (or new) construction practices, as well as to considerthe influence of retrofitting on the response of existing structures. Furthermore,analytical methods can take advantage of advances in seismic hazardassessment, such as the derivation of seismic hazard maps in terms of spectralordinates (e.g., INGV-DPC S1, 2007), different from macroseismic intensity orPGA. However, generally speaking analytical methods need a larger amount ofdetailed data and a higher computational effort, compared with empiricalmethods. Therefore, the effective increase in accuracy of vulnerabilityassessment, when analytical methods are adopted, should be checked by meansof a comparison with observed damage data. Further critical issues in theapplication of analytical methods have to be carefully considered: first of all,the degree of confidence in the capability of a numerical model to accuratelypredict the response of real structures and, in particular, the confidence in thecorrelation between the assumed analytical damage index (such as theinterstorey drift or a cyclic damage index) and the actual structural damage.Also, many of the collapses observed after seismic events are due toconstructive errors and deficiencies, which normally are not considered in ananalytical model (e.g., Verderame et al., 2010).

8 Chapter I – Assessing seismic vulnerability of reinforced concrete buildingsEmpirical and analytical methods can be used complementing each other, ashappens in so-called “hybrid” methods. Moreover, relationships betweenseismic intensity and expected damage for different structural typologies canalso be based on expert-judgement.A very comprehensive and detailed review of seismic vulnerabilityassessment methodologies can be found in (Calvi et al., 2006). In the following,main vulnerability assessment procedures are illustrated, referring toReinforced Concrete (RC) buildings.1.2 EMPIRICAL METHODSFirst developments of seismic vulnerability assessment of building stockstook place in 1970s, through empirical methods based on macroseismicintensity; at the time, the major part of hazard maps adopted this kind ofmeasure for the seismic intensity.Different types of empirical methods for the seismic vulnerabilityassessment of buildings can be distinguished:− Damage Probability Matrices (DPMs), expressing in a discrete formthe conditional probability of reaching a damage level D = j due to aground motion of intensity I = i, P ij = P [ D = j | I = i ];− vulnerability functions, expressing in a continuous form theprobability P ij = P [ D ≥ j | I = i ];− methods based on a so-called “Vulnerability Index”;− screening methods.1.2.1. Damage Probability MatricesFirst DPMs have been proposed in (Whitman et al., 1973), see Figure1.2.1.1. for a given structural typology, the probability of being in a given stateof structural and non-structural damage is provided. For each damage state, thedamage ratio is provided too, representing the ratio between the cost of repairand the cost of replacement. These DPMs are compiled for different structural

10 Chapter I – Assessing seismic vulnerability of reinforced concrete buildings1998).Figure 1.2.1.2. Vulnerability classes adopted in (Di Pasquale et al., 2005)According to EMS-98 scale six vulnerability building classes (A to F, seeFigure 1.2.1.3) are defined, then for each class a qualitative description ( “few”,“many” and “most”, see Figure 1.2.1.4) of the proportion of buildings sufferinga given level of damage (1 to 5, see Figure 1.2.1.5) is provided as a function ofthe seismic intensity level, ranging from V to XII. Hence, DPMs are implicitlydefined in EMS-98 scale. Nevertheless, they are incomplete (the proportion ofbuildings suffering a given damage level for a given seismic intensity is notprovided for all possible combinations of damage levels and seismic intensities)and vague (proportion of buildings is described only qualitatively)

Chapter I – Assessing seismic vulnerability of reinforced concrete buildings 11Figure 1.2.1.3. Vulnerability classes according to EMS-98 scale (Grünthal, 1998)Figure 1.2.1.4. Definition of quantities “few”, “many” and “most” according to EMS-98 scale(Grünthal, 1998)

12 Chapter I – Assessing seismic vulnerability of reinforced concrete buildingsFigure 1.2.1.5. Definition of damage grades to RC buildings according to EMS-98 scale(Grünthal, 1998)

Chapter I – Assessing seismic vulnerability of reinforced concrete buildings 13Giovinazzi and Lagomarsino (2004) start from these matrices and overcometheir limits of incompleteness and vagueness, then relate the obtained DPMs tothe building stock through a vulnerability index.1.2.2. Continuous vulnerability curvesRelationships between seismic intensity and expected damage based onempirical data can also be derived in a continuous form.Orsini (1999) elaborates the data of the damage survey carried out after the1980 Irpinia earthquake in order to evaluate, for each municipality, a value ofseismic intensity according to the Parameterless Scale of Intensity (PSI)proposed by Spence et al. (1991). The main hypothesis at the basis of the PSImodel is that the intensity at which the structures belonging to a singlevulnerability class overcome a given damage threshold is continuouslydistributed according to a Gaussian model. The use of PSI allows the definitionof continuous vulnerability functions depending on a macroseismic intensityparameter, tackling the problem that macroseismic intensity is not a continuousvariable. After determining PSI values for each municipality, Orsini (1999)proposes vulnerability curves for apartment units as a function of thiscontinuous parameter.Sabetta et al. (1998) derive vulnerability curves depending on PGA, AriasIntensity and effective peak acceleration based on the elaboration of about50000 building damage surveys from past Italian earthquakes, by calculatingfor each municipality a mean damage index as the weighted average of thefrequencies of each damage level for each structural class.Rota et al. (2008) select more than 91000 damage survey forms from pastItalian earthquakes out of a total amount of 164000 ones, (i) disregarding thedata affected by important information missing and (ii) including only datarelated to municipalities surveyed for at least 60%, thus avoiding a biasedsample. The authors subdivide these data into 23 different building typologiesand 10 ground motion intervals. Both PGA and Housner intensity areconsidered as ground motion parameters; their values are estimated for each

14 Chapter I – Assessing seismic vulnerability of reinforced concrete buildingsmunicipality using the attenuation law of Sabetta and Pugliese (1987, 1996) forrock conditions, with the parameters (magnitude and epicentral coordinates) ofthe earthquake of interest. The adopted damage scale is similar to the EMS-98scale, consisting of five levels of damage plus the case of no damage. DPMs areextracted from the data for all of the 23 considered vulnerability classes,according to the defined damage scale and seismic intensity scale. Hence,continuous vulnerability curves are obtained by fitting with lognormaldistributions the data evaluated in form of DPMs; also, when carrying out thisfitting, for each sample (given a building class, a seismic intensity and adamage level) the inverse of the estimated standard deviation is used as aweight expressing the reliability of the single sample.It is to be noted that when the seismic intensity is measured by means of aparameter related to the spectral acceleration or spectral displacement at thefundamental period of vibration (e.g., Rossetto and Elnashai, 2003), differentfrom macroseismic intensity or PGA, the vulnerability curves show a betterprediction capacity, because taking into consideration the relationship betweenthe frequency content of the ground motion and the dynamic characteristics ofthe building stock.1.2.3. Vulnerability Index methodThe “Vulnerability Index” method is first proposed in (Benedetti andPetrini, 1984; GNDT, 1993). The index I v is evaluated by means of a fieldsurvey form where “scores” K i (from A to D) are assigned to eleven parametershaving a high influence on building vulnerability (e.g., plan and elevationconfiguration, type of foundation, structural and non-structural elements); then,the index is defined as the weighted sumI11= ∑ K W(1.2.3.1)v i ii=1according to the importance assigned to each parameter.Based on observed damage data from past earthquakes, for different values of

Chapter I – Assessing seismic vulnerability of reinforced concrete buildings 15this vulnerability index a relationship can be calibrated between seismicintensity and damage ratio (see Figure 1.2.3.1).Figure 1.2.3.1. Vulnerability functions to relate damage ratio and PGA for different values ofvulnerability index (adapted from Guagenti and Petrini (1989)) (from (Calvi et al., 2006))The use of Vulnerability Index Method was quite widespread; it was alsoadopted in different projects such as RISK-UE (Mouroux and Le Brun, 2006)and “Progetto Catania” (Faccioli et al., 1999; Faccioli and Pessina, 2000).1.2.4. Screening methodsAccording to the Japanese Seismic Index Method (JBDPA, 1990), theseismic performance of the building is represented by a seismic performanceindex, I S , evaluated by means of a screening procedure. The procedure can becarried out according to three different levels of detail. I S is calculated for eachstorey in every frame direction according to the following expression:I= E S T(1.2.4.1)S 0 Dwhere E 0 , S D and T correspond to the basic structural performance, to thestructural design and to the time-dependent deterioration of the building,respectively. E 0 is given by the product between C and F, respectively

16 Chapter I – Assessing seismic vulnerability of reinforced concrete buildingsrepresenting the ultimate strength and the ductility of the building, dependingon the failure mode, the total number of storeys and the position of theconsidered storey. S D accounts for irregularity in stiffness and/or massdistribution. A field survey is needed to define T. The calculated seismicperformance index I S is compared with the seismic judgement index I S0 todetermine the degree of safety of the building. I S0 represents a storey shear forceand is given byIS0= E ZGU(1.2.4.2)Swhere E S conservatively increases with the decreasing accuracy of the screeningprocedure, Z is a zone index modifying the ground motion intensity assumed atthe site of the building, G accounts for local effects such as ground-buildinginteraction or stratigraphic and topographic amplification and U is a kind ofimportance factor depending on the function of the building. In the 1998revised version of the Japanese Building Standard Law the index IS0is taken asthe spectral acceleration (in terms of g) at the period of the considered building,and it should be distributed along the height of the structure according to atriangular distribution.Preliminary assessment methods based on screening procedures have beenproposed in Turkey, too, during last years. Some methods require thedimensions of the lateral load resisting elements to be defined: the “PriorityIndex” proposed by Hassan and Sozen (1997) is a function of a wall index (areaof walls and infill panels divided by total floor area) and a column index (areaof columns divided by total floor area); the “Capacity Index” proposed byYakut (2004) depends on orientation, size and material properties of the lateralload-resisting structural system as well as the quality of workmanship andmaterials and other features such as short columns and plan irregularities. TheSeismic Safety Screening Method (SSSM) by Ozdemir et al. (2005) derivesfrom the Japanese Seismic Index Method (JBDPA, 1990): in this method, too,the seismic capacity of a building is represented by a seismic index value whichis a function of structural strength and ductility; this index value has to be

Chapter I – Assessing seismic vulnerability of reinforced concrete buildings 17compared with a seismic demand index value – representing the seismic hazardof the zone where the building is located – for assessing the degree of safety ofthe building.1.3 ANALYTICAL METHODSSinghal and Kiremidjian (1996) estimate vulnerability curves and DPMs fordifferent RC frames (from Low-Rise, Mid-Rise and High-Rise classes,respectively) through nonlinear dynamic analyses and using the Monte Carlosimulation technique (see Figure 1.3.1).Figure 1.3.1. General framework of the methodology adopted in (Singhal and Kiremidjian,1996)The uncertainties associated with structural capacities and demands aremodelled. Uncertainty in capacity is simulated assuming as random variablesthe compressive strength of concrete and the yield strength of steel. Uncertaintyin seismic demands is accounted for by simulating 100 artificial time histories.Then, the conditional probability of reaching or exceeding a damage state given

18 Chapter I – Assessing seismic vulnerability of reinforced concrete buildingsa ground motion intensity is determined by the Monte Carlo simulation method.100 Latin hypercube samples are used for the nonlinear dynamic analyses ateach ground motion level (expressed in terms of spectral acceleration value).After performing nonlinear dynamic analyses, for each level of ground motionthe statistics of the Park and Ang (1985) damage index are used to obtain theparameters of a lognormal probability distribution function at that groundmotion level (see Figure 1.3.2).Figure 1.3.2. Probability distribution of Park and Ang’s damage index at S a =3g (Singhal andKiremidjian, 1996)The lognormal probability functions at each level of ground motion are thenused to obtain the probabilities of reaching or exceeding a damage state,adopting given threshold values for the different damage states (see Figure1.3.3).

Chapter I – Assessing seismic vulnerability of reinforced concrete buildings 19Figure 1.3.3. Ranges of Park and Ang's damage index for different damage states (Singhal andKiremidjian, 1996)Discrete points representing the probabilities of different damage states for agiven spectral acceleration value are evaluated from the probabilitydistributions of the damage measure. Hence, smooth vulnerability curves areobtained fitting lognormal distribution functions to these points (see Figure1.3.4).Figure 1.3.4. Vulnerability curves for Mid-Rise frames (Singhal and Kiremidjian, 1996)The relationship between the Modified Mercalli Intensity (MMI) and theaverage spectral acceleration (that is, the conditional probability of a spectralacceleration at a specified MMI value) in each period band, which is assumedto be lognormal, is developed in the paper based on average spectral

20 Chapter I – Assessing seismic vulnerability of reinforced concrete buildingsacceleration values of the ground motions recorded on firm sites and the MMIvalues from these earthquakes at the respective recording stations (see Figure1.3.5).Finally, DPMs are evaluated from the fragility curves by calculating theprobability of reaching or exceeding a given damage state for a given MMIintensity (see Figure 1.3.6). This probability is obtained by convolving (i) theprobability of reaching or exceeding the given damage state for a specifiedMMI and spectral acceleration and (ii) the conditional probability of a spectralacceleration at specified MMI.Figure 1.3.5. Correlation between MMI intensity and spectral acceleration over period range0.5-0.9 s (Singhal and Kiremidjian, 1996)Figure 1.3.6. Damage Probability Matrix for Mid-Rise frames (Singhal and Kiremidjian, 1996)

Chapter I – Assessing seismic vulnerability of reinforced concrete buildings 21A similar approach is adopted in (Masi, 2003), where three main structuraltypologies are examined: bare frames, regularly infilled frames and pilotisframes, designed for gravity loads only. Structural models are generatedthrough a simulated design procedure considering current practice and codes inforce at the age of construction. Nonlinear dynamic analyses with groundmotions of various levels of intensity are carried out. Based on the obtainedresults, each type of building can be assigned to a different vulnerability classof EMS-98 scale.Rossetto and Elnashai (2005) derive vulnerability curves for a low-riseinfilled RC frame with inadequate seismic provisions according to thefollowing methodology: a population of 25 buildings is generated from a singlebuilding through consideration of material parameter uncertainty; uncertainty indemand is accounted for through the use of 30 different accelerograms; for eachof the generated buildings, an adaptive pushover analysis is carried out, and theperformance point is found following the Capacity Spectrum framework ofassessment, for all the accelerograms; a damage scale experimentally calibratedto maximum inter-storey drift is adopted. Hence, the results of the populationassessment are used to generate second-order response surfaces, one for eachdamage state. Vulnerability curves are generated from response surfacesthrough re-sampling. The derived curves show good correlation withobservational post-earthquake damage statistics.In (Cosenza et al., 2005) a procedure to evaluate the seismic capacity of abuilding class is proposed that enables to reduce dispersion of results dependingon the level of knowledge. A building class is defined in terms of age ofconstruction and number of storeys. The level of knowledge of the buildingstock is accounted for through a “specification” of building classes in differentorders depending on the level of knowledge of the parameters. RC rectangularshaped frame buildings are considered.For each class, a number of building models is generated by means of a

22 Chapter I – Assessing seismic vulnerability of reinforced concrete buildingssimulated design procedure, based on the probabilistic distribution of thestructural (geometrical and mechanical) parameters. Seismic capacity isdetermined in terms of base shear coefficient and global drift for each of thegenerated buildings of the building class, through a mechanics-based approach:3n z predefined mechanisms, where n z is the number of storeys, are considered(see Figure 1.3.7) and the corresponding base shear, V bi , is calculated for eachmechanism assuming a linear distribution of horizontal seismic forces.Figure 1.3.7. Predefined collapse mechanisms (Cosenza et al., 2005)The ultimate roof displacement ∆ ui is determined as a function of the ultimaterotation θ u of the structural elements:( H H )∆ = θ ⋅ − (1.3.1)u,1 u n k∆u,2= θu ⋅ Hk(1.3.2)( H )∆ = θ ⋅ − (1.3.3)u,3 u kHk − 1The collapse mechanism is identified by the lowest value of V bi . Then, thecapacity of the building is finally evaluated in terms of base shear coefficientC b,i (= ratio between the base shear V b,i and the seismic weight W) andcorresponding lateral (drift u ) i (= ratio between the ultimate roof displacement∆ u,i and the building height H n ) for the determined collapse mechanism:CVb,ib,i= (1.3.4)W

Chapter I – Assessing seismic vulnerability of reinforced concrete buildings 23( drift )∆u,iu= (1.3.5)iHnStarting from the capacity of the analyzed buildings, the response surfacemethod is adopted and the influence of each parameter is investigated. Capacitycurves expressing the probability of having a capacity lower than the assignedvalue are obtained through a Monte Carlo simulation technique. The influenceof the knowledge level on the probability of reaching a fixed capacity thresholdis shown, too.However, this study only provides cumulative frequency distributions ofcapacity parameters (base shear coefficient and ultimate roof drift) within abuilding class. No vulnerability curve, relating a seismic demand measure to theprobability of reaching or exceeding a given damage state, is provided.In (Iervolino et al., 2007) a complete seismic risk assessment framework ispresented, where the mechanisms-based approach is overcome.In order to investigate the building class capacity, n geometrical and mechanicalcharacteristics of the buildings are identified as random variables. Then, apossible range of variation and a corresponding “scanning step” are assumedfor each one of this variables. A simulated design procedure, a nonlinear FEmodelling of the structure and a Static PushOver (SPO) analysis are carried outfor all of the resulting combinations of values. Hence, response surfaces areobtained for the capacity parameters T (period), C S (strength) and C d(displacement capacity) of the equivalent SDOF system (see Figure 1.3.8),expressed as function of the assumed random variables.

24 Chapter I – Assessing seismic vulnerability of reinforced concrete buildingsFigure 1.3.8. Capacity parameters (Iervolino et al., 2007)Seismic demand is provided by Probabilistic Seismic Hazard Analysis (PSHA).Hence, a calculation of seismic risk can be carried out through a Monte Carlosimulation technique, according to the following steps:- sampling of N values of the n input random variables describing differentgeometrical and mechanical building characteristics according to theProbability Density Functions (PDFs) respectively assigned;- evaluation of N arrays of capacity parameters {T, C S , C d } as a function ofthe sampled random variables by linearly interpolating between the pointsobtained from the SPO analyses;- sampling of N values of elastic spectral displacement demand S d,e accordingto the probability distribution given by the PSHA;- evaluation of the corresponding N values of median inelastic displacementdemand Sd,i = Sd,e ⋅ CRaccording to the Capacity Spectrum Methodassessment procedure (Fajfar, 1999);- sampling of N values of the random variableεC Rrepresenting thevariability of the inelastic displacement demand, according to the assignedPDF, thus giving the N final values of the displacement demandD = S d,i⋅ε CR;- comparison between the N values of displacement capacity C d and thecorresponding N values of displacement demand D, thus leading to thenumber N f of buildings for which the capacity is exceeded by the demand;

Chapter I – Assessing seismic vulnerability of reinforced concrete buildings 25Nf- estimation of the failure probability as Pf= .NHAZUS (HAZard in United States) is an earthquake loss estimationmethodology including many components. It was developed by the FederalEmergency Management Agency (FEMA) under agreements with the NationalInstitute of Building Sciences (NIBS) (FEMA, 2001; Kircher et al., 1997a;Kircher et al., 1997b; Whitman et al., 1997).Estimates of building damage are used as inputs to other damage modules.Most importantly, building damage is used as an input to a number of lossmodules (see Figure 1.3.9).Figure 1.3.9. Building-related modules of HAZUS methodology (FEMA, 2001)HAZUS damage functions for ground shaking have two basic components:capacity curves and fragility curves.Capacity curves are defined by two control points: the yield capacity and theultimate capacity. The yield capacity accounts for design strength, redundanciesin design, conservatism in code requirements and expected (rather thannominal) strength of materials. Design strengths of model building types arebased on the requirements of US seismic code provisions or on an estimate oflateral strength for buildings not designed for earthquake loads. The ultimate

26 Chapter I – Assessing seismic vulnerability of reinforced concrete buildingscapacity represents the maximum strength of the building when the globalstructural system has reached a full mechanism. Up to yield, the buildingcapacity curve is assumed to be linear with stiffness based on an estimate of theexpected “elastic” period of the building. From yield to the ultimate point, thecapacity curve transitions in slope from an essentially elastic state to a fullyplastic state. The capacity curve is assumed to remain plastic past the ultimatepoint (see Figure 1.3.10).Figure 1.3.10. Example building capacity curve and control points (FEMA, 2001)36 different building structural typologies are considered. For each typology,values of the parameters defining the capacity curves are provided. As anexample, see Figure 1.3.11 and Figure 1.3.12 for C1M building class (Mid-RiseConcrete Moment Frame).

Chapter I – Assessing seismic vulnerability of reinforced concrete buildings 27Figure 1.3.11. “Elastic” period values and average inter-story drift ratios of capacity curvecontrol points and structural damage state thresholds (fragility medians) for C1M 1 buildingclass (FEMA, 2001)Figure 1.3.12. Capacity curves and structural damage-state thresholds (fragility medians) forfive seismic design levels (Special High, High, Moderate, Low and Pre-Code) for C1M buildingclass (FEMA, 2001)Capacity Spectrum Method is adopted in HAZUS to evaluate the demandcorresponding to a given seismic intensity. To this end, the inelastic demand

28 Chapter I – Assessing seismic vulnerability of reinforced concrete buildingsspectrum is obtained reducing the 5%-damped elastic response spectrum bymeans of an effective damping value which is defined as the total energydissipated by the building during peak earthquake response and is the sum of anelastic damping term, β E , and a hysteretic damping term, β H , associated withpost-yield, inelastic response and influenced by ground motion duration. Then,peak response displacement and acceleration are determined from theintersection between the demand spectrum and the building’s capacity curve(see Figure 1.3.13).Figure 1.3.13. Example demand spectrum construction and calculation of peak responsedisplacement (D) and acceleration (A) (FEMA, 2001)HAZUS provides fragility curves for damage to structural system, nonstructuralcomponents sensitive to drift and non-structural components (andcontents) sensitive to acceleration. Fragility curves are lognormal functionsdefined by a median value of the demand parameter, which corresponds to thethreshold of that damage state, and by the variability associated with thatdamage state. For example, the spectral displacement S d that defines thethreshold of a particular damage state ds is given by

Chapter I – Assessing seismic vulnerability of reinforced concrete buildings 29Sd= Sd,ds⋅εds(1.3.6)where S d,ds is the median value of spectral displacement of damage state ds andε ds is a lognormal random variable with a unit median value and a logarithmicstandard deviation β ds , which controls the slope of the fragility curve andaccounts for the variability and uncertainty associated with capacity curveproperties, damage states and ground shaking.Four damage states are defined: Slight, Moderate, Extensive and Complete (seeFigure 1.3.14). Median values of spectral displacement associated with eachdamage state are evaluated calculating the average interstorey drift ratio (i.e.,roof displacement divided by building height) corresponding to the step ofpushover analysis at which a certain fraction of structural elements reaches acertain deformation limit. The value of this fraction is defined as the repair orreplacement cost of components at limit divided by the total replacement valueof the structural system.Figure 1.3.14. Example fragility curves for Slight, Moderate, Extensive and Complete damage(FEMA, 2001)The lognormal standard deviation β ds , which describes the total variability offragility-curve damage state ds, is given by three contributions:

30 Chapter I – Assessing seismic vulnerability of reinforced concrete buildings( CONV [ , ]) 2( ) 2β = β β + β (1.3.7)ds C D T,dswhere β C is the lognormal standard deviation parameter that describes thevariability of the capacity curve, β D is the lognormal standard deviationparameter that describes the variability of the demand spectrum and β T,ds is thelognormal standard deviation parameter that describes the variability of thethreshold of damage state ds. Since the demand spectrum is dependent onbuilding capacity, a convolution process is required to combine their respectivecontributions to total variability, while the third contribution to total variability,β T,ds , is assumed mutually independent of the first two and is combined with theresults of the convolution process using the square-root-sum-of-the squares(SRSS) method. The convolution process involves a complex numericalcalculation that would be very difficult for most users to perform. To avoid thisdifficulty, sets of pre-calculated values of damage state Beta’s are proposed.These Beta values are given as a function of building height group, post-yielddegradation of the structural system, damage state threshold variability andcapacity curve variability.Estimation of β C and β T,ds must be made by users on a judgmental basis, basedon the consideration that these variability values are influenced by uncertaintyin capacity curve properties and thresholds of damage states and by buildingpopulation (i.e., individual building or group of buildings): relatively lowvariability of damage states would be expected for an individual building withwell known properties (e.g., complete set of as-built drawings, material testdata, etc.) and whose performance and failure modes are known withconfidence. Relatively high variability of damage states would be expected fora group of buildings whose properties are not well known and for which theuser has low confidence in the results (of pushover analysis) that representperformance and failure modes of all buildings of the group.Giovinazzi (2005) proposes a method for seismic risk assessment based onthe assumption that, dealing with a territorial vulnerability assessment, building

Chapter I – Assessing seismic vulnerability of reinforced concrete buildings 31seismic response can be represented by simplified bilinear capacity curvesdefined by three parameters: the yield acceleration, the yield period of vibrationand the structural ductility capacity.The yield acceleration can be derived as a function of the seismic code designlateral force, multiplied by another factor in order to consider median values ofmaterial strength instead of nominal ones. The period can be evaluated throughsimplified expressions proposed by code. The ductility capacity can be derivedfrom the behaviour factor adopted in design, if any; otherwise, for buildingsnon-specifically designed to have dissipation capacity, a value of 2.5 is arbitraryassumed.For non designed structures, the author states that bilinear capacity curve can bederived taking into account the geometrical and the technological featurescharacterizing on the average the typology (number of floors, code level,material strength, drift capacity, age, etc.) and hypothesizing a certain collapsemode.Displacement demand assessment for a given seismic intensity is carried outaccording to the Capacity Spectrum Method.Four damage states are considered. Mean values of the correspondingdisplacement threshold are proposed as a function of the yielding and ultimatedisplacements, based on expert judgement, and are verified on the basis of theresults of pushover analyses performed on prototype buildings.In order to define fragility curves for the considered damage states, uncertaintyin the estimate has to be evaluated. To this end, a different approach fromHAZUS is proposed: the overall uncertainty in the damage estimation isevaluated in order to represent the same dispersion of observed damage datathat are well fitted by binomial distributions. Repeating this procedure fordifferent buildings typologies a lognormal standard deviation is found,depending on the ductility corresponding the mean damage values.Grant et al. (2006) also adopt a code-based approach to the evaluation ofbuilding seismic vulnerability. In order to carry out a first, rapid and very

32 Chapter I – Assessing seismic vulnerability of reinforced concrete buildingssimplified step of a multi-level screening procedure aimed at defining prioritiesand timescales for seismic intervention in school buildings, authors evaluate thePGA capacity from the code-prescribed seismic input at the age of construction,based on the assumption of a “perfect” code compliance. To this aim, startingfrom the design inelastic acceleration capacity prescribed by the seismic code inforce at the age of construction, a sort of “back-analysis” is applied, thuscalculating the corresponding PGA, also accounting for modern seismic coderequirements including adjustments for ductility capacity (i.e., the behaviourfactor) and building importance. In a very conservative (but unrealistic) way theauthors also assume that buildings designed for Gravity Loads only have a nullseismic capacity. Following this procedure, the seismic vulnerability can beevaluated in terms of a “PGA deficit” obtained as the difference between theevaluated PGA capacity and the PGA demand, which is derived from modernseismic hazard studies.However, a quite critical shortcoming can affect a procedure that evaluateseismic capacity based on the assumption of a perfect code compliance withseismic codes in force at the age of construction, since the actual seismiccapacity of a building stock can differ greatly from the prediction of such a codeprescription-based model. At least, factors accounting for material overstrengthshould be accounted for (e.g., Giovinazzi, 2005). Moreover, designconservatism approximations usually should lead to a higher capacity,compared with code prescriptions. Hence, a code-based procedure maysystematically underestimate seismic capacity. This approach may be justifiedas conservative, but actually a seismic vulnerability assessment for a large scaleearthquake loss model should not be conservative; it should rather provide aseismic capacity estimation as reliable as possible.Ordaz et al. (2000) adopt a vulnerability analysis procedure where thedamage level is expressed as a function of the maximum interstorey drift, whichis evaluated as a function of the spectral acceleration. The relationship between

Chapter I – Assessing seismic vulnerability of reinforced concrete buildings 33the maximum expected interstorey drift and the spectral acceleration demand isevaluated through a simplified model based on the analogy with equivalentcantilever beams subjected to shear and flexural deformations. In this model,coefficients are used to account, among others, for the structural type, for theheight of the structure and for the ratio between inelastic and elastic demand.Moreover, further coefficients are used to account for the increase in seismicvulnerability due to some factors including, for instance, irregularities inelevation and/or in plan or the presence of short columns.Calvi (1999) first proposes an approach for the evaluation of thevulnerability of building classes based on the Displacement-Based method (e.g.,Priestley, 1997).For each limit state, a displacement shape is assumed and a correspondingdisplacement capacity is evaluated, depending on the attainment of a localdeformation limit [material strain capacity -> section curvature capacity ->element drift capacity -> building displacement capacity (on the equivalentSDOF model)]. A possible range of variation for the evaluated capacity isdefined. At the same time, a possible range of variation for the period ofvibration (secant to the displacement capacity) is defined, too. Hence, for eachlimit state, rectangles representing the possible “positions” of the pointsrepresenting the building capacity in a period-displacement plane are obtained.A uniform probability density function over the rectangles is assumed,describing the variability of the capacity.Seismic demand is represented by displacement response spectra adjusted toinclude the nonlinear response, wherein a reduction of the spectral ordinates isapplied to account for the energy dissipation capacity of the structure as afunction of the target displacement and the structural response.Capacity and demand can be directly compared to each other as a function ofthe period: the rectangle area below the demand spectrum represents theexpected proportion of buildings reaching (or exceeding) the limit statecapacity (see Figure 1.3.15).

34 Chapter I – Assessing seismic vulnerability of reinforced concrete buildingsFigure 1.3.15. An example of the intersection of capacity areas and demand spectrum (Calvi,1999)The methodology proposed by Calvi (1999) is subsequently developed(Pinho et al., 2002; Glaister and Pinho, 2003; Crowley et al., 2004; Crowley etal., 2006) leading to the Displacement-Based Earthquake Loss Assessment(DBELA) procedure.The main improvements to the original procedure by Calvi (1999) may besummarized in (i) the theoretical improvement of structural and non-structuraldisplacement capacity equations, (ii) the derivation of an equation betweenyield period and height for European buildings both with and without infillpanels (Crowley and Pinho, 2004, 2006) and (iii) the development of a fullyprobabilistic framework accounting for uncertainties in geometrical andmechanical properties, in capacity models and in demand spectrum.In DBELA the displacement capacity can be expressed as a function of thebuilding height; this relationship can be transformed into a direct relationshipbetween displacement capacity and period, through the substitution of anequation relating the height of a building to its limit state period. Hence, a

Chapter I – Assessing seismic vulnerability of reinforced concrete buildings 35direct comparison is possible at any period between the displacement capacityof a building class and the displacement demand predicted from a responsespectrum (see Figure 1.3.16).Figure 1.3.16. Deformation based seismic vulnerability assessment procedure (Glaister andPinho, 2003)The probabilistic treatment of the uncertainties involved in the assessmentprocedure leads to the definition of a Joint Probability Density Function (JPDF)of displacement capacity and period (see Figure 1.3.17), which was originallyassumed to be uniform (Calvi, 1999).Figure 1.3.17. Joint Probability Density Function (JPDF) of displacement capacity andperiod (Crowley et al., 2004)

36 Chapter I – Assessing seismic vulnerability of reinforced concrete buildingsThe Simplified Pushover-Based Earthquake Loss Assessment (SP-BELA)by Borzi et al. (2008a) combines the definition of a pushover curve using asimplified mechanics-based procedure – similar to (Cosenza et al., 2005) – todefine the base shear capacity of the building stock with a displacement-basedframework similar to that in DBELA, such that the vulnerability of buildingclasses at different limit states can be obtained.Simplified pushover curves are derived according to the following procedure: aprototype structure representing the building class is defined first, for which thecollapse mechanism and, therefore, the collapse multiplier under a lineardistribution of lateral forces is determined. Based on limit conditions given interms of element chord rotations, the building displacement capacity (in termsof the equivalent SDOF) is evaluated for different Limit States. Then, theperiod of vibration for each Limit State is calculated, corresponding to thesecant stiffness to the displacement capacity.In order to derive vulnerability curves using this type of analytical procedure, aset of random variables is defined – together with the corresponding probabilitydistributions – including geometrical dimensions, material properties anddesign loads.Seismic demand is defined in terms of inelastic displacement demand spectra,and the uncertainty in this demand is taken into account assuming the cornerperiods of the spectrum and the spectral amplification coefficient as randomvariables.A Monte Carlo simulation approach is adopted, and random variables aregenerated through a Latin Hypercube Sampling procedure. Hence, vulnerabilitycurves can be derived for a class of buildings and for different Limit States,carrying out the following steps:- definition of a number of building samples through the generation ofassumed random variables;- definition of building capacity through a pushover curve for each generatedbuilding;- definition of the displacement demand;

Chapter I – Assessing seismic vulnerability of reinforced concrete buildings 37- comparison between demand and capacity to define the number of buildings– out of the generated population – exceeding the given Limit Stateconditions.SP-BELA has been further developed in order to approximately account for thepresence of infill panels in (Borzi et al., 2008b). Two possible distributions ofthe infill panels are considered: a uniform distribution along the height of thebuilding or a “pilotis” distribution. It is assumed that the panels have aninfluence on the lateral resistance of the building up to the yield limit state.When the frames evolve into the nonlinear range, the panels are considered tocollapse and, therefore, they no longer contribute to the base shear resistance.The behaviour of the single strut representing the infill panel is assumed to belinear up to failure. The influence of the panels is not considered in defining thedisplacement capacity on the pushover curve as the panels are often notperfectly in contact with the frames and they are assumed to play a role on theoverall building performance only after the frames have already been deformedbeyond their elastic limit. On the other hand, the panels are assumed to collapsebefore the frames reach the significant damage limit condition.Hence, the only way the influence of infill panels is accounted for is that theyare assumed to increase the lateral strength of the building up to the yielding ofthe RC structure. In other terms, the presence of infill panels leads to a lowervalue of the secant period to the yielding Limit State by increasing the yieldstrength, thus decreasing the corresponding failure probability within theadopted Displacement-Based assessment framework. No influence at all isconsidered on other Limit States.However, authors do not clarify how the presence of elements characterized bya brittle behaviour (such as infill trusses) can be accounted for in amechanisms-based approach, where all the structural elements should have anelastic-perfectly plastic behaviour.

38 Chapter I – Assessing seismic vulnerability of reinforced concrete buildingsVC (Vulnerabilità Calcestruzzo armato, reinforced concrete vulnerability),by Dolce and Moroni (2005), is a simplified procedure – implemented in aspreadsheet software – for the vulnerability assessment of RC buildings. TwoLimit States are considered: Slight Damage and Collapse. The vulnerability isexpressed as the PGA values leading the attainment of these Limit States. Theprocedure is based on the evaluation of the storey strength at each storey and onthe application of a ductility coefficient accounting for the inelasticdisplacement capacity.Soft-storey (concentration of the inelastic demand only in columns in onestorey) is the only collapse mechanism considered. In authors’ opinion, this isthe most probable collapse mechanism for existing RC buildings, due tofrequent weak column/strong beam conditions.Infill elements can be taken into account, both in terms of stiffness andstrength.For the definition of Slight Damage Limit State an interstorey drift limit, basedon Italian code prescriptions, is assumed. An elastic behaviour is assumed up tothis limit. Hence, interstorey shear stiffness has to be evaluated. To this end, thesum of column stiffness values is calculated, also considering the influence ofthe restrain condition given by the beams; a cracked stiffness is considered, too.If infill panels are present, their contribution is taken into account assuming thestiffness model provided by Italian code. Hence, a value of interstorey shearleading to the attainment of Slight Damage Limit State (V OPER ) is evaluated ateach storey, corresponding to the prescribed interstorey drift limit.For Collapse Limit State the ultimate value of interstorey shear strength (V COLL )at each storey is evaluated. The ultimate interstorey shear strength is calculatedas the sum of the ultimate shear strength of each column, given by the flexuralcapacity of the column section, also considering the influence of the restraincondition given by the beams on the moment distribution along the elementand, therefore, on the corresponding shear value. Possible shear failures areconsidered, too. If infill panels are present, their contribution to the ultimateshear strength is taken into account considering different possible collapse

Chapter I – Assessing seismic vulnerability of reinforced concrete buildings 39mechanisms of the panels. Subsequently, this value is multiplied by acoefficient accounting for the inelastic displacement capacity in order toevaluate the interstorey shear value leading to Collapse in a spectral elasticapproach, thus implicitly applying the equal rule between overstrength andductility (R=µ).The procedure can be summarized in the following steps (each step is carriedout in both building directions):- at each storey, interstorey shear leading to Slight Damage drift limit (V OPER )and ultimate interstorey shear strength (V COLL ) are evaluated, as abovedescribed;- the interstorey shear demand distribution is evaluated, assuming a baseshear demand equal to the weight of the structure (that is, a pseudoaccelerationequal to 1g) and a linear distribution of lateral displacements;- at each storey, the ratios between V OPER and V COLL and the interstorey sheardemand are evaluated, representing the pseudo-acceleration values S D(OP)and S D(COLL) (expressed in g) leading to the attainment of a shear demandequal to V OPER and V COLL , respectively;- at each storey, the PGA values corresponding to S D(OP) and S D(COLL) areevaluated by means of different coefficients: α PM (accounting for theparticipating mass ratio of the first mode), α AD (aimed at evaluating thePGA from the spectral pseudo-acceleration depending on the period ofvibration and the shape of the demand spectrum), α DS (accounting for thestructural dissipation capacity) and α DUT (accounting for the inelasticdisplacement capacity). Obviously, α DUT is equal to 1 for Slight DamageLimit State. For Collapse Limit State, a coefficient α DUT,pil is evaluated foreach column as a function of the axial load ratio; it is assumed equal to 1 ifthe column behaviour is controlled by shear. Then, α DUT is given by aweighted average of α DUT,pil extended to all the columns in the storey. α DUTcan be reduced by means of coefficients accounting for the presence of asoft storey or for irregularities in strength/stiffness/mass distribution. If thepresence of infill panels is taken into account α DUT is assumed equal to 1.5

40 Chapter I – Assessing seismic vulnerability of reinforced concrete buildingssince in this case in authors’ opinion the failure mechanism is controlled bybrittle interaction mechanisms between structural and non-structuralelements;- for both Limit States, the minimum PGA value between all the valuescalculated at each storey and in each direction is evaluated, representing thePGA capacity of the building.1.4 HYBRID METHODSHybrid methods allow to produce DPMs and vulnerability curves as acombination of analytical data from mechanical models and empirical datafrom observed damage, thus allowing, for example, to calibrate analyticalmodels or to provide for the lack of empirical damage data at certain intensitylevels for the geographical area under consideration.In (Kappos et al., 1995; Kappos et al., 1998) DPMs are provided which arepartially derived from observed damage data from past earthquakes, through thevulnerability index procedure, and partially obtained from nonlinear dynamicanalyses carried out on building models representing different building classes.In order to include such analytical results into the DPMs, an empiricalcorrelation between intensity and PGA values at which the accelerograms werescaled is used, and a correlation is also established between an analytical globaldamage index obtained from the analyses and the damage expressed as the costof repair. 6 structural models representing existing Greek buildings, 10accelerograms and 2 intensities are considered, thus leading to a total number of120 nonlinear dynamic analyses. The damage results are then combined withthe observed damage from the 1978 earthquake in Thessaloniki.In (Singhal and Kiremidjian, 1998) the analytical vulnerability curvesproposed in (Singhal and Kiremidjian, 1996) for Low-Rise RC frames areupdated based on the observational data obtained on 84 buildings damagedduring the 1994 Northridge earthquake, by means of a Bayesian updatingtechnique accounting for the reliability of different data sources.Nevertheless, special attention should be addressed to the treatment of

Chapter I – Assessing seismic vulnerability of reinforced concrete buildings 41uncertainties when using hybrid methods since analytical and empiricalvulnerability data include different sources of uncertainty and are thus notdirectly comparable. Hence, in order to improve an analytical model through acomparison with an empirical model, it probably would be better to calibratethe former in order to obtain only median values equal to the ones provided bythe latter. In this way, each source of uncertainty can be properly taken intoaccount through a specific and explicit modelling (Calvi et al., 2006).1.5 EXPERT JUDGEMENT-BASED METHODSAn example of Damage Probability Matrices derived from expert judgementcan be found in ATC-13 (ATC, 1985), where DPMs are provided which werederived from the judgement of more than 50 senior earthquake engineeringexperts. Each expert provided, according to his engineering judgement andexperience, an estimate of low, best and high values of the damage ratio foreach of 36 different building classes, as a function of the seismic intensityexpressed according to the MMI scale. These values were assumed ascorresponding to 5 th , 50 th and 95 th percentiles, respectively, of a lognormaldistribution representing the estimated damage factor for a given seismicintensity. The estimates provided by the experts were also weighted accordingto the experience and confidence level of each expert for the consideredbuilding class.

42 Chapter I - Assessing the seismic vulnerability of reinforced concrete buildingsREFERENCES− ATC, 1985. Earthquake damage evaluation data for California. ReportATC-13, Applied Technology Council, Redwood City, California,USA.− Benedetti D., Petrini V., 1984. Sulla vulnerabilità di edifici in muratura:proposta di un metodo di valutazione. L’industria delle Costruzioni,149(1), 66-74. (in Italian)− Borzi B., Pinho R., Crowley H., 2008a. Simplified pushover-basedvulnerability analysis for large scale assessment of RC buildings.Engineering Structures, 30(3), 804-820.− Borzi B., Crowley H., Pinho R., 2008b, The influence of infill panels onvulnerability curves for RC buildings. Proceedings of the 14 th WorldConference on Earthquake Engineering, Beijing, China, October 12-17.Paper 09-01-0111.− Braga F., Dolce M., Liberatore D., 1982. A statistical study on damagedbuildings and an ensuing review of the MSK-76 scale. Proceedings ofthe 7 th European Conference on Earthquake Engineering, Athens,Greece. Pp. 431-450.− Calvi G.M., 1999. A displacement-based approach for vulnerabilityevaluation of classes of buildings. Journal of Earthquake Engineering,3(3), 411-438.− Calvi G.M., Pinho R., Magenes G., Bommer J.J., Restrepo-Veléz L.F.,Crowley H., 2006. The development of seismic vulnerability assessmentmethodologies for variable geographical scales over the past 30 years.ISET Journal of Earthquake Technology, 43(3), 75-104.− Colombi M., Borzi B., Crowley H., Onida M., Meroni F., Pinho R., 2008.Deriving vulnerability curves using Italian earthquake damage data.Bulletin of Earthquake Engineering, 6(3), 485-504.

Chapter I – Assessing the seismic vulnerability of reinforced concrete buildings 43− Cosenza E., Manfredi G., Polese M., Verderame G.M., 2005. A multilevelapproach to the capacity assessment of existing RC buildings.Journal of Earthquake Engineering, 9(1), 1-22.− Crowley H., Colombi M., Borzi B., Faravelli M., Onida M., Lopez M.,Polli D., Meroni F., Pinho R., 2009. A comparison of seismic risk mapsfor Italy. Bulletin of Earthquake Engineering, 7(1), 149-190.− Crowley H., Pinho R., 2004. Period-height relationship for existingeuropean reinforced concrete buildings. Journal of EarthquakeEngineering, 8(1), 93-119.− Crowley H., Pinho R., 2006. Simplified equations for estimating theperiod of vibration of existing buildings. Proceedings of the 1 stEuropean Conference on Earthquake Engineering and Seismology,Geneva, Switzerland, September 3-8. Paper No. 1122.− Crowley H., Pinho R., Bommer J.J., 2004. A probabilistic displacementbasedvulnerability assessment procedure for earthquake lossestimation. Bulletin of Earthquake Engineering, 2(2), 173-219.− Crowley H., Pinho R., Bommer J.J., Bird, J.F., 2006. Development of adisplacement-based method for earthquake loss assessment. ROSEResearch Report No. 2006/01, IUSS Press, Pavia, Italy.− Di Pasquale G., Orsini G., 1997. Proposta per la valutazione di scenari didanno conseguenti ad un evento sismico a partire dai dati ISTAT. Attidell’VIII convegno ANIDIS “L’ingegneria sismica in Italia”, Taormina,Italy, September 21-24. Vol. 1, pp. 477–486. (in Italian)− Di Pasquale G., Orsini G., Romero R.W., 2005. New developments inseismic risk assessment in Italy. Bulletin of Earthquake Engineering,3(1), 101-128.− Dolce M., Masi A., Marino M., Vona M., 2003. Earthquake damagescenarios of the building stock of Potenza (southern Italy) including siteeffects. Bulletin of Earthquake Engineering, 1(1), 115-140.− Dolce M., Moroni C., 2005. La valutazione della vulnerabilità e delrischio sismico degli edifici pubblici mediante le procedure VC

44 Chapter I - Assessing the seismic vulnerability of reinforced concrete buildings(vulnerabilità c.a.) e VM (vulnerabilità muratura), Atti del Dipartimentodi Strutture, Geotecnica, Geologia applicata all’ingegneria, N. 4/2005.(in Italian)− Faccioli E., Pessina V. (editors), 2000. The Catania project: earthquakedamage scenarios for a high risk area in the Mediterranean. CNR-Gruppo Nazionale per la Difesa dai Terremoti, Rome, Italy.− Faccioli E., Pessina V., Calvi G.M., Borzi B., 1999.A study on damagescenarios for residential buildings in Catania city. Journal ofSeismology, 3(3), 327-343.− Fajfar P., 1999. Capacity spectrum method based on inelastic demandspectra. Earthquake Engineering and Structural Dynamics, 28(9), 979-993.− FEMA, 2001. HAZUS99 Technical Manual. Service Release 2. FederalEmergency Management Agency, Washington, D.C., USA.− Giovinazzi S., 2005. The vulnerability assessment and the damagescenario in seismic risk analysis. PhD Thesis, Technical UniversityCarolo-Wilhelmina at Braunschweig, Braunschweig, Germany andUniversity of Florence, Florence, Italy.− Giovinazzi S., Lagomarsino S., 2004. A macroseismic method for thevulnerability assessment of buildings. Proceedings of the 13 th WorldConference on Earthquake Engineering, Vancouver, Canada, August 1-6. Paper No. 896.− Glaister S., Pinho R., 2003. Development of a simplified deformationbasedmethod for seismic vulnerability assessment. Journal ofEarthquake Engineering, 7(SI1), 107-140.− GNDT, 1993. Rischio sismico di edifici pubblici. Parte I: aspettimetodologici. CNR-Gruppo Nazionale per la Difesa dai Terremoti,Rome, Italy.− Grant D., Bommer J.J., Pinho R., Calvi G.M., 2006. Defining prioritiesand timescales for seismic intervention in school buildings in Italy.ROSE Research Report No. 2006/03, IUSS Press, Pavia, Italy.

Chapter I – Assessing the seismic vulnerability of reinforced concrete buildings 45− Grünthal G., 1998. Cahiers du Centre Européen de Géodynamique et deSéismologie: Volume 15 – European Macroseismic Scale 1998.European Center for Geodynamics and Seismology, Luxembourg.− Hassan A.F., Sozen M.A., 1997. Seismic vulnerability assessment of lowrisebuildings in regions with infrequent earthquakes. ACI StructuralJournal, 94(1), 31-39.− Iervolino I., Manfredi G., Polese M., Verderame G.M., Fabbrocino G.,2007. Seismic risk of R.C. building classes. Engineering Structures,29(5), 813-820.− INGV-DPC S1, 2007. Progetto S1. Proseguimento della assistenza alDPC per il completamento e la gestione della mappa di pericolositàsismica prevista dall'Ordinanza PCM 3274 e progettazione di ulteriorisviluppi. Istituto Nazionale di Geofisica e Vulcanologia – Dipartimentodella Protezione Civile, http://esse1.mi.ingv.it (in Italian)− JBDPA, 1990. Standard for seismic capacity assessment of existingreinforced concrete buildings. Japanese Building Disaster PreventionAssociation, Ministry of Construction, Tokyo, Japan.− Kappos A.J., Pitilakis K., Stylianidis K.C., 1995. Cost-benefit analysis forthe seismic rehabilitation of buildings in Thessaloniki, based on ahybrid method of vulnerability assessment. Proceedings of the 5 thInternational Conference on Seismic Zonation, Nice, France, October17-19. Vol. 1, pp. 406-413.− Kappos A.J., Stylianidis K.C., Pitilakis K., 1998. Development of seismicrisk scenarios based on a hybrid method of vulnerability assessment.Natural Hazards, 17(2), 177-192− Kircher C.A., Nassar A.A., Kustu O., Holmes W.T., 1997. Developmentof building damage functions for earthquake loss estimation.Earthquake Spectra, 13(4), 663-682.− Kircher C.A., Reitherman R.K., Whitman R.V., Arnold C., 1997.Estimation of earthquake losses to buildings. Earthquake Spectra, 13(4),703-720.

46 Chapter I - Assessing the seismic vulnerability of reinforced concrete buildings− Masi A., 2003. Seismic vulnerability assessment of Gravity LoadDesigned R/C frames. Bulletin of Earthquake Engineering, 1(3), 371-395.− Mouroux P., Le Brun B., 2006. Presentation of RISK-UE project. Bulletinof Earthquake Engineering, 4(4), 323-339.− Ordaz M., Miranda E., Reinoso E., Pérez-Rocha L.E., 2000. Seismic Lossestimation model for Mexico City. Proceedings of the 12 th WorldConference on Earthquake Engineering, Auckland, New Zealand,January 30-February 4. Paper No. 1902.− Orsini G., 1999. A model for buildings’ vulnerability assessment usingthe Parameterless Scale of Seismic Intensity (PSI). Earthquake Spectra,15(3), 463-483.− Ozdemir P., Boduroglu M.H., Ilki A., 2005. Seismic safety screeningmethod. Proceedings of the International Workshop on SeismicPerformance Assessment and Rehabilitation of Existing Buildings(SPEAR), Ispra, Italy, April 4-5. Paper No. 23.− Park Y.J., Ang A.H.S., 1985. Mechanistic seismic damage model forreinforced concrete. ASCE Journal of Structural Engineering, 111(4),722-739.− Pinho R., Bomber J.J., Glaister S., 2002. A simplified approach todisplacement-based earthquake loss estimation analysis. Proceedings ofthe 12 th European Conference on Earthquake Engineering, London, UK,September 9-13. Paper No. 738.− Priestley M.J.N., 1997. Displacement-based seismic assessment ofreinforced concrete buildings. Journal of Earthquake Engineering, 1(1),157-192.− Rossetto T., Elnashai A., 2003. Derivation of vulnerability functions forEuropean-type RC structures based on observational data. EngineeringStructures, 25(10), 1241-1263.

Chapter I – Assessing the seismic vulnerability of reinforced concrete buildings 47− Rossetto T., Elnashai A., 2005. A new analytical procedure for thederivation of displacement-based vulnerability curves for populations ofRC structures. Engineering Structures, 7(3), 397-409.− Rota M., Penna A., Strobbia C., Magenes G., 2008. Direct derivation offragility curves from Italian post-earthquake survey data. Proceedings ofthe 14 th World Conference on Earthquake Engineering, Beijing, China,October 12-17. Paper 09-01-0148.− Sabetta F., Goretti A., Lucantoni A., 1998. Empirical fragility curvesfrom damage surveys and estimated strong ground motion. Proceedingsof the 11 th European Conference on Earthquake Engineering, Paris,France, September 6-11.− Sabetta F., Pugliese A., 1987. Attenuation of peak horizontal accelerationand velocity from Italian strong-motion records. Bulletin of theSeismological Society of America, 77(5), 1491-1513.− Sabetta F., Pugliese A., 1996. Estimation of response spectra andsimulation of nonstationary earthquake ground motions. Bulletin of theSeismological Society of America, 86(2), 337-352.− Singhal A., Kiremidjian A.S., 1996. Method for probabilistic evaluationof seismic structural damage. ASCE Journal of Structural Engineering,122(12), 1459-1467.− Singhal A., Kiremidjian A.S., 1998. Bayesian updating of fragilities withapplication to RC frames. ASCE Journal of Structural Engineering,124(8), 922-929.− Spence R.J.S., Coburn A.W., Sakai S., Pomonis A., 1991. Aparameterless scale of seismic intensity for use in the seismic riskanalysis and vulnerability assessment. International Conference onEarthquake, Blast and Impact, Manchester, UK, September 19-20. Pp.19-30.− Verderame G.M., De Luca F., Ricci P., Manfredi G., 2010. Preliminaryanalysis of a soft storey mechanism after the 2009 L’Aquila earthquake.

48 Chapter I - Assessing the seismic vulnerability of reinforced concrete buildingsEarthquake Engineering and Structural Dynamics. DOI:10.1002/eqe.1069− Whitman R.V., Anagnos T., Kircher C.A., Lagorio H.J., Lawson R.S.,Schneider P., 1997. Development of a national earthquake lossestimation methodology. Earthquake Spectra, 13(4), 643-661.− Whitman R.V., Reed J.W., Hong S.T., 1973. Earthquake DamageProbability Matrices. Proceedings of the 5 th World Conference onEarthquake Engineering, Rome, Italy, June 25-29. Vol. 2, pp. 2531-2540.− Yakut A., 2004. Preliminary seismic performance assessment procedurefor existing RC buildings. Engineering Structures, 26(10), 1447-1461.

Chapter II – Seismic behaviour of existing reinforced concrete buildings 49Chapter IISeismic behaviour of existing reinforced concretebuildings2.1 GENERAL REMARKSOrdinary reinforced concrete structures cannot sustain large earthquakesremaining in elastic field: they have to be enough ductile to dissipate energywithstanding large deformations into inelastic field without collapsing. Thiscould appear like a trivial issue, but it is the main idea at the basis of the majorbreakthrough in earthquake engineering philosophy: the shift from Force-Basedto Deformation-Based approach and the formulation of “Capacity Design”principles (Hollings, 1968a,b; Paulay and Priestley, 1992). According to theseprinciples, when designing a reinforced concrete structure for earthquake loads,a desired collapse mechanism has to be established first. This mechanism has tobe the most energy-dissipating possible, i.e., under this mechanism the structurehas to show the largest displacement (ductility) capacity. To this end, among allthe possible mechanisms, the one that is characterized by the lowest localductility demand, given equal the global ductility (i.e., the one that ischaracterized by the highest global ductility, given equal the local ductilitydemand), is chosen, thus leading to the well-known global collapse mechanism(see Figure 2.1.1).

50 Chapter II – Seismic behaviour of existing reinforced concrete buildingsFigure 2.1.1. Comparison of energy-dissipating mechanisms (Paulay and Priestley, 1992)Furthermore, the “strength hierarchy” principle has to be respected, ensuringthe development of inelastic deformations in the highest possible number ofductile elements and not in elements with lower rotational capacity (that is, inbeams and not in columns, due to the different axial load) and providing anoverstrength to undesired failure mechanisms – such as shear failure, bucklingof longitudinal reinforcement, anchorage failure or beam-column joint failure –since these kinds of brittle failure mechanisms would limit or even inhibit thedevelopment of ductile, energy-dissipating mechanisms (see Figure 2.1.2), suchas the flexural ones.Figure 2.1.2. The chain analogy: the strength of brittle links has to be higher than the strength ofductile links, in order to ensure a ductile failure mechanism to develop instead of a brittle one(Paulay and Priestley, 1992)

Chapter II – Seismic behaviour of existing reinforced concrete buildings 51These concepts lead to a series of design prescriptions. For instance, a shearstrength higher than the flexural strength has to be provided to each element,independent of the force demand evaluated from analysis, in order to preventany possibility of shear failure. The development of inelastic deformations inbeams rather that in columns, thus avoiding a local column-sway (less energydissipating)collapse mechanism (see Figure 2.1.1), is ensured providing anhigher flexural strength to column elements compared to beam elements (weakbeam/strong column condition).Prescriptions are provided not only to avoid the onset of brittle failuremechanisms, but also to increase the ductility capacity: higher the materialstrain ductility, higher the section curvature ductility, higher the elementrotational ductility, higher the global structural ductility.At material level, for instance, a higher ductility of concrete is given by ahigher confinement: to this end, prescriptions about spacing and anchoragedetail of transverse reinforcement in plastic hinge region are of importance. Therepresentation of the beneficial influence of these prescriptions at material orsection level is often completely conventional and far from the actual structuralbehaviour. As an example, an upper limit to longitudinal reinforcement ratio isprescribed in order to the increase the section curvature capacity, but at largedisplacements the plane section assumption in critical regions is quite far fromreality, and it makes no sense to talk about section curvature. However, theseprescriptions at material or section level do have a direct beneficial effect onelement ductility capacity. A way to account for this effect has to be found,although it is not easy to be modelled. From this point of view, experimentalactivity is of fundamental importance.At element level, an increase in ductility capacity can be achieved (or better,a limitation in ductility capacity can be avoided) through prescription aimed atavoiding the onset of brittle failure mechanisms such as buckling ofcompressed longitudinal reinforcement or anchorage failure.At structural level, a regular distribution of mass, stiffness and strength isalso prescribed, in order to avoid a collapse mechanism characterized by a

52 Chapter II – Seismic behaviour of existing reinforced concrete buildingslocalization of inelastic displacement demand since this kind of mechanismwould provide – as already illustrated – a low global ductility. For the samereason, modern seismic codes also prescribe a local increase in design seismicdemand to account for the effects of an irregular distribution of nonstructuralelements such as infill walls (e.g., “pilotis” effect).Most of the existing RC buildings in seismic areas were not designed incompliance with the above illustrated principles, even if they were designed forseismic loads. As far as Italy is concerned, Capacity Design method was fullyadopted only by very recent seismic codes (see Section 2.5.2), while a majorpart of the building stock was constructed in compliance with older seismiccodes or even for gravity loads only since not all the national territory wasclassified yet as seismic.As a result, even if an existing RC building was properly designedaccording to an old seismic code, anyhow it does not have the same (local andglobal) ductility as a contemporary building since its design procedure did notrespect some fundamental principles of modern earthquake engineering (e.g.,strength hierarchy).Furthermore, some critical issues have to be considered when capacitymodels are formulated for elements that were not designed according to theabove illustrated principles (i.e., substandard elements). For instance, ductiledeformation mechanisms can differ greatly from the same mechanisms incontemporary elements.In this Chapter, specific issues about the (ductile) deformation mechanismsof substandard elements are discussed in Section 2.2, with emphasis on RCcolumns with smooth bars.Then, main capacity models for shear resistance of RC members and forbeam-column joints are briefly reported and discussed (Sections 2.3, 2.4).Finally, an analysis of structural damage to RC buildings in L’Aquila afterthe 6 th April 2009 earthquake is presented, together with an overview of pastseismic code prescriptions, thus highlighting the typical deficiencies of existingRC buildings through observed damage (Section 2.5).

Chapter II – Seismic behaviour of existing reinforced concrete buildings 532.2 MEMBERS CONTROLLED BY FLEXURAL AND AXIAL LOADSIn this Section, specific issues about ductile deformation mechanisms of RCmembers are discussed, with emphasis on members with smooth bars. As amatter of fact, this kind of reinforcement is widely spread among existing RCbuildings, and its presence can highly influence the deformation mechanisms ofRC members.The results reported herein were published in (Verderame et al., 2010).A discussion about code formulations for the assessment of deformationcapacity of RC members is carried out in Section 2.2.1.Then, an experimental-based study on ultimate deformation capacities ofcolumn with smooth bars is presented, leading to a new proposal about codeprescriptions (Section 2.2.2).Bond between concrete and reinforcing bars can significantly influencedeformation mechanisms of RC members. Hence, an experimental study onbond capacities of smooth bars is reported, together with the formulation of acapacity model (Section 2.2.3).The deformation capacity of substandard RC members may be affected bylimitations due to the absence of proper seismic details. Among these,transverse reinforcement details (i.e., stirrup spacing and anchorage) are ofimportance. In Section 2.2.4 this issue is analyzed through the results of anexperimental campaign.In Section 2.2.5 the fixed-end rotation mechanism is investigated through anumerical model of a column element including the end hooked bars,representing a typical anchorage detail for this kind of elements.2.2.1. Code provisions for the assessment of ultimate deformation capacityThe use of non-linear analysis methods to determine the seismic capacity ofRC buildings requires knowledge of the actual post-elastic rotational capacitiesof each element (beams, columns) both in monotonic field, for non-linear staticanalysis, and in cyclic field, for non-linear dynamic analysis. In monotonicfield, a series of parameters (yielding, peak resistance, ultimate state) has to be

54 Chapter II – Seismic behaviour of existing reinforced concrete buildingsdefined, in order to define the response curve of the element. In cyclic field,hysteretic rules and strength and stiffness degradation models have to bedefined; they significantly influence the assessment of ultimate rotationalcapacity. Nevertheless, these rules are not easy to define, due to the number ofgeometrical and mechanical parameters and to the uncertainties involved. Forexample, the type of loading influences in a not negligible way the response ofthe RC element. Most of the code prescriptions only define the deformationcapacity at characteristic envelope points, such as the elastic limit (yielding)and the ultimate condition (collapse); therefore, based on these prescriptions, itis not possible to completely define the strength degradation of the monotonicenvelope, nor the hysteretic behaviour through appropriate rules.Generally, deformation at yielding is evaluated as a chord rotation,accounting for different contributions corresponding to bending, shear andfixed-end rotation deformation mechanisms.The rotational capacity is generally evaluated referring to a fixed strengthdecay (20%) with respect to the peak resistance, evaluated on the forcedisplacementenvelope curve. It is clear that this definition is stronglyinfluenced by the maximum resistance condition, as well as the post-peakdegradation, monotonic or cyclic. It is difficult to define a relationship betweenthe element parameters and the rotational capacity, due to the complexphenomena influencing the post-elastic deformation behaviour and to thenatural variability affecting these phenomena.European code (CEN, 2005), consistent with the methodologies developedin literature, proposes two main approaches: a mechanical-empirical approach,based on plastic hinge length concept, and a purely empirical approach.According to the USA code approach (referring in particular to ASCE/SEI41 update provisions (Elwood et al., 2007)), deformation capacity is evaluatedfrom a dataset of empirical data (Berry et al., 2004), assuming a categorizationof columns based on failure mode and selecting target probabilities of failurefor each failure mode.In this Section, both European and USA code prescriptions for the

Chapter II – Seismic behaviour of existing reinforced concrete buildings 55evaluation of deformation capacity of RC members – with a special focus onthe assessment of existing buildings – are reported and discussed, together withtheir background theory.2.2.1.1. EC8 part 3.3 – empirical approachEurocode 8–Part 3 at Section A.3.2.2 (Limit State of Near Collapse)provides expressions for the evaluation of ultimate element capacity of RCelements. The value of total chord rotation capacity under cyclic loading,following an empirical approach, is given by [EC8 - Eq. (A.1)]:0.35 ⎛ fyw⎞⎜αρsxf ⎟⎝ c ⎠ 100ρd25 (1.25 )( ′)( )1 νθum= 0.016 ⋅ (0.30 ) ⎢ fc ⎥γelmax 0.01;ω⎛ L⎜⎝ hV⎞⎟⎠⎡ max 0.01;ω⎣⎤⎦0.225(2.2.1.1)where γ el , equal to 1.5 for primary seismic elements and to 1.0 for secondaryseismic elements, is meant to convert mean values of chord rotation to meanminus-one-standard-deviationones. The code also provides another expressionfor the evaluation of the plastic part of the ultimate chord rotation [EC8 - Eq.(A.3)]:0.35 ⎛ fyw⎞αρsx0.2 L⎛ V ⎞ ⎜ f ⎟⎝ c ⎠ 100ρdfc25 (1.275 )( ′)( )1 ⎡max 0.01;ω0.0145 (0.25 )⎣plνθum= θum − θy= ⋅ ⎢ ⎥γelmax 0.01;ω⎜⎝h⎟⎠⎤⎦0.3(2.2.1.2)To evaluate the total chord rotation, the plastic part calculated according tothis formula should be added to the rotation at yielding [EC8 - Eq. (A.10)].The values of chord rotation calculated according to (2.2.1.1) and (2.2.1.2)apply to elements with ribbed bars, seismically detailed and without lapping oflongitudinal bars in the vicinity of the end region where yielding is expected(plastic hinge region).The correction coefficient applied to members with ribbed bars without

56 Chapter II – Seismic behaviour of existing reinforced concrete buildingsseismic detailing is equal to 0.825 for both formulas. If the longitudinal ribbedbars are lapped, expressions (2.2.1.1) and (2.2.1.2) should be applied doublingthe mechanical compression reinforcement ratio ( ω′). Moreover, if the laplength is less than the minimum valuel ou, min :⎡f yw ⎤l ou,min= dbLfyL / ⎢(1.05+ 14.5α1ρsx ) fc⎥(2.2.1.3)⎣fc⎦Another reduction factor equal to ( lo / lou,min ) should be applied, calibratedonly for expression (2.2.1.2), that is only for the plastic part of chord rotation.Corrections applied to the chord rotation at yielding are given at SectionA.3.2.4(3) of the code; they are omitted here for the sake of brevity.In elements with smooth bars the chord rotation evaluated according to(2.2.1.1) should be multiplied by 0.575, while the plastic part of chord rotationgiven by (2.2.1.2) should be multiplied by to 0.375. It is worth noting that bothcoefficients already include the reduction factor equal to 0.825, accounting forthe lack of seismic detailing. If longitudinal bars are lapped in members withsmooth bars, another coefficient has to be adopted, depending on the lap lengthl ) and the shear span ( L ). For total chord rotation, it is given by:( o[ min(50,l / d )](1− l / L )V0.0025180+o bL o V(2.2.1.4)while for the only plastic part it is:[ min(50,l / d )](1− l / L )0.0035 60 + o bL o V(2.2.1.5)Moreover, shear span in expressions (2.2.1.1) and (2.2.1.2) should bereduced by the lap length l o , assuming that the ultimate condition is controlledby the region right after the end of the lap.A document has been presented (“Corrigenda to EN 1998-3” – DocumentCEN/TC250/SC8/N437A (CEN, 2009)) changing some provisions of Eurocode8 – part 3 (CEN, 2005), also including prescriptions about ultimate deformationcapacity of members with smooth bars, which have been illustrated herein. Thecoefficients 0.575 and 0.375, applied to Eqs. (2.2.1.1) and (2.2.1.2) for

Chapter II – Seismic behaviour of existing reinforced concrete buildings 57elements with smooth bars, have been changed into 0.80 and 0.75 respectively.In both cases, these coefficients already include the reduction factor accountingfor the lack of seismic detailing, which has been changed from 0.825 to(1/1.20=0.833). Formulations (2.2.1.4) and (2.2.1.5), for elements with lappingof longitudinal smooth bars, have been significantly changed, too. Expression(2.2.1.4), applied to total ultimate chord rotation, has been replaced by:[ min(40,l / d )]0.019 10 +o bL(2.2.1.4a)Expression (2.2.1.5), applied to the plastic part of ultimate chord rotation,has been replaced by:0bL.019min(40,lo / d )(2.2.1.5a)In these cases, coefficients do not include the reduction factor accountingfor the lack of seismic detailing – equal to 1/1.20 – which has to be applied.The deformation capacity of elements with smooth bars – evaluated bymeans of coefficients applied to Eq. (2.2.1.1) or Eq. (2.2.1.2) – according to(CEN, 2009) is higher than previously prescribed by (CEN, 2005).In the following, both the formulations given in draft 2005 of Eurocode 8 –part 3 and the later proposed changes will be reported. They will by referred toas (CEN, 2005) and (CEN, 2009) respectively.Background theoryFormulas for the evaluation of rotational capacity can be obtained with atotally empirical approach, based on experimental data, with pure numericalregression analyses.In (Haselton and Deierlein, 2007), based on 255 experimental tests fromPEER database (Berry et al., 2004), empirical expressions for characteristicparameters of a RC element model (e.g., stiffness, rotation capacity, etc.), alsoincluding cyclic behaviour. These parameters are chosen according to the modelproposed in (Ibarra et al., 2005). Empirical expressions for the ultimatedeformation capacity are also proposed in (Rossetto, 2002; Zhu et al, 2007).This kind of formulations can also be derived from a small number of

58 Chapter II – Seismic behaviour of existing reinforced concrete buildingsexperimental data, when a specific typology of RC element is investigated. In(Lam et al., 2003), based on a few number of experimental tests, expressionsfor the assessment of deformation capacity of rectangular RC columns with lowlateral confinement and high-axial load are proposed.A different approach is proposed in (Peruš et al., 2006; Peruš et al., 2007).Authors elaborate a method for the prediction of flexural deformation capacity,but also of the whole force-drift envelope, by means of CAE method (a specialtype of multi-dimensional non-parametric regression) applied to a subset ofFardis and PEER databases. This method shows a better prediction capacitycompared to EC8 formulations.Among the different empirical expressions proposed in literature, theexpression proposed in (Panagiotakos et al., 2001) represents a reference for theabove illustrated code formulas (CEN, 2005). This experimental databaseconsists in 633 cyclic tests and 242 monotonic tests on beams, columns andwalls, which do not present brittle failure mechanisms. The relationship is alinear regression of the logarithm ofθ u on the control variables or theirlogarithms, without coupling. Only control variables which turn out to bestatistically significant for the prediction of θ u are retained. Separate regressionanalyses for monotonic tests and for cyclic ones are performed. To obtain amore representative experimental database, with particular regard to memberswith unsymmetric reinforcement well represented in monotonic tests, anotherregression analysis on all 875 tests is performed, leading to the followingexpression:θu= αst⋅αcyc⎛ αsl⎞⎛α⋅⎜1+⎟⎜1−⎝ 2.3 ⎠⎝3( 0.01;ω )( 0.01;ω )ν ⎡ max ′ ⎤(0.20 ) ⎢fcmax⎥⎣⎦0.275wall⎛ L⎜⎝ hV⎞⎟⎠⎞⎟⎠0.451.1⎛ fyw ⎞⎜100αρsx⎟⎝ fc ⎠(1.30100ρ d)(2.2.1.6)The ratio between the experimental ultimate rotation and the numericalvalue provided by (2.2.1.6) has mean equal to 1.06, median equal to 1.00 and

Chapter II – Seismic behaviour of existing reinforced concrete buildings 59CoV of 47%.During years, together with the extension of the experimental database, thecoefficients in this expression have been slightly modified. The last proposal,given in (Fardis, 2007), is based on 1307 monotonic and cyclic tests:θu= αst⋅(1− 0.43αcyc( 0.01;ω )( 0.01;ω )ν ⎡ max ′ ⎤(0.30 ) ⎢fcmax⎥⎣⎦⎛ αsl⎞⎛3) ⋅⎜1+⎟⎜1−α⎝ 2 ⎠⎝80.225⎛ L⎜⎝ hV⎞⎟⎠0.3525wall⎞⎟⎠⎛ fyw ⎞⎜ αρsx ⎟⎝ fc ⎠(1.25100ρ d)(2.2.1.7)The mean value of the ratio between the experimental ultimate rotation andthe numerical value provided by (2.2.1.7) is 1.05, the median is equal to 0.995and the CoV is of 42.8%. The comparison between the coefficients of variationclearly shows the better prediction capacity of (2.2.1.7), due to the growth ofexperimental knowledge state.In the same work, a regression analysis for the only plastic part is alsopresented, which was already proposed in (CEB-FIB, 2003) based on 1100experimental tests. The expression is:θplu= αplst⋅(1− 0.52αcyc( 0.01;ω )( 0.01;ω )ν ⎡ max ′ ⎤(0.25 ) ⎢max⎥⎣⎦⎛ αsl⎞) ⋅⎜1+⎟⎝ 1.6 ⎠0.300.20fc⎛ L⎜⎝ h( 1−0.4α)V⎞⎟⎠0.3525wall⎛ fyw ⎞⎜ αρsx ⎟⎝ fc ⎠(1.275100ρ d)(2.2.1.8)The mean value of the ratio between the experimental ultimate rotation andthe corresponding numerical prediction is 1.05, the median is equal to 0.995and the CoV is of 42.7%, against the 47% in the first proposal (see Eq. 2.2.1.6).Expressions (2.2.1.1) and (2.2.1.2) proposed in EC8 almost perfectly agreewith (2.2.1.7) and (2.2.1.8), assumingslip),α wall =0 (only beams and columns) and α st =α cyc =1 (cyclic loading), α sl =1 (withplstα =0.0185 (hot-rolledductile steel).Consistent with the characteristic of tests included in the experimental

60 Chapter II – Seismic behaviour of existing reinforced concrete buildingsdatabase, the proposed expressions for the ultimate rotational capacity shouldbe applied only to members with ribbed bars, with seismic detailing andwithout lapping of longitudinal bars in the vicinity of plastic hinge region, thatis, to members which are not representative of existing buildings. Authorsdefine correction coefficients allowing to extend the use of these expressions tomembers with different characteristics. These coefficients are calibrated tocounterbalance the mean error evaluated through the comparison betweenvalues from expressions (2.2.1.7) and (2.2.1.8) and results of experimental testson non-conforming members, not included in the original (primary) database.This approach, certainly approximated, is necessary because of the smallnumber of experimental data for these members. Because of the low number ofthese data, it seems to be allowed to suppose that their inclusion in the databasewould have not led to any significant change in the regression expression.Moreover, applying the primary expression to members of different typologies,only using a multiplicative coefficient, is the same as postulating that theultimate rotation depends on the control parameters by the same way,independently of the specific characteristics of considered elements.Nevertheless, the assumed methodology seems to be the only one that can befollowed, due to the few experimental data now available for this kind ofelements. A higher reliability can be obtained only by extending theexperimental database, so that a wider range of loading conditions andgeometrical and mechanical characteristics can be covered. In Table 2.2.1.1correction coefficients and the extension of the corresponding experimentaldatabases used for calibrations are reported.

Chapter II – Seismic behaviour of existing reinforced concrete buildings 61Element Typew/o seismicdetailing and w/continuousribbed barsw/o seismicdetailing w/hooked smoothbars and w/ orw/o lap-splicingover plastichingelengthw/o seismicdetailing w/hooked smoothbars and w/ orw/o lap-splicingover plastichingelengthCorrectionFactor# ofdata0.85 270.825 42( ( ))0.015 ⋅ 10 + min 40;lodb15(1 / 1.20 ⋅ 0.019 ⋅ 10+min 40;lodb(-Mean - MedianCoV(corrected data)(-) – (1.00)(-)(1.00) – (1.005)(33.6%)(1.07) – (0.975)(32%)(-) – (-)(-)Table 2.2.1.1. Correction factors for non-detailed membersReference(Panagiotakoset al., 2002;CEB-FIB,2003)(Biskinis andFardis, 2004;CEN, 2005)(Fardis, 2006)(CEN, 2009)2.2.1.2. EC8 part 3.3 – mechanical approachAccording to (CEN, 2005), the ultimate rotation may also be calculatedfollowing an equivalent mechanical approach through the evaluation of theplastic ultimate section curvature φ − φ ) , assumed to be constant over theplastic hinge length( u yL pl , which is empirically calibrated. Hence, the ultimaterotational capacity may be evaluated according to [EC8 - Eq. (A.4)]:θum1=γel⎛⎜θ⎝y+ ( φu− φy)Lpl⎛ L⎜1− 0.5⎝ LplV⎞⎞⎟⎟⎠⎠(2.2.1.9)Section curvatures at ultimate and at yielding are calculated based on thefirst principles, with the constitutive relationships given by Eurocode 2 (CEN,2004). If the concrete confinement model given in 3.1.9 in Eurocode 2 is

62 Chapter II – Seismic behaviour of existing reinforced concrete buildingsassumed, the plastic hinge length is equal to [EC8 - Eq. (A.5)]:dbLfyL pl = 0.10LV+ 0.17h + 0.24(2.2.1.10)fcIf the confinement model proposed by Eurocode 8 – part 3 is adopted, betterrepresenting the effects of confinement under cyclic loading, the plastic hingelength is given by:LdbLfy= 0.11(2.2.1.11)30fVL pl + 0.20h +cFor expressions (2.2.1.10) and (2.2.1.11) no correction factor accounting forthe above mentioned deficiencies is given. Therefore, they should only beapplied to members with ribbed bars, seismically detailed and without lappingof longitudinal bars.Background theoryFrom a phenomenological standpoint, the plastic hinge region can beidentified with the zone of the element where yielding of reinforcement andconcrete crushing take place. The plastic hinge length used in the evaluation ofthe element rotational capacity is, instead, purely conventional. It onlyrepresents the length over which ultimate section curvature, assumed to beconstant, is integrated, following an equivalent bending approach, to calculatethe effective chord rotation including shear and fixed-end rotation contributionsto the overall deformability of the member; the curvature is calculated based onBernoulli’s plane section assumption.The plastic hinge length can not be evaluated based on a purely mechanicalapproach. As a matter of fact, based on section equilibrium conditions and fullinteractionhypothesis, in a post-peak phase the curvature should increase onlyat the base section of the element (zero length hinge problem) (Daniell et al.,2008; Haskett et al., 2009). Moreover, a purely mechanical approach, leading tothe evaluation of flexural deformability, would not account for other

Chapter II – Seismic behaviour of existing reinforced concrete buildings 63deformation mechanisms such as shear deformability and slippage ofreinforcing bars from the connection element. These contributions are notnegligible at all. Shear mechanisms may contribute in the overall post-elasticmember deformability up to 30% (Fenwick and Megget, 1993), whilst the endrotation due to the slippage of reinforcing bars may contribute up to 40%(Sezen, 2002).Therefore, researchers over years have empirically calibrated the plastichinge length over which theoretical ultimate section curvature is integrated,aiming at achieving the best agreement with experimental values of ultimatechord rotation.Following this approach, rotational capacity of an element may be expressedas:θ = θ + ( φ − φ ) L(2.2.1.12)uyuwhere the plastic hinge lengthydifferent deformation mechanisms:plpl,flexpl,shearplpl,slipL pl is made up of three terms, corresponding toL = L + L + L(2.2.1.13)Table 2.2.1.2 reports main formulations that have been proposed over years,starting from the first fundamental work by Baker (1956). These expressionsshow that the shear span L V and the section depth h are the major variablesinfluencing the plastic hinge length, while the term corresponding to fixed-endrotation is generally proportional to diameter and yielding strength oflongitudinal reinforcement bars. First proposed formulations are mainlycalibrated based on experimental tests on beam elements, therefore the fixedendrotation contribution is not clearly evaluated. In recent formulations,calibrated also on column elements, this contribution is clearly representedinstead.

64 Chapter II – Seismic behaviour of existing reinforced concrete buildingsReference Plastic hinge length (L pl )(Baker, 1956) ( ) 1 4k k k ⋅ z d ⋅ d1 2 3(Mattock, 1964)d ⎡ ⎛ '1 1.14 ⎞⎛⎛1 1⎤− ⎞ ⎞⋅ ⎢ + ⎜ − ⎟⎜−⎜ ⎟⎥2 ⎢ ⎝ d ⎠⎜⎜ q b ⎟ 16.2 ⎟⎥⎣⎝ ⎝ ⎠ ⎠⎦(Corley, 1966)d z+ 0.22 d(Mattock, 1967)d+ 0.05z2(Park, 1982) 0.4h(Priestley et al., 1987) 0.08L+ 6dv b(Paulay et al., 1992) 0.08L + 0.022d fv b y(Panagiotakos et al., 2001)0.12L + 0.014 α d f for cyclic loadingv sl b y0.18L + 0.021 α d f for monotonic loadingv sl b y(Fardis, 2007)0.09L+ 0.2 h for cyclic loadingv0.04L+ 1.2 h for monotonic loadingvTable 2.2.1.2. Empirically derived plastic hinge lengthsMoreover, in (2.2.1.12) the ultimate condition is given in terms of curvatureφ u , depending, based on plane section hypothesis, on steel or concrete failure.Nevertheless, the evaluation of ultimate curvature is not easy or univocal, dueto the influence of some aspects as concrete confinement, spalling of theconcrete cover or buckling of compressive reinforcing bars. For example, theuse of different confinement models may significantly influence thedetermination of the ultimate curvature, therefore the plastic hinge length canassume very different values.The plastic hinge formulation proposed in (Panagiotakos et al., 2001) is themost interesting among the expressions presented in literature. It is based on anextensive experimental database, which will be discussed in the next paragraph.

Chapter II – Seismic behaviour of existing reinforced concrete buildings 65θuThe ultimate chord rotation is given by:φyL=3V+ ( φu− φy)Land the plastic hinge lengthpl⎛ L⎜1− 0.5⎝ LplV⎞⎟⎠(2.2.1.14)L pl is given as a linear function of shear span(bending contribution) and of the product ( f y d bL)(fixed-end contribution):Lpl= αL+ β(fd )(2.2.1.15)VybLCoefficients α and β are derived from a regression analysis onexperimental data; they are equal, respectively, to 0.12 and to 0.0014 for cyclictests and to 0.18 and 0.0021 for monotonic ones. The ultimate curvatureL Vφ u isevaluated accounting both for the concrete confinement and for the spalling ofthe concrete cover. In particular, for cyclic tests the mean and median of theexperimental-to-predicted ratio for expression (2.2.1.14), using (2.2.1.15), areequal to 1.23 and 0.99 respectively, with a Coefficient of Variation (CoV) of83%; while for monotonic tests the mean and median are equal to 1.37 and 1.01respectively, with a CoV of 94%.The last plastic hinge expression proposed by (Fardis, 2007), based on amore extensive experimental database, is depending not on the shear spanbut also on the height h of the section. Moreover, the fixed-end rotationcontribution is evaluated with a separate term:θu= θwith:Ly⎛ Lpl⎞+ ( θ u,slip − θ y,slip ) + ( φ u − φ y )Lpl⎜1− 0.5⎟(2.2.1.16)⎝ LV⎠= 0.09L 0.20h(2.2.1.17)pl V +where:φyLV⎛ h ⎞ φydbLfyθ y = + 0.0013 1 1.5 +3⎜ +L⎟(2.2.1.18)⎝ V ⎠ 8 fcL V

66 Chapter II – Seismic behaviour of existing reinforced concrete buildingsφydbLfyθ y,slip =(2.2.1.19)8 fcφudbLfyθ u,slip =(2.2.1.20)16 fcThe use of the illustrated relationships, together with the confinement modelshown in the same work, leads to an experimental-to-predicted ratio with meanand median, on a database of 1307 experimental tests, equal to 1.105 and 0.994respectively, with a CoV of 53.6%.Expressions (2.2.1.14) e (2.2.1.16), although providing a differentevaluation of the fixed-end contribution, present the same control variables ofthe code expression (2.2.1.9), which directly shows, in the calculation of plastichinge length, the dependence on all the above mentioned parameters.2.2.1.3. ASCE/SEI 41 approachASCE/SEI 41 (2007) is the latest in a series of documents developed toassist engineers with the seismic assessment and rehabilitation of existingbuildings (FEMA 273, 1997; FEMA 356, 2000). A document has beenproposed (Elwood et al., 2007) for updating provisions related to existingreinforced concrete buildings. Based on experimental data and empiricalmodels, this document also provides a revision of deformation capacityparameters for older-type RC columns. This proposal is described in thefollowing.RC columns with 135 degree hooked transverse reinforcement arecharacterized by three different failure modes:• Condition i: Flexure failure (flexural yielding without shear failure)• Condition ii: Flexure-shear failure (shear failure following flexuralyielding)• Condition iii: Shear failure (shear failure before flexural yielding)depending on the ratio between the plastic shear (which represents the demand

Chapter II – Seismic behaviour of existing reinforced concrete buildings 67shear, corresponding to the flexural strength of the element) V p and the nominalshear strength V n , as reported in Table 2.2.1.3.V /(V / k)0.60ACI conformingdetails with 135°hooksTransverse Reinforcement DetailsClosed hoopswith 90° hooksOther (includinglap-splicedtransversereinforcement)p n≤ Condition i Condition ii Condition ii1.00≥ Vp /(Vn/ k) > 0.60 Condition ii Condition ii Condition iiiV /(V / k)1.00p n> Condition iii Condition iii Condition iiiTable 2.2.1.3. Categorization of failure modes for older-type RC columns (Elwood et al., 2007)The nominal shear strength V n is evaluated according to (Sezen andMoehle, 2004), see Section 2.3, while parameter k is defined to be equal to 1.00for displacement ductility less than 2, to be equal to 0.60 for displacementductility exceeding 6 (more conservative compared to the original assumptionof 0.70), and to vary linearly for intermediate displacement ductilities.To provide further confidence of achieving a flexural failure, Condition i islimited to columns with a transverse reinforcement ratiothan 0.002, and a spacing-to-depth ratio lower than 0.5."ρ = Av/ bwsgreaterFor Vp /(Vn/ k) ≤ 0. 60 , the Condition is adjusted from i to ii for columnswith 90 degree hooks or lap-spliced transverse reinforcement. For1.00≥ Vp /(Vn/ k) >0.60 , the Condition is adjusted from ii to iii only for lapspicedtransverse reinforcement.Moreover, another Condition is considered (Condition iv): “failurecontrolled by inadequate development or splicing”, assuming that this failuremode takes place when the calculated steel stress at the splice exceeds the steelstress specified by equation:f2/3⎛ lb⎞s = 1.25⎜ f y(2.2.1.21)ld⎝⎟ ⎟ ⎠

68 Chapter II – Seismic behaviour of existing reinforced concrete buildingswhere f s is the maximum stress that can be developed in the bar for the straightdevelopment, hook, or lap-splice length l b provided, f y the nominal yieldstrength of reinforcement and l d the length required by ACI 318 (2005).In particular, according to ACI 318, the development length for deformedbars in tension terminating in a standard hook (l dh ) is determined from thefollowing expression:ldh0.02ψefy= 0.80 db(2.2.1.22)λ fcwhereψ e and λ are taken as 1.0 while 0.80 is the modification factor due to thepresence of 180 degree hooks. For smooth straight bars, hooked bars, and lapsplicedbars, development and splice lengths is taken as twice the valuesdetermined in accordance with ACI 318.Based on these prescriptions, a Condition is identified for the column andcorresponding values of capacity parameters a and b (see Figure 2.2.1.1) areprovided, depending on different parameters:P− , where P is the axial load level, transverse reinforcementA f '−−gcratio, A g is the gross cross-sectional area and f’ c is the concretecompressive strength;Avρ " = , where A v is the area of transverse reinforcement in theb swdirection of applied shear, b w is the width of the columnperpendicular to the applied shear and s is the spacing of thetransverse reinforcement;Vν = , where V is the shear demand and d is the effective depth.b dwAs an example, see Figure 2.2.1.2, where parameters a and b for Condition iproposed by (Elwood et al., 2007) are reported and compared with the previousFEMA 356 prescription. For Conditions iii and iv, parameter a is set equal to 0.

Chapter II – Seismic behaviour of existing reinforced concrete buildings 69Figure 2.2.1.1. Generalized force-deformation relations for RC elements (ASCE/SEI 41)Figure 2.2.1.2. Comparison between parameters a and b for Condition i and the previous FEMA356 prescription, for columns with conforming (a) and non-conforming (b) transversereinforcement, according to FEMA 356 definition (Elwood et al., 2007)

70 Chapter II – Seismic behaviour of existing reinforced concrete buildingsBackground theoryFirst of all, for the purpose of determining a values, it was assumed that thispoint corresponds to the plastic rotation at which the lateral resistance hasdegraded to 80% of the measured peak shear force, thus assuming the samedefinition employed in EC8 approach.Hence, target probabilities of failure were established based on judgementregarding the consequence of each failure mode. Due to the degradation of axialcapacity with the development of a shear-failure plane, the a values for columnsthat are expected to fail in flexure-shear or shear (Conditions ii and iii,respectively) were selected to achieve a probability of failure less than 15%.Because columns experiencing flexural failures are more likely to be able tomaintain axial loads beyond initial loss of lateral strength, the target probabilityof failure was relaxed for flexure-controlled columns (Condition i), with avalues selected to achieve a probability of failure less than 35%.Results from laboratory tests compiled by Berry et al. (2004) – on columnswith ribbed bars – were used to assess the adequacy of the proposed modellingparameters and check the probabilities of failure assuming a lognormaldistribution for the plastic rotation. For Conditions i and ii the failureprobabilities based on the assumed a values resulted equal to 30% (instead of35%) and 6% (instead of 15%), respectively. However, a high dispersion of theexperimental-to-predicted capacity ratio is observed.The decrease in deformation capacity due to the absence of seismic detailsis reflected, for instance, in the prescription of adjusting the Condition (from ito ii) for columns with 90 degree hooks characterized by Vp /(Vn/ k) ≤ 0. 60 .If experimental data are not available for the determination of deformationcapacity (e.g., columns with lap-spliced transverse reinforcement, characterizedby .00 ≥ V /(V / k) 0. 60 ), Condition is adjusted (from ii to iii) to achieve a1p n>higher conservatism.When the failure Condition is determined for columns with smooth barsending in standard hooks, the development length is taken as twice the values

Chapter II – Seismic behaviour of existing reinforced concrete buildings 71determined in accordance with ACI 318. This prescription may lead toclassifying a column as “controlled by inadequate development or splicing”(Condition iv, a=0) even if the column actually has a deformation capacity intoinelastic field. As a matter of fact, an anchorage detail of a smooth bar – madeup of a straight portion of bar ending in a 180 degree hook – can be veryeffective, even allowing the development of steel ultimate strength, althoughthe low bond capacities along the straight bar, thank to the load carryingcapacity of the hook (Fabbrocino et al., 2005).From this point of view, a less conservative but more realistic evaluation ofthe deformation capacity of members with smooth bars ending in standardhooks is provided by EC8 (CEN, 2005).2.2.1.4. Critical reviewThe expressions for the ultimate rotational capacity, as clearly shown in theprevious paragraphs, are necessarily calibrated on experimental data, due to thecomplex nature of mechanisms affecting the post-elastic behaviour of RCmembers and their interaction.All the approaches presented in literature and in Code are characterized byhigh values of the coefficient of variation of the experimental-to-predictedcapacity ratio.The high dispersion affecting these models is not only due to the naturalexperimental variability, but also to the difficulty in completely modelling witha simple formulation the interaction between the complex phenomenainfluencing the post-elastic deformation behaviour of RC element.Panagiotakos and Fardis (2001), based on the analysis of subgroups of tests,homogenous for geometrical and mechanical characteristics and for loadingconditions, quantify the CoV associated with the only natural variability in12.5%.The limited prediction capacity of these expressions is also due toimpossibility of introducing in the control variables some parameters whichcertainly affect the rotational capacity. The major among these parameters is the

72 Chapter II – Seismic behaviour of existing reinforced concrete buildingsload path, that is, the energy dissipated in hysteretic cycles. This aspect hasbeen experimentally investigated by (Pujol et al., 2006), who analyzed theinfluence of displacement history on the decay of element resistance capacity.The experimental tests show that, given equal the geometrical and mechanicalcharacteristics and the applied axial load (that is, all the input parameters ofcode and literature regression formulations), it is possible to predetermine thevalue of element chord rotation corresponding to a conventional drop of 20% ofpeak resistance, by imposing a given load path (see Figure 2.2.1.3).Panagiotakos and Fardis, in the above mentioned work, try to explicitlyaccount for the effect of cyclic loading by another regression, where the type ofloading is evaluated with a variable expressing the equivalent number ofinelastic imposed cycles ( ∑| θ i | θ u ), instead of the coefficient ( α cyc ).Nevertheless, contrary to expectations, the inclusion of this parameter makesworse the prediction capacity of the formulation. The CoV of the ratio betweenthe experimental and the predicted value, in fact, increases up to 51%. On theother hand, the usual structural modelling approaches do not allow to introducethe dissipated energy in the control variables.A critical analysis of expressions (2.3.4.19) and (2.3.4.20), based onmechanical considerations regarding the absence of a direct relationshipbetween the median estimation of the ultimate rotation and some parametersthat certainly influence the member capacity, seems to be without foundation.Due to the purely statistical nature of the expression, in fact, the retaining ofthese variables turns out to be not significant because of their strong correlationwith other parameters, already present in the formulation (Panagiotakos et al.,2001).It is worth noting that the higher coefficient of variation affecting the hybridmechanical-empirical formulation (plastic hinge length) with respect to thepurely empirical one is probably related to the difficulty in expressing theultimate rotation as a function of element characteristics based on a statisticalregression analysis restrained to a mechanical relationship.

Chapter II – Seismic behaviour of existing reinforced concrete buildings 73Figure 2.2.1.3. Influence of displacement history on ultimate chord rotation (Pujol et al., 2006)

74 Chapter II – Seismic behaviour of existing reinforced concrete buildings2.2.2. A proposal for a new correction coefficient applied to the EC8capacity formulation for RC columns with smooth barsSmooth reinforcing bars have been widely used in the construction ofEuropean RC buildings. In Italy and in the whole Mediterranean area their usewas widely spread up to 1970s, in north-American countries and in NewZealand constructions with smooth bars are present until 1950. The widespreading of RC buildings with smooth bars among existing buildings can bededuced if it is considered that 50% of Italian existing buildings has beenconstructed between earliest 1940s and latest 1970s, when RC structures withsmooth bars were the prevailing construction typology.The correct evaluation of deformation capacity of RC elements has toaccount for the effective bond capacities between reinforcing bars and thesurrounding concrete; for members with smooth bars, low bond capacitiesdirectly influence the three main deformation mechanisms: bending, shear andfixed-end rotation.As shown by experimental evidence, the scarce capacities of load transferbetween the reinforcing bars and the surrounding concrete (see Section 2.2.3)makes the deformation contribution associated with the fixed-end rotationeffect very important (see Section 2.2.5). This contribution, in fact, due to thecyclic and post-elastic decay of bond capacities, may represent up to (80-90)%of overall deformability of the element (Verderame et al., 2008a,b).Bond capacities also influence the development of cracks along the element.A lower number of wider cracks is observed when bond decreases. This greatlyinfluences both shear and bending deformability, reducing the former andincreasing the latter.Therefore, formulations able to provide a reliable assessment of ultimatedeformation capacity of elements with smooth bars are of a particular interestfor assessment of existing RC buildings.In this Section, referring to the purely empirical formulation proposed in(CEN, 2005), the applicability of this formulation to non-conforming elementswith smooth bars is evaluated. In particular, experimental data for the

Chapter II – Seismic behaviour of existing reinforced concrete buildings 75assessment of deformation capacity of RC elements with smooth bars arepresented in Section 2.3.4.2. Based on these data, in Section 2.3.4.3 correctioncoefficients applied to the EC8 empirical formulation for elements with smoothbars, with or without lapping of longitudinal reinforcement, are proposed.2.2.2.1. Deformation capacity of RC columns with smooth barsThe ultimate rotational capacities for columns with smooth bars, accordingto the European code (CEN, 2005), as already shown at Section 2.2.1.1, isevaluated by applying a correction coefficient, based on experimental data, tothe capacity formulations calibrated on members with ribbed bars andseismically detailed.Most of literature data about the experimental behaviour of RC elementscomes from test executed on members with ribbed bars. During last years, theneed for a reliable assessment of seismic capacity of existing structures hasproduced an increasing number of experimental campaigns aimed at the studyof behaviour of non-conforming elements.In Table 2.2.2.1, experimental results of columns with smooth bars (Bousiaset al., 2005; Fardis et al., 2006; Faella et al., 2008; Verderame et al., 2008b),including recent tests (Di Ludovico et al., 2010) carried out in the laboratory ofthe Department of Structural Engineering at the University of Naples FedericoII, in the research project ReLUIS-DPC 2005-2008 Linea 2, are reported.Based on these data, it will be possible to extend the experimental databasefor the calibration of correction coefficients applied to the regressionrelationships for the evaluation of ultimate rotational capacity of members withsmooth bars.Tested columns with lapping of longitudinal reinforcement are included inthis database only if hooks are provided at the end of lapped bars. Literatureoffers experimental data on members without this anchorage detail (Ilki et al.,2004; Yalcin et al., 2008); in these cases, brittle lap splice failures are present.Therefore, in the following these data will not be considered.

76 Chapter II – Seismic behaviour of existing reinforced concrete buildingsn test Reference loading l o /d bL θ u,exp /θ u1 cyclic 15 0.332 cyclic 15 0.623 cyclic 25 0.39Bousias et al., 20054 cyclic 25 0.415 cyclic 100 0.586cyclic 100 0.607 cyclic 100 0.548 cyclic 100 0.74Fardis et al., 20069 cyclic 100 0.8310cyclic 100 1.2511 cyclic 43 0.7712 Faella et al., 2008 cyclic 43 0.7913cyclic 43 0.8514 cyclic 40 1.2615 cyclic 40 0.8316 cyclic 40 0.60Verderame et al., 2008b17 cyclic 100 1.2118 cyclic 100 1.1319cyclic 100 0.8120 cyclic 100 1.4121 Di Ludovico et al., 2010 cyclic 100 1.4222cyclic 100 1.76Table 2.2.2.1. Ratios between experimental ultimate rotations and corresponding theoreticalvalues2.2.2.2. Calibration of correction factorThe correction coefficient applied to EC8 expressions for the ultimaterotation of members with smooth bars is calibrated, based on experimental datareported in Table 2.2.2.1. The correction coefficient will be calibratedaccording to the methodology already illustrated at 2.2.1.1, with regard to thefollowing expression:uypluθ = θ + θ(2.2.2.1)whereplθ u is evaluated according to Eq. (2.2.1.2), with γel=1.The considered database is made up only of cyclic tests. As a matter of fact,ultimate rotational capacity given by code prescriptions (CEN, 2005) is meantto be cyclic. Monotonic tests could be included in the database for the

Chapter II – Seismic behaviour of existing reinforced concrete buildings 77calibration of correction coefficient only by means of a coefficient accountingfor the type of loading, asαcyc, applied to the expression of the ultimaterotation. On the other hand, this would be the same as postulating that thereduction in rotational capacity due to cyclic loading, evaluated by thiscoefficient, is, on average, not depending on bond capacities. As a matter offact, this coefficient, as previously illustrated, is calibrated on a database madeup of members with ribbed bars; therefore, the evaluation of the correctioncoefficient should be executed supposing that the reduction given byαcyccanalso be extended to members with smooth bars.Nevertheless, first experimental results highlight that the reduction in rotationalcapacity due to cyclic loading is lower for columns with smooth bars comparedto columns with ribbed bars; this is shown, in particular, by test results from theUniversity of Naples (Verderame et al., 2008a,b; Di Ludovico et al., 2010).Figure 2.2.2.1 reports the ratio θ / θ ) between cyclic and monotonic( u,cycu, monexperimental ultimate rotations for each possible couple of tests, given equalthe axial load level, the longitudinal reinforcement detail (with or withoutlapping) and the geometrical and mechanical characteristics of the elements,versus the axial load level ν . The reduction in cyclic rotational capacity clearlyincreases as the axial load level increases.1.00.80.60.4(θ u,cyc / θ u,mon )0.69 smooth bars0.57 ribbed bars(Fardis, 2007 )0.2smooth barsribbed barsnormalized axial load, ν0.00.00 0.05 0.10 0.15 0.20 0.25 0.30Figure 2.2.2.1. Ratio between cyclic and monotonic rotational capacities versus the axial loadlevel from Verderame et al. (2008a,b) and Di Ludovico et al. (2010)

78 Chapter II – Seismic behaviour of existing reinforced concrete buildingsHowever, the ratio θ / θ ) has a mean equal to 0.69 with a CoV=0.17( u,cycu, monfor columns with smooth bars, independently of the axial load level and thelongitudinal reinforcement detail. On the contrary, the average value of ratio,for columns with ribbed bars and seismically detailed, is equal to 0.57 asindicated in (Fardis, 2007); it is to be noted that this value is confirmed by theonly couple of tests characterized by ribbed longitudinal reinforcement.Therefore, due to the uncertainties related to the inclusion of monotonic tests,the correction coefficient will now be calibrated based on the only cyclic tests.Table 2.2.2.1 reports the description of the database, including the lap lengthand the ratio between the experimental ultimate rotation and the correspondingtheoretical value ( θratiou ,exp/ θθ u ,exp / θuversus the lap length o / dbLu), according to (2.2.1.1); Figure 2.2.2.2 shows thel .2.01.81.61.41.21.00.80.60.40.20.0θ u,exp / θ u# 22 testslap length, l o /d bL0 10 20 30 40 50 60 70 80 90 100 110 120Figure 2.2.2.2. Ratio θ exp /θ u versus lap length l o /d bLThe ratio ( θu ,exp/ θu) for members without lapping of longitudinal bars(conventionally reported as lo / dbL= 100 ) has mean equal to 1.03 and medianequal to 0.98, with a CoV=0.39. Therefore, based on the experimental tests,

Chapter II – Seismic behaviour of existing reinforced concrete buildings 79expression (2.2.2.1) shows a very good agreement with the cyclic rotationalcapacity of elements with smooth bars without lapping of longitudinalreinforcement.The use of expression (2.2.2.1) for members with lapping of longitudinal barsoverestimates even more the experimental rotational capacity; in fact, the ratio( θ u ,exp / θu) for members with lapping of longitudinal bars has mean equal to0.69 and median equal to 0.69, with a CoV=0.41. With regard to members withlapping of longitudinal bars, a linear regression performed on the ratio( θ u ,exp / θu) gives the following expression for the correction coefficient:κ = .020 (l / d )(2.2.2.2)1 0 ⋅ o bLThe ratio has mean equal to 1.07 and median equal to 0.93, with a CoV=0.38.Based on mean and median values shown by columns with continuouslongitudinal reinforcement, it is possible to provide one expression for thecorrection coefficient, both for elements with and without lapping oflongitudinal bars:κ= 0.020 min(50, lo / dbL)(2.2.2.3)The ratio θ u,exp/( κ ⋅ θu) , calculated on all tests in the experimental database,has mean equal to 1.06, median equal to 0.96 and a CoV=0.38 while formembers without lapping of longitudinal bars it has mean equal to 1.03 andmedian equal to 0.98, with a CoV=0.39.Figure 2.2.2.3 reports the ratio between the experimental ultimate rotation andthe corresponding theoretical value ( θu ,expcorrection coefficient given by (2.2.2.3), applied to (2.2.2.1)./ θu), together with the proposed

80 Chapter II – Seismic behaviour of existing reinforced concrete buildings2.01.81.61.4θ u,exp / θ u# 22 tests1.21.00.80.60.020·min(50,l o /d bL )0.40.2lap length, l o /d bL0.00 10 20 30 40 50 60 70 80 90 100 110 120Figure 2.2.2.3. Proposed correction factorIt is possible to compare the proposed coefficient, evaluated on 22 tests, withthe coefficient proposed by (Fardis, 2006), evaluated on 15 tests, with thecoefficient given by (CEN, 2005), evaluated on 6 tests, and with update to(CEN, 2005) proposed by (CEN, 2009). The correction coefficient suggested in(Fardis, 2006) is not far from the proposed coefficient given by (2.2.2.2) formembers with lapping of longitudinal reinforcement.On the other hand, the coefficient adopted by (CEN, 2005) shows aconsiderable conservativeness. According to this prescription, the ultimaterotation of members with a lap length equal to l o has to be evaluated based onthe assumption that the ultimate condition is controlled by the region right afterthe end of the lap. Hence, expression (2.2.2.1) should be multiplied byexpression (2.2.1.4). In this coefficient, a further reduction in the ultimaterotation is given by the term ( 1−lo/ LV) , expressing a reduction in the shearspanLVby the lap length ol . Moreover, shear span should be reduced by thelap length also in expressions (2.2.1.2).With regard to members without lapping of longitudinal bars, based on theproposed correction coefficient the ultimate rotational capacity of members

Chapter II – Seismic behaviour of existing reinforced concrete buildings 81with smooth bars is equal to that of members with ribbed bars and seismicallydetailed. On the contrary, according to the expression proposed in (Fardis,2006), the ratio between the former and the latter is equal to 0.75, whilst codeprescriptions (CEN, 2005) suggest 0.575.Expression proposed in (CEN, 2009), as previously noted, is very similar to theexpression given by (Fardis, 2006).Figure 2.2.2.4 shows a comparison between different correction coefficientsapplied to (2.2.2.1); it is to be noted that the coefficient given by (CEN, 2005)is represented not taking into account the shear span reduction.2.01.81.61.41.21.00.80.60.4θ u,exp / θ u# 22 testsproposed (Eq.23)(CEN, 2005)(CEN, 2009)(Fardis, 2006)0.2lap length, l o /d bL0.00 10 20 30 40 50 60 70 80 90 100 110 120Figure 2.2.2.4. Comparison between the proposed correction coefficient and the ones reportedin (CEN, 2005), (Fardis, 2006) and (CEN, 2009)2.2.2.3. Discussion of resultsThe extension of the experimental database allowed to re-calibrate thecorrection coefficients applied to the assessment of the ultimate rotationalcapacity of elements with smooth bars, with or without lapping of longitudinalreinforcement.The expression of correction coefficient proposed herein highlights theconservativeness of EC8 (CEN, 2005) proposal, which is based on very few

82 Chapter II – Seismic behaviour of existing reinforced concrete buildingsexperimental tests. Moreover, EC8 assumes that, when lapping of longitudinalreinforcement is present, the ultimate condition is controlled by the region rightafter the end of the lap, so that the shear span and, therefore, the rotationalcapacity are further reduced. This assumption is not confirmed by theexperimental results reported in (Verderame et al., 2008a,b; Di Ludovico et al.,2010); the highest plastic demand, in fact, always concentrates at the basesection of the element.The changes in correction coefficients proposed by (CEN, 2009) – probablybased on the proposal of (Fardis, 2006) – result in a less conservative and morereliable evaluation of ultimate deformation capacity of members with smoothbars.Despite the difficulties in the choice of the most reliable expression for thecorrection coefficient, recent experimental results (Di Ludovico et al., 2010)clearly highlight the higher rotational capacity of members with smooth barswith compared to members with ribbed bars, equal for structural characteristicsand details. As a matter of fact, the comparison between the ultimate rotationsof the elements highlights that the capacity of members with smooth bars arehigher, on average, by 35% compared with the corresponding members withribbed bars.From a mechanical standpoint, the higher ultimate rotational capacity ofcolumns with smooth bars may be explained by the comparison between twoopposite mechanisms: the increase in deformability caused by the fixed-endrotation mechanism, particularly exalted due to the low bond capacities; on theother hand, the higher degradation of global resistance due to the increase indeformation demand on concrete in compression, localized at the base of theelement and associated with the concentrated rotation (rocking effect).According to experimental evidence, the former seems to prevail on the latter,leading to an overall increase of ultimate rotational capacity compared withmembers with higher bond capacities.However, it is to be noted that the stirrup spacing in critical region (orbetter, the ratio between stirrup spacing and longitudinal bars diameter) can

Chapter II – Seismic behaviour of existing reinforced concrete buildings 83highly influence the deformation capacity through the buckling phenomenon.(see Section 2.2.4) This issue can be highlighted, for instance, observing thedifferences in ultimate rotation capacity between University of Naples databaseand Bousias database.Furthermore, the post-elastic development of a high slippage, concentratedin a low number of wide cracks, represents not only a source of deformabilitybut also a permanent damage for the RC element (Verderame et al., 2008b).Moreover, the higher influence of fixed-end rotation mechanism on behaviourof elements with smooth bars, compared to elements with ribbed bars, alsoleads to a decrease in the energy dissipation capacity. As a matter of fact, RCmembers with smooth bars tested under cyclic loading reported in (Di Ludovicoet al., 2010), at the same displacement demand, show a dissipated energy about30% lower, on average, than the energy dissipated by the correspondingmembers with ribbed bars, equal for geometrical characteristics and appliedaxial load. This issue should be carefully considered since it could potentiallylead to an underestimate of the seismic demand.Further conservatism should be addressed to the assessment of seismiccapacity of members with smooth bars because of the particularly highuncertainties involved in modelling their deformation mechanisms. This is due,for example, to the difficulties in evaluating the influence of rocking effect andto the high variability affecting bond capacities (Verderame et al., 2009a,b),also influenced by possible corrosion (Fang et al., 2006).Finally, the absence of an effective anchorage of reinforcing bars by meansof end hooks may limit the deformation capacity (Yalcin et al., 2008) and insome cases the strength (Ilki et al., 2004) of the element.

84 Chapter II – Seismic behaviour of existing reinforced concrete buildings2.2.3. Bond behaviour of smooth bars: experimental and analyticalinvestigationThe development of bond stresses between smooth bars and concrete can beexplained by different mechanisms: for low values of slip, chemical adhesionand micro-interlocking are present, subsequently a purely frictional mechanismis activated.In this Section, results form experimental tests (see Figure 2.2.3.1, Table2.2.3.1) carried out in the laboratory of the Department of StructuralEngineering (DIST) at the University of Naples Federico II are reported. Theresults reported herein were published in (Verderame et al., 2009a). Monotonicand cyclic pullout tests were carried out; in the latter case, different values ofmaximum imposed displacements were adopted in order to evaluate theinfluence of slip amplitude on the mechanisms of bond deterioration. Also, apull-out test was carried out characterized by five cycles for each of the targetvalues of the slip previously considered.reinforcing barφ=12 mmplastic pipe235 mmL b = 120mm500 mmspecimen30 235 mm(a)Figure 2.2.3.1. Geometry of the pull-out specimen (a), test setup (b) (Verderame et al., 2009a)(b)

Chapter II – Seismic behaviour of existing reinforced concrete buildings 85Specimen Loading type Imposed displacement [mm] n° of cycles n° of testsM_01M_02monotonic - - 2C_0.5_01C_0.5_02cyclic ± 0.5 5 2C_2.0_01C_2.0_02cyclic ± 2.0 5 2C_4.0_01C_4.0_02cyclic ± 4.0 5 2C_8.0_01C_8.0_02cyclic ± 8.0 5 2C_01 cyclic ± 0.5 - ± 2.0± 4.0 - ± 8.0 5 + 5 + 5 +5 1Table 2.2.3.1. Experimental program (Verderame et al., 2009a)Results from pull-out tests show, in monotonic field, a first ascending branchwhich in correspondence with very low values of the relative slippage reachesmaximum values of the bond resistance. With the increase in slippage the bondstrength reduces and tends towards the value of minimum friction contribution.The value of the friction bond resistance should remain constant or slightlydecrease as the slippage increases. The parameters characterizing the monotonicenvelope of the experimental bond–slip relationship are the bond stress and slipat the peak condition (τ b,max , s max ) and the value of minimum frictional bondstress (τ b,f ) (see Figure 2.2.3.2).τ b bond stress [MPa]τb,fτb,maxs maxslip [mm]Figure 2.2.3.2. Characteristic parameters of experimental monotonic bond-slip relationship(Verderame et al., 2009a)

86 Chapter II – Seismic behaviour of existing reinforced concrete buildingsIn spite of their high variability, values of these parameters, in averageterms, seem to reflect well the literature indications about bond performances ofplain bars (see Table 2.2.3.2).τ b,max s maxτ b, f/ ττ b,max/ fcτ b,f/ fcb ,f b, maxSpecimen[MPa] [mm] [MPa]M_01 1.64 0.34 0.68 0.41 0.17 0.41M_02 1.58 0.15 0.61 0.40 0.15 0.39C_0.5_01 2.15 0.15 - 0.54 - -C_0.5_02 1.15 0.12 - 0.29 - -C_2.0_01 1.50 0.20 - 0.38 - -C_2.0_02 1.03 0.22 - 0.26 - -C_4.0_01 1.15 0.17 0.49 0.29 0.12 0.43C_4.0_02 0.83 0.14 0.30 0.21 0.08 0.36C_8.0_01 0.61 0.07 0.25 0.15 0.06 0.41C_8.0_02 0.75 0.10 0.43 0.19 0.11 0.57Mean 1.24 0.17 0.46 0.31 0.12 0.43CoV 0.38 0.45 0.37 0.38 0.37 0.18Table 2.2.3.2. Characteristic parameters of experimental monotonic bond-slip relationship(Verderame et al., 2009a)τIn cyclic field, experimental results show a significant degradation of bondcapacities. Shape of hysteretic cycles is characterized by a reloading phase, bothin positive and negative field, showing a slight reduction for slip valuesapproaching zero and a subsequent increase in bond stress towards themaximum imposed slip. It is possible to describe this trend by means of threecharacteristic parameters: bond values corresponding to the initial, the medium(that is, zero-slip condition) and the final point of each semi-cycle. Theseparameters show a high variability, represented both by the absence ofsymmetry between positive and negative semi-cycles, in the same test, and bythe variability of these values between different tests. However, it is generallypossible to recognize a decreasing trend of bond stresses both with the numberof cycles and with the maximum imposed slip.Example results from a cyclic test, together with the schematisation of the

Chapter II – Seismic behaviour of existing reinforced concrete buildings 87typical hysteretic behaviour, are reported in Figure 2.2.3.3.τ b bond stress1.5Pull-out testC_2.0_02τ b bond stress [MPa]first inversion of slip1.0τ b,un0.5τ b,rel + (1)τ b,rel + (n)τ b,un - (n)τ b,un - (1)τ b,o + (1)τ b,o + (n)τ b,o - (n)τ b,o - (1)τ b,un + (1)τ + b,un (n)slipτ b,rel - (n)τ b,rel - (1)0.0-0.5slip [mm]-1.0-4 -3 -2 -1 0 1 2 3 4(a)(b)Figure 2.2.3.3. Schematisation of the bond-slip relationship of the bonded bar subjected tocyclic load (a), characteristic parameters of cyclic bond-slip relationship (b) (Verderame et al.,2009a)Based on these experimental results, a bond stress-slip relationship forsmooth bars is proposed, both in monotonic and cyclic field, which waspublished in (Verderame et al., 2009b).The monotonic envelope presents a first ascending branch up to a peakstrength value corresponding to very low values of slippage; during this phase,chemical-physical adhesion, mechanical microinterlocking and also the frictioncomponent contribute to the bond strength. Then, a softening branch related tothe progressive degradation of friction mechanism is present; finally, ahorizontal branch is present, corresponding to a constant value equal to theminimum frictional component value of bond resistance. The monotonicenvelope of the bond-slip relationship has to be defined through theexperimental evaluation of five parameters: parameter α, related to the shape ofthe ascending branch; the couple of values (τ b,max , s max ), corresponding to thepeak resistance condition; parameter p, representing the slope of the softeningbranch expressed as a quote of the secant stiffness (τ b,max /s max ); and the

88 Chapter II – Seismic behaviour of existing reinforced concrete buildingsfrictional bond strength value τ b,f . The proposed cyclic model is defined throughtwo parameters: cyclic (τ b,c ) and residual (τ b,r ) bond stresses. Under cyclicexcitations the bond stress τ b,c is assumed to be constant and equal to the 35%of the monotonic frictional bond resistance, independent of the number and themagnitude of the cycles. Then, in correspondence with values of slip higherthan the maximum one previously attained, τ-slip curve does not reach themonotonic envelope curve, but a reduced value τ b,r , equal to the 68% of themonotonic frictional bond resistance. All the characteristic parameters of theconstitutive bond-slip relationship are then expressed proportionally to thesquare root of the cylindrical compressive strength of concrete (see Figure2.2.3.4).τb,maxτ= 0. 31⋅f= 0. 13⋅fb, f ccτ b,maxτ ḇτ b,maxτ b,fτ b,cτ b,rslip- τ b,c-τ b,r-τ b,fττb,rb,c= 0. 09 ⋅ f= 0. 05⋅fccFigure 2.2.3.4. Summary of model parameters. (Verderame et al., 2009b)

Chapter II – Seismic behaviour of existing reinforced concrete buildings 892.2.4. The influence of transverse reinforcement anchorage detail onconfined concrete behaviourThe absence of a proper anchorage detail in transverse reinforcement canlead to a limitation of confinement effect on concrete, thus leading to a lowermaterial ductility and, finally, to a lower element ductility. This issue wasexperimentally investigated (Cosenza et al., 2009): monotonic experimentaltests were carried out on column elements (250x250x800 mm) with smoothbars, both for longitudinal and transverse reinforcement. 4φ12 longitudinal barswere present. The transverse reinforcement (8 mm diameter stirrups) wascharacterized by different anchorage details, that is, 135 degree hooks (incompliance with modern seismic detailing prescriptions) and 90 degree hooks(reflecting design and constructive practice of existing RC buildings). Threedifferent stirrup spacing values were considered: 100, 200 and 300 mm (seeFigure 2.2.4.1). Steel yield strength was equal to f y =335 MPa and f yw =430 MPafor longitudinal and transverse reinforcement, respectively. Compressivestrength of unconfined concrete was equal to f co =27.8 MPa, evaluated on 0-0-#1 Specimen (with no reinforcement). A summary of experimental results isshown in Figure 2.2.4.2.Experimental tests highlighted that:- concrete compressive strength increases with the volumetric ratio oftransverse reinforcement, with no significant influence of anchoragedetail;- post-peak softening response is strongly influenced by buckling oflongitudinal reinforcement, which in turn is influenced by stirrupspacing (higher the stirrup spacing, earlier this phenomenon takesplace);- progressive opening and loss of effectiveness of 90 degree anchoragedetail is registered together with the buckling of longitudinalreinforcement (see Figure 2.2.4.3);- nevertheless, no significant influence of anchorage detail is clearlyshown, neither on post-peak softening response.

90 Chapter II – Seismic behaviour of existing reinforced concrete buildingsLongitudinalreinforcementTransversereinforcementSpecimenAnchorage VolumetricA s f y A sw Spacingdetail ratio ρ w[mm 2 ] [MPa] [mm 2 ] [mm] [-] [%]0-0-#1 - - - - - -300-135-#1 452 355 50 300 135° 0.2667300-135-#2 452 355 50 300 135° 0.2667300-135-#3 452 355 50 300 135° 0.2667300-90-#1 452 355 50 300 90° 0.2667300-90-#2 452 355 50 300 90° 0.2667300-90-#3 452 355 50 300 90° 0.2667200-135-#1 452 355 50 200 135° 0.4000200-135-#2 452 355 50 200 135° 0.4000200-135-#3 452 355 50 200 135° 0.4000200-90-#1 452 355 50 200 90° 0.4000200-90-#2 452 355 50 200 90° 0.4000200-90-#3 452 355 50 200 90° 0.4000100-135-#1 452 355 50 100 135° 0.8000100-135-#2 452 355 50 100 135° 0.8000100-135-#3 452 355 50 100 135° 0.8000100-90-#1 452 355 50 100 90° 0.8000100-90-#2 452 355 50 100 90° 0.8000100-90-#3 452 355 50 100 90° 0.8000φ8@300 φ8@200 φ8@100 φ8@300 φ8@200 φ8@100135 degree hooks 90 degree hooksFigure 2.2.4.1. Experimental program (Cosenza et al., 2009)

Chapter II – Seismic behaviour of existing reinforced concrete buildings 91(a) (b) (c)Figure 2.2.4.2. Summary of experimental results for stirrup spacing equal to 100 (a), 200 (b)and 300 (c) mm (Cosenza et al., 2009)100-90° 200-90° 300-90°Figure 2.2.4.3. Evidence of longitudinal bar buckling and opening of 90 degree anchoragehooks (Cosenza et al., 2009)

92 Chapter II – Seismic behaviour of existing reinforced concrete buildings2.2.5. Numerical modelling of RC members with smooth barsA numerical investigation of the deformation mechanism of columns withsmooth bars is carried out (Verderame et al., 2008c) through a two-componentmonotonic and cyclic model implemented in FORTRAN®, where (i) theflexural displacement (∆ flex ) is evaluated by means of a distributed plasticityfiber model and (ii) the fixed-end rotation contribution (θ base ) is evaluated as therotation given by the slip of the anchored bars (see Figure 2.2.5.1). At eachstep, the total lateral displacement is given by ∆ tot =∆ flex +θ base·L, where L is thecolumn height.concreteφ (curvature)steels 1 s 2d-d’θ baseσ 1 σ 2s 1 θ bases 2Figure 2.2.5.1. Two-component column model: flexural displacement is given by a distributedplasticity fiber model, fixed-end rotation is evaluated as depending on bar slip from anchorageA typical anchorage detail for smooth bars was represented by a straightportion of bar ending with a 180 degree circular hook. When a strain (that is, astress) value is imposed at the end of the hooked bar, a corresponding slippageof reinforcement takes place, given both by the deformability contribution of

Chapter II – Seismic behaviour of existing reinforced concrete buildings 93the straight bar (strongly dependent on bond capacities, both in elastic and inpost-elastic field) and by the concentrated deformability contribution due to theslip of the end anchorage detail (hook) (Fabbrocino et al., 2004; Fabbrocino etal., 2005) (see Figure 2.2.5.2a).slip1σ1=f(εs1)θbaseσ2=f(εs2)slip2(a)(b)Figure 2.2.5.2. Two-component model of a hooked smooth bar (Fabbrocino et al., 2004) (a);Evaluation of fixed-end rotation θ base as a function of slip from anchored bars (b)The onset of this slippage in longitudinal reinforcement, in correspondencewith the end section of the element, leads to the effect of deformability increaseknown as “fixed-end rotation”. In order to evaluate this contribution, theanchorage detail is modelled through a two-component finite difference model,where both contributions are taken into account. To this end, hysteretic modelsrepresenting the bond-slip relationship and the steel stress-strain relationshipare needed for the straight bonded bar, together with another hysteretic modelproviding the hook as a function of the corresponding stress. Hence, at eachstep, the steel strain values in top and bottom longitudinal reinforcement layers– at the end section of the element – are imposed as a boundary condition forthe models representing the anchorage details. The resulting slip values lead toa rigid rotation at the end of the element (see Figure 2.2.5.2b).

94 Chapter II – Seismic behaviour of existing reinforced concrete buildingsFor the hysteretic rules of the bond-slip relationship, see Section 2.2.3. Thebond capacities in post-elastic field are based on original and literature(Fabbrocino et al., 2004) experimental studies.Numerical results show a good agreement with experimental data, both inglobal (overall deformability, pinching effect) and local (base rotation) terms, inmonotonic and cyclic field (see Figures 2.2.5.3 to 5), thus confirming the keyrole played by fixed-end rotation mechanism in determining the deformabilityof RC members with smooth bars.force [kN]5045403530252015105experimentalnumerical w/o fixed-end rotationnumerical w/ fixed-end rotation00 20 40 60 80 100 120 140 160 180displacement [mm]Figure 2.2.5.3. Comparison between numerical and experimental (M270-B1 and M270-B2 testsfrom (Verderame et al. 2008a)) monotonic force-displacement relationships, with or withoutconsidering fixed-end rotation contribution

Chapter II – Seismic behaviour of existing reinforced concrete buildings 95force [kN]50403020100-10-20-30-40-50experimentalnumerical w/o fixed-end rotationnumerical w/ fixed-end rotation120100806040200-20-40-60-80-100-120displacement [mm]Figure 2.2.5.4. Comparison between numerical and experimental (C270-A1 test from(Verderame et al. 2008b)) cyclic force-displacement relationships, with or without consideringfixed-end rotation contributionw exp ,s num [mm]161412108642experimentalnumerical0-2-100 -80 -60 -40 -20 0 20 40 60 80 100displacement [mm]Figure 2.2.5.5. Comparison between the numerical slip values at the end section of the elementand the corresponding experimental crack width values (C270-A1 test from (Verderame et al.2008b))

96 Chapter II – Seismic behaviour of existing reinforced concrete buildings2.3 MEMBERS CONTROLLED BY SHEARIn this Section, main truss models for the evaluation of shear strength of RCmembers are presented.Capacity models for shear strength of RC members account for differentcontributions, corresponding to different post-cracking resistance mechanisms:first, the primary contribution (V s ) given by web reinforcement in tension,according to the truss analogy; then, resistance mechanisms developed inconcrete (V c ) are considered, such as dowel action or frictional interlockingbetween cracked interfaces. A distinction can be made between the models thatinclude the contribution of axial compression to shear strength in V c and themodels that consider this contribution as a distinct term (V P ).Moreover, capacity models have to take into account the degradation ofshear strength in members subjected to cyclic inelastic displacement; thisdegradation is usually expressed as a function of the maximum ductilitydemand. Hence, assuming V R as shear strength and V flex as flexural strength,V R decreases with the ductility demand increasing. If V R,i is the initial shearstrength (for zero ductility demand) and V R,r is the residual shear strength (thatis, the shear strength corresponding to the maximum degradation due toductility demand), three different conditions can take place (see Figure 2.3.1):• V flex < V R,r : no shear failure occurs, the element deformationcapacity can entirely develop (ductile behaviour, or behaviourcontrolled by flexure);• V R,r < V flex < V R,i : a shear failure may occur before ductile failurebut after flexural yielding (limited ductility behaviour, or behaviourcontrolled by shear-flexure interaction);• V R,i < V flex : a shear failure occurs before flexural yielding, no ductilemechanism can develop (brittle behaviour, or behaviour controlledby shear).

Chapter II – Seismic behaviour of existing reinforced concrete buildings 97Figure 2.3.1. Interaction between shear strength and ductility (Priestley et al., 1994)In (Priestley et al., 1994) an empirical-based model is proposed, where theshear strength is given by three contributions:AwfywD'VR = Vs + Vc + VP = cot 30° + k fc ⋅ 0.8Ag+ P tan α (2.3.1)sThe evaluation of V s (where A w is the cross-sectional area of transversereinforcement, f yw is the yield strength of transverse reinforcement, D’ is thedistance between the centrelines of transverse reinforcement and s is thespacing of transverse reinforcement) is based on a truss mechanism assuming a30 degree angle between the diagonal compression struts and the columnlongitudinal axis.In the evaluation of V c (where f c is the concrete compressive strength and A g isthe gross cross-sectional area) a coefficient k is applied (see Figure 2.3.2) inorder to account for the degradation of concrete resistance mechanisms due tothe inelastic flexural demand.Finally, in V P , which is the shear strength contribution given by axialcompression P, α represents the inclination of diagonal compression struts (dueto P) with member axis (see Figure 2.3.3).

98 Chapter II – Seismic behaviour of existing reinforced concrete buildingsFigure 2.3.2. Degradation of concrete shear strength with ductility (Priestley et al., 1994)(a)Figure 2.3.3. Shear strength contribution given by axial compression P: α angle is different inreversed bending (a) and in single bending (b) (Priestley et al., 1994)(b)In (Sezen and Moehle, 2004) a model is proposed, based on experimentaldata, for the evaluation of shear strength in lightly reinforced concrete columns.Shear strength is given by:A f d ⎛ 0.5 f P ⎞V = V + V = k + k 1+0.8As ⎜ a d 0.5 fcA ⎟⎝g ⎠w yw cR s c gwhere d is the effective depth and a is the shear span.(2.3.2)

Chapter II – Seismic behaviour of existing reinforced concrete buildings 99The concrete contribution V c is evaluated focusing the attention on diagonaltension capacity, and assuming that onset of diagonal tension cracking takesplace when the nominal principal tension stress acting on the element reachesthe nominal tensile strength (evaluated as0.5 fc). Hence, aspect ratio a/d isalso taken into account since elements with increasing a/d show decreasingshear strength.The authors find out that the traditional expression for V s (that is, based on theassumption of 45 degree inclined compressed struts) provides a good estimationof experimental data, given the assumed expression for V c .The degradation factor depending on inelastic displacement demand (k) isapplied not only to concrete resistance mechanisms but also to transversereinforcement contribution since, from a phenomenological standpoint,concrete degradation also leads to a decrease in V s contribution through loss ofanchorage and reduction in bond capacity for transverse reinforcement.The contribution of axial compression to shear strength is not taken intoaccount in a distinct term.EC8-part 3 (CEN, 2005) adopts the shear capacity model proposed in(Biskinis et al., 2004), based on a dataset of 239 experimental tests. For a/dhigher than 2 (slender elements), shear strength is given by:1V = ⎡V + (1 − 0.05min(5; µ )) ⋅ V + V( )plR P ∆ c sγ ⎣elwith⎤⎦(2.3.3)d − xVP= min(P;0.55Acf c)(2.3.4)2aaVc = 0.16 max(0.5;100 ρtot )(1 − 0.16 min(5; ))Ac f(2.3.5)cdVs = ρw ⋅bw ⋅ z ⋅ fyw(2.3.6)where γ el , equal to 1,15 for primary seismic elements and 1,0 for secondary

100 Chapter II – Seismic behaviour of existing reinforced concrete buildingsseismic elements, is meant to convert mean values of shear strength to meanminus-one-standard-deviationones,plµ∆is the plastic part of ductility demand, xis the compression zone depth, ρ tot is the total longitudinal reinforcement ratio,ρ w is the transverse reinforcement ratio, b w is the width of the cross section andz is the length of the internal lever arm.In this model the contribution of axial compression is explicitly taken intoaccount, assuming that the inclination of diagonal compression struts withmember axis is given by (d-x)/2a.In existing RC buildings not designed according to the strength hierarchyconcept, no ratio between shear and flexural strength was established a priori.Hence, the onset of a shear failure roughly depends on the ratio between theamount of longitudinal reinforcement (providing flexural strength) and theamount of transverse reinforcement (providing shear strength). Higher thisratio, higher the probability that the element exhibit a brittle behaviour. Fromthis point of view, a shear failure can be even more likely to occur in a oldseismic designed building rather than in a gravity load designed building sincein the former it is likely to have a much higher amount of longitudinalreinforcement compared to the latter, but not a much higher amount oftransverse reinforcement.This is also due to the so-called “threshold-based” design method fortransverse reinforcement: in old technical codes (e.g., RDL 2229/1939, DIN1045/1959, B4200/1953, ACI 318/1951, CP 114/1958) a value of allowabletangential stress was assumed (e.g., τ c0 ) and, if the design stress demand did notexceed this value, only a minimum amount of transverse reinforcement wasprescribed, thus leading to inadequate shear strength.Moreover, some critical issues may affect the development of shear strengthin existing building without proper seismic details: for instance, the absence ofa 135 degree hook anchorage in transverse reinforcement can lead to theopening of the stirrups under repeated cyclic loading, thus resulting in a halfcuttingof their contributions to shear strength (Biskinis et al., 2004).

Chapter II – Seismic behaviour of existing reinforced concrete buildings 101Generally speaking, shear capacity in RC members is given by twocontributions, corresponding to two different mechanisms: the truss mechanism(to which are referred the capacity models reported herein) and the tied archmechanism. It is to be noted that in members with smooth bars, characterizedby very low bond capacities (see Section 2.2.3) – and, therefore, also by a lowernumber of wider cracks, compared to elements with ribbed bars – thecontribution associated with the tied arch mechanism may become prevalentwith respect to the truss mechanism, see Figure 2.3.4.(a)(b)Figure 2.3.4. Variation of internal stress flow according to perfect bond (a) or perfect unbond(b) condition (Pandey and Mutsuyoshi, 2005)

102 Chapter II – Seismic behaviour of existing reinforced concrete buildings2.4 BEAM-COLUMN JOINTSIn a beam-column joint with transverse reinforcement, the shear capacity isgiven by two contributions, respectively corresponding to strut-mechanism(shear is concentrated in a single diagonal compressed concrete strut, see Figure2.4.1b) and truss-mechanism (the shear force due to the bond stress along thelongitudinal steel reinforcement inside the joint is in equilibrium with a trussmechanism given by concrete struts and vertical and horizontal tiescorresponding to joint panel reinforcement).Nevertheless, transverse reinforcement in beam-column joint panel area, incompliance with Capacity Design principles, has been prescribed only by recentseismic codes (e.g., Circ. M.LL.PP. 65, 1997, see Section 2.5.2). Hence, in thefollowing only capacity models for beam-column joints without transversereinforcement will be reported, thus referring to the strut-mechanism as the onlypossible resistance mechanism.(a)(b)Figure 2.4.1. Mechanism of shear transfer at an interior beam-column joint withoutreinforcement: (a) Force from beams and columns acting on joint core; (b) Strut-mechanism(Paulay and Priestley, 1992)

Chapter II – Seismic behaviour of existing reinforced concrete buildings 103Truss failure may occur by crushing of the strut, by splitting of the nodalregion, or by bond failure along the anchorage of a tie (CEB-FIB, 2003).In Figure 2.4.1a the forces acting on an interior beam-column joint panel arereported. The horizontal shear force V jh is equal to:V = C + C + T − V = T + T − V(2.4.1)''jh s2 c2 1 c 1 2 cbecause the horizontal equilibrium equation referred to the end section ofthe beam yields to:Cs2 + Cc2 = T2(2.4.2)The vertical shear force can be similarly given by an equilibrium equation,but an enough accurate evaluation can be given by:Vhbjv= Vjh(2.4.3)hcwhere h b is the beam depth and h c is the column depth.A first approach to evaluate the shear capacity of a beam-column jointwithout transverse reinforcement consists in principal stress limits according toconcrete strength. Direct limits on the shear stress, according to (Hakuto et al.,2000) and reported in many International Codes (ACI 352, 2002; AIJ, 1999) arenot accurate because they do not account for the vertical axial force in thecolumn. The principal stresses p in the joint panel can be given by Mohr’sCircle assuming uniform normal and transverse stresses, f a e v jh respectively,according to the following equation:p2−fa⎛ fa⎞= ± +2⎜2⎟⎝ ⎠v2jh(2.4.4)Equation (2.4.4) allows the horizontal joint shear to be evaluated at the firstdevelopment of diagonal cracking:ffv = p 1 + ⇒ V = k f 1+ b h(2.4.5)aajh t jh 1 c j jpt k1 fc

104 Chapter II – Seismic behaviour of existing reinforced concrete buildingswhere the tensile limit stress p t is assumed to be proportional to k 1 times thesquare root of concrete compressive strength, where k 1 is empirically evaluated.It is clearly shown in (2.4.5) that axial load delays the diagonal cracking in thejoint panel. The joint shear causing compressed concrete strut crushing,assuming the compressive limit stress p c to be proportional to k 2 times theconcrete compressive strength, is equal to:ffv = p 1 − ⇒ V = k f 1 − b h(2.4.6)aajh c jh 2 c j jpck2fcwhere k 2 is empirically evaluated.In the case of interior joints without transverse reinforcement, the values fork 1 e k 2 (Priestley, 1997) are 0.29 e 0.50, respectively. In the case of exteriorjoints, the proposed value for k 1 according to Priestley depends on thelongitudinal bars anchoring details and it is 0.29 if the longitudinal bars are bentat 90° outside the joint or 0.42 if they are anchored inside the joint. In the caseof exterior joints with smooth bars the value for k 1 equal to 0.20 is suggested(Calvi et al., 2002). In the cited works, deterioration models are provided toaccount for k 1 and k 2 variability based on ductility demand.According to European Code EC8 (CEN, 2005) the evaluation of thehorizontal maximum shear acting in the joint panel (shear demand) can beperformed through the following two expressions, respectively for exterior andinterior joints:Vjhd = γrd ⋅ As1 ⋅fyd − VC(2.4.7)Vjhd= γrd ⋅ (As1 + As1) ⋅fyd − VC(2.4.8)where A s1 is the area of the beam top reinforcement, A s2 is the area of the beambottom reinforcement, V C is the column shear force, obtained from the analysisin the seismic design situation, γ Rd is a factor to account for overstrength due tosteel strain-hardening and should be not less than 1.2. The EC8 formulation forpredicting the joint shear capacity is made up of two separated steps. First, there

Chapter II – Seismic behaviour of existing reinforced concrete buildings 105is an expression to evaluate the compression capacity of the strut that can berecognized in the joint panel under seismic actions and, then, an expressiondevoted to verify the tensile strength of the joint in order to avoid diagonalcracking. The horizontal shear demand should not exceed a value that couldcause the compression failure of the joint:νV = η f 1 − b ⋅ hηdjhd cd j jc(2.4.9)where η = 0.60 (1-f ck /250) for interior joints and η = 0.48 (1-f ck /250) forexterior joints, practically meaning that the strength of exterior joints is 0.8(0.48/0.60) times that one of interior joints (assuming the same joint materialsand detailing); ν d is the normalised axial force in the column above the joint, f ckis given in MPa, h jc is the distance between the extreme layers of columnreinforcement, b j is the effective width of the joint.The Italian code (DM 14/1/2008) deals separately with joints belonging tonew and existing buildings, the former ones being evaluated as in EC8. As forexisting buildings, IC contains two expressions devoted to verify beam-columnjoint without seismic provisions, that is without hoops in the panel. Theseexpressions allow to calculate the maximum diagonal compression (2.4.10) andtensile (2.4.11) stresses in the concrete joint core that must be below givenvalues related to the concrete strength f c :2 2N ⎛ N ⎞ ⎛ V ⎞nσnt= − + ≤ 0,3 fcfcin MPa2A ⎜ g2A ⎟ ⎜ gA ⎟⎝ ⎠ ⎝ g ⎠( )(2.4.10)N2 2⎛ N ⎞ ⎛ V ⎞nσnc= + + ≤2A ⎜ g2A ⎟ ⎜ gA ⎟g⎝ ⎠ ⎝ ⎠0,5fc(2.4.11)where N is the axial force acting on the upper column, A g is the gross area ofthe joint panel horizontal section and V n the horizontal shear acting in the jointpanel evaluated taking into account both the column shear and the shear

106 Chapter II – Seismic behaviour of existing reinforced concrete buildingstransmitted by the beam reinforcing bars.It is worth noting that a joint failure criterion based on tensile principalstress limit results to be over conservative. As a matter of fact, the joint panel isable to transfer noticeable shear forces also in a cracked phase due to thediagonal strut mechanism. The joint failure should be always related to thecompressed strut crushing. In the case of high axial loads, the compressed strutcrushing can be attained before the joint panel cracking (Paulay and Priestley,1992).The experimental evaluation of k 2 coefficient in equation (2.4.6) has toaccount for the real stress field in the joint, that is complex to be evaluated incracked phase, for the compressive strength deterioration due to diagonaltensile strains (Collins et al., 1980), and for the detailing of steel barsanchorage.The latter is a key aspect in the case of exterior joints, to guarantee thedevelopment of the compressed strut (Priestley, 1997): when beamreinforcement is anchored by bending away from the joint (see Figure 2.4.2a)diagonal struts in the joint cannot be stabilized and joint failure occurs at anearly stage.It is to be noted that, in order to allow the truss mechanism to develop,tension ties must be able to develop up to the node of the truss, independent ofbond capacity (i.e., smooth or ribbed reinforcement) (CEB-FIB, 2003).However, some specific issue about smooth reinforcement have to behighlighted, mainly related to the anchorage detail. For instance, when the baris compressed the end hook anchorage mobilizes a pushout cone, potentiallyleading to a splitting failure (Calvi et al., 2002; CEB-FIB, 2003), see Figure2.4.3.

Chapter II – Seismic behaviour of existing reinforced concrete buildings 107Figure 2.4.2. Breakdown of unreinforced exterior joints (Priestley, 1997)Figure 2.4.3. Cone (wedge) splitting failures in various old-type joints (CEB-FIB, 2003)

108 Chapter II – Seismic behaviour of existing reinforced concrete buildings2.5 STRUCTURAL PERFORMANCE OF RC BUILDINGS AFTERTHE 6 TH APRIL 2009 L’AQUILA EARTHQUAKE, ITALYOn 6 th April 2009 an earthquake of magnitude M w = 6.3 occurred in theAbruzzo region; the epicentre was very close to the city of L’Aquila (about 6km away). The event produced casualties and damage to buildings, lifelines andother infrastructures. An analysis of the main damage that RC buildings showedafter the event is presented in this Section. An analysis of the existing RCbuilding stock in the area is carried out (Section 2.5.1), together with a reviewof the most important seismic codes in force in the last 100 years in Italy(Section 2.5.2). Comparison of the current design provisions of the Italian andEuropean codes with previous standards allows the main weaknesses of theexisting building stock to be determined (Section 2.5.3). Damage to structuraland elements are finally analyzed thanks to photographic material collected inthe first week after the event (Section 2.5.4). The observations reported in thisSection were published in (Ricci et al., 2010).2.5.1. Reinforced concrete buildings in L’AquilaThe layout of the ancient city of L’Aquila is characterized by two majorstreets crossing at right-angles at a place called “Quattro Cantoni”. Thehistorical centre (Figure 2.5.1.1) is situated on a raised hill overlooking thesurrounding area. It is encircled by medieval walls, which still stand almostcompletely undamaged.The first structures beyond the ancient perimeter were the sports facilities inViale Gran Sasso, built in the 1930s. However, urbanization accelerated afterWorld War II, especially during the 1960s and 1970s, following the opening ofthe highway to Rome. In 1965 and 1975 two urban plans were enacted.Expansion mainly occurred in on the north-western side of the city, leading in afew years to the complete saturation of the urban area bounded by the samehighway (Figure 2.5.1.1). Later expansion radiated out from the historicalcentre on all sides, except to the south-west, the course of the Aterno river(Figure 2.5.1.1).

Chapter II – Seismic behaviour of existing reinforced concrete buildings 109The current urban structure of L’Aquila is that of an historical centresurrounded by densely-packed suburbs, comprising the quarters of Pettino,Santa Barbara and Torrione, and less densely populated areas in the North-Western, including Coppito, Sant'Antonio and Torretta quarters. The remainingarea within the city’s administrative boundaries includes several villages in thesurrounding area.Figure 2.5.1.1. L’Aquila: historical centre (black line), the Aterno river (blue line) and thehighway (yellow line) (Google Earth©)According to data from the Italian National Institute of Statistics (Istitutonazionale di statistica, ISTAT), see Figure 2.5.1.2, collected in 2001, whichrepresent the most recent official source for information about the buildingstock in Italy, and hence in the L’Aquila area, 24% of buildings are reinforcedconcrete structures, 68% masonry structures and 8% structures of unspecifiedtype (Figure 2.5.1.2b). Data that identify age of construction of the buildings(Figure 2.5.1.2a) indicate that 55% of the entire stock was built after 1945. Alow overall incidence of RC structures shows that after 1945 new masonrystructures were still being built and that the number of RC structures increasedgradually over time. Based on the distribution of number of storeys (Figure2.5.1.2c), only 5% of the buildings have more than three storeys. Assuming thatall buildings with more than three storeys are RC structures, it may still be

110 Chapter II – Seismic behaviour of existing reinforced concrete buildingsinferred that the vast majority of L’Aquila RC buildings are no more than threestoreys tall.100%80%60%40%20%0%1991(a)100%80%60%40%20%0%R.C. masonry other1 2 3 ≥ 4(b)(c)Figure 2.5.1.2. 2001 census ISTAT data for L’Aquila: (a) age of construction, (b) building type,(c) number of storeysIf the interstorey height is considered to vary between 3.0 and 3.5 meters,approximate formulation provided by the Eurocode (CEN, 2003) for RC framestructures gives for three-storey buildings a fundamental period of 0.4 seconds.Working hypotheses assumed in this Section, which were useful in definingpoints of comparison between codes, are mostly confirmed by representativesamples of buildings employed in other field campaigns carried out for thesame earthquake (e.g., Liel and Lynch, 2009).According to previous observations, in the following Section 2.5.3, whencomparing different Italian Code spectral shapes, the comparison is focused on

Chapter II – Seismic behaviour of existing reinforced concrete buildings 111period values that range from 0 to 0.4 seconds. The latter assumption allows acomparison between constant acceleration branches of the spectra. A generalreview of design prescriptions in recent decades is employed to identify themain weaknesses of the building stock and to finally compare seismic demandgiven by codes with the demand of the earthquake event considered in thisSection.2.5.2. Overview of past seismic code provisionsL’Aquila and its neighbourhood were first legally recognized as a seismiczone in 1915. A specific law (RDL 573, 1915) was passed after the catastrophicseismic event occurring in January 1915 that struck Abruzzo (the Marsicaearthquake) killing more than 29,000 people. This law provided that newconstructions would have been designed taking into account seismic loads:horizontal forces were equal to 1/8 and 1/6 of gravity loads respectively at thefirst and second level of the building.In 1927 (RDL 431, 1927) a more detailed seismic classification wasintroduced; this classification divided the Italian seismic area into two differentcategories; L’Aquila belonged to the less restricted one (second category).Seismic provisions were simply achieved by limiting the number of storeys: forthe second category zone the 1927 law allowed construction of three-storeybuildings, and for specific situations even four-storey buildings were accepted.Horizontal forces were equal to 1/10 of the storey weight for structures up to 15meters tall or 1/8 for structures higher than this limit. This code gave specificprescriptions for RC structures including prescriptions for dimensions of beamand column sections and the least amount of steel reinforcement required.In the following years, between 1930 and 1937, three seismic codes wereenacted (RDL 682, 1930; RDL 640, 1935; RDL 2105, 1937) and their mainconcern was the evaluation of seismic forces. For seismic vertical action theadditional load was determined as equal to 1/3 of the structural weight, thusreducing the amount applied in the 1915 regulations. In second category zonesthe ratio between seismic horizontal forces and vertical forces due to gravity

112 Chapter II – Seismic behaviour of existing reinforced concrete buildingsloads (base shear coefficient) was initially 0.05 (RDL 640, 1935) and then 0.07(RDL 2105, 1937). These prescriptions were confirmed in 1962 (Legge 1684,1962) with less restrictive limits about building height and setting themaximum number of storeys at seven. Under this law further areas of thecountry were classified as seismic.In 1975 (DM 40, 1975) a fundamental innovation was introduced into theanalytical procedure: for the first time within Italian regulations the dynamicproperties of the structures were considered. Starting from this year, seismicaction could be determined by means of static and dynamic analyses. In thestatic analysis, the resultant of lateral force distribution applied to the buildingwas given by Eq. 2.5.2.1, where W is the total weight of the structural masses;R the response coefficient, assumed as a function of the fundamental period ofthe structure; coefficient C represents the seismic action (Eq. 2.5.2.2), and isdefined by means of S, the seismic intensity parameter. Coefficients ε and βrespectively express soil compressibility (ε=1.00-1.30) and the possiblepresence of structural walls (β =1.00-1.20).Fh= C⋅ R ⋅ε ⋅β⋅ W(2.5.2.1)S − 2C = (2.5.2.2)100Fh= 0.07 ⋅ W(2.5.2.3)For second category zones, S was assumed equal to 9. If coefficients ε and βwere considered equal to 1, respectively corresponding to stiff soil and absenceof structural walls, a structure, whose fundamental period was lower than 0.8seconds, was characterized by a base shear coefficient (F h /W) of 0.07 and it wasthe same as that adopted up to 1975 (see Eq. 2.5.2.3).The coefficient given by the product of C and R should be interpreted as adesign inelastic acceleration demand: it took into account dynamic properties ofthe structure and a strength reduction factor evaluated upon dissipative capacityof the structure. Nevertheless, lateral forces applied to the building were

Chapter II – Seismic behaviour of existing reinforced concrete buildings 113proportional to the height of the slab at each storey determined from thefoundation level, assuming a linear distribution with an “inverted triangular”shape that is more suitable to represent the actual dynamic behaviour of thestructure, compared with previous code prescriptions.New generation codes explicitly express this kind of dissipative capacity ofthe structures; Eurocode 8 (CEN, 2003) does it by means of the “behaviourfactor”. According to the Eurocode 8 definition, the behaviour factor q is anapproximation of the ratio of the seismic forces that the structure wouldexperience if its response was completely elastic with 5% viscous damping tothe seismic forces that may be used in the design, with a conventional elasticanalysis model, still ensuring a satisfactory response of the structure. Thevalues of q, which also account for the influence of the viscous damping beingdifferent from 5%, are given for various materials and structural systemsaccording to the relevant ductility classes.Regarding seismic input, even if different new seismic design codes wereapproved (DM 24/1/1986; DM 16/1/1996), no changes have been introducedregarding this aspect since 1975. On the other hand, in this period, the LimitState method was introduced and, for Ultimate Limit State assessment, designacceleration was supposed to be increased by a factor of 1.50, thus obtaining anacceleration of (1.50×0.07g), equal to 0.105g.Furthermore, it is worth noting that the first prescriptions close to theperformance-based seismic design approach, such as the attainment of bothproper local and global ductility capacity, were provided in 1997 with anexplanatory document attached to the 1996 code (Circ. M.LL.PP. 65, 1997). Inthis document there were limits for longitudinal and transverse reinforcement ofbeams and columns with specific prescription in the end zone of each structuralelement (critical region). In the 1997 document, additional prescriptions wereprovided regarding proper anchorage of bars, and it was prescribed to lengthenlongitudinal and transverse reinforcement of the column in beam-column joints.The latter prescription regarding beam-column joints was aimed at giving aproper local ductility to the element. Although this document (Circ. M.LL.PP.

114 Chapter II – Seismic behaviour of existing reinforced concrete buildings65, 1997) represented an important step towards performance-based designcriteria in Italy, lack in prescriptions about regularity criteria in plan andelevation is still recognizable and these criteria remained qualitative, withoutany specific quantitative definition to help in regularity classification.In the 2003 seismic code (OPCM 3274, 2003) and its followingmodifications (OPCM 3431, 2005) an innovative seismic input definition wasintroduced, representing the first real upgrade towards the Eurocode 8approach. In this document an elastic spectrum was provided with a definedshape in which the only value to be changed, considered a function of theseismic zone, was the anchorage Peak Ground Acceleration (PGA) on stiff soiltype (ground type A). L’Aquila belonged to the second category and the PGAvalue on ground type A was 0.25g. This spectrum was to be amplifiedconsidering site specific characteristics, taking into account other ground typesand topographic conditions. The elastic acceleration spectrum was to bereduced by the q factor value depending on the specific structural type, thusobtaining a design acceleration spectrum. This document explicitly introducedin Italy the strength hierarchy concept, ensuring the development of inelasticdeformations in the highest possible number of ductile elements and not inelements with lower rotational capacity (that is, in beams and not in columns,due to the different axial load), but also providing over-strength to brittle failuremechanisms with respect to ductile ones. Furthermore, proper quantitativedefinition of regularity criteria in plan and in elevation was introduced, fixingmaximum variation of mass, stiffness and strength over building height.The most recent Italian code (DM 14/1/2008) defines maximumacceleration expected at the site no longer with division in terms of seismiczones but as a function of geographic coordinates of the site. For L’Aquila(latitude 42.38; longitude 13.35), the PGA is 0.261 g on ground type A for a10% probability of exceedance in 50 years. In the case of L’Aquila, 2003 and2008 PGA values are very close to each other.

Chapter II – Seismic behaviour of existing reinforced concrete buildings 1152.5.3. Spectral considerationsSeismic demand defined by previous codes can be considered equal to thelowest seismic capacity of structures designed according to them. The seismicdemand of old codes can be easily compared with the current code seismicdemand and actual seismic demand registered during the 2009 L’Aquila event.Eurocode 8 (CEN, 2003) and the Italian Code (DM 14/1/2008) provide aNewmark-Hall functional expression for the elastic spectrum. By means ofofficial Italian hazard data, given the specific geographic coordinates andground type, the elastic spectrum may be defined for the considered site.Material, reinforced concrete in this study, and ductility class are necessary todefine the behaviour factor q (see Section 2.5.2); the latter is employed to passfrom the elastic spectrum to the design spectrum.Both Eurocode 8 and the Italian code provide two ductility classesdepending on the hysteretic dissipation capacity. Both classes correspond tobuildings designed, dimensioned and detailed in accordance with specificearthquake-resistant provisions, enabling the structure to develop stablemechanisms associated with large dissipation of hysteretic energy underrepeated reversed loading, without suffering brittle failures.Design spectrum defined by the Italian Code (DM 14/1/2008) for the LifeSafety Limit State can be compared with the 1996 Ultimate Limit State spectralshape; the former was evaluated for both ductility classes, namely high ductilityclass (CD “A”) and low ductility class (CD “B”), assuming a behaviour factor qdetermined for new design RC frame structures (see Figure 2.5.3.1a).Another interesting comparison can be made between the 1996 inelasticspectral shape and design response spectra evaluated for existing RC structuresconsidering extreme values of q factor (1.5-3.0) according to the current Italianseismic code (Circ. M.LL.PP. 617, 2009), see Figure 2.5.3.1b. Indeed, bothEurocode 8 and the Italian Code provide different values of behaviour factor qfor new design and existing buildings, presuming that the latter cannot becharacterized by properly high hysteretic dissipation capacity.According to the Ultimate Limit State spectrum adopted in Italy between

116 Chapter II – Seismic behaviour of existing reinforced concrete buildings1975 and 1996, a constant value of 0.105g was assumed for spectral ordinatesbetween 0 and 0.8 seconds. This value for design inelastic acceleration can bereasonably considered representative of the minimum base shear coefficient ofthe great majority of L’Aquila RC buildings, if properly designed according tocodes until 2003 and given ISTAT data (see Figure 2.5.1.2a).Comparing constant acceleration branches of the various spectra shown inFigure 5a it may be noted that a building designed in CD “A”, and regular inplan and elevation, so characterized by a q factor of 5.85, according to thecurrent Italian Code, is designed for the same seismic demand as in the oldcodes. However, it has to be considered that previous codes provided neitherdesign rules nor detailed structural prescriptions able to ensure global and localductility required by the current code, which allows adoption of a q factor of5.85.Generally, existing structures are unable to show a highly ductile behaviourand it is not possible to ensure that the structure develops stable mechanismsassociated with large dissipation of hysteretic energy. This is why actual codesconsiderably limit q in such cases, allowing it in the range (1.5-3.0). The choiceof a value in this range should be made according to regularity criteria and theemployment of material properties. Hence, a proper comparison has to becarried out between the current seismic demand spectra provided for existingstructures and the former code spectrum (see Figure 2.5.3.1b). The lattercomparison leads to a ratio of at least 2 between the current seismic demandand the old seismic demand.Design procedures and details according to new generation codes, such asEurocode, (BS EN 1990, 2002), for the Ultimate Limit State, considering thesecond reliability class (RC2), according to the same Eurocode definition (BSEN 1990, 2002), lead to an annual failure probability not higher than 1⋅ 10 −6 .A ratio of current to old code demands, as calculated above, of at least 2,does not mean Life Safety limits are exceeded for all buildings; on the otherhand, the percentage of building failure over the whole population, in this case,would definitely be higher than1⋅ 10 −6 .

Chapter II – Seismic behaviour of existing reinforced concrete buildings 1170.50a/g0.50a/g0.400.40D.M. 2008 (q=1.50)0.30D.M. 2008 (CD"B")0.300.20(D.M. 1975 - D.M.1996)D.M. 2008 (CD"A")0.20(D.M.1975 - D.M.1996)D.M. 2008 (q=3.00)0.100.10T [sec]0.000.00 0.50 1.00 1.50 2.00 2.50 3.00(a)2.00 a/gAQK-EWAQG-EWAQA-EW1.60AQV-EWAQK-NSAQG-NS1.20AQA-NSAQV-NS0.80D.M. 2008 - TR 475D.M. 2008 - TR 975T [sec]0.000.00 0.50 1.00 1.50 2.00 2.50 3.00(b)2.00 a/gAQK-ZAQG-Z1.60AQA-ZAQV-ZD.M. 2008 - TR 4751.20D.M. 2008 - TR 9750.800.400.40T [sec]0.000.00 0.50 1.00 1.50 2.00 2.50 3.00T [sec]0.000.00 0.50 1.00 1.50 2.00 2.50 3.00(c)(d)Figure 2.5.3.1. Inelastic old code spectra compared with current code spectra for new designstructures (a) and existing structures (b). Current elastic code spectra compared with recordedsignal spectra for horizontal (c) and vertical component (d)If the elastic demand spectra of the registered signals are compared with thecurrent code’s elastic demand spectra, determined for different return periods(T R 475 and 975 years) on ground type A, it may be noted that the spectra of theregistered signals exceed code demand in most of the frequency rangeconsidered. Figure 2.5.3.1c compares elastic spectra determined fromhorizontal components of the registered signals in stations AQK, AQG, AQAand AQV, while Figure 2.5.3.1d compares vertical components of the same

118 Chapter II – Seismic behaviour of existing reinforced concrete buildingssignals with the vertical code spectra.2.5.4. Field survey of structural damageIn this Section the main structural damage to RC structures after theL’Aquila earthquake is presented. Photographic documentation (Verderame etal., 2009c) was produced on the days immediately following the 6 th April 2009mainshock. Generally speaking, damage to structural elements is not sofrequent and it seldom involves the whole structural system.The main structural damage that involved RC columns can be easilyrecognized as failure caused by mechanisms that capacity design rules tend toavoid or at least to limit. During an earthquake, columns are characterized byhigh flexural and shear demand; maximum flexural demand combined withaxial force produced by gravity loads and seismic loads are located at the end ofthe element; in these zones (critical regions) rotational ductility demandconcentrates. Therefore, it is necessary to give an adequate rotational capacityand to avoid buckling of compressed longitudinal reinforcements.Modern seismic codes, such as Eurocode 8 (CEN, 2003), provideprescriptions to increase rotational capacity of the section: the upper limit onthe longitudinal reinforcement percentage leads to a higher ultimate curvatureof the section; proper hoop spacing and cross-tie presence give, due to a moreefficient confinement action on concrete, an additional increase in sectioncurvature capacity; finally, proper spacing between hoops avoids buckling inlongitudinal reinforcement, or at least fixes an acceptable upper bound limit forwhich this phenomenon occurs.However, the prescriptions and structural details presented above are typicalof modern design concepts that first appeared in Italy in 1997. It is thereforepossible to find RC columns with longitudinal reinforcement percentageexceeding 4% limit or hoops closed with 90 degree hooks, or with insufficientlythick spacing (15-20 cm).

Chapter II – Seismic behaviour of existing reinforced concrete buildings 119(a)(b)Figure 2.5.4.1. Column with smooth bars and poor transverse reinforcement (a); damage to acolumn due to axial force and bending moment (b)Figure 2.5.4.1a presents a corner column of an RC building in the historicalcentre of L’Aquila, probably erected between 1950 and 1960. Damage occurredat the bottom end section of the element. The presence of smooth bars and asmall hoop diameter (6 mm), closed with 90 degree hooks, can be observed, butthe most significant detail is the absence of any transverse reinforcement in thefirst 30–40cm of the element immediately adjacent to the beam-column jointregion. Figure 2.5.4.1b shows a circular column belonging to a building in theresidential zone of Pettino, built in the 1980s: typical damage due to axial forceand bending moment is recognizable; the concrete cover was crushed due tohigh compression strains and longitudinal bar buckling. In this case hoopspacing is, once again, not thick enough, as in the case of Figure 2.5.4.1a, butprobably in this case the column was designed in accordance with codeprescriptions at the time of construction.

120 Chapter II – Seismic behaviour of existing reinforced concrete buildings(a)(b)(c)(d)Figure 2.5.4.2. Shear failure of: (a) rectangular and (b) circular (b) columns, (c) columnadjacent to partial infilling panels, (d) squat column adjacent to basement level concrete walls

Chapter II – Seismic behaviour of existing reinforced concrete buildings 121High shear demand can produce brittle failures with an outstandingreduction in column dissipative capacity. In order to prevent brittle failures,shear demand has to be determined according to flexural capacity of theelement; applying to shear demand an amplifying coefficient to allow forvariability in steel properties (CEN, 2003) can prevent brittle failureoccurrence. These prescriptions have been laid down since 2003 in the Italiancode; no control of the failure mechanism used to be applied before this codewas released. All the above considerations can be confirmed by brittle failure ofthe columns reported in Figure 2.5.4.2.With regard to the rectangular column in Figure 2.5.4.2a, whose section is30×100 cm 2 , belonging to a 1980s’ building, shear failure is evident, involvingthe top end section. Transverse reinforcement has hoop spacing ofapproximately 15-20cm, and is definitely under-designed with respect tocolumn section size, that is, with respect to the inertia of the section, thusleading to premature shear failure of the element. The brittle failure mechanismis highlighted by the crushing of the concrete within the reinforcement and thecomplete opening of the third and fourth hoops from the top end of the element.Figure 2.5.4.2b shows shear failure of a 30cm-diameter circular column; inthis case it is possible to recognize insufficient hoop spacing, which leads to thetypical diagonal cracking typical of shear failure mechanisms and longitudinalbar buckling in the column.In order to stress the non-secondary role played by column – infillinteraction in determining brittle failures in the structural elements, Figure2.5.4.2c shows the damage that columns present in these kinds of situation. It ispossible to recognize the brittle failure in the column due to the localinteraction with the concrete infill partially covering the bay frame, reaching1/3 of the total column height. Partial infilling that effectively interacts with thecolumn reduces the slenderness of the element and consequently produces ahigher shear demand that exceeds column shear capacity. This kind ofphenomenon involves all the columns interacting with the concrete partialinfilling.

122 Chapter II – Seismic behaviour of existing reinforced concrete buildingsFigure 2.5.4.2d gives an example of a basement that is partially below theground level. According to common building practice, basement levels arecharacterized by walls, often realized in concrete, aimed at a retaining functionof the adjacent embankment; concrete wall height is limited with respect tocolumn height to allow the fitting of windows. This structural solution leads toa strict reduction in column slenderness with a consequent increase in sheardemand; moreover, decreasing shear span can modify the shear span ratio of theelement up to a squat column behaviour. This situation is of no secondaryimportance since the shear resistance mechanism of a squat column differs withrespect to the typical behaviour of a slender element. Differences between shearcapacity formulations proposed in Eurocode 8 (CEN, 2005) for existingbuildings for slender and squat columns testify to the difference between shearfailure mechanisms. Hence, if local interaction between the column andconcrete wall is not allowed for, premature brittle failure due to excessiveconcrete compression can often occur.Figure 2.5.4.3. Shear failure in squat columns of the staircaseColumns belonging to staircases can easily show brittle failures as well.Most common staircase types generally possess discontinuity elements in theregular RC frame scheme composed by beams and columns. Indeed, on oneside a staircase consists of inclined axis elements (beam or slab); on the other,

Chapter II – Seismic behaviour of existing reinforced concrete buildings 123squat columns are created by the intersection of inclined axis elements with thecolumn.Staircase elements lend a considerable lateral stiffness to the wholestructural system, first due to axial stiffness of the inclined elements andsecondly to higher lateral stiffness of squat columns. These contributions areeasily appreciable via linear analyses. On the other hand, staircase elements canrepresent a weak point because they possess higher shear demand that can leadto brittle failure mechanisms.Figure 2.5.4.3 shows a staircase composed by inclined beams; the squatcolumn in the corner has typical shear failure. Poor transverse reinforcement,both in terms of hoop spacing and diameter, can be recognized.Figure 2.5.4.4. Failure in reinforced concrete wallsShear failures were found in reinforced concrete as well. As an example, inFigure 2.5.4.4 two reinforced concrete walls, respectively with two differentshape factors, are shown; damage consists of a spread diagonal cracking. Lowlongitudinal and transverse reinforcement percentages can be recognized,

124 Chapter II – Seismic behaviour of existing reinforced concrete buildingsespecially compared with minimum values prescribed by design codes based oncapacity design approach.(a)(b)(c)(d)Figure 2.5.4.5. Joint failure with evidence of (a) longitudinal bar buckling and (b) diagonalcracking failure in concrete joint panel; (c) (d) failure mechanisms at joint – column interfacesurface

Chapter II – Seismic behaviour of existing reinforced concrete buildings 125Beam-column joints can completely change the structural behaviour of thewhole building and their failure should necessarily be avoided in a properseismic design approach: such elements possess brittle failure mechanisms. Ingeometrically very small beam-column joints, demand coming from beams andcolumns is concentrated and both the concrete panel and longitudinal bars aresubjected to high gradients of shear and flexural demand.Joint failure mechanisms are mainly governed by shear and bondmechanisms; force distribution, which allows shear and moment transfer,produces diagonal cracking and hence joint failure due to diagonal compressionin the concrete is quite likely to occur, thus producing a reduction in strengthand stiffness in the connection.Generally speaking, joint design is limited by concrete compressive stress;the diagonal stress induced by the elements meeting in the joint cannot exceedconcrete compressive stress. In order to keep structural continuity whenconcrete cracking occurs, a proper transverse reinforcement along the wholeelement should be provided. The presence of transverse reinforcement allowsstresses to be transferred by means of a strut and tie mechanism, even if thecracking phase has passed in the concrete. The latter mechanism can bedeveloped if longitudinal reinforcement, transverse reinforcement and concretestruts contribute to truss formation. If capacity design prescriptions arefollowed, preventing brittle failure in joints gives the chance to develop moreductile mechanisms in the other structural elements.Specific design rules for beam-column joints appeared in the Italian designprescriptions only in 2003 (OPCM 3274, 2003). Indeed, in the explanatorydocument to the 1996 code (Circ. M.LL.PP. 65, 1997) the transversereinforcement in the joints was simply required to be at least equal to the hoopspacing in the columns.Damage from the 6 th April 2009 earthquake clearly shows how hazardousfailure of joints can be. Figure 2.5.4.5a shows an external beam-column joint,characterized by an extensive cracking in the joint panel. The absence oftransverse reinforcement leads to local buckling of the longitudinal bars that

126 Chapter II – Seismic behaviour of existing reinforced concrete buildingsconsequently results in concrete cover spalling. Interestingly, the absence ofproper transverse reinforcement in the joint also leads to a loss of anchorage inbeam longitudinal reinforcement.Figure 2.5.4.5b shows typical diagonal cracking failure in a concrete panelbelonging to an external joint. Cracking begins at the intersection between thejoint and upper column and ends at the intersection between the joint and lowercolumn, producing the loss of monolithic connection. Absence of hoops, in thissituation too, leads to buckling in the external longitudinal bars and involveslower column bars without transverse reinforcement in the first 30–40cm.Another noteworthy aspect in RC damage after the L’Aquila earthquake is apeculiar loss of connection at the lower joint-column interface; this aspect isemphasized and becomes a critical issue when there is insufficient longitudinaland transverse reinforcement both within the joint and at the column end.Generally speaking, the presence of a separation (previously present orotherwise) at the interface between the column and beam-column joint, if bothelements – column and joint – are well designed, complying with modernseismic prescriptions, should not prevent the development of a ductile failuremechanism in the column. According to current code prescriptions, (i) aminimum amount of longitudinal reinforcement, evenly distributed around theperiphery of the section, and (ii) an adequate, effectively anchored transversereinforcement, both in the beam-column joint and at the column end, have to beadopted, thus avoiding brittle failure along the interface section betweencolumn and joint (Paulay and Priestley, 1992).Figure 2.5.4.5c reports a brittle failure mechanism due to the lack of transverseand longitudinal reinforcement that led to loss of continuity at the intersectionbetween the joint and lower column, being the probable final cause of thefailure. Figure 2.5.4.5d shows a clear separation in concrete at the joint-columninterface; in this case, due to a complete spalling of the concrete cover, thereinforcement in the element may be recognized and it may be noted that thefirst hoop in the column is partially open. The lack of transverse reinforcementin the element made the separation at the joint-column interface critical.

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Chapter II – Seismic behaviour of existing reinforced concrete buildings 133− Park R., Priestley M.J.N., Gill W.D., 1982. Ductility of square-confinedconcrete columns. ASCE Journal of Structural Division, 108(ST4), 929-950.− Paulay T., Priestley M.J.N., 1992. Seismic design of reinforced concreteand masonry buildings. John Wiley & Sons, New York, USA.− Peruš I., Fajfar P., 2007. Prediction of the force-drift envelope for RCcolumns in flexure by the CAE method. Earthquake Engineering andStructural Dynamics. 36(15), 2345-2363.− Peruš I., Poljanšek K., Fajfar P., 2006. Flexural deformation capacity ofrectangular RC columns determined by the CAE method. EarthquakeEngineering and Structural Dynamics. 35(12), 1453-1470.− Priestley M.J.N., 1997, Displacement-based seismic assessment ofreinforced concrete buildings. Journal of Earthquake Engineering, 1(1),157-192.− Priestley M.J.N., Park R., 1987. Strength and ductility of concrete bridgecolumns under seismic loading. ACI Structural Journal, 84(1), 61-76.− Priestley M.J.N., Verma R., Xiao Y., 1994. Seismic shear strength ofreinforced concrete columns. ASCE Journal of Structural Engineering,120(8), 2310-2329.− Pujol S., Sozen M.A., Ramirez J.A., 2006. Displacement history effectson drift capacity of reinforced concrete columns. ACI StructuralJournal, 103(2), 253-262.− Regio Decreto Legge n. 573 del 29/4/1915. Che riguarda le normetecniche ed igieniche da osservarsi per i lavori edilizi nelle localitàcolpite dal terremoto del 13 gennaio 1915. G.U. n. 117 dell’11/5/1915.(in Italian)− Regio Decreto Legge n. 431 del 13/3/1927. Norme tecniche ed igienichedi edilizia per le località colpite dai terremoti. G.U. n. 82 dell’8/4/1927.(in Italian)

134 Chapter II – Seismic behaviour of existing reinforced concrete buildings− Regio Decreto Legge n. 682 del 3/4/1930. Nuove norme tecniche edigieniche di edilizia per le località sismiche. G.U. n. 133 del 7/6/1930.(in Italian)− Regio Decreto Legge n. 640 del 25/3/1935. Nuovo testo delle normetecniche di edilizia con speciali prescrizioni per le località colpite daiterremoti. G.U. n. 120 del 22/5/1935. (in Italian)− Regio Decreto Legge n. 2105 del 22/11/1937. Norme tecniche di ediliziacon speciali prescrizioni per le località colpite dai terremoti. G.U. n. 298del 27/12/1937. (in Italian)− Regio Decreto Legge n. 2229 del 16/11/1939. Norme per la esecuzionedelle opere in conglomerate cementizio semplice od armato. G.U. n. 92del 18/04/1940. (in Italian)− Ricci P., De Luca F., Verderame G.M., 2010. 6th April 2009 L’Aquilaearthquake, Italy: reinforced concrete building performance. Bulletin ofEarthquake Engineering. DOI: 10.1007/s10518-010-9204-8− Rossetto T., 2002. Prediction of deformation capacity of non-seismicallydesigned reinforced concrete members. Proceedings of the 7 th U.S.National Conference on Earthquake Engineering, Boston, USA, July 21-25.− Sezen H., 2002. Seismic behavior and modeling of reinforced concretebuilding columns. PhD Dissertation, Department of Civil andEnvironmental Engineering, University of California, Berkeley,California, USA.− Sezen H., Moehle J.P., 2004. Shear strength model for lightly reinforcedconcrete columns. ASCE Journal of Structural Engineering, 130(11),1692-1703.− Verderame G.M., Fabbrocino G., Manfredi G., 2008a. Seismic responseof RC columns with smooth reinforcement. Part I: Monotonic tests.Engineering Structures, 30(9), 2277-2288.

Chapter II – Seismic behaviour of existing reinforced concrete buildings 135− Verderame G.M., Fabbrocino G., Manfredi G., 2008b. Seismic responseof RC columns with smooth reinforcement. Part II: Cyclic tests.Engineering Structures, 30(9), 2289-2300.− Verderame G.M., Ricci P., Manfredi G., Cosenza E. 2008c. La capacitàdeformativa di elementi in c.a. con barre lisce: modellazione monotonae ciclica, Atti del convegno ReLUIS “Valutazione e riduzione dellavulnerabilità sismica di edifici esistenti in c.a.”, Rome, Italy, May 29-30. Pp. 589-600.− Verderame G.M., Ricci P., De Carlo G., Manfredi G., 2009a. Cyclic bondbehaviour of plain bars. Part I: Experimental investigation. Constructionand Building Materials, 23(12), 3499-3511.− Verderame G.M., De Carlo G., Ricci P., Fabbrocino G., 2009b. Cyclicbond behaviour of plain bars. Part II: Analytical investigation.Construction and Building Materials, 23(12), 3512-3522.− Verderame G.M., Iervolino I., Ricci P,. 2009c. Report on the damages onbuildings following the seismic event of 6th of April 2009 time 1.32(UTC) – L’Aquila M=5.8, V1.20. http://www.reluis.it/− Verderame G.M., Ricci P., Manfredi G., Cosenza E., 2010. Ultimatechord rotation of RC columns with smooth bars: some considerationsabout EC8 prescriptions. Bulletin of Earthquake Engineering. DOI:10.1007/s10518-010-9190-x− Yalcin C., Kaya O., Sinangil M., 2008. Seismic retrofitting of R/Ccolumns having plain rebars using CFRP sheets for improved strengthand ductility. Construction and Building Materials, 22(3), 295-307.− Zhu L., Elwood K.J., Haukaas T., 2007. Classification and seismic safetyevaluation of existing reinforced concrete columns. ASCE Journal ofStructural Engineering, 133(9), 1316-1330.

136 Chapter II – Seismic behaviour of existing reinforced concrete buildings

Chapter III – Influence of infills on seismic behaviour of reinforced concrete buildings 137Chapter IIIInfluence of infills on seismic behaviour ofreinforced concrete buildings3.1 INTRODUCTIONInfill walls are usually employed in reinforced concrete buildings forpartition use and for thermal/acoustic insulation. Hence, they are considered asnon-structural elements; nevertheless, post-earthquake damage observation,experimental and numerical research have shown that their influence on seismicbehaviour of RC buildings can be not negligible at all. Modern seismic codes(e.g. FEMA 356, 2000; CEN, 2004a; DM 16/1/1996; DM 14/1/2008) prescribeto account for the possible influence of infills on seismic behaviour of RCframes, both at local and global level. Even though the awareness about thisissue in earthquake engineering is not very recent, it is likely to state thatpractically no existing RC building was designed accounting for the presence ofthese elements.Generally speaking, infill walls can provide a considerable contribution to aRC structure in terms of strength and stiffness. However, their post-peakresponse is usually quite brittle. Moreover, many uncertainties affect theevaluation of their behaviour; the first (and obvious) reason is that this kind ofelements are not designed to have a specific behaviour under seismic action.Different collapse modes are possible, both in-plane and out-of-plane. Also,

138 Chapter III – Influence of infills on seismic behaviour of reinforced concrete buildingsmany differences in materials and constructive methods are observed.The interaction between infill panels and RC structural elements underseismic action develops at global level, leading to an increase in lateral stiffnessand base shear capacity, but also at local level, potentially leading to brittlefailure mechanisms in surrounding elements such as columns or beam-columnjoints.It is not easy to determine whether infill influence on seismic behaviour ofRC buildings is beneficial or not, on the whole. Probably, the best syntheticdescription of this issue can be drawn from the conclusions reported in (Dolšekand Fajfar, 2001): the infill walls can have a beneficial effect on the structuralresponse, provided that they are placed regularly throughout the structure, andthat they do not cause shear failures of columns.In this Chapter, main issues about the influence of infills on seismicbehaviour of RC buildings are discussed. To this end, the behaviour of an infillpanel and its local interaction with the surrounding RC members are discussedfirst (Section 3.2). Hence, the influence of infills on global behaviour of RCstructures is illustrated, also through experimental results from literature(Section 3.3). Finally, an analytical study on the influence of infills on period ofvibration of RC buildings is presented (Section 3.4).3.2 BEHAVIOUR OF RC FRAMES WITH MASONRY INFILLSFundamental issues about the behaviour of RC frames with masonry infillsare reported herein. Very extensive and comprehensive reviews can be found in(Crisafulli, 1997; Shing and Mehrabi, 2002).The in-plane lateral response of an infill panel can be described through thetypical behaviour shown by experimental tests on one bay-one storey infilledRC frames (e.g., Stylianidis, 1985; Pires, 1990; Mehrabi et al., 1996; Mosalamet al., 1997; Colangelo, 2003).

Chapter III – Influence of infills on seismic behaviour of reinforced concrete buildings 139(a)(b)(c)Figure 3.2.1. Cyclic lateral load-displacement response of “weak” (a) or “strong” (b) infilledRC frames; Monotonic lateral load-displacement response of bare, “weak” infilled or “strong”infilled RC frames (c) (Mehrabi et al., 1996)First, the response of the infilled RC frame is influenced, obviously, by thematerial characteristics of the infill panel (see Figure 3.2.1). Thesecharacteristics are influenced both by mortar and masonry unit properties;nevertheless, when evaluating the behaviour of an infilled RC frame thematerial mechanical characteristics are usually referred to the equivalenthomogeneous material, and are expressed through different parameters such asthe Young’s elastic modulus, the shear elastic modulus, the compressivestrength or the shear cracking stress. These parameters are usually determinedfrom vertical or diagonal (i.e., with different angles between the bed joint

140 Chapter III – Influence of infills on seismic behaviour of reinforced concrete buildingsdirection and the applied load) tests on masonry specimens. However, materialtypes and constructive methods can vary greatly in infill panels. Hence, highuncertainties and dispersion affect the determination of these characteristicswhen they have to be evaluated in order to model the influence of infill panelson structural behaviour (see Section 3.2.4).Behaviour of an infilled RC frame is also strongly influenced by theinteraction between the masonry panel and the surrounding RC structure, bothin terms of stiffness and strength.Generally, some distinct phases in the response of an infilled frame can bedistinguished, focusing the attention on the monotonic envelope of a typicallateral force-displacement curve.In a first phase, for very low values of lateral displacement, the response ofthe infilled frame strictly depends on interface conditions between the panel andthe surrounding elements. In non-integral infilled frames, due to shrinkage ofthe mortar or to constructive problems, there is a lack of contact between thetwo elements, thus leading to high reduction in the initial stiffness (Crisafulli,1997). On the contrary, in integral infilled frames the initial response is givenby a monolithic behaviour of the whole composite system, ensured by bondcapacities at the interface between the panel and the frame (see Figure 3.2.2).Figure 3.2.2. Force-displacement response of integral and non-integral infilled frames(Crisafulli, 1997)

Chapter III – Influence of infills on seismic behaviour of reinforced concrete buildings 141As far as integral infilled frames are concerned, with increase in lateral loaddifferences in deformational characteristics between the panel and the RCframe cause cracking and separation at the interface between the two materials,leading to a first stiffness decrease in the force-displacement response. Thisseparation occurs for variable load levels, depending also on the interfaceconditions; however, it is expected to take place for very low drift values.Afterwards, an increase in the stress state narrowed in the opposite compressionangles and along the diagonal of the panel takes place, together with a diagonalcracking; contact areas between the frame and the panel further decrease (seeFigure 3.2.3).(a)(b)Figure 3.2.3. Normal and shear stresses acting on a loaded corner (a); increase in the stress statealong the diagonal of the panel (b) (Crisafulli, 1997)As the lateral load further increases, cracking and damage in the panelgradually increase up to the attainment of the maximum lateral strength of theinfilled frame. This mechanism is usually referred to as “truss mechanism”, dueto the clear analogy between the diagonal of the panel, along whichcompression stresses concentrates, and a compressed diagonal truss. Theinteraction between the compressed truss and the surrounding RC membersdevelops in corner contact areas whose dimensions are mainly influenced by theratio between the stiffness of the panel and the stiffness of the RC frame. Thisinteraction strictly influences the distribution of forces in RC members (see

142 Chapter III – Influence of infills on seismic behaviour of reinforced concrete buildingsFigure 3.2.4). Shear and axial force variation in columns are of particularimportance.Figure 3.2.4. Bending moment, shear and axial force diagrams for a typical infilled RC frame(Crisafulli, 1997)After the peak, the experimental curve shows a different softening behaviourdepending on the type of the panel failure and on the post-elastic response ofthe frame.Nevertheless, the above described truss mechanism – which initiallydevelops after the separation between the infill panel and the RC frame – mayor may not evolve into a primary load-resistance mechanism, mainly dependingon the interaction between the panel and the surrounding RC frame. Differentfailure modes may take place, different from diagonal cracking of the panel,such as corner crushing or horizontal shear sliding. The failure mechanism ofthe infill panel may also influence the failure mechanism of the surrounding RCframe, for instance, by determining the location of plastic hinge in columns (seeFigure 3.2.5).

Chapter III – Influence of infills on seismic behaviour of reinforced concrete buildings 143Figure 3.2.5. Failure mechanisms of infilled frames (Shing and Mehrabi, 2002)

144 Chapter III – Influence of infills on seismic behaviour of reinforced concrete buildings3.2.1. Influence of openingsPresence of openings is another issue which should be carefully consideredwhen evaluating the behaviour of an infilled RC frame, although it is not easyat all to be modelled. Numerical (e.g., Mosalam, 1996; Asteris, 2003) andexperimental (e.g., Mosalam et al., 1997; Kakaletsis and Karayannis, 2009)studies were carried out to investigate the influence of openings on the lateralforce-displacement behaviour of an infilled RC frame. A general reduction instiffness and strength is observed, mainly depending on the opening percentage(expressed as the ratio between the opening area and the total panel area), butalso on the opening position (Asteris, 2003). However, the evaluation of thisreduction can differ greatly from one model to another. Presence of openingscan also influence the developments of stress flows in the panel, leading to theformation of resistance mechanism different from the standard single truss (seeFigure 3.2.1.1).Figure 3.2.1.1. Single- (a) and multi- (b) diagonal truss formation (Mondal and Jain, 2008)

Chapter III – Influence of infills on seismic behaviour of reinforced concrete buildings 1453.2.2. Brittle failure in RC members due to local interaction with infillsThe local interaction between the panel and the adjacent beam and columnelements consists in a normal and shear stress transfer – developed in a contactarea (see Figure 3.2.3) whose dimensions are influenced by several factors –leading to a severe force variation in RC members (see Figure 3.2.4). Asalready highlighted, this interaction can lead to brittle failure mechanisms, bothin columns and in beam-column joints. In particular, the resulting shear forceacting on a column may be significantly larger than the expected value resultingfrom section flexural strength, given by equilibrium of the element. Hence,even a column expected to have a ductile behaviour (see Section 2.3) mayexperience a shear failure. Moreover, a detrimental decrease in axial load takesplace. It is to be noted that the column shear span to be considered whenevaluating the behaviour resulting from interaction with an infill panel issignificantly lower than the column height, thus leading to a squat-elementbehaviour.Figure 3.2.2.1. Shear failure in a column adjacent to partial infilling panels (see Section 2.5.4)

146 Chapter III – Influence of infills on seismic behaviour of reinforced concrete buildingsMoreover, a shear failure mechanism can take place in the squat columnresulting from the interaction with a partial infill (see Figure 3.2.2.1).(a)(b)Figure 3.2.2.2. Diagonal cracking failure in a beam-column joint due to shear forces and“opening” moment due to interaction with the infill panel (Crisafulli, 1997) (a); observed failureof an unreinforced external joint after the 2009 L’Aquila earthquake (see Section 2.5.4) (b)In beam-column joints, the interaction with the infill panel can lead todiagonal cracking failure of the joint panel even before cracking of the adjacentbeam section (see Figure 3.2.2.2). Sliding shear failure may also take place atthe interface between column element and joint panel (Verderame et al.,2010a).It is to be noted that all of these brittle failure mechanisms may be avoided,or at least significantly limited, adopting the seismic details prescribed bymodern seismic codes according to Capacity Design principles, such astransverse reinforcement (i) in beam-column joints and (ii) at the ends of thecolumns (with proper spacing). Although these prescriptions are aimed (i) atavoiding joint failure due to flexural forces from beams and columns and (ii) atproviding higher ductility in critical (plastic hinge) region, respectively, theycan also avoid brittle failure mechanisms due to forces from local interaction

Chapter III – Influence of infills on seismic behaviour of reinforced concrete buildings 147with infill panels.However, modern seismic code also provide specific prescriptions aimed atavoiding brittle failure mechanisms due to interaction between RC columns andinfill panels. For instance, EC8-part I (CEN, 2004a), at Section 5.9, prescribesto consider the shear force acting on the column as the smaller of (i) thehorizontal component of the strut force of the infill, assumed to be equal to thehorizontal shear strength of the panel, and (ii) the shear force determinedaccording to the Capacity Design rule – that is, on the basis of the equilibriumof the column under end moment resistances – assuming that the plastic hingesdevelop at the two ends of the contact length, which is assumed to be equal tothe full vertical width of the diagonal strut of the infill.Moreover, if the height of the infill is smaller than the clear length of theadjacent columns, the same code prescribes to consider the entire length of thecolumns as critical region, thus providing a proper amount of transversereinforcement, and to assume that the plastic hinges develop at the two ends ofthe length of the column not in contact with the infill when evaluating the shearforce from the equilibrium of the column under moment resistances (see Figure3.2.2.3).Figure 3.2.2.3. Partial masonry infill in concrete frame (Paulay and Priestley, 1992)

148 Chapter III – Influence of infills on seismic behaviour of reinforced concrete buildings3.2.3. Out-of-plane behaviourSo far, in-plane behaviour of infill panels has been described, since itproduces relevant interaction mechanisms with surrounding RC elements;nevertheless, out-of-plane failure mechanisms are of importance, too, since theysignificantly influence the own damage vulnerability of infill elements (seeFigure 3.2.3.1).Out-of-plane resistance is mainly due to the formation of an archingmechanism, which is highly influenced by panel slenderness (Shing andMehrabi, 2002). Moreover, experimental tests showed that the interactionbetween in-plane and out-of-plane resistance has no significant influence(Flanagan and Bennett, 1999).(a)(b)Figure 3.2.3.1. In-plane and out-of-plane forces acting on an infill panel (Crisafulli, 1997) (a);observed out-of-plane failure of an external infill layer after the 2009 L’Aquila earthquake (b)3.2.4. Models for the analysis of infilled RC framesModels reproducing the in-plane lateral force-displacement behaviour ofinfill panels are used to evaluate the influence of these elements on structuralresponse. They can be divided in two categories: micro-models and macromodels.

Chapter III – Influence of infills on seismic behaviour of reinforced concrete buildings 149Micro-models are essentially based on Finite Element (FE) method. Theinfill panel is discretized in a number of sub-elements, representing anequivalent homogeneous material or a two-phase (mortar and masonry units)material. Contact element are also employed to model the boundary interactionbetween infill panel and reinforced concrete. By means of these models, localeffects such as cracking, crushing and contact interaction can be evaluated. FEanalyses are usually employed to investigate numerically the influence ofdifferent parameters (e.g., presence of openings) on the response of singleinfilled frames with a relatively low number of elements (Mosalam, 1996;Asteris, 2003).Nevertheless, the computational effort and the refined modelling required bythis approach do not fit the needs of a structural analysis aimed at evaluatingthe global behaviour of a RC building with infill walls. To this aim, macromodelsare employed. Most of them are based on the equivalent strut concept,due to the mechanical behaviour usually shown by an infill panel after theseparation from the surrounding RC frame, as already illustrated. Equivalentstrut concept was first introduced by Polyakov (1956); first models based onthis concept were aimed at evaluating the increase in the stiffness of a framedue to the presence of a masonry infill panel by experimentally calibrating thewidth of the equivalent strut, which was usually assumed to have the samethickness and the same compressive elastic modulus of the panel (e.g., Holmes,1961; Stafford Smith, 1966; Mainstone, 1971).However, equivalent strut models allow to simulate the lateral forcedisplacementbehaviour of an infilled frame in a wide range of loading, bymeans of an appropriate characterization of the strut force-displacementrelationship (usually implicitly referring to a diagonal cracking failuremechanisms). Several models were proposed, providing not only the monotonicenvelop of the strut force-displacement relationship, but also the rulesdescribing the hysteretic behaviour.

150 Chapter III – Influence of infills on seismic behaviour of reinforced concrete buildingsFigure 3.2.4.1. Single-strut model for infilled frames (Crisafulli, 1997)Once the strut force-displacement relationship has been determined, it isassigned to diagonal truss elements (carrying load in compression) thatrepresent the infill panels in the numerical structural model. The most simpleway to model an infill panel by means of an equivalent strut is the use of asingle-strut model (see Figure 3.2.4.1). This approach allows to account for theaxial force variation in RC columns due to the interaction with the adjacentpanel.Nevertheless, a single-strut model is not able to fully capture the localinteraction between the panel and the adjacent RC elements, leading, forinstance, to an increase in shear demand in columns. To this aim, multi-strutmodels were proposed, where the diagonal elements representing the infillpanel (i) connect points different from the opposite corners, thus modelling theactual extension of the contact area, and (ii) are placed not only concentrically(i.e., parallel to the diagonal of the panel) but also eccentrically, thus effectivelyrepresenting the force demand in adjacent beams and columns (FEMA 356,2000).In spite of a not very higher computational and modelling effort, thesemodels allow to account for the influence of infills on the seismic behaviour ofinfilled RC structures in a quite more realistic way, not only at local but also atglobal level.

Chapter III – Influence of infills on seismic behaviour of reinforced concrete buildings 151In the following, main macro-models for the evaluation of behaviour ofinfilled RC frames are presented. The adequacy of different models to predictthe response of an infilled frame – depending, for instance, on the stage ofbehaviour and the failure mechanism – is discussed.Klingner and Bertero (1976)In (Klingner and Bertero, 1976), a simple single-strut model is proposed (seeFigure 3.2.4.2) based on experimental tests on 1/3 scale RC frames infilled withreinforced masonry units. However, in authors’ opinion, some of the results areapplicable to other panel materials as well.In this model, the monotonic envelop is represented by a linear elasticbranch up to the maximum strength followed by an exponential degradingcurve where the strength is proportional to e γv , where v is the axial deformationin the strut (compression is negative) and γ is a parameter expressing therapidity in strength deterioration; a tensile force different from zero can beconsidered in tension, too.In cyclic field, no degradation of the skeleton curve is modelled. Theunloading stiffness is constant, too, and equal to the elastic stiffness. Adegradation of the reloading stiffness is modelled by assuming that the forcedisplacementreloading joints the skeleton curve for a displacement equal to themaximum displacement previously attained, in compression or in tension.

152 Chapter III – Influence of infills on seismic behaviour of reinforced concrete buildingsFigure 3.2.4.2. Equivalent strut model proposed in (Klingner and Bertero, 1976)Panagiotakos and Fardis (1996)In the infill model proposed by Panagiotakos and Fardis (Panagiotakos andFardis, 1996; Fardis, 1997) the monotonic envelope of the lateral forcedisplacementcurve is given by four branches:- the first branch corresponds to the linear elastic behaviour up to the firstcracking, and the stiffness is given byKG Aw wel= (3.2.4.1)hwwhere A w is the cross-sectional area of the infill panel, G w is the elasticshear modulus of the infill material and h w is the clear height of theinfill panel. According to the authors, this assumption gives the bestagreement with experimental initial stiffness values reported byStylianidis (1985) and Pires (1990).The shear cracking strength is given byF= τ A(3.2.4.2)cr cr wwhere τ cr is the shear cracking stress;

Chapter III – Influence of infills on seismic behaviour of reinforced concrete buildings 153- the second branch follows the first cracking, up to the point ofmaximum strength. The maximum strength is given byFmax= 1.30⋅ F(3.2.4.3)crand the corresponding displacement is evaluated assuming that thesecant stiffness up to this point is given by Mainstone’s formula(Mainstone, 1971), that is, assuming an equivalent strut width given by:( ) 0.4−b = 0.175 λ h d(3.2.4.4)w h w wwhere d w is the clear diagonal length of the infill panel and λ h is thewell-known coefficient accounting for the ratio between stiffness ofmasonry panel and RC frame (Stafford Smith, 1966; Stafford Smith andCarter, 1969), given by:E t sin 2θw wλh= 4(3.2.4.5)4EcIphwwhere E w is the Young’s elastic modulus of the infill material, t w is thethickness infill panel, θ is the slope of diagonal of infill to horizontaland E c I p is the flexural stiffness of RC columns adjacent to the infillpanel.Similar to initial elastic stiffness, this assumption is based on thecomparison with experimental secant-to-maximum stiffness valuesreported in Stylianidis (1985) and Pires (1990).The authors also say that a representative value for the post-crackingtangent stiffness could be Kpost− cracking= 0.03⋅ Kel(Panagiotakos andFardis, 1996);- the third branch is the post-capping degrading branch, up to the residualstrength. Its stiffness depends on the elastic stiffness through theparameter α:Ksoft= −α K(3.2.4.6)el

154 Chapter III – Influence of infills on seismic behaviour of reinforced concrete buildingsthe value of this parameter has to be arbitrarily assumed. However, theauthors give some indication (Panagiotakos and Fardis, 1996): the rangeof values for a should be between 0.005 and 0.1, although a value of 0.1is unrealistically high (very brittle infill), while a value of 0.01 may bemore realistic yet still conservative (well constructed infill);- the fourth branch is the horizontal branch corresponding to the residualstrength. This strength is given byFres= β F(3.2.4.7)maxwith β between 0.05 and 0.1.In cyclic field, a degradation of the strength envelope (depending oncumulated displacement) and of unloading and reloading stiffness is modelled,through different experimentally-calibrated parameters, allowing to model thepinching effect too.Figure 3.2.4.3. Lateral force-displacement relationship of an infill panel, as proposed in (Fardis,1997)Authors provide a lateral force-displacement relationship for the infill panel(see Figure 3.2.4.3) that may be employed in infill modelling through theequivalent strut concept, by simply projecting this relationship on the axis ofthe inclined strut.

Chapter III – Influence of infills on seismic behaviour of reinforced concrete buildings 155However, it is to be noted that in authors’ opinion (Fardis, 1997) it is notphysically appealing to adopt an equivalent strut approach for the calculation ofthe stiffness before cracking. At this stage, that is, for very low values of thelateral drift, the response of the infilled frame is not affected by non-linearitydue to the separation at the interface between the masonry panel and thesurrounding frame, which has not occurred yet. The behaviour of the infilledframe can be still considered as monolithic (Fiorato, 1970), and no trussmechanism has taken place yet. Hence, for instance, no significant variation ofthe axial load in adjacent RC columns (given by the presence of an equivalentdiagonal strut) should be modelled.As a matter of fact, the simple expression assumed in this model for theevaluation of the elastic stiffness is based on the assumption that, under thelateral load, the panel deformation follows a pure shear behaviour.Crisafulli (1997)In (Crisafulli, 1997), two strut models with different degree of refinementare proposed.A single strut model is proposed first, suitable for the evaluation of theglobal response of an infilled structure. In this model the strut resistance alsodepends on the expected failure mode of the panel. The hysteretic behaviour ismodelled through different parameters influencing, for instance, the slope ofunloading or reloading curves.Hence, a more refined multi-strut model is proposed, in order to achieve abetter representation of the effect of the masonry panel on the surroundingframe, depending on the type of failure. When a diagonal tension cracking isexpected (usually followed by the compressive failure of the diagonal strut), seeFigure 3.2.4.4a, a model with three concentric struts is proposed.

156 Chapter III – Influence of infills on seismic behaviour of reinforced concrete buildings(a)(b)(c)(d)Figure 3.2.4.4. Failure modes and corresponding multi-strut models: diagonal tension cracking(a), corner crushing (b), stepped shear sliding (c) and horizontal shear sliding (d) (Crisafulli,1997)

Chapter III – Influence of infills on seismic behaviour of reinforced concrete buildings 157In this model, the distance h z is evaluated as z/2, where the contact length z,in turn, is evaluated according to (Stafford Smith 1966; Stafford Smith andCarter, 1969):πz = (3.2.4.8)2 ⋅λhIf a corner crushing is expected, see Figure 3.2.4.4b, the author proposes toadopt a model where the central strut is divided into two parts with differentarea, in order to consider approximately the increase of axial stresses occurringin the corners of the panels. If a shear failure of the masonry panel by steppeddebonding of the mortar joint is expected, see Figure 3.2.4.4c, a model isproposed accounting separately for the compressive and shear behaviour ofmasonry using a double truss mechanism and a shear spring in each direction.In this case h z is between z/2 and z/3. If a horizontal sliding shear failure isexpected the same model can be adopted modifying h z in h/2, see Figure3.2.4.4d.Of course, the definition of further parameters, compared with the previouslyillustrated single-strut model, is needed for the application of this kind ofmodels.Chrysostomou et al., (2002)Chrysostomou et al. (2002) propose a multi-strut model with threeconcentric struts per direction. The proposed force-displacement relationshipdepends on parameters that have physical meaning and can be adapted toexperimental data. The effects of openings, lack of fit and interface conditionscan also be modelled by assigning proper values to the model parameters. Incyclic field, strength and stiffness degradation is modelled.The position of the off-diagonal struts depends on the contact length, whichis given as a function of parameter α (see Figure 3.2.4.5). Actually, accordingto authors, contact length should not have a unique and constant value duringthe analysis. Hence, the chosen value should best represent the final position of

158 Chapter III – Influence of infills on seismic behaviour of reinforced concrete buildingsplastic hinge formation in RC members due to interaction with the infill panel.Figure 3.2.4.5. Six-strut idealization of infill walls (Chrysostomou et al., 2002)Lateral force-displacement relationships and stiffness for infill panel areprovided first. Hence, axial force-displacement relationships and stiffness forthe central strut and for the off-diagonal struts are evaluated. Obviously, thesum of the forces and stiffnesses of the three struts adds to the force andstiffness of the panel.The definition of axial force-displacement relationships and stiffness for thecentral strut is aimed at reproducing the faster deterioration of the centraldiagonal part of the panel, either due to corner crushing or due to tensioncracking along the diagonal; following the deterioration of the compressiondiagonal, more load is carried by the off-diagonal part of the panel. Therefore,parameters are defined that influence the force and stiffness distributionbetween the central and lateral struts, thus allowing to model, for example, thecrushing of the central strut when the peak load of the infill panel is reached,which is usually the case for non-integral infilled frames (Liauw and Kwan,1984).Hence, axial force-displacement relationships and stiffness for the offdiagonalstruts are evaluated. To this aim, the principle of virtual displacementsis applied to evaluate the distribution of forces between the central strut and theoff-struts, for each displacement value

Chapter III – Influence of infills on seismic behaviour of reinforced concrete buildings 1593.3 EXPERIMENTAL BEHAVIOUR OF INFILLED RCSTRUCTURESGlobal structural behaviour of a RC building is influenced by the presence ofinfill walls in different ways: roughly, an increase in lateral stiffness and in baseshear capacity are observed. It is to be noted that, when describing the influenceof infills on the lateral force-displacement global response, the influence of theabove illustrated shear failure mechanisms in columns or beam-column jointswill be neglected, because considered as the result of a local interaction.The increase in lateral stiffness leads to a modification of the dynamicproperties, resulting in a lower period of vibration (see Section 3.4).The increase in lateral strength should reasonably have a beneficial effect onseismic capacity, but the brittle post-peak behaviour generally shown by infillpanels is reflected in a brittle global lateral force-displacement response. Ageneral reduction in global displacement demand is observed, even though thisdemand tends to concentrate at the bottom of the structure.These considerations are valid if the infill panels are regularly placedthroughout the structure, in plan and in elevation. Otherwise, the presence ofinfill walls may lead to a detrimental localization of inelastic displacementdemand (see Figures 3.3.1, 3.3.2), resulting in less ductile (less energydissipating)and potentially catastrophic collapse mechanisms.This is reflected by modern seismic code (e.g., EC8-part I (CEN, 2004a) atSection 4.3.6), which prescribe to avoid strong irregularities in distribution ofinfills, both in plan and elevation, or – if such irregularities are present – toaccount for them by conventionally increasing the seismic demand (e.g.,increasing the seismic action effects in the vertical elements of the storey wherea drastic reduction of infills is present, compared to the others).Moreover, the own damage vulnerability of infill elements is also consideredwhen assessing seismic safety. To this aim, for Damage Limitation Limit Statethe interstorey drift ratio is limited to 0.005 if “non-structural elements of brittlematerials attached to the structure” are present.However, it is worth noting that the influence of infills on structural

160 Chapter III – Influence of infills on seismic behaviour of reinforced concrete buildingsbehaviour cannot be analyzed without considering the seismic behaviour thatthe corresponding bare structure would show, that is, the design procedure.Figure 3.3.1. Torsional collapse mechanism due to an irregular infill distribution in plan (Bragaand Petrangeli, 1976)

Chapter III – Influence of infills on seismic behaviour of reinforced concrete buildings 161Figure 3.3.2. Soft-storey collapse mechanism due to an irregular infill distribution in elevation(Braga and Petrangeli, 1976)Literature does not offer many experimental results showing the behaviourof RC structures with infill panels. In this Section, main studies from literatureare reported, illustrating the influence of infills on stiffness, strength andcollapse mechanism of RC structures.

162 Chapter III – Influence of infills on seismic behaviour of reinforced concrete buildingsNegro and Verzeletti (1996)Negro and Verzeletti (1996) carried out pseudo-dynamic tests on a full-scalefour-storey RC building (see Figure 3.3.3) designed according to Eurocodes 2and 8, in ductility class High – complying the weak beam/strong columnprinciple – for a PGA equal to 0.3g. Three tests were carried out, withoutinfills, with uniformly distributed infills and with infills in all storey but thefirst, respectively.(a)(b)Figure 3.3.3. Layout of the tested frame (Negro and Verzeletti, 1996)An artificially generated earthquake derived from the 1976 Friuli earthquakewas employed in the tests, with nominal acceleration 50% larger than the valueadopted in design (PGA=1.5x0.3=0.45g).During the first test carried on the bare frame the structure performed asexpected, respecting the weak beam/strong column mechanism. The damagewas limited and uniformly distributed. A decrease in frequency of vibrationbefore and after the test was observed (from 1.78 to 0.82 Hz).

Chapter III – Influence of infills on seismic behaviour of reinforced concrete buildings 163Figure 3.3.4. Uniformly infilled frame (Negro and Verzeletti, 1996)After the first test, infill walls were uniformly placed throughout thestructure (see Figure 3.3.4). The fundamental frequency changed to 3.34 Hz.During the test, the masonry panels at the first and second storeys werecompletely destroyed, while the panels at the third storey suffered extensivedamage, and the ones at the upper storey remained almost intact, thushighlighting a non-uniform interstorey displacement demand distribution.After the second test, the masonry panels were demolished and replacedwith new ones, leaving the first storey bare (see Figure 3.3.5). The fundamentalfrequency was 1.6 Hz. The test resulted in soft-storey mechanism, characterizedby a concentration of drift at the first storey, with some damage suffered by thepanels of the second storey only.

164 Chapter III – Influence of infills on seismic behaviour of reinforced concrete buildingsFigure 3.3.5. Soft-storey infilled frame (Negro and Verzeletti, 1996)If maximum base share values from the three tests are compared, it isobserved that the maximum base shear for the soft-storey structure is onlyslightly larger than that of the bare frame, while the maximum base shear forthe uniformly infilled frame was almost 50% than that of the bare frame, thushighlighting the noticeable contribution of infills to the lateral strength of thestructure.The distribution of displacement demand along the height of the structure inthe three tests can be observed from the interstorey drift profiles (see Figure3.3.6).If compared with the bare structure, presence of uniformly distributed infillsleads to a decrease in displacement demand, but also to a concentration of thisdemand in lower storeys. The worst behaviour is shown by the soft-storeystructure, where the highest displacement demand at the first storey and themost irregular demand distribution are observed, compared with other tests.

Chapter III – Influence of infills on seismic behaviour of reinforced concrete buildings 165Figure 3.3.6. Maximum interstorey drift profiles (Negro and Verzeletti, 1996)Pinto et al. (2002)Pseudo-dynamic tests were carried out within the ICONS project on planefour-storey three-bay RC frames, with and without infills. The frames wererepresentative of existing European RC buildings; they were designed for abase shear coefficient equal to 0.08, with no compliance with Capacity Designprinciples. In the infilled frame, masonry panels were uniformly distributedalong the height of the structure and openings were present in two of the threebays (see Figure 3.3.7).

166 Chapter III – Influence of infills on seismic behaviour of reinforced concrete buildingsFigure 3.3.7. Plan and elevation view of the infilled RC frame

Chapter III – Influence of infills on seismic behaviour of reinforced concrete buildings 167100010004 th storey800[kN]4 th storey800[kN]600600400400200200[mm]0-80 -60 -40 -20 0 20 40 60 80-200[mm]0-80 -60 -40 -20 0 20 40 60 80-200-400-400-600-600-800-800-1000-1000100010003 rd storey800[kN]3 rd storey800[kN]600600400400200200[mm]0-80 -60 -40 -20 0 20 40 60 80-200[mm]0-80 -60 -40 -20 0 20 40 60 80-200-400-400-600-600-800-800-1000-1000100010002 nd storey800[kN]2 nd storey800[kN]600600400400200200[mm]0-80 -60 -40 -20 0 20 40 60 80-200[mm]0-80 -60 -40 -20 0 20 40 60 80-200-400-400-600-600-800-800-1000-1000100010001 st storey800[kN]1 st storey800[kN]600600400400200200[mm]0-80 -60 -40 -20 0 20 40 60 80-200[mm]0-80 -60 -40 -20 0 20 40 60 80-200-400-400-600-600-800-800-1000(a)(b)Figure 3.3.8. Comparison between interstorey displacement-shear experimental relationships forbare (a) and infilled (b) RC frames-1000

168 Chapter III – Influence of infills on seismic behaviour of reinforced concrete buildingsInput signals for pseudo-dynamic tests were artificial accelerogramscharacterized by PGA values corresponding to different return periods.In Figure 3.3.8 interstorey displacement-shear experimental relationships forbare and infilled frames for the same seismic intensity (given by a PGAcorresponding to a 975 years return period) are reported.The bare frame collapsed under a column-sway mechanism at the thirdstorey, where the maximum displacement demand can be observed.The infilled frame showed a noticeable increase in stiffness and strength,compared with the bare one, resulting in a severe decrease in displacementdemand, which was higher at lower storeys.Dolce et al. (2005)Dolce et al. (2005) carried out shake table tests on 1/3.3-scale plane RCframes (see Figure 3.3.9), designed according to the European seismic code(EC8–part I) for low-ductility and 0.15 g PGA seismic intensity, in order tostudy their behaviour with or without different kinds of energy dissipating andre-centring bracing systems. Two unretrofitted specimens were tested: a bareframe and a masonry infilled frame.Figure 3.3.9. Geometrical characteristic of 1/3.3 scale RC structural models (Dolce et al., 2005)

Chapter III – Influence of infills on seismic behaviour of reinforced concrete buildings 169Both models were subjected to two alternate series of tests, namely seismictests and random tests. Seismic tests were aimed at evaluating the structuralresponse under seismic motion, represented by an artificially generatedaccelerogram of increasing intensity (PGA). Random tests were aimed atevaluating the frequency of vibration. Hence, both the equivalent (during theseismic excitation) and the fundamental (after the seismic excitation, under lowintensity) frequencies of vibration were evaluated. The latter providesinformation about the damage suffered by the structure during the seismicevent, but the former is of importance for displacement-based methods.Structural collapse occurred for 0.48 and 0.9g PGA for bare and infilledmodel, respectively, thus highlighting the beneficial role of infill elements, ifuniformly distributed and accurately realized.Figure 3.3.10. Frequency of vibration due to seismic tests with increasing intensity for bareframe and masonry infilled frame (Dolce et al., 2005)

170 Chapter III – Influence of infills on seismic behaviour of reinforced concrete buildingsFigure 3.3.10 shows the changes in the frequency of vibration due to seismictests with increasing intensity for both models. Comparing the frequencies ofvibration of the two models the stiffness increase due to infill presence isclearly shown by an initial fundamental frequency about 2.5 times higher (9.03and 3.65 Hz, respectively). The decrease in frequency of vibration was almostlinear for the bare model, up to collapse. For the infilled model, the decreasewas linear at lower seismic intensities but followed a power law after asignificant damage in infill panels occurred. For both models the gap betweenequivalent and fundamental frequency of vibration tends to increase during thetests, due to the progression of structural and non-structural damage.Figure 3.3.11 shows the profiles of maximum absolute displacements andmaximum interstorey drifts. Comparing the maximum displacement andinterstorey drift demand for each seismic intensity level, two main conclusionscan be drawn:- the roof drift at collapse was greater than 3% for the bare model andabout equal to 2.5% for the infilled model. Hence, the displacementcapacity of the infilled structure was substantially lower;- an evident damage concentration at the first storey, with increasingseismic intensity, was observed. Authors highlighted that thisconcentration is a consequence of the constant resistance of the infilledframe along the height.

Chapter III – Influence of infills on seismic behaviour of reinforced concrete buildings 171Figure 3.3.11. Profiles of maximum absolute displacements and maximum interstorey drifts forbare frame and masonry infilled frame (Dolce et al., 2005)

172 Chapter III – Influence of infills on seismic behaviour of reinforced concrete buildingsShing et al. (2009)Shing et al. (2009) carried out shake-table tests on two 2/3-scale, three-story,two-bay, infilled RC frames (see Figure 3.3.12). One was tested without retrofitmeasures and the other had infill strengthened in the first and second stories.Results from the test on the unreinforced specimen are reported herein.The structure was designed as an exterior frame of a RC building designedfor gravity loads only, according to obsolete code prescriptions. Infills wereuniformly distributed along the height, and in one bay openings were present.(a)(b)Figure 3.3.12. Elevation view of tested frame (a) and shake table test setup (b) (Shing et al.,2009)In the shake-table tests, the specimen was subjected to a sequence of scaledground motion records (Gilroy from the 1989 Loma Prieta earthquake and theNS component of the 1940 El Centro earthquake) , see Figure 3.3.13.Damage was localized at the bottom storey. The weak first storey isolatedthe second storey from severe seismic force. Shear failure developed in themiddle column during the 120% Gilroy, see Figure 3.3.14b. Severe damagewith shear failures developed in the exterior columns occurred when thespecimen was subjected to the 250% El Centro, see Figure 3.3.14d.

Chapter III – Influence of infills on seismic behaviour of reinforced concrete buildings 173Figure 3.3.13. First storey interstorey drift-shear demand for different ground motion intensities(Shing et al., 2009)Figure 3.3.14. First storey damage for different ground motion intensities (Shing et al., 2009)

174 Chapter III – Influence of infills on seismic behaviour of reinforced concrete buildingsPujol and Fick (2010)Pujol and Fick (2010) carried out experimental tests on a full scale threestoreyRC structure designed for gravity loads only. The structure had two baysin the direction of loading and one bay in the opposite direction. Tests were firstcarried out on the bare structures. Hence, brick infill walls were added to thedamaged structure, which was tested again. The load was applied indisplacement control at the top slab. Hence, loads at the other two levels wereadjusted to 2/3 (at the floor of the third storey) and 1/3 (at the floor of thesecond storey) of the load applied at the top level, thus imposing step by step afixed linear shape of the lateral load pattern. Following this procedure,displacement cycles with increasing amplitude were applied to the structure.The bare structure initially had a fundamental period of vibration equal to0.5 s. The test on this structure was stopped at a roof drift of 3%. For a roofdrift equal to 2.8% a punching shear failure took place at the connectionbetween a column and the slab at the second storey, where the largestinterstorey drift demand was observed.Hence, the structure was modified adding unreinforced brick walls. Thefundamental period of vibration of the (partially) infilled structure was equal to0.2 s, thus highlighting the higher stiffness due to the addition of infill walls.Then another experimental test was carried out, imposing displacement cycleswith increasing amplitude. Also in this case the largest interstorey drift demandwas observed at the second storey.Results from both tests are compared in Figure 3.3.15. The increase instrength due to the addition of infill walls is clearly shown. Authors highlightthat this noticeable increase remains effective up to 1.5% of roof drift.An image of the tested structure is reported in Figure 3.3.16.

Chapter III – Influence of infills on seismic behaviour of reinforced concrete buildings 175Figure 3.3.15. Comparison of results from first and second test (Pujol and Fick, 2010)Figure 3.3.16. Tested structure after the second test (Pujol and Fick, 2010)

176 Chapter III – Influence of infills on seismic behaviour of reinforced concrete buildings3.4 ANALYTICAL INVESTIGATION OF ELASTIC PERIOD OFINFILLED RC MRF BUILDINGSIt has been highlighted how the presence of infill walls leads to a higherlateral stiffness of RC buildings, resulting in a modification of dynamicproperties, that is, in a lower period of vibration.In this Section, this issue is investigated from a numerical standpoint, bymeans of modal analyses carried out on 3D numerical RC Moment ResistingFrame (MRF) building models, varying structure morphology (height, surfacearea, ratio between plan dimensions) and infill characteristics. Simplifiedformulas based on regression analysis of obtained numerical data are presentedand discussed. These relationships are also compared with similar literaturenumerical expressions and empirical data from experimental measurements onexisting buildings.The results illustrated in this Section were published in (Ricci et al., 2010).3.4.1. The period of RC buildingsIn an equivalent static approach, the evaluation of seismic forces is based onthe period of vibration of the structure. However, the period of vibration is notan unique and constant characteristic. The stiffness degradation experienced bythe structure during the response to a seismic event causes the “lengthening” ofthe period: as the degree of damage (both structural and non-structural)increases, the period increases too. In order to obtain a realistic estimate ofseismic demand, many authors propose to evaluate the period of vibrationbased on empirical data from existing buildings subjected to earthquakes.Seismic codes often adopt formulas obtained in this way.Moreover, during last years numerical and experimental efforts were madein order to evaluate period-height relationships for RC buildings accounting forthe stiffness contribution of infill walls.In this Section, empirical-based expressions for evaluating the period ofvibration of RC MRF SW buildings are illustrated; moreover, the description ofliterature experimental campaigns and numerical models aimed at the

Chapter III – Influence of infills on seismic behaviour of reinforced concrete buildings 177assessment of dynamic behaviour of RC buildings with infill walls is reported.3.4.1.1 Empirical estimate of period of RC MRF buildingsExpression proposed by Eurocode 8 (CEN, 2004a) and first appeared inATC3-06 (ATC, 1978):T0.75= CtH(3.4.1.1)is derived from Rayleigh’s method, and C t is calibrated in order to achieve thebest fit to experimental data. ATC3-06, based on Gates and Foth’s study(1978), proposed for this coefficient the value 0.025 as a lower limit forevaluating the period of vibration of RC MRF buildings. The evaluation of thisvalue was based on periods computed from motions recorded in 14 buildingsduring the San Fernando earthquake in 1971. The value of C t was subsequentlychanged into 0.030, that is, 0.074 if the height is expressed in metres, verysimilar to the value 0.075 adopted by EC8:0.75T = 0.075H(3.4.1.2)In (Bertero et al., 1988), starting from an accurate analysis of buildingsstudied by Gates and Foth, the authors partially modify their database andpropose to assume C t equal to 0.035, as a lower bound for period of vibration ofthe only structural components of the building, corresponding to the stage whenthe stiffness contribution of non-structural elements can be considered to benegligible due to their damage level.In (Goel and Chopra, 1997a) the authors calibrate numerical values ofcoefficients α and β in the expression:T= α H β(3.4.1.3)based on strong motion accelerograms from 27 RC buildings recorded duringdifferent seismic events. The best agreement with all experimental data, inaverage terms, is given by:0.90T = 0.053H(3.4.1.4)

178 Chapter III – Influence of infills on seismic behaviour of reinforced concrete buildings3.4.1.2 Empirical estimate of period of RC SW buildingsIn RC SW buildings the lateral load resistance is mainly provided by shearwalls. Hence, a significant contribute to the overall lateral stiffness, too, isgiven by walls. The period of vibration of these buildings can be evaluated withgood approximation as the period of an equivalent cantilever (Goel and Chopra,1998). If the only shear deformability is accounted for, this period is equal to:T = 4mHκ ⋅GHAS(3.4.1.5)where m H is the uniformly distributed mass per unit height, κ is a factoraccounting for the shape of the transverse section (equal to 5/6 for a rectangularsection), G is the shear elastic modulus and A S is the area of the transversesection (Goel and Chopra, 1997b). The area A S can be expressed as the productof the thickness t by L x(y) , that is the plan dimension of the equivalent cantileverparallel to the considered direction along which the fundamental period isevaluated:T 4m H Hκ⋅G t ⋅ L LHx(y)= = αx(y)x(y)(3.4.1.6)Different codes adopt this kind of formula, with an experimentally calibratedvalue for α. In (ATC, 1978) it is proposed to assume α equal to 0.05 fordimensions expressed in feet, that is, 0.09 for dimensions in metres. In (Goeland Chopra, 1998) the authors propose the following expression:ρ H HTx(y)= 40= ακ⋅G A Ae,x(y)e,x(y)(3.4.1.7)where ρ is the average mass density, defined as the ratio between the totalbuilding mass and the total building volume, andAeis the equivalent sheararea, defined as the percentage on the total plan area of A e , which accounts forthe presence of several uncoupled shear walls, considering also their flexural

Chapter III – Influence of infills on seismic behaviour of reinforced concrete buildings 179deformability (Goel and Chopra, 1997b). Based on Eq. (3.4.1.7), the authorscarry out a regression analysis on 17 measured period values from 9 RC SWbuildings subjected to seismic excitations. The best agreement with allexperimental data, independent of the peak ground acceleration experienced bythe buildings, is given by:T = 0.0077H(3.4.1.8)AeMoreover, the authors point out the poor correlation between H / D and themeasured period, where D is the plan dimension parallel to the direction alongwhich the period is evaluated.3.4.1.3 Empirical estimate of period of infilled RC buildingsThe above illustrated formulas for estimating the fundamental period of RCbuildings are based on experimental data from USA structures subjected toearthquakes of different intensity. Generally speaking, European RC buildingsare significantly different from USA RC buildings, both in terms of structuralsystem and non-structural elements (such as internal and external infills).During last years, experimental studies were carried out aimed at theassessment of dynamic properties of this type of buildings, especially inMediterranean area. Measurement techniques used in these studies were mainlybased on low amplitude motion, that is, microtremors or ambient noise.Therefore, due to low intensity of the source of excitation, measured periodsrepresent with good approximation the linear dynamic properties of thestructures, since phenomenon of period lengthening – caused by non-linearity inbehaviour of structural and non-structural materials and components (such asinfill walls, too) – should not have occurred during the experimentalmeasurements. Empirical relationships proposed in these studies highlight agood agreement with each other.These relationships provide period values much lower than previouslyillustrated works (e.g. Gates and Foth 1978; Goel and Chopra, 1997a; Goel and

180 Chapter III – Influence of infills on seismic behaviour of reinforced concrete buildingsChopra, 1998; Bertero et al., 1988). Moreover, experimental data show the highinfluence of infill presence on period of vibration (Oliveira and Navarro, 2010).In (Oliveira, 2004) a database is presented, made up of measured periods ofvibration from Portuguese buildings, evaluated by means of microtremors. Themajority of these buildings are located on firm soil types. Among them, theauthors select 130 RC buildings with infill brick walls, obtaining that the bestfit to experimental period data is given byTx= 0.012H and Ty= 0.013H , inlongitudinal and transversal directions respectively. If an interstorey heightequal to 3 meters is assumed, these relationships change into Tx= 0.037N andTy= 0.039N , where N is the total number of storeys.Although on a smaller number of buildings, the same authors also show thatthe absence of infill walls leads to a period of vibration at least double, for thesame height, compared with buildings where infill walls are present.In (Navarro and Oliveira, 2006), based on a subset of 37 RC buildings withinfill walls from the same database, monitored with very sensitive sensors, theauthors evaluate the period of vibration as T = ( 0.043 ± 0.001)N .In (Gallipoli et al., 2010) empirical data for periods of vibration of 244 RCbuildings located in Italy and in Balkan area, evaluated by means of ambientnoise measurements, are presented. The period-height relationship is given byT 0.016H = .In (Oliveira and Navarro, 2010) further expressions proposed by differentauthors for evaluating the fundamental period are presented, based onexperimental data from buildings located in Mediterranean area (France andSpain), having in common a RC structural system with infill wall panels.According to these expressions – also evaluated by means of low amplitudemotion measurement techniques – fundamental period is included, again,between 0.015H and 0.017H .

Chapter III – Influence of infills on seismic behaviour of reinforced concrete buildings 1813.4.1.4 Numerical estimate of period of infilled RC buildingsIn (Crowley and Pinho, 2006) the authors propose period-heightrelationships for RC MRF buildings with infill walls, considering both grossand yield stiffness of RC sections. These equations are obtained as linearregressions of period values evaluated by modelling eleven case-study buildingsdesigned only for vertical loads or according to obsolete seismic codes. Thepresence of infills is accounted for by means of equivalent diagonal struts,according to (Liauw and Kwan, 1984). The presence of openings is taken intoaccount, too, by means of the expressions proposed in (Bertoldi et al., 1994).For uncracked infilled buildings, if a gross stiffness for RC element sections isconsidered, the following expression is obtained:Te= 0.038H(3.4.1.9)For cracked RC buildings, the yield period – evaluated assuming a crackedstiffness for RC element sections – is given by:Ty= 0.055H(3.4.1.10)Masi and Vona (2008), by means of a simulated design procedure, elaboratestructural models of a class of infilled RC buildings. The design procedure isdefined for gravity loads only. The stiffness reduction due to the cracking ofmember sections is evaluated by adopting different values of the effectiveinertia. Infills are represented by equivalent diagonal struts according to(Mainstone, 1974); presence of openings is not taken into account. Thevariability in the distribution of infill elements is considered too. A totalnumber of 648 analyses is performed. For infilled buildings with gross oryielded inertia of RC members, respectively, the period (along the transversaldirection) is given by:Te= 0.050H(3.4.1.11)andTy= 0.055H(3.4.1.12)

182 Chapter III – Influence of infills on seismic behaviour of reinforced concrete buildingsKose (2009), through a sensitivity analysis, finds out that the mainparameters affecting the period of vibration of an infilled RC building,accounting also for the presence of shear walls, are the percentage of shearwalls on the total floor area, the percentage of infill walls on the total panel areaand the number of bays (in order of importance). Amanat and Hoque (2006)also perform a sensitivity analysis on the period of vibration of RC buildingswith infills, concluding that the main parameters affecting the period, besidesthe height, are the number and the length of bays and the amount of infills,while the stiffness of RC members does not have a great influence.3.4.2. Modelling of infill stiffnessBased on the consideration that in integral infilled RC frames, in a firstphase, for very low values of lateral displacement, the initial response is givenby a monolithic behaviour of the whole composite system, ensured by bondcapacities at the interface between the panel and the frame (see Section 3.2), in(Fiorato et al., 1970) the evaluation of the initial stiffness of the infilled frame isbased on the linear elastic response of the equivalent composite cantileverbeam. This response results from the interaction between the two elements, andthe applied lateral load is distributed between them based on the ratio betweentheir stiffness. Authors evaluate the overall displacement assuming that theflexural deformability is due to the monolithic response of the compositesystem, while the shear deformability contribution is only due to the infillpanel. Therefore, the resulting stiffness is given by:K =11 1+GwAw3EI3h hw(3.4.2.1)where A w is the cross-sectional area of the infill panel, G w is the elastic shearmodulus of the infill material, h w is the clear height of the infill panel, E is theelastic Young’s modulus of the frame-panel composite material, I is the

Chapter III – Influence of infills on seismic behaviour of reinforced concrete buildings 183moment of inertia of the total frame-panel cross section and h is the distancefrom top of base beam to mid-height of the first-storey beam. The theoreticalvalue of the initial stiffness evaluated according to Eq. (3.4.2.1) seems to wellapproximate, in the early range of loading, the lateral load-deflection curves ofinfilled frames tested by the authors (Fiorato et al., 1970).The approach proposed in (Fardis, 1997), see Eq. 3.2.4.1 at Section 3.2.4, isquite similar, from a theoretical standpoint. In this case it is assumed that, underthe lateral load, the panel deformation follows a pure shear behaviour, and nointeraction between the panel and the surrounding elements is taken intoaccount. The infill is modelled as a system in parallel with the RC frame.Many other models for the evaluation of the infill stiffness, based on theequivalent strut approach (see Section 3.2.4), are proposed in literature.Holmes (1961) arbitrary proposes to assume this width equal to 1/3 of thediagonal length. In (Mainstone, 1971), the author, based on experimental data,proposes different formulas expressing the width of the equivalent strutcorresponding to secant stiffness at first cracking and ultimate strengthconditions. In particular, the equivalent strut width for the evaluation of thesecant stiffness to the first cracking is given by Eq. 3.2.4.4 at Section 3.2.4.In (Paulay and Priestley, 1992) the authors assume that the width of theequivalent strut is equal to 0.25 times the diagonal length of the panel. Thisvalue is proposed in order to estimate the secant stiffness corresponding to alateral load equal to 50% of the maximum load capacity of the infilled frame,that is, after separation between masonry panel and RC frame has occurred. Asa matter of fact, in authors’ opinion the evaluation of the period in a seismicdemand assessment should be based on the structural stiffness corresponding tothis stage.Liauw and Kwan (1984) build up numerical models of non-integral infilledframes, thus deducing that the width of the equivalent strut has to be expressedas a function ofhwcos θ. Then, based on experimental stiffness values given in(Barua and Mallick, 1977), the authors find out the following expression:

184 Chapter III – Influence of infills on seismic behaviour of reinforced concrete buildingsbw0.95hwcos θ=λhw(3.4.2.2)The experimental data fitted by Eq. (3.4.2.2) are evaluated according to theprocedure proposed in (Stafford Smith, 1967). In this work the author describesa typical load-displacement curve of an infilled frame. In particular, heidentifies two zones: a first one characterized by an irregular behaviour, wherethe stiffness is considered to be unpredictable, and a second one where theresponse is quasi-linear (see Figure 3.4.2.1). First phase is essentially due to theinitial lack of fit between the panel and the frame, while during the secondphase a firm bearing develops between the two elements. Stiffness of theinfilled frame, according to author’s proposal, is evaluated in the latter range ofloading. The considerations reported by the author clearly refer to the behaviourof non-integral infilled frames. The value calculated by means of the abovedescribed procedure can be reasonably considered to be lower than the initialstiffness shown by an integral infilled frame.Figure 3.4.2.1. Schematic representation of load-deflection curves recorded in tests (Baruaand Mallick, 1977)Above described models are compared in Figure 3.4.2.2. A one-bay one-storeyinfilled frame is considered, with (300×300)mm columns and a (300×500)mmbeam, and a (4.00×3.00)m infill; panel thickness is assumed equal to 200 mm.Elastic Young’s modulus of concrete is given equal to E c =30000 MPa. Lateralstiffness of the infilled frame is reported, according to the illustrated formulas,

Chapter III – Influence of infills on seismic behaviour of reinforced concrete buildings 185depending on the shear elastic modulus of the infill G w . The ratio G w /E w isgiven equal to 0.30.Expressions proposed in (Fardis, 1997) and in (Fiorato et al., 1970) clearlyprovide higher stiffness values compared with remaining ones. As a matter offact, the expression given in (Fiorato et al., 1970) is aimed at the assessment ofthe infilled frame stiffness in the earliest range of loading, when cracking of thepanel and separation at the interface between panel and surrounding frame havenot taken place yet. The expression proposed by Fardis (1997), even if in asimplified way, evaluates the infill stiffness in a pre-cracking phase, too.On the contrary, the other described formulas evaluate a secant stiffness value,up to first cracking (Mainstone, 1971) or to 50% of the maximum load (Paulayand Priestley, 1992) conditions, or a not properly initial stiffness value referredto non-integral infilled frames (Liauw and Kwan, 1984).Hence, in this study, in order to evaluate the infill stiffness in a pre-crackingphase, the expression proposed by Fardis (Eq. 3.2.4.1) is adopted.800700600K [kN/mm]F∆Fardis, 1997Fiorato et al., 1970Paulay and Priestley, 1992Liauw and Kwan, 1984Mainstone, 1971500K=F/∆400300200100G w [MPa]0600 800 1000 1200 1400 1600 1800 2000Figure 3.4.2.2. Comparison of infilled frame stiffness according to different literature models

186 Chapter III – Influence of infills on seismic behaviour of reinforced concrete buildings3.4.3. Numerical estimate of period of infilled RC MRF buildingsA numerical investigation of period of vibration of infilled RC MRFbuildings is carried out through a parametric study on a class of buildings. Eachbuilding is generated according to a series of geometrical and mechanicalparameters. The considered buildings are designed for gravity loads only; thistypology represents a wide part of the existing RC building stock. As a matterof fact, the 43% of the Italian territory is classified as exposed to seismic riskand, within this portion, only the 40% of structures have been designedaccording to seismic guidelines (De Marco et al., 2000). The structural model isdefined by means of a simulated design procedure, carried out according tocode prescriptions and design practices at the age of construction, that is,between 1950s and 1970s (RDL 2229, 1939). The presence of uniformlydistributed external infill panels is taken into account.3.4.3.1 Building populationModelled buildings have a rectangular shape in plan, defined by a surfacearea (A b ) equal to 200, 400 or 600 square meters. This range is based on in-situsurveys carried out during last years in different Italian cities, in order to collectdata for the assessment of seismic vulnerability of the existing RC buildingstock (Cosenza et al., 2003; Pecce et al., 2004; Polese et al., 2008). For eachvalue of A b , longitudinal and transversal dimensions (L x and L y respectively)are evaluated from the ratio (L x /L y ), assumed equal to 1, 3/2, 2 and 5/2. Figure3.4.3.1 shows plan dimensions L x and L y depending on surface area A b , for eachvalue of the ratio (L x /L y ).

Chapter III – Influence of infills on seismic behaviour of reinforced concrete buildings 187L x /L y =1 L x /L y =3/224.5020.0014.1420.0016.3311.5514.1420.0024.5017.3224.5030.00A b200m 2400m 2L x /L y =2 L x /L y =5/2600m 217.3214.1410.0015.4912.658.9420.0028.2834.6422.3631.6238.73Figure 3.4.3.1. Morphology and plan dimensions of analyzed buildingsStarting from the global dimensions in plan L x and L y , all possiblecombinations of number of bays in longitudinal and transversal directions (n x ,n y ) are determined assuming a bay length (a x , a y ) between 3.5 and 6.0 meters(Simurai, 2010). A staircase is present, centred respect to the longitudinaldimension and 3 meters wide; inclined axis beams parallel to the transversaldirection are present in the staircase. The number of storeys is between two andeight; the interstorey height is equal to a z =3.0 meters.The concrete compressive strength f c is assumed equal to 20 MPa; Young’smodulus E c is given by 22.000 (f c /10) 0.3 (CEN, 2004b).Given the illustrated parameters, the structural model of the building is definedby means of a simulated gravity loads design procedure (Cosenza et al., 2005;Verderame et al., 2010c). The structural configuration follows the parallelplane frames system: frames in longitudinal direction resist to gravity loadsfrom slabs, and in transversal direction only two frames at the two ends arepresent (see Figure 3.4.3.2a). Slab way is always parallel to the transversaldirection. Element dimensions are calculated according to the allowable

188 Chapter III – Influence of infills on seismic behaviour of reinforced concrete buildingsstresses method; the design value for maximum concrete compressive stress isassumed equal to 5.0 and 7.5 MPa for axial load and axial load combined withbending respectively. Design values of dead and live gravity loads areevaluated. Column dimensions are calculated according only to the axial load,beam dimensions are determined from bending due to loads from slabs.Infills are considered as uniformly distributed in external frames of eachbuilding, see Figure 3.4.3.2b. Clear dimensions of infill panels – height h w andlength l w – are evaluated taking into account beam and column dimensionsrespectively. The panel thickness s w is assumed equal to 200 mm,corresponding to a double layer brick infill (120+80)mm thick, which can beconsidered as typical of a non-structural infill masonry wall (Bal et al., 2007).Elastic shear modulus G w is equal to 1350, 1080 or 1620 MPa, which can beassumed, respectively, as the median value and the median value minus andplus one time the standard deviation for hollow clay brick panels (with hollowpercentage lower than 45%), according to the actual Italian seismic code(Circolare 617, 2009). The assumed range of values for G w is also consistentwith the value of 1240 MPa provided in (Fardis, 1997), based on wallette testscarried out at the University of Pavia on specimens made up of hollow claybricks with a void ratio of 42%, selected as representative of typical light nonstructuralmasonry.Stiffness of infills is evaluated according to two hypotheses:(i) uncracked infills, adopting Eq. (3.2.4.1) proposed in (Fardis, 1997),similar to the expression proposed in (Fiorato et al., 1970). Theperiod values are compared with the empirical formulas for existinginfilled RC buildings, based on in-situ experimental results obtainedby means of microtremors (Section 3.4.1.3);(ii) cracked infills, adopting Eq. (3.2.4.4) proposed in (Mainstone, 1971)for the evaluation of the secant stiffness to the first cracking. Theperiod values are compared with literature formulas based on similarnumerical analyses (Section 3.4.1.4).

Chapter III – Influence of infills on seismic behaviour of reinforced concrete buildings 189Period is evaluated both with and without presence of openings. The openingpercentage is assumed equal to 20%, which can be considered as representative,on average, of window presence (Bal et al., 2007). For uncracked infills (case i)the stiffness is reduced by 25%; this reduction is evaluated according to thesimple method proposed in (Fiorato et al., 1970) for the initial elastic stiffnessof masonry infilled panels with openings. For cracked infills (case ii) areduction factor equal to 0.38 is applied to Mainstone’s formula, according to(Asteris, 2003).The total number of considered buildings, given by the variation of morphology(L x /L y ), surface area (A b ), plan dimensions (L x , L y ), bay length (a x , a y ), numberof storeys (N) and infill mechanical characteristics (G w ), is equal to 672.infill wallL y a ya ycolumnbeamslab waya ystairstairinfill walla x a x 3.00a x a xl w l w l w l wL xL x(a)(b)Figure 3.4.3.2. Plan building model: structural configuration (a), external infill configuration(b)3.4.3.2 Evaluation of periodFor each building, a modal analysis was performed on a three-dimensionalnumerical model of the structure and fundamental periods of vibration inlongitudinal (X) and transversal (Y) directions were calculated.Masses were evaluated from a load analysis carried out on every building. Ateach floor level a master joint was defined, corresponding to the position of thecentre of masses; the total floor mass was attributed to this joint, both in termsof translational and rotational Degree Of Freedom (DOF), in longitudinal and

190 Chapter III – Influence of infills on seismic behaviour of reinforced concrete buildingstransversal directions and around the vertical axis respectively. Hence, the3N×3N mass diagonal matrix ([M]) of the entire structure relative to theseDOFs was defined, where N is the number of storeys.A three-dimensional numerical model of the structure was built up by means ofOpenSees software (McKenna et al., 2004). Infill panels were represented byshear links connecting the opposite joints of each bay in the external frames.These links were characterized by the elastic stiffness calculated by means ofEq. (14) (uncracked infills) or Eq. (15) (cracked infills), based on the cleardimensions of the panel and its parametric mechanical characteristics. Grossstiffness was attributed to RC element sections.A rigid diaphragm constraint was assigned to joints of each floor slab and the3N×3N stiffness matrix ([K]) related to the same DOFs was defined, imposingunit generalized displacements at the N previously defined master joints.An eigenvalue analysis was performed by means of MATLAB ® software, inorder to evaluate the 3N natural vibration frequencies (ω i ) of the structure andthe related modal displacement vectors ({Ψ} i ), solving the following equation:2[ ] [ ] { } { }( K − ω M ) Ψ = 0(3.4.3.1)The i th period of vibration was given by:Ti2π= (3.4.3.2)ωiHence, the fundamental periods of vibration T x and T y were evaluated as theperiods characterized by the higher participating mass ratios in longitudinal andtransversal directions respectively.3.4.4. Analysis of resultsIn this Section, results of modal analyses carried out on buildings defined inSection 3.4.3.1 are presented and discussed. Numerical expressions obtained byregression of analytical data are presented and compared with main literatureformulas, previously illustrated in Section 3.4.1.

Chapter III – Influence of infills on seismic behaviour of reinforced concrete buildings 191Results for buildings with uncracked external infills (case i), based on thestiffness model proposed in (Fardis, 1997), both with and without the presenceof openings, are analyzed first.The influence of internal infills is also considered. The period of a buildingwith internal infills is evaluated depending on the period of the correspondingbuilding without internal infills.Then, numerical results for buildings with cracked external infills (case ii),based on the secant stiffness model proposed in (Mainstone, 1971), arediscussed.3.4.4.1. Uncracked infillsFigures 3.4.4.1a and 3.4.4.1b report the fundamental period of vibration Tversus the height H for longitudinal (X) and transversal (Y) directionsrespectively, for buildings with uncracked infills without openings.First of all, numerical values of period – for the same height – vary even by100%, in both considered directions.The period in longitudinal direction (T x ) is clearly lower than in transversaldirection (T y ). This is certainly due to the difference in dimensions L x and L y :unless the case (L x /L y =1), the longitudinal dimension L x is higher than thetransversal dimension L y , up to (L x /L y =5/2).1.0Period T x [sec]1.0Period T y [sec]0.80.80.60.60.40.40.20.2H [m]0.00 5 10 15 20 25 30H [m]0.00 5 10 15 20 25 30Figure 3.4.4.1. Period-height relationship for buildings with uncracked infills without openings:longitudinal (a) and transversal (b) directions

192 Chapter III – Influence of infills on seismic behaviour of reinforced concrete buildingsGenerally speaking, in infilled buildings a significant contribution to theoverall lateral stiffness is given by infills along the considered direction. If theonly plan dimension opposite to the considered direction changes, the buildingarea changes too, leading to a different total mass, while the lateral stiffness ofthe building does not change significantly because the stiffness contribution ofinfills along the considered direction remains constant. Therefore, a variation inperiod valuevariation inTx(y)is expected, roughly proportional to the square root of theLy(x). On the contrary, if the only plan dimension along theconsidered direction changes, the total mass and the infill contribution to lateralstiffness change in the same way, not leading to a significant variation in periodvalue. The latter consideration, in particular, is consistent with (Goel andChopra, 1998), where a poor correlation between H L x(y ) and Tx(y)ispointed out by the authors.In the present building population, for buildings with equal surface area, asthe ratio (L x /L y ) increases, the former dimension increases and the latterdecreases, respectively leading to an increase in lateral stiffness in longitudinaldirection and to a decrease in lateral stiffness in transversal direction, while thetotal building mass remains about constant. Then, given equal the surface area,as (L x /L y ) increases, a decrease in T x and an increase in T y are expectedcompared with the case (L x /L y =1).As a matter of fact, the lateral stiffness for buildings with (L x /L y =1) is verysimilar in both directions, thus leading to a ratio (T x /T y ) close to 1. The periodin transversal direction T y is almost linear with the period in longitudinaldirection T x , given equal the ratio (L x /L y ), and increases with (L x /L y ), see Figure3.4.4.2a.These considerations are consistent with Eq. (3.4.1.7), adopted by severalseismic codes (e.g. ATC, 1978) for the evaluation of fundamental period of RCSW buildings. This expression can be applied to the present numerical data. Ifspecific values are assumed for coefficient α in longitudinal and transversaldirections, the following expressions are obtained:

Chapter III – Influence of infills on seismic behaviour of reinforced concrete buildings 193TxH= α x(3.4.4.1)LxTyH= α y(3.4.4.2)Lyleading to:TyαLy x= Tx(3.4.4.3)α x LyAccording to Eq. (3.4.4.3), T y is proportional to T x , given equal the ratio(L x /L y ), and increases with this value.The value of ratio2y Tx)α α can be observed from Figure 3.4.4.2b, whereyx( T versus (L x /L y ) is reported. Unless a moderate variability, α y α x is,on average, equal to 1 for each of the considered values of the ratio between L xand L y . Based on this result, an unique value α = α = α can be assumed,independent of the considered direction. This is consistent with literatureproposals for RC SW buildings, as reported in Eq. (3.4.1.7).yx0.70.60.50.40.30.2T y [sec]5/223/2(L x /L y )0.1T x [sec]00 0.1 0.2 0.3 0.4 0.5 0.6 0.713.02.52.01.51.0(T y /T x ) 2y = 1.00xR 2 = 0.9900.5(L x /L y )0.00.0 0.5 1.0 1.5 2.0 2.5 3.0Figure 3.4.4.2. Comparison between longitudinal (T x ) and transversal (T y ) periods for differentvalues of the ratio (L x /L y ) (a); value of ratio α y α x (b)

194 Chapter III – Influence of infills on seismic behaviour of reinforced concrete buildingsThese considerations highlight a similarity between the elastic dynamicresponse of infilled RC MRF buildings and RC SW buildings. As a matter offact, some geometric parameters – such as height (H) and plan dimensions (L x ,L y ) – seem to influence in a similar way the period of vibration for these twostructural typologies. In both cases, a significant contribution to the lateralstiffness of the building is given by walls; hence, the period is wellapproximated by the period of an equivalent cantilever, see Section 3.4.1. Thisis also consistent with the assumption made in (Fiorato et al., 1970), where theinitial stiffness of an infilled frame is evaluated by modelling the frame as anequivalent composite cantilever, see Section 3.4.2.Hence, a regression analysis is carried out on numerical data according toexpression (3.4.1.7). Evaluation of coefficient α is based on all data,independent of the considered direction ( α = αy= αx); to this end, for eachbuilding the period T x(y)is reported depending on the ratio H L x(y ), seeFigure 3.4.4.3. Then, α is estimated via ordinary least square regression,obtaining:HT x(y) = 0.063(3.4.4.4)Lx(y)with H and L x(y)expressed in meters.In Figure 3.4.4.3 the numerical data are reported and expression (3.4.4.4) isplotted, versus the ratio H L x(y ) . The low prediction capacity of Eq. (3.4.4.4)is clearly shown. Given a value of H L x(y )noticeably variable, even by 100%., the analytical period values are

Chapter III – Influence of infills on seismic behaviour of reinforced concrete buildings 1951.00.80.6Period T x(y) [sec]y = 0.063xR 2 = 0.7120.40.2H/(L x(y) ) 1/20.00 2 4 6 8 10Figure 3.4.4.3. Simplified formula for period of buildings with uncracked infills versusHL x(y)As above mentioned, the scarce prediction capacity of the ratio H L x(y ) isalso highlighted in (Goel and Chopra, 1998) for the period of RC SW buildings.The authors, based on analytical procedures, propose Eq. (3.4.1.7) as a moreadequate expression to predict the period value. Eq. (3.4.1.7) is a rearrangementof Eq. (3.4.1.5), because it considers not only the shear deformability but alsothe flexural deformability.In this study, consistently with the purely shear nature of the stiffness modeladopted for uncracked infills (Fardis, 1997), the contribution of flexuraldeformability considered in Eq. (3.4.1.7) is not taken into account.Therefore, the following expression is assumed as alternative to Eq. (3.4.4.4):Tx(y)H= α(3.4.4.5)Ax(y)where A x(y)is the ratio (in percentage) between the infill area (roughlyevaluated including column dimensions) along the considered direction x(y)and the building area. Based on infill distribution in considered buildings (seeFigure 3.4.3.2b), this ratio can be expressed as( )Ax(y) = ⎡⎣2⋅sw ⋅ Lx(y)( Lx ⋅ Ly) ⎤⎦ ⋅ 100 = 2⋅sw Ly(x)⋅100. Then, Eq. (3.4.4.5)

196 Chapter III – Influence of infills on seismic behaviour of reinforced concrete buildingsbecomes:HTx(y)= 0.020(3.4.4.6)Ax(y)where H is the building height expressed in meters. Eq. (3.4.4.6), given theexpression ofAx(y), highlights a direct dependence between Tx(y)and Ly(x),consistently with the considerations reported at the beginning of the presentSection. Figure 3.4.4.4a reports the numerical data and the plot of Eq. (3.4.4.6),versus the ratio H A x(y ). The high prediction capacity of Eq. (3.4.4.6) isclearly shown. The higher estimate capacity of Eq. (3.4.4.6) compared with Eq.(21) is due to the parameter A x(y), accounting for the variability in floor massand storey stiffness. As a matter of fact, both the surface area ( L x ⋅ L y ) –proportional to the floor mass by unit area mass m S – and the infill area –proportional to the storey infill stiffness by shear modulus G w and height h w –are included in A x(y). The low variability of analytical period, given equalH A x(y) , is mainly due to the specific stiffness of infills, that is, to G w ,which is not included in A x(y).If the periodTx(y)is expressed as depending on H GwA x(y)(see Figure3.4.4.4b), the prediction capacity further increases, thus demonstrating theinfluence of shear modulus G w . Therefore, it is likely to assume that theremaining variability can be explained by the variability in bay length.Moreover, it is to be noted that coefficient α in Eq. (3.4.4.6) is equal to 0.020,while in Eq. (3.4.1.8) it is equal to 0.0077 for RC SW buildings. The differencein the order of magnitude between these values can be explained by thedifference in shear modulus between concrete ( G ) and infills ( Gin coefficients α . If an elastic moduluscw), includedE c =25000 MPa is assumed, withν=0.20, the shear modulus is equal to G = E 2(1 + ν)= 10400 MPa. Ifcc

Chapter III – Influence of infills on seismic behaviour of reinforced concrete buildings 197Gw=1350 MPa, the ratio(0.020/0.0077)=2.60.G G is equal to 2.78, not far fromcw1.0Period T x(y) [sec]1.0Period T x(y) [sec]y = 0.713x0.8y = 0.020x0.8H/(A x(y) ) 1/2 H/(G w A x(y) ) 1/2R 2 = 0.940R 2 = 0.9810.60.60.40.40.20.20.00.00 5 10 15 20 25 30 0 0.2 0.4 0.6 0.8 1Figure 3.4.4.4: Simplified formula for period of buildings with uncracked infills versusH Ax(y)(a) and versusw x(y)H G A (b)Based on the analyzed data, the lateral stiffness of buildings with uniformlydistributed uncracked infills is mainly due to the only infill contribution, andthe contribution of the RC structure (frames and stairs) can be considered asnegligible.Further regression analyses are carried out on numerical data, in order to makea comparison with literature formulas. In particular, the period is assumed asdepending on the power of the height ( T = αH), as linearly depending on theheight ( T = αH) and on the number of storeys ( T = αN).Evaluation of coefficients α and β is based on all data, independent of theconsidered direction. The obtained period-height relationships – with H inmeters – are respectively:0.85T = 0.022H(3.4.4.7)T = 0.014H(3.4.4.8)T = 0.043N(3.4.4.9)β

198 Chapter III – Influence of infills on seismic behaviour of reinforced concrete buildingsThe prediction capacity of Eqs. (3.4.4.7), (3.4.4.8) and (3.4.4.9) is clearly low,if compared with Eq. (3.4.4.6), see Figure 3.4.4.5. The high variability ofperiods, given a value of height, is due to the dependence of period ongeometrical parameters not included in these expressions. Nevertheless, it is tobe noted that their prediction capacity is not lower than the prediction capacityof Eq. (3.4.4.4).1.0Period T [sec]1.0Period T [sec]0.80.60.4y = 0.014xR 2 = 0.731y = 0.022x 0.85R 2 = 0.8040.80.60.4y = 0.043xR 2 = 0.7310.20.2H [m]0.00 5 10 15 20 25 30Number of storeys, N0.00 2 4 6 8 10Figure 3.4.4.5. Simplified formulas for period of buildings with uncracked infills depending onheight H (a) and number of storeys N (b)If coefficient α in ( T = αH) is evaluated separately for longitudinal (X) andtransversal (Y) direction, Eq. (3.4.4.8) changes into:T x = 0.012H(3.4.4.10)T y = 0.016H(3.4.4.11)Expressions proposed up to here are based on period of infilled RC MRFbuildings without openings. The presence of openings, assumed to be uniformlydistributed and corresponding to an opening percentage of 20%, leads to adecrease in stiffness of infills by 25%, thus increasing the period of vibration ofbuildings.If presence of openings is taken into account, Eq. (3.4.4.6) – expressing theperiod as depending on the infill percentage area A x(y)– changes into the

Chapter III – Influence of infills on seismic behaviour of reinforced concrete buildings 199following:HT x(y) = 0.023(3.4.4.12)Ax(y)The increase in the value of period is, on average, of 15%, technicallycorresponding to the square root of the ratio between the infill stiffness withand without openings. Hence, even if openings are present and uniformlydistributed, the lateral stiffness of the building is well represented by the onlystiffness contribution of infills.Period-height relationships can be obtained again, by new numericalregressions on period values accounting for the presence of openings. Anincrease in coefficient α can be noted.If Eqs. (3.4.4.7), (3.4.4.8) and (3.4.4.9) are evaluated independent of thedirection, the following expressions are obtained:0.85T = 0.025H(3.4.4.13)T = 0.016H(3.4.4.14)T = 0.049N(3.4.4.15)while Eqs. (3.4.4.10) and (3.4.4.11), depending on the considered direction, are:T x = 0.014H(3.4.4.16)T y = 0.019H(3.4.4.17)Influence of internal infillsAbove illustrated results show that the lateral stiffness of infilled buildings,with or without openings, is well represented by the stiffness contribution ofinfills, since the stiffness contribution of RC structure can be considered asnegligible. Stiffness of infills is well represented by the infill area, given equalthe height h w and the shear modulus G w .

200 Chapter III – Influence of infills on seismic behaviour of reinforced concrete buildingsIn the following, based on these considerations, the influence of internal infillson the fundamental period of buildings is approximately evaluated. Internalinfills, as well as external infills, increase lateral stiffness of buildings; this isevaluated by the increase in infill area, that is, in parameter A x(y).Internal infills are assumed as symmetrically distributed in plan, along bothdirections. Shear modulus G w and height h w are assumed equal to externalinfills. The thickness is assumed equal to s w =100 mm. The reduction in thevalue of period, compared with the case when only external infills are present,can be estimated as proportional to the square root of the increase in stiffness,that is, in infill area due to the presence of internal infills. In both directions, itis assumed that the overall linear dimension of internal infills is equal toexternal infills (Crowley and Pinho, 2010). Based on this assumption, given thelower thickness of internal infills, due to their presence the total infill areaincreases by 50%.Therefore, the period of both internally and externally infilled buildings is equalto 2 /3 = 0. 82 times the period of only externally infilled buildings. Inparticular, if the presence of openings is not taken into account:T = 0.011H(3.4.4.18)or:T = 0.035N(3.4.4.19)while, if openings are present:T = 0.013H(3.4.4.20)or:T = 0.040N(3.4.4.21)3.4.4.2. Cracked infillsIn this Section, results of modal analyses carried out according to the hypothesisof cracked infills – by means of the secant stiffness model proposed in

Chapter III – Influence of infills on seismic behaviour of reinforced concrete buildings 201(Mainstone, 1971) – are presented. Cracking of infills leads to a severe decreasein their stiffness, that is, to an increase in the fundamental period in bothdirections, compared with the uncracked condition.If the presence of openings is not considered, the period increases, on average,by 120%. If openings are present, the period increases even by 160%. Thepresence of openings leads to a higher increase in values of period, because thedecrease in infill stiffness due to their presence is more severe for crackedcondition than for uncracked condition.A regression analysis is carried out according to the expression T = αH, inorder to make a comparison with similar formulas, see Section 3.4.1.4.Simplified expressions for period of buildings with cracked infills withoutopenings, in longitudinal and transversal directions, are respectively given by:T x= 0.026H(3.4.4.22)T y= 0.036H(3.4.4.23)If presence of openings is considered, period is given by:T x= 0.034H(3.4.4.24)T y= 0.048H(3.4.4.25)Simplified formulas for period of buildings with cracked infills, independent ofthe considered direction, are provided, without openings (Figure 3.4.4.6a):T = 0.031H(3.4.4.26)and with openings (Figure 3.4.4.6b):T = 0.041H(3.4.4.27)

202 Chapter III – Influence of infills on seismic behaviour of reinforced concrete buildings1.81.51.2Period T [sec]y = 0.031xR 2 = 0.6911.81.51.2Period T [sec]y = 0.041xR 2 = 0.6530.90.90.60.60.3H [m]0.00 5 10 15 20 25 300.3H [m]0.00 5 10 15 20 25 30Figure 3.4.4.6. Simplified formulas for period of buildings with cracked infills without (a) andwith (b) openingsExpressions for period of buildings with cracked infills, with and withoutopenings, provide an upper and a lower bound, respectively, for the expressiongiven in (Crowley and Pinho, 2006) for uncracked infilled buildings (Eq.(3.4.1.9)).This is probably due to the infill stiffness assumed by the authors: the value ofsecant stiffness given by the model proposed in (Liauw and Kwan, 1984) forE w =1500 MPa (Crowley and Pinho, 2006) is quite similar to the infill stiffnessgiven by (Mainstone, 1971) in the assumed range of variation for G w .Moreover, the authors do not build three-dimensional models of consideredbuildings, but only two-dimensional models of representative frames (bare,fully infilled or infilled with openings). The dynamic response of the building,in terms of fundamental period of vibration, is obtained as a weighted averageof the two-dimensional response of modelled frames, based on the meanfrequency of occurrence of each type of frame within a typical building,provided by (Bal et al., 2007).Finally, Eq. (3.4.1.11), proposed in (Masi and Vona, 2008), is different aboutby 40% from the expression for transversal period of infilled buildings withoutopenings. This is probably due to a difference in the assumed value of infillshear modulus G w .

Chapter III – Influence of infills on seismic behaviour of reinforced concrete buildings 2033.4.5. Comparison with literature formulasIn this Section, proposed expressions for fundamental period of infilledbuildings are compared with literature empirical and numerical expressions.Comparison is carried out according to two main issues: structural typology andintensity of excitation used for the experimental measurement of period.Therefore, numerical formulas proposed herein for period of buildings withuncracked infills are compared with literature regressions of experimental dataobtained by means of techniques based on low amplitude motion –microtremors or ambient noise – previously introduced in Section 3.4.1.3.These experimental studies were carried out on infilled RC buildings inMediterranean area, similar to analyzed buildings in structural typology andinfill characteristics. Due to the nature of the applied measurement techniques,it is likely to assume that these relationships provide a not lengthened value ofthe period, corresponding to a linear behaviour of structural materials andcomponents.Main considered period-height relationships are reported in (Oliveira, 2004;Navarro and Oliveira, 2006; Gallipoli et al., 2010). Moreover, expressionsprovided by (Kobayashi et al., 1996; Dunand et al., 2002), reported in (Oliveiraand Navarro, 2010), respectively concerning Spanish and French buildings, areconsidered.These relationships express period value depending on height or number ofstoreys, usually independent of the building plan direction. Therefore, in thefollowing, a numerical-experimental comparison will be carried out accordingboth to height and to number of storeys.Figure 3.4.5.1 reports proposed linear relationships for buildings withuncracked infills and literature experimental relationships. Only highest andlowest experimental period values are reported and the area between thesebounds is painted in grey for an easier understanding. Proposed analyticalexpressions include only externally infilled buildings (in red), with or withoutopenings, and both internally and externally infilled buildings (in blue), with or

204 Chapter III – Influence of infills on seismic behaviour of reinforced concrete buildingswithout openings. A very good agreement between numerical and experimentalrelationships is shown.Numerical relationships for both internally and externally infilled buildings(in blue) fully fit the range of experimental values. The assumption of presenceof only externally infills (in red) leads to higher values of period.1.00.80.6Period T [sec]with int.infills - w/o openingswith int.infills - with openingsw/o int.infills - w/o openingsw/o int.infills - with openingsDunand et al., 2002Oliveira, 2004 - long.1.00.80.6Period T [sec]with int.infills - w/o openingswith int.infills - with openingsw/o int.infills - w/o openingsw/o int.infills - with openingsOliveira, 2004 - transv.Kobayashi et al., 19960.40.40.20.2H [m]0.00 5 10 15 20 25 30 35 40number of storeys, N0.00 2 4 6 8 10 12 14Figure 3.4.5.1. Comparison between proposed and experimental period-height (a) andperiod-number of storeys (b) relationships (area between highest and lowest experimentalperiod values is painted in grey)It is to be noted that modelled RC MRF buildings were designed for gravityloads only. For these buildings, it was shown that the contribution of the RCstructure to the overall lateral stiffness is negligible, if infills are present.However, empirical data were evaluated both on buildings designed for gravityloads only and on buildings designed for seismic loads, even if according toobsolete code prescriptions.In (Gallipoli et al., 2008) the period database of 65 Italian RC buildings isprovided (a first subset of the data set presented in (Gallipoli et al., 2010)),reporting the town and the age of construction of each building. The authorsindicate that the town of Potenza was classified for the first time as a seismiczone after the 1980 Irpinia earthquake; hence, pre-1981 buildings weredesigned for gravity loads only. Two separated regressions were carried out on

Chapter III – Influence of infills on seismic behaviour of reinforced concrete buildings 205pre- and post-1980 building data from this town, leading to period-heightrelationships respectively given by T = 0.015Hand T = 0.014H, see Figure3.4.5.2.The design procedure of the RC structure does not seem to influencesignificantly the experimental data. As a matter of fact, seismic designed RCstructures have a higher lateral stiffness – that is, a lower period of vibration(Verderame et al., 2010b) – compared with gravity loads designed structures,due to higher element section dimensions; nevertheless, in infilled buildings,this effect of stiffness increase is strongly reduced by presence of infills. In(Angel, 2007) the author carries out eigenvalue analyses on existing and newinfilled RC MRF buildings, obtaining much lower values for the period ofvibration in the latter case. Nevertheless, a so large scatter is probably due tothe mechanical characteristics assumed for infill panels: the author supposesthat in existing buildings the panels are made of light non-structural masonry,and that in new buildings the same panels are made up of perforated concreteblocks, characterized by a diagonal compressive strength eight times higher.1.0Period T [sec]0.80.6pre-1980post-1980y = 0.015xy = 0.014x0.40.2H [m]0.00 10 20 30 40 50Figure 3.4.5.2. Periods of gravity load designed (pre-1980) and seismic designed (post-1980) buildings in the town of Potenza, from (Gallipoli et al., 2008)

206 Chapter III – Influence of infills on seismic behaviour of reinforced concrete buildingsThe good numerical-experimental agreement demonstrates that thehypothesis of uncracked infill stiffness is consistent with the displacementcondition of infills under low amplitude motion sources of excitation.Furthermore, it is worth noting that the analytical value of period shouldrepresent a lower bound for the empirical value, since experimentalmeasurements are influenced by soil flexibility, leading to an increase in period(Muriá-Vila and González, 1995). On the contrary, rigid-base hypothesis leadsa stiffer system, that is, to a lower period.Despite the good numerical-experimental agreement – in average terms – itis to be noted that the period of an infilled building depends not only on heightbut also on percentage of infill area, opening percentage and distribution, andinfill mechanical characteristics. This is shown by the high variability, givenequal the height, of experimental values of period (Oliveira and Navarro, 2010;Gallipoli et al., 2008), see Figure 3.4.5.2, but also by the high variability ofnumerical values of period, see Figure 3.4.4.1, due to the dependence on theabove mentioned parameters.Analytical evaluation of elastic period of infilled buildings has to be basedon uncracked infill stiffness hypothesis. If a non-initial infill stiffness value isassumed, obtained numerical formulas (Crowley and Pinho, 2006; Masi andVona, 2008) overestimate, even by 200%, empirical data, see Figure 3.4.5.3.1.81.51.2Period T [sec]proposedCrowley and PinhoMasi and Vona0.90.60.3H [m]0.00 5 10 15 20 25 30 35 40Figure 3.4.5.3. Comparison between proposed, experimental and numerical literatureperiod-height relationships (area between highest and lowest experimental period values ispainted in grey)

Chapter III – Influence of infills on seismic behaviour of reinforced concrete buildings 207This is probably the main reason of the large numerical-experimental scatterpointed out in (Masi and Vona, 2008), where a ratio about equal to 3 isregistered between the theoretical values provided by the proposed formulationand empirical values of period.Furthermore, a period calculated by assuming a cracked (secant) stiffness ateach storey does not represent the actual dynamic properties of a damagedinfilled RC building, neither in a simplified way, and it can not be employed inthe seismic assessment of this kind of buildings (Crowley and Pinho, 2006).As a matter of fact, the distribution of damage in infills (that is, the distributionof infill secant stiffness) is not uniform along the height of the building, as it isconsidered in these formulations, but tends to concentrate in one storey at thebottom of the building, especially if the building is seismically under-designedand strongly influenced, also in non-linear field, by the presence on infillpanels, as already highlighted in literature by means of experimental tests (Pintoet al., 2002) and numerical non-linear analyses (Dolšek and Fajfar, 2001) oninfilled RC frames or buildings.The overcoming of the elastic limit, both in infill and RC elements, leads to alengthening in the period of vibration, as much as the amplitude of motionincreases. Nevertheless, these effects become much more complex in MDOFsystems (Oliveira and Navarro, 2010).

208 Chapter III – Influence of infills on seismic behaviour of reinforced concrete buildingsREFERENCES− Amanat K.M., Hoque E., 2006. A rationale for determining the naturalperiod of RC building frames having infill. Engineering Structures,28(4), 495-502.− Angel J.P., 2007. Verification of some Eurocode 8 rules for simplifiedanalysis of structures. M.Sc. Dissertation, ROSE School, Pavia, Italy.− Asteris P.G., 2003. Lateral stiffness of brick masonry infilled planeframes. ASCE Journal of Structural Engineering, 129(8), 1071-1079.− ATC, 1978. Tentative provisions for the development of seismicregulations for buildings. Report No. ATC3-06, Applied TechnologyCouncil, Palo Alto, California, USA.− Bal I.E., Crowley H., Pinho R., Gulay F.G., 2007. Structuralcharacteristics of Turkish RC building stock in Northern Marmararegion for loss assessment applications. ROSE Research Report No.2007/03, IUSS Press, Pavia, Italy.− Barua H.K., Mallick S.K., 1977. Behaviour of mortar infilled steel framesunder lateral load. Building and Environment, 12(4), 263-272.− Bertero V.V., Bendimerad F.M., Shah H.C., 1988. Fundamental period ofreinforced concrete moment-resisting frame structures. Report No. 87,Department of Civil and Environmental Engineering, StanfordUniversity, Stanford, California, USA.− Bertoldi S.H., Decanini L.D., Santini S. Via G., 1994. Analytical modelsin infilled frames. 10 th European Conference on EarthquakeEngineering. August 28-September 2, Vienna, Austria.− Braga F., Petrangeli M.P., 1976. Considerazioni sul comportamento degliedifici civili con struttura in cemento armato. L'Industria Italiana delCemento, anno XLVI, nn. 7-8, pp. 485-502. (in Italian)− CEN, 2004a. European Standard EN1998-1:2004. Eurocode 8: Design ofstructures for earthquake resistance. Part 1: general rules, seismic

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210 Chapter III – Influence of infills on seismic behaviour of reinforced concrete buildings− De Marco R., Martini M.G., Di Pasquale G., Fralleone A., Pizza A.G.,2000. La classificazione e la normativa sismica italiana dal 1909 al1984. Servizio Sismico Nazionale. (in Italian)− Decreto Ministeriale del 16/1/1996. Norme tecniche per le costruzioni inzone sismiche. G.U. n. 29 del 5/2/1996. (in Italian)− Decreto Ministeriale del 14/1/2008. Approvazione delle nuove normetecniche per le costruzioni. G.U. n. 29 del 4/2/2008. (in Italian)− Dolce M., Cardone D., Ponzo F.C., Valente C., 2005. Shaking table testson reinforced concrete frames without and with passive control systems.Earthquake Engineering and Structural Dynamics, 34(14), 1687-1717.− Dolšek M., Fajfar P., 2001. Soft storey effects in uniformly infilledreinforced concrete frames. Journal of Earthquake Engineering, 5(1), 1-12.− Dunand F., Bard P.Y., Chatelain J.L., Guéguen P., Vassail T., Farsi M.N.,2002. Damping and frequency from randomdec method applied to insitu measurements of ambient vibrations. Evidence for effective soilstructure interaction. Proceedings of the 12 th European Conference onEarthquake Engineering, London, UK, September 9-13. Paper No. 869.− Fardis M.N., 1997. Experimental and numerical investigations on theseismic response of RC infilled frames and recommendations for codeprovisions. Report ECOEST-PREC8 No. 6. Prenormative research insupport of Eurocode 8.− FEMA 356, 2000. Prestandard and commentary for the seismicrehabilitation of buildings, FEMA Publication No. 356, prepared by theAmerican Society of Civil Engineers for the Federal EmergencyManagement Agency, Washington, D.C., USA.− Fiorato A.E., Sozen M.A., Gamble W.L., 1970. An investigation of theinteraction of reinforced concrete frames with masonry filler walls.Report No. UILU-ENG 70-100, University of Illinois, Urbana-Champaign, Illinois, USA.

Chapter III – Influence of infills on seismic behaviour of reinforced concrete buildings 211− Flanagan R.D., Bennett R.M., 1999. In-plane behaviour of structural claytile infilled frames. ASCE Journal of Structural Engineering, 125(6),590-599.− Gallipoli M.R., Mucciarelli M., Vona M., 2008. Empirical estimate offundamental frequencies and damping for Italian buildings. EarthquakeEngineering and Structural Dynamics, 38(8), 973-988.− Gallipoli M.R., Mucciarelli M., Šket-Motnikar B., Zupanćić P., Gosar A.,Prevolnik S., Herak M., Stipčević J., Herak D., Milutinović Z.,Olumćeva T., 2010. Empirical estimates of dynamic parameters on alarge set of European buildings. Bulletin of Earthquake Engineering,8(3), 593-607.− Gates W.E., Foth V.A., 1978. Building period correlation. Report to theApplied Technology Council. Applied Technology Council, Palo Alto,California, USA.− Goel R.K., Chopra A.K., 1997a. Period formulas for moment-resistingframe buildings. ASCE Journal of Structural Engineering, 123(11),1454-1461.− Goel R.K., Chopra A.K., 1997b. Vibration properties of buildingsdetermined from recorded earthquakes motions. Report No. UCB-PEER1997-14, University of California, Berkeley, California, USA.− Goel R.K., Chopra A.K., 1998. Period formulas for concrete shear wallbuildings. ASCE Journal of Structural Engineering, 124(4), 426-433.− Holmes M., 1961. Steel frames with brickwork and concrete infilling.Proceedings of the Institution of Civil Engineering, 19, 473-478.− Kakaletsis D.J., Karayannis C.G., 2009. Experimental investigation ofinfilled reinforced concrete frames with openings. ACI StructuralJournal, 106(2), 132-141.− Klingner R.E., Bertero V.V., 1976. Infilled frames in earthquake-resistantconstruction. Report No. UCB-PEER 1976-32, University of California,Berkeley, California, USA.

212 Chapter III – Influence of infills on seismic behaviour of reinforced concrete buildings− Kobayashi H., Vidal F., Feriche D., Samano T., Alguacil G., 1996.Evaluation of dynamic behaviour of building structures withmicrotremors for seismic microzonation mapping. 11 th WorldConference on Earthquake Engineering, Acapulco, México, June 23-28.Paper No. 1769.− Kose M.M., 2009. Parameters affecting the fundamental period of RCbuildings with infill walls. Engineering Structures, 31(1), 93-102.− Liauw T.C., Kwan K.H., 1984. Nonlinear behaviour of non-integralinfilled frames. Computers and Structures, 18(3), 551-560.− Mainstone R.J., 1971. On the stiffnesses and strengths of infilled frames.Proceedings of the Institution of Civil Engineering, Supplement IV, 57-90.− Mainstone R.J., 1974. Supplementary note on the stiffness and strength ofinfilled frames. Current Paper CP13/74, Building ResearchEstablishment, London, UK.− Masi A., Vona M., 2008. Estimation of the period of vibration of existingRC building types based on experimental data and numerical results. In:Mucciarelli M., Herak M., Cassidy J. Increasing seismic safety bycombining engineering technologies and seismological data. WB/NATOPublishing Unit. Chapter 3.3, 207-226. Springer.− McKenna F., Fenves G.L., Scott M.H., 2004. OpenSees: Open System forEarthquake Engineering Simulation. Pacific Earthquake EngineeringResearch Center. University of California, Berkeley, California, USA.http://opensees.berkeley.edu− Mehrabi A.B., Shing P.B., Schuller M.P., Noland J.L., 1996.Experimental evaluation of masonry-infilled RC frames. ASCE Journalof Structural Engineering, 122(3), 228-237.− Mondal G., Jain S.K., 2008. Lateral stiffness of masonry infilledReinforced Concrete (RC) frames with central opening. EarthquakeSpectra, 24(3), 701-723.

Chapter III – Influence of infills on seismic behaviour of reinforced concrete buildings 213− Mosalam K.M., 1996. Modeling of the nonlinear seismic behavior ofgravity load designed frames. Earthquake Spectra, 12(3), 479-492.− Mosalam K.M., White R.N., Gergely P., 1997. Static response of infilledframes using quasi-static experimentation. ASCE Journal of StructuralEngineering, 123(11), 1462-1469.− Muriá-Vila D., González A.R., 1995. Propiedades dinámicas de edificiosde la Ciudad de México. Revista Mexicana de Ingeniería Sísmica, 51,25-45. (in Spanish)− Navarro M., Oliveira C.S., 2006. Experimental techniques for assessmentof dynamic behaviour of buildings. In: Oliveira, C.S., Roca, A., Goula,X., Assessing and managing earthquake risk. Volume 2, Part II, Chapter8, 159-183. Springer.− Negro P., Verzeletti G., 1996. Effect of infills on the global behaviour ofR/C frames: energy considerations from pseudodynamic tests.Earthquake Engineering and Structural Dynamics, 25(8), 753-773.− Oliveira C.S., 2004. Actualização das bases-de-dados sobre frequênciaspróprias de estruturas de edifícios, pontes, viadutos e passagens depeões a partir de medições expeditas in-situ. 5 th Portuguese Conferenceon Earthquake Engineering, University of Minho, Guimarães, Portugal.(in Portuguese)− Oliveira C.S., Navarro M., 2010. Fundamental periods of vibration of RCbuildings in Portugal from in-situ experimental and numericaltechniques. Bulletin of Earthquake Engineering, 8(3), 609-642.− Panagiotakos T.B., Fardis M.N., 1996. Seismic response of infilled RCframes structures. 11 th World Conference on Earthquake Engineering,Acapulco, México, June 23-28. Paper No. 225.− Paulay T., Priestley M.J.N., 1992. Seismic design of reinforced concreteand masonry buildings, John Wiley & Sons, New York, USA.− Pecce M., Polese M., Verderame G.M., 2004. Seismic vulnerabilityaspects of RC buildings in Benevento. Proceedings of the Workshop onMultidisciplinary Approach to Seismic Risk Problems. Sant’Angelo dei

214 Chapter III – Influence of infills on seismic behaviour of reinforced concrete buildingsLombardi, Italy, September 22. In: Pecce M., Manfredi G., Zollo A.,2004. The many facets of seismic risk. Pp. 134-141. CRdC AMRA.− Polese M., Verderame G.M., Mariniello C., Iervolino I., Manfredi G.,2008. Vulnerability analysis for gravity load designed RC buildings inNaples – Italy. Journal of Earthquake Engineering, 12(S2), 234-245.− Pinto A.V., Verzeletti G., Molina J., Varum H., Coelho E., 2002. Pseudodynamictests on non-seismic resisting RC frames (infilled frame andinfill strengthened frame tests). Report EUR, EC, Joint Research Centre,Ispra, Italy.− Pires F., 1990. Influencia das paredes de alvenaria no comportamiento deestruturas reticuladas de betao armado subjectas a accoes horizontaes.Ph.D. Thesis, LNEC, Lisbon, Portugal. (in Portuguese)− Polyakov S.V., 1956. Masonry in framed buildings (an investigation intothe strength and stiffness of masonry infilling). Gosudarstvennoeizdatel’stvo Literatury po stroitel’stvu I arkhitekture, Moscow. (Englishtranslation by G. L. Cairns, National Lending Library for Science andTechnology, Boston, Yorkshire, England, 1963).− Pujol S., Fick D., 2010. The test of a full-scale three-story RC structurewith masonry infill walls. Engineering Structures, 32(10), 3112-3121.− Regio Decreto Legge n. 2229 del 16/11/1939. Norme per la esecuzionedelle opere in conglomerate cementizio semplice od armato. G.U. n. 92del 18/04/1940. (in Italian)− Shing P.B., Mehrabi A.B., 2002. Behaviour and analysis of masonryinfilledframes. Progress in Structural Engineering and Materials, 4(3),320-331.− Shing P.B., Stavridis A., Koutromanos I., Willam K., Blackard B.,Kyriakides M.A., Billington S.L., Arnold S., 2009. Seismic performanceof non-ductile RC frames with brick infill. ATC & SEI 2009 Conferenceon Improving the Seismic Performance of Existing Buildings and OtherStructures, San Francisco, USA.

Chapter III – Influence of infills on seismic behaviour of reinforced concrete buildings 215− Simurai, 2010. Technical report to the SIMURAI project – StrumentiIintegrati per il MUlti Risk Assessment territoriale in ambienti urbaniantropizzatI (Integrated instruments for large scale multi risk assessmentin urban anthropic environment), supported by the Italian Ministry ofEducation, University and Research, scientific coordinator Prof.Gaetano Manfredi.− Stafford Smith B., 1966. Behaviour of square infilled frames. ASCEJournal of Structural Division, 92(1), 381-403.− Stafford Smith B., 1967. Methods for predicting the lateral stiffness andstrength of multi-storey infilled frames. Building Science, 2(3), 247-257.− Stafford Smith B., Carter C., 1969. A method of analysis for infilledframes. Proceedings of the Institution of Civil Engineering, 44, 31-48.− Stylianidis K.C., 1985. Experimental investigation of the behaviour of thesingle-story infilled R.C. frames under cyclic quasi-static horizontalloading (parametric analysis). Ph.D. Thesis, University of Thessaloniki,Thessaloniki, Greece.− Verderame G.M., De Luca F., Ricci P., Manfredi G., 2010a. Preliminaryanalysis of a soft storey mechanism after the 2009 L’Aquila earthquake,Earthquake Engineering and Structural Dynamics. DOI:10.1002/eqe.1069− Verderame G.M., Iervolino I., Manfredi G., 2010b. Elastic period of substandardreinforced concrete moment resisting frame buildings. Bulletinof Earthquake Engineering, 8(4), 955-972.− Verderame G.M., Polese M, Mariniello C., Manfredi G., 2010c. Asimulated design procedure for the assessment of seismic capacity ofexisting reinforced concrete buildings. Advances in EngineeringSoftware, 41(2), 323-335.

216 Chapter III – Influence of infills on seismic behaviour of reinforced concrete buildings

Chapter IV – Numerical investigation of seismic capacity of RC buildings with infills 217Chapter IVNumerical investigation of seismic capacity ofreinforced concrete buildings with infills4.1 INTRODUCTIONDuring last decades, a growing attention has been addressed to the influenceof infills on the seismic behaviour of RC buildings, also supported by theobservation of damage to RC buildings with infills after severe earthquakes(e.g., Kocaeli 1999 (EERI, 2000)). The importance of this issue was widelyrecognized by earthquake engineering researchers, leading to first full-scaleexperimental tests on infilled RC frames (e.g., Negro and Verzeletti, 1996) andcode prescriptions about the consideration of infills in seismic design (e.g.,CEN, 1995). As a result, from the second half of 1990s on, several valuablenumerical efforts have been made to investigate the seismic behaviour of RCframes with infills through nonlinear analyses.In this Chapter, a review of main numerical studies from literature ispresented first. Hence, a numerical investigation on the influence of infills onthe seismic behaviour of a case-study Gravity Load Designed building is carriedout by means of Static Push-Over analyses, within the N2 spectral assessmentframework. Different infill configurations are considered (Bare, Uniformlyinfilled and Soft-storey infilled), and a sensitivity analysis is carried out, thusevaluating the influence of main material and capacity parameters on seismic

218 Chapter IV – Numerical investigation of seismic capacity of RC buildings with infillsresponse for different Limit States. Fragility curves are obtained, through theapplication of a Response Surface Method. Finally, a comparison between theseismic capacity assessment based on “exact” models and on correspondingShear Type models is carried out, in view of the simplified approach developedin Chapter V.4.2 NUMERICAL INVESTIGATION OF SEISMIC BEHAVIOUR OFINFILLED RC BUILDINGS: STATE-OF-THE-ARTIt is to be noted that, when evaluating the influence of infills on the seismicresponse of infilled RC structures by means of nonlinear analyses, the possibleinfluence of brittle failure mechanisms – especially due to local interactionbetween infill panels and surrounding RC members, see Section 3.2 – is usuallynot considered, rather focusing the attention on the flexure-controlled behaviourof RC members. Sometimes, for specific case-study structures, this is justifiedby the observation of experimental behaviour (e.g., Dolšek and Fajfar,2008a,b).Fardis and Panagiotakos (1997b) presented a comprehensive study based onnonlinear dynamic analyses carried out (i) on idealized SDOF infilled frames,(ii) on the numerical model of an infilled four-storey RC structureexperimentally tested ((Negro and Verzeletti, 1996), see Section 3.3) and (iii)on RC structures with different number of storeys (4, 8 or 12) (Fardis andPanagiotakos, 1997a) and infill configuration (Bare, Fully infilled or Pilotis). Itis worth noting that structures were designed for seismic loads according toEurocode 8, complying with the weak beam/strong column principle. Inparticular, based on numerical results from (iii), infill influence was deemedbeneficial on seismic response, except for very brittle or irregularly distributedinfills. However, the detrimental effect of an irregular infill distribution wasmore pronounced at ground motion intensities much higher than that of thedesign motion. In medium-high rise reinforced concrete frame buildings, the

Chapter IV – Numerical investigation of seismic capacity of RC buildings with infills 219presence of infills and even irregularities in their arrangement in elevation had avery small effect on the global and local seismic response, also due to the lowshear strength of the infills in comparison to the total strength and base shear ofthe building. The influence of code prescriptions accounting for the presence ofan irregular distribution of infills (increasing design seismic demand in softstoreys)was analyzed, too, and authors even came to the conclusion that theseprescriptions were too conservative.Kappos (1998) carried out nonlinear dynamic analyses on a case study tenstoreyinfilled RC frame considering different infill configurations (Bare, Fullyinfilled and Pilotis) and different strength values for infill material (Low andHigh). Frames were designed according to Eurocode 8, in intermediate ductilityclass and for a PGA equal to 0.25g (without applying the specific codeprescriptions accounting for the infill presence). Hence, nonlinear dynamicanalyses were carried out assuming as input motions different accelerogramsnormalized to the code design spectrum. Results highlighted a rather uniformdistribution of interstorey drift demand in the bare frame, a tendency ofdecreasing drift demand with the height in the fully infilled frame and a verylarge demand at the first (soft-) storey, drastically reducing at upper storey, inthe Pilotis frame, as expected. Hence, under the same seismic action, the bestperformance (in terms of lowest interstorey drift demand) was shown by theFully infilled frame. This was also reflected by the large amount of energydissipated by infill elements. The worst behaviour, in terms of maximum localductility demand, was shown by the Pilotis frame.Negro and Colombo (1997) carried out a numerical-experimentalcomparison with the results of the pseudo-dynamic tests on the four-storey RCbuilding reported in (Negro and Verzeletti, 1996) (see Section 3.3). Authorshighlighted the detrimental effect of localization of ductility demand due to anirregular infill distribution, as expected. However, authors pointed out that adetrimental effect on seismic behaviour may be expected also from a uniform

220 Chapter IV – Numerical investigation of seismic capacity of RC buildings with infillsinfill distribution since storey-level sidesway mechanisms take place after thefailure of the panels at that storey, thus leading to a similar effect of localizationof ductility demand. This effect may or may not be counterbalanced by thebeneficial effect due to the increase in stiffness, strength and energy dissipationcapacity provided by infills.Fajfar and Drobnič (1998) also presented a comparison between nonlineardynamic analyses and the results from the same test (Negro and Verzeletti,1996), coming to similar conclusions. Moreover, authors carried out StaticPush-Over analyses on the numerical models of tested structures and executed aspectral assessment of the seismic demand by means of the N2 method. Anidealized bilinear force-displacement relationship was used to represent thenumerical response also for the infilled structure, in spite of the degradingbehaviour due to the failure of infills (see Figure 4.2.1). To this aim, thestiffness of the idealized bilinear relationship was determined as the averagestiffness of bare frames and uniformly infilled frames, while the ultimatestrength approximately corresponded to the average strength of the uniformlyinfilled structure in the displacement range of interest.Figure 4.2.1. Base shear-top displacement relationships determined by pushover analyses (solidlines) and idealized bilinear relationships (dotted lines) used in the N2 method (Fajfar andDrobnič, 1998)

Chapter IV – Numerical investigation of seismic capacity of RC buildings with infills 221Dolšek and Fajfar (2000, 2002) presented an investigation of modellingissues about the behaviour of infilled RC frames, confirming that a detrimentaleffect on seismic behaviour may be due not only to an irregular infilldistribution but also to a regular one. As a matter of fact, in the latter case,although reducing the displacement demand in structural elements, presence ofinfills may lead to an undesirable storey mechanism, which may represent apotential danger in the case of long duration ground motion. Furthermore,authors pointed out that the major issues about the modelling of infilledstructures were the determination of the characteristics of the equivalent strutsrepresenting the infill, due to the high uncertainties involved in thisdetermination, and the characteristics of ground motion. Hence, the need for thedevelopment of simplified procedures providing rough estimates of seismicresponse of infilled structures and allowing quick analysis of a number ofvariants was highlighted.In Dolšek and Fajfar (2001) – starting from the observation of damage toinfilled RC buildings after the 1999 Kocaeli earthquake – nonlinear dynamicanalyses were carried out on numerical models representing two differentstructures, one (“contemporary”) designed for a base shear coefficient equal to0.15 and complying with Capacity Design principles (e.g., weak beam/strongcolumn condition) and the other one (“existing”) designed for a base shearcoefficient equal to 0.08 and without applying Capacity Design principles.These models represented the test structures reported in (Negro and Verzeletti,1996) and (Pinto et al., 2002), respectively (see Section 3.3). Both structureswere uniformly infilled, considering two different cases for infill mechanicalcharacteristics, namely “weak” and “strong” infills. Nonlinear dynamic analyseswere carried out with increasing ground motion intensity. Numerical resultshighlighted that uniformly distributed infills led to a beneficial reduction indisplacement demand up to a certain intensity of ground motion, but if thisthreshold (that increased with the infill strength) was exceeded a soft storeymechanism occurred at one of the bottom storeys, resulting in a sudden increase

222 Chapter IV – Numerical investigation of seismic capacity of RC buildings with infillsin (localized) displacement demand. In the contemporary RC frame theobserved displacement demand was generally lower if compared with theexisting, but a concentration of displacement demand was anyhow observed atthe bottom of the structure when weak infills were considered. Hence, theconditions for a collapse due to the formation of such a collapse mechanism inuniformly infilled structure were (i) a high ground motion intensity, (ii) a lowglobal and local ductility of the bare frame and (iii) a low infill strength.A fundamental work for the assessment of seismic performance of infilledRC frames was presented by Dolšek and Fajfar (2004a). In this study, a R-µ-Trelationship for the evaluation of inelastic displacement demand starting fromelastic demand spectra was presented, which was evaluated on SDOF systemscharacterized by the typical idealized force-displacement envelope of an infilledRC frame, different from the usual elasto-plastic system (see Figure 4.2.2).Figure 4.2.2. Force-displacement envelope of the SDOF system (Dolšek and Fajfar, 2004a)The first, equivalent elastic part represented both the initial elasticbehaviour and the behaviour after cracking has occurred in both the frame andthe infills. The second part, corresponding to the horizontal branch, representedyielding. The third part represented the strength degradation of the infills. Then,the horizontal branch represents the stage when infills are failed and only theRC frame resists the horizontal actions.

Chapter IV – Numerical investigation of seismic capacity of RC buildings with infills 223A parametric study was carried out executing nonlinear dynamic analyseson the considered SDOF system with three sets of 7 accelerograms, varyingdifferent parameters:- T/T C : ratio between the period of the SDOF system and the cornerperiod of the ground motion;- r u : ratio between the residual strength and the maximum strength(F 3 /F 1 , see Figure 4.2.2);- µ s : ductility at the beginning of the degradation (D 2 /D 1 );- µ u : ductility at the end of the degradation (D 3 /D 1 ).First two sets of accelerograms were used to evaluate the R-µ-Trelationship, the third one was used to validate the same relationship.Based on obtained results, an increase in ductility demand was observedwith r u decreasing. Moreover, it was observed that µ u had a negligible influenceon ductility demand. Hence, this parameter was not included in the proposedrelationship, which is shown in Figure 4.2.3.Based on the proposed R-µ-T relationship, seismic assessment of infilledRC buildings can be included within the spectral framework of the N2 method,through Static Push-Over analyses.The applicability of such relationship was validated in a companion paper(Dolšek and Fajfar, 2005) through a comparison between a seismic assessmentcarried out by means of the N2 method, employing such relationship, and theresults obtained by Incremental Dynamic Analysis (IDA) on two uniformlyinfilled case study RC structures, one contemporary and one existing (see(Dolšek and Fajfar, 2001)). In this study, a methodology to evaluate theidealized multi-linear curve from the Push-Over curve for infilled RC buildingswas also proposed.

224 Chapter IV – Numerical investigation of seismic capacity of RC buildings with infillsFigure 4.2.3. Comparison between the R-µ-T relationship for an infilled RC frame proposed in(Dolšek and Fajfar, 2004a) and the R-µ-T relationship for an elasto-plastic system withoutstrength degradation (from (Dolšek and Fajfar, 2008a))It can also be observed that, from a qualitative standpoint, based on thisrelationship, the sudden increase in displacement demand observed when asoft-storey occurs in uniformly infilled structures for a seismic demandexceeding a certain threshold (Dolšek and Fajfar, 2001) may be explained notonly by the localization of the displacement demand, but also by the typicalbrittle behaviour shown by the structural response when this is controlled by theresponse of a storey where the infills fail; such a strength drop is representedthrough the parameter r u .The N2 method extended with the above illustrated relationship was appliedto the seismic assessment of infilled RC frames also in (Dolšek and Fajfar,2008a). In this work, a case study RC frame was considered, based on a tested

Chapter IV – Numerical investigation of seismic capacity of RC buildings with infills 225structure (see (Pinto et al., 2002)), and was analyzed in different configurations:Bare, Partially Infilled (infills with openings) and Fully Infilled. Based onnumerical results, authors pointed out again that infills may significantly reducedamage, but only up to a certain intensity of ground motion. Above thisthreshold level, a small increase in the ground motion intensity leads to a verysignificant drop of strength, due to the failure of infills, resulting in a severeincrease in displacement demand.In the companion paper (Dolšek and Fajfar, 2008b) the seismic assessmentof infilled RC frames is considered in a probabilistic framework, combining theSAC/FEMA method for a probability assessment in closed form (Cornell et al.,2002) with the N2 method. In the paper, the relationship between seismicdemand (represented by an Engineering Demand Parameter (EDP)) and seismicintensity (represented by an Intensity Measure (IM)) is not represented by IDAcurves but by IN2 curves, obtained applying the N2 method for increasinglevels of seismic intensity (Dolšek and Fajfar, 2004b). Hence, an evaluation ofthe influence of infills on seismic response could be made in terms of failureprobability, for different Limit States. Based on obtained results, the beneficialinfluence of infills was even more evident than in the companion paper (Dolšekand Fajfar, 2008a). When evaluating failure probabilities, authors observed that,despite the higher inherent uncertainty in their capacity and response, regularinfilled frames were less sensitive to randomness and uncertainty. Nevertheless,authors highlighted that different kind of failures, which were not considered inthe study (such as brittle failure mechanisms due to local interaction betweeninfills and structural elements), may change the results leading to the illustratedconclusions.Another study assessing the seismic performance of RC frames with infillswas proposed by Dymiotis et al. (2001). In this paper, the seismic reliability ofan infilled RC frame was evaluated focusing the attention on uncertainties inmaterial characteristics (both in reinforced concrete and in masonry infills) andon deformation capacity of RC members. The considered frame was designed

226 Chapter IV – Numerical investigation of seismic capacity of RC buildings with infillsaccording to Eurocode 8 (CEN, 1995), for the intermediate ductility class and adesign PGA equal to 0.25g. Seismic performance was evaluated at two LimitStates (Serviceability (SLS) and Ultimate (ULS)). Vulnerability curves wereevaluated through nonlinear dynamic analyses carried out for different levels ofground motion intensity. Two configurations were considered: Uniformlyinfilled and Pilotis frame. Results for Bare frame were available from aprevious study (Dymiotis et al., 1999). Authors observed that the Pilotis framewas more vulnerable than the Uniformly infilled frame, at both Limit States.Compared with the Bare frame, the Uniformly infilled frame was lessvulnerable at SLS but more vulnerable at ULS. The Pilotis frame resulted as themost vulnerable system at both SLS and ULS (see Figure 4.2.4).Figure 4.2.4. Comparison between vulnerability curves for Bare, Uniformly infilled and Pilotisframes for Serviceability and Ultimate Limit States (Dymiotis et al., 2001)Seismic performance of infilled RC frames were also studied by Madan andHashmi (2008), considering seven and fourteen-storey infilled RC framessubjected to near-fault ground motions. Sattar and Liel (2010) evaluated

Chapter IV – Numerical investigation of seismic capacity of RC buildings with infills 227vulnerability curves at collapse for a four- and a eight-storey old seismicdesigned RC frame, in Bare, Uniformly infilled and Pilotis configurations. IDAanalyses were performed; modelled uncertainty only consisted in record-torecord variability. For both four- and eight-storey frames, the Uniformly infilledconfiguration resulted as the most vulnerable, whereas the Bare frame resultedas the less vulnerable.In conclusion, based on the illustrated numerical studies, often supported byexperimental data or observed damage, the following general conclusions canbe drawn:- an irregular distribution of infills (soft-storey effect) results in a worseseismic performance through a detrimental localization of inelasticdisplacement demand in the storey where infills are not present;- a regular distribution of infills may lead to a beneficial reduction indisplacement demand compared with the bare structure, especially ifthe seismic demand intensity does not overcome a certain threshold(e.g., for Damage Limitation Limit State);- as the seismic demand intensity increases (e.g., for Collapse LimitState), a detrimental localization of inelastic displacement demandtakes place also in the case of uniform infill distribution since thedisplacement demand tends to concentrate in one storey, thus resultingin a worse seismic performance compared with the bare structure;- previous considerations are strongly dependent (i) on the design of thebare structure, both in terms of strength (e.g., base shear coefficient)and application of Capacity Design principles such as weakbeam/strong column condition, and (ii) on the strength of infills.

228 Chapter IV – Numerical investigation of seismic capacity of RC buildings with infills4.3 SEISMIC CAPACITY ASSESSMENT OF A FOUR-STOREY GLDBUILDING WITH DIFFERENT INFILL CONFIGURATIONSIn this Section, the influence of infills on the seismic behaviour of existingRC buildings is evaluated on a case-study Gravity Load Designed building withdifferent infill configurations are considered (Bare, Uniformly infilled andPilotis). Seismic response is evaluated through Static Push-Over analyses.Seismic demand is assessed by means of the N2 method.In Section 4.3.1 the case study building is described, together with theadopted modelling and analysis method.The results of a sensitivity analysis evaluating the influence of mainmaterial and capacity parameters on the seismic response of the building arepresented in Section 4.3.2.A comparison between the seismic capacity of the building in different infillconfigurations is shown in Section 4.3.3.In Section 4.3.4 a comparison between the seismic capacity assessmentbased on “exact” models and on corresponding Shear Type models is carriedout, in view of the simplified approach developed in next Chapter.4.3.1. Case study structure: numerical modelling and analysis methodologyThe case study structure is a Gravity Load Designed building, defined bymeans of a simulated design procedure according to code prescriptions anddesign practices in force in Italy between 1950s and 1970s (RDL 2229, 1939;Verderame et al., 2010a). The building is symmetric in plan, both inlongitudinal (X) and in transversal (Y) direction. It is a four-storey building,with five bays in longitudinal direction and three bays in transversal direction.Interstorey height is equal to 3.0 m, bay length is equal to 4.5 m. The structuralconfiguration follows the parallel plane frames system: gravity loads from slabsare carried only by frames in longitudinal direction. Beams in transversaldirection are present only in the external frames. Slab way is always parallel tothe transversal direction. Element dimensions are calculated according to the

Chapter IV – Numerical investigation of seismic capacity of RC buildings with infills 229allowable stresses method; the design value for maximum concretecompressive stress is assumed equal to 5.0 and 7.5 MPa for axial load and axialload combined with bending, respectively. Column dimensions are calculatedaccording only to the axial load, beam dimensions and reinforcement aredetermined from bending due to loads from slabs. Reinforcement in columnscorresponds to the minimum amount of 0.8% of the section area, as prescribedby code (RDL 2229, 1939). Reinforcing bars are smooth.Three hypotheses are made for the infill:- Case 1: infill panels are uniformly distributed along the height(Uniformly infilled frame, see Figure 4.3.1.1).- Case 2: first storey is bare and upper storeys are infilled (Pilotis frame,see Figure 4.3.1.2).- Case 3: no infill panel is present (Bare frame, see Figure 4.3.1.3).Infills panels, if present, are uniformly distributed in all the external framesof the building. Panel thickness is equal to 20cm. Presence of openings is nottaken into account.Figure 4.3.1.1. Uniformly infilled frame

230 Chapter IV – Numerical investigation of seismic capacity of RC buildings with infillsFigure 4.3.1.2. Pilotis frameFigure 4.3.1.3. Bare frameNonlinear response of RC elements is modelled by means of a lumpedplasticity approach: beams and columns are represented by elastic elementswith rotational hinges at the ends. A three-linear envelope is used, characteristic

Chapter IV – Numerical investigation of seismic capacity of RC buildings with infills 231points are cracking, yielding and ultimate. Section moment and curvature atcracking and yielding are calculated on a fiber section, for an axial load valuecorresponding to gravity loads. The behaviour is assumed linear elastic up tocracking and perfectly-plastic after yielding. Rotations at yielding and ultimateare evaluated through the formulations given in (Fardis, 2007) (see Section2.2.1.1, Eq. 2.2.1.7). No reduction of ultimate rotation for the lack of seismicdetailing is applied, due to the presence of smooth reinforcement (see Section2.2.2).Infill panels are modelled by means of equivalent struts. The adopted modelfor the envelope curve of the force-displacement relationship is the modelproposed by Panagiotakos and Fardis (see Section 3.2.4). The ratio betweenpost-capping degrading stiffness and elastic stiffness (parameter α) is assumedequal to 0.03. The ratio between residual strength and maximum strength(parameter β) is assumed equal to 0.01.Nonlinear Static Push-Over (SPO) analyses are performed on the case studybuilding both in X and Y direction. The assumed lateral load pattern isproportional to the displacement shape of the first mode. Lateral response isevaluated in terms of base shear-top displacement relationship.Structural modelling, numerical analyses and post-processing of damagedata, including the 3D graphic visualization of the deformed shape, areperformed through the “PBEE toolbox” software (Dolšek, 2010), combiningMATLAB® with OpenSees (McKenna et al., 2004). The functions for infillelements were added by the author of this thesis during a cooperation stay at theInstitute of Structural Engineering, Earthquake Engineering and Construction(IKPIR) of the Faculty of Civil and Geodetic Engineering, at the University ofLjubljana.When the lateral response is characterized by a strength degradation due toinfill failure, a multi-linearization of the pushover curve is carried out byapplying the equal energy rule respectively between the initial point and themaximum resistance point, between the maximum resistance point and thepoint corresponding to the last infill failure, between the point corresponding to

232 Chapter IV – Numerical investigation of seismic capacity of RC buildings with infillsthe last infill failure and the point corresponding to the first RC elementconventional collapse.When the lateral response is not characterized by a strength degradation(because infill elements are not present or not involved in the collapsemechanism) an elasto-plastic bi-linearization is carried out by applying theequal energy rule between the initial point and the maximum resistance point.Moreover, the procedure proposed in (Dolšek and Fajfar, 2005) to improvethe accuracy of the displacement demand assessment in the case of low seismicdemand is applied, by approximating the first part of the pushover curve by abilinear curve rather than a linear one and applying specific R-µ-T relationshipsin this range of behaviour, as proposed by the authors.Two limit states are defined: Damage Limitation (DL), corresponding to thedisplacement when the last infill reaches its maximum resistance thus startingto degrade (Dolšek and Fajfar, 2008a) or when the first yielding in RC membersoccurs, and Near Collapse (NC), corresponding to the first conventionalcollapse in RC members.Then, the IN2 curves (Dolšek and Fajfar, 2004b) for the equivalent SDOFsystems are obtained by assuming as Intensity Measure both the elastic spectralacceleration at the period of the equivalent SDOF system (S ae (T eff )) and thePeak Ground Acceleration (PGA). Values of these seismic intensity parameterscorresponding to characteristic values of displacement (ductility) demand(including the considered Limit States) are calculated, based on the R-µ-Trelationships given in (Dolšek and Fajfar, 2004a) or in (Fajfar, 1999) fordegrading or non-degrading response, respectively.Elastic spectra are the Uniform Hazard Newmark-Hall demand spectraadopted in Italian code (DM 14/1/2008) – provided in (INGV-DPC S1, 2007) –for a high seismic city in Southern Italy (Avellino, Lon.: 14.793 Lat.: 40.915).Soil type A (stiff soil) and 1 st topographic category are assumed (noamplification for stratigraphic or topographic effects).It is worth noting that a double iterative procedure is required to evaluateS ae (T eff ) and PGA from the characteristic parameters of equivalent SDOF

Chapter IV – Numerical investigation of seismic capacity of RC buildings with infills 233system – namely the ductility at the point of interest (µ), the period (T eff ) andfor degrading systems also the ductility at the beginning of the degradation (µ s )and the ratio between the residual strength and the maximum strength (r u ) – forthe following reasons:- the spectral shape depends on some parameters, such as the cornerperiod (T C ) and the ratio between the spectral acceleration on theconstant branch and the PGA (F 0 ), which are not constant with theseismic intensity (i.e., with the return period), hence also the ratiobetween S ae (T eff ) and PGA changes with the seismic intensity;- some characteristic parameters of the elastic spectrum, such as T C , areinput parameters for the R-µ-T relationship, but also depends on theresults obtained from the R-µ-T relationship since they depends on theseismic intensity.Due to the fact that the ratio between S ae (T eff ) and PGA is not constant, theIN2 curves in terms of S ae (T eff ) or in terms of PGA may have different shapes.Demand spectra are provided in (INGV-DPC S1, 2007) in terms ofparameters PGA, F 0 and T C * (which is multiplied by another coefficientdepending on stratigraphic characteristics, C C , to obtain T C ) for a range ofreturn periods from 30 to 2475 years. For intermediate values of seismicintensity, an interpolation procedure is proposed (DM 14/1/2008). Nevertheless,in this study there is the need to extend elastic demand spectra above and belowthe extreme values, as in (Crowley et al., 2009). To this aim, the formulationsproposed for the interpolation procedure are also used to extrapolate the abovementioned parameters out of the given range of values.In order to evaluate the influence of material characteristics and elementcapacity on the seismic response of the case study structure, the followingparameters are selected as Random Variables to carry out a sensitivity analysis(Section 4.3.2) and an based on the Response Surface Method (Section 4.3.2):- Concrete compressive strength f c ;

234 Chapter IV – Numerical investigation of seismic capacity of RC buildings with infills- Steel yield strength f y ;- Infill shear elastic modulus G w ;- Rotation at yielding in RC members θ y ;- Rotation at ultimate in RC members θ u .A lognormal distribution is assumed for all of the Random Variables. Eachdistribution is defined through the central (median) value and the Coefficient ofVariation (CoV).For the concrete compressive strength, reference values come from astatistical analysis on the mechanical properties of concrete employed in Italyduring 1960s (Verderame et al., 2001).For the steel yield strength, values are referred to Aq50 steel typology, themost widely spread in Italy during 1960s (Verderame et al., 2010b).The determination of infill material characteristics is affected by highdifficulties and uncertainties, and literature does not offer an enough largeamount of experimental data. In this study, a median value of 1240 MPa for theshear elastic modulus G w is adopted, provided in (Fardis, 1997), based onwallette tests carried out at the University of Pavia on specimens made up ofhollow clay bricks with a void ratio of 42%, selected as representative of typicallight non-structural masonry. Nevertheless, there are further infill mechanicalcharacteristics to be determined in order to define, according to the adoptedmodel, the load-displacement relationship of the infill trusses, namely theelastic Young’s modulus E w and the shear cracking stress τ cr . A certain amountof correlation certainly exists between these parameters, although it is not easyat all to be determined. In this study, a fully correlation is assumed, based onthe proposal of the Italian code (Circolare 617, 2009) for the mechanicalcharacteristics of hollow clay brick panels. Hence, the ratio between E w and G wis assumed equal to 10/3, whereas τ cr is assumed as linearly dependent on G w ,assuming τ cr equal to 0.3 and 0.4 MPa for G w equal to 1080 and 1620 MPa,respectively. As far as the modelling of uncertainty in infill mechanicalcharacteristics is concerned, some indications can be drawn from literature: in(Dymiotis et al., 2001) the authors state that “the model uncertainty in

Chapter IV – Numerical investigation of seismic capacity of RC buildings with infills 235predicting the masonry capacity may be accounted for effectively through theuse of two model uncertainty factors. These relate to the maximum shear stressand the area under the τ-γ envelope curve up to γ = 3γ max ”. In particular, theauthors refer to the envelope for infill response proposed in (Valiasis, 1989).Referring to these parameters the authors write that “the model uncertaintyvariables X m,τmax and X m,A , which are ratios of experimental to analyticalvalues, may be described by lognormal distributions with mean values of 0.88and 0.95 and coefficients of variation (COV) of 26 and 19%, respectively”. In(Rossetto and Elnashai, 2005) the authors assume for the random variable“infill compressive strength” a lognormal distribution with a CoV equal to 0.20.They write that “the probability distribution functions assigned to eachmaterial property for the assessment of the example infilled frame population[…] were determined through consideration of numerous tests on Europeanconstruction materials dating from the assumed time of construction, (e.g. Pipaand Carvalho, Petersons, amongst others)”, but they do not specify clearlywhat was the reference used to establish the assumed value of CoV for the infillcompressive strength. In (Calvi et al., 2004) the authors describe theexperimental results from 20 experimental test on small size wallettes. Theywrite that “the low absolute values for compression and tensile strength and thevery large dispersion of the stiffness values […] are considered to berepresentative of infill panels commonly constructed in the Mediterraneanarea”. CoV values of 0.25 and 0.36 are provided for the tensile strength and forthe shear elastic modulus, respectively. Based on these indications, a CoV equalto 0.30 is assumed for G w .As far as deformations at yielding and ultimate in RC members areconcerned, median and CoV values are evaluated starting from the valuescalculated through the formulations proposed in (Fardis, 2007) and usingmedian and CoV values of the experimental-to-predicted ratio, as illustrated bythe author.A summary of median and CoV values for the selected Random Variables isreported in Table 4.3.1.1.

236 Chapter IV – Numerical investigation of seismic capacity of RC buildings with infillsR.V. Median Value Reference Distrib. CoV Referencef cf y25.0 MPa369.7 MPaVerderame et al.,2001Verderame et al.,2010bLognormal 0.31Lognormal 0.08Verderame et al.,2001Verderame et al.,2010bG w 1240 MPa Fardis, 1997 Lognormal 0.30 -θ yθ u1.015*calculatedFardis, 2007Fardis, 2007Lognormal 0.331(Eq. 2.20a, Table 2.4)(Table 2.4)0.995*calculatedFardis, 2007Fardis, 2007Lognormal 0.409(Eq. 3.27a, Table 3.2)(Table 3.2)Table 4.3.1.1. Summary of median and CoV values for the selected Random Variables4.3.2. Sensitivity analysisBased on the assumed Random Variables, a sensitivity analysis is carriedout to investigate the influence of each variable on the seismic capacity of thecase study structure. To this aim, two models are generated for each randomvariable assuming median-minus-1.7-standard-deviation and median-plus-1.7-standard-deviation values for the considered variable, and median values for theremaining variables. The choice of these values will be better explained in nextSection, when the Response Surface Method will be used for the generation ofvulnerability curves for the case study structure.In addition to these analyses, another one is carried out assuming medianvalues for all of the variables (Model #1).In the following, obtained results are presented and discussed for Uniformlyinfilled, Pilotis and Bare frames, in both longitudinal (X) and transversal (Y)directions and at Damage Limitation and Near Collapse Limit States. The [topdisplacement, S ae (T eff )] and [top displacement, PGA] points on IN2 curvescorresponding to DL and NC Limit State are reported as yellow and red circles,respectively.

Chapter IV – Numerical investigation of seismic capacity of RC buildings with infills 237The results will be reported according to the following notation:VariableSymbolElastic period [sec]T elMDOF displacement capacity at last infill maximum [m]∆ limMDOF displacement capacity at first yielding in RC members [m]∆ fRCyMDOF displacement capacity at first RC element collapse [m]∆ collapseMaximum base shear [kN]V b,maxModal participation factorΓEffective mass [t] m*Period of the equivalent SDOF system [sec]T effDisplacement at yielding of the equivalent SDOF system [m]S dyDuctility at the beginning of the degradationµ sDuctility at the end of the degradationµ uMaximum inelastic acceleration capacity (=S ay ) [g]C s,maxMinimum inelastic acceleration capacity [g]C s,minRatio between C s,min and C s,maxr uDuctility at last infill maximumµ limDuctility at first yielding in RC membersµ fRCyDuctility at first RC element collapseµ collapseElastic spectral acceleration (at T eff ) leading to ductility demand equal to µ s [g] S ae,sElastic spectral acceleration (at T eff ) leading to last infill maximum [g]S ae,limElastic spectral acceleration (at T eff ) leading to first yielding in RC members [g] S ae,fRCyElastic spectral acceleration (at T eff ) leading to collapse [g]S ae,collapseRatio between S ae,s and S ayR sRatio between S ae,lim and S ayR limRatio between S ae,fRCy and S ayR fRCyRatio between S ae,collapse and S ayR collapsePeak ground acceleration leading to ductility demand equal to µ s [g]PGA sPeak ground acceleration leading to last infill maximum [g]PGA limPeak ground acceleration leading to first yielding in RC members [g]PGA lfRCyPeak ground acceleration leading to collapse [g]PGA collapseChange in PGA collapse compared with Model #1 [%]∆ PGA,NCChange in PGA lim compared with Model #1 [%]∆ PGA,limChange in PGA fRCy compared with Model #1 [%]∆ PGA,fRCyIt is to be noted that the influence of each single variable, which will beillustrated through the sensitivity analysis, not only depends on the influence ofthe variable on the seismic response, but also depends on the assumed

238 Chapter IV – Numerical investigation of seismic capacity of RC buildings with infillsdispersion for that variable. As a matter of fact, the amount of dispersionconsidered for the variable (through the assigned Coefficient of Variation) leadsto consider – as Lower and Upper limits – values more or less distant from thecentral (median) value. A variable characterized by a lower uncertainty (i.e., alower CoV) will have median-minus-1.7-standard-deviation and median-plus-1.7-standard-deviation values closer to the median value, and vice versa.Hence, the amount of the change in PGA capacity due to the change in eachvariable, compared with the model where median values are assigned to allvariables (Model #1), should be interpreted taking into account also the CoVvalue assigned to each variable.

Chapter IV – Numerical investigation of seismic capacity of RC buildings with infills 2394.3.2.1 Uniformly Infilled frameX direction2.52S ae(T eff) [g]1.510.500 0.02 0.04 0.06 0.08 0.1 0.12 0.14Top displacement in X direction [m]Figure 4.3.2.1. Pushover and IN2 curves for Model #1 (Uniformly Infilled frame – X direction)Figure 4.3.2.2. Deformed shape and element damage for Model #1 at NC (Uniformly Infilledframe – X direction)

240 Chapter IV – Numerical investigation of seismic capacity of RC buildings with infillsSensitivity analysisthufcVariableGwfythyUpper valueLower value-60 -40 -20 0 20 40 60Change in PGA at collapse (%)Figure 4.3.2.3. Results of sensitivity analysis for NC LS (Uniformly Infilled frame – Xdirection)Pushover and IN2 curves for Model #1 in X direction are reported in Figure4.3.2.1. Results of sensitivity analysis for NC and DL Limit States are reportedin Figures 4.3.2.3 and 4.3.2.8, respectively.The building collapses under a soft-storey mechanism at the 1 st storey in allcases except when a lower value is assumed for infill mechanicalcharacteristics: in this case there is a soft-storey mechanism at the 2 nd storey.The sensitivity analysis shows that θ u has the highest influence on the PGAat collapse. This is clearly due to the fact the displacement capacity at collapseis directly given by the rotational capacity of columns, given the soft-storeycollapse mechanism. Thus, an increase in θ u results in an increase in ∆ collapse ,that is, an increase in µ collapse , leading to higher values of S ae,collapse (see Figure4.3.2.4) and, hence, of PGA collapse (see Figure 4.3.2.5). Vice versa if θ udecreases.f c influences the collapse capacity through the value of θ u : given equal theaxial load, as f c increases the axial load ratio decreases and the rotational

Chapter IV – Numerical investigation of seismic capacity of RC buildings with infills 241capacity of the columns increases, thus leading to a higher global ductility. Viceversa if f c decreases.When E w , G w and τ cr increase, several effects can be observed: the increasein stiffness and strength leads to a lower T eff and a higher C s,max ; C s,min does notchange significantly, hence a decrease in r u is observed. ∆ collapse does not changesignificantly, but the decrease in S dy leads to an increase in µ collapse .In R-µ-T relationships, as T eff decreases, given equal the ductility µ, Rdecreases too; as µ increases, given equal the period T eff , R increases. If theeffective stiffness of the equivalent system increases but the strength and thedisplacement capacity do not change (i.e., only a decrease in S dy is observed),both these effects are observed (decrease in T eff and increase in µ) but the lattertends to prevail over the former, leading to a higher R.Nevertheless, in our case the increase in µ collapse is only given by thedecrease in S dy , whereas the decrease in T eff is given not only by the lower S dybut also by the higher C s,max . Hence, the effect of the decrease in T eff prevailsover the increase in µ collapse , finally leading to a lower value of R.Moreover, the detrimental effect of the decrease in r u also leads to a lowervalue of R. Hence, these effects globally lead to a much lower value of R collapse ;however, the higher base shear capacity C s,max leads to a value of S ae,collapse onlyslightly lower, compared with Model #1 (see Figure 4.3.2.6). Nevertheless, dueto the decrease in T eff , this lower value of S ae,collapse corresponds to a highervalue of PGA collapse (see Figure 4.3.2.7).When E w , G w and τ cr decrease, the building collapses under a soft-storeymechanism at the 2 nd storey instead of the 1 st one. From a qualitativestandpoint, a higher infill strength leads to a more uniform distribution ofmaximum interstorey shear strength along the height of the building: moreuniform is this distribution, higher is the probability to have a soft storeymechanism at the 1 st storey, where the shear demand is higher. For the samereasons, a lower infill strength may lead to the formation of a soft-storeymechanism at the 2 nd storey instead of the 1 st one. At the 2 nd storey the strengthof RC columns is lower, thus leading to a lower value of the residual strength

242 Chapter IV – Numerical investigation of seismic capacity of RC buildings with infillsC s,min , which is essentially due to the contribution of RC frame due to thefailure of infills.Opposite observations, compared with the previous case, can be made: thedecrease in stiffness and strength leads to a higher T eff and a lower C s,max ;hence, an increase in r u is observed. ∆ collapse does not change significantly, butthe increase in S dy leads to a decrease in µ collapse . These effects globally lead to amuch higher value of R collapse ; however, the lower base shear capacity C s,maxleads to a lower value of S ae,collapse compared with Model #1 (see Figure4.3.2.6), also resulting in a lower PGA collapse (see Figure 4.3.2.7).The only parameter significantly influenced by f y is the residual base shearC s,min . An increase in f y results in a higher C s,min , thus leading to a higher r u .This beneficial effect results in a higher R collapse , leading to higher values ofS ae,collapse and PGA collapse . Vice versa if f y decreases.The rotation at yielding θ y has no significant influence on PGA capacity atcollapse.

Chapter IV – Numerical investigation of seismic capacity of RC buildings with infills 2433.532.5S ae(T eff) [g]21.510.500 0.05 0.1 0.15 0.2 0.25 0.3 0.35Top displacement in X direction [m]Figure 4.3.2.4. Pushover and IN2 curves in terms of S ae (T eff ) for Models #10, #1 and #11:Lower, Median and Upper values for θ u (Uniformly Infilled frame – X direction)1.41.21PGA [g]0.80.60.40.200 0.05 0.1 0.15 0.2 0.25 0.3 0.35Top displacement in X direction [m]Figure 4.3.2.5. IN2 curves in terms of PGA for Models #10, #1 and #11: Lower, Median andUpper values for θ u (Uniformly Infilled frame – X direction)

244 Chapter IV – Numerical investigation of seismic capacity of RC buildings with infills2.52S ae(T eff) [g]1.510.500 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16Top displacement in X direction [m]Figure 4.3.2.6. Pushover and IN2 curves in terms of S ae (T eff ) for Models #6, #1 and #7: Lower,Median and Upper values for infill mechanical characteristics (Uniformly Infilled frame – Xdirection)0.90.80.70.6PGA [g]0.50.40.30.20.100 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16Top displacement in X direction [m]Figure 4.3.2.7. IN2 curves in terms of PGA for Models #6, #1 and #7: Lower, Median andUpper values for infill mechanical characteristics (Uniformly Infilled frame – X direction)

Chapter IV – Numerical investigation of seismic capacity of RC buildings with infills 245Sensitivity analysisGwfcVariablefythythuUpper valueLower value-60 -40 -20 0 20 40 60Change in PGA at last infill maximum (%)Figure 4.3.2.8. Results of sensitivity analysis for DL LS (Uniformly Infilled frame – Xdirection)As far as PGA capacity at last infill maximum is concerned, from aqualitative standpoint, the same trend observed for PGA capacity at collapsewith the infill mechanical characteristics are observed. Hence, a beneficialeffect of an increase in stiffness and strength is observed.When f c increases, C s,max increases too, mainly due to the highercontribution of RC columns – due to their higher stiffness and strength – to themaximum base shear, which corresponds to the attainment of the maximumstrength in the infills in the storey involved in collapse and is attained for thesame displacement. On the whole, the change in f c does not influencesignificantly R lim , but the increase in C s,max leads to higher values of S ae,lim andPGA lim . Vice versa if f c decreases.Remaining parameters do not have a significant influence on PGA lim .

246 Chapter IV – Numerical investigation of seismic capacity of RC buildings with infillsY direction21.81.61.4S ae(T eff) [g]1.210.80.60.40.200 0.02 0.04 0.06 0.08 0.1 0.12 0.14Top displacement in Y direction [m]Figure 4.3.2.9. Pushover and IN2 curves for Model #1 (Uniformly Infilled frame – Y direction)Figure 4.3.2.10. Deformed shape and element damage for Model #1 at NC (Uniformly Infilledframe – Y direction)

Chapter IV – Numerical investigation of seismic capacity of RC buildings with infills 247Sensitivity analysisthufcVariableGwfythyUpper valueLower value-60 -40 -20 0 20 40 60Change in PGA at collapse (%)Figure 4.3.2.11. Results of sensitivity analysis for NC LS (Uniformly Infilled frame – Ydirection)Pushover and IN2 curves for Model #1 in Y direction are reported in Figure4.3.2.9. Results of sensitivity analysis for NC and DL Limit States are reportedin Figures 4.3.2.11 and 4.3.2.14, respectively.The building collapses under a soft-storey mechanism at the 2 nd storey in allcases except when a lower value is assumed for f c and when an upper value isassumed for infill mechanical characteristics. In these cases, the storey involvedby the collapse mechanism is the 1 st one. As already highlighted, a lowerstiffness and/or strength of the RC structure and a higher strength of infills leadto a more uniform distribution of maximum interstorey shear strength along theheight of the building: more uniform is this distribution, higher is theprobability to have a soft storey mechanism at the 1 st storey, where the sheardemand is higher. The attention has to be focused not only on the strength ofthe RC structure, but also on its stiffness. As a matter of fact, in infilled RCframes the soft-storey collapse mechanism generally takes place at the storeywhere – under the given distribution of lateral forces – the maximum ratiobetween the interstorey shear demand and the interstorey shear strength takes

248 Chapter IV – Numerical investigation of seismic capacity of RC buildings with infillsplace. From a qualitative standpoint, the latter value is provided by the strengthcontribution of infills, corresponding to their maximum resistance and attainedfor rather low displacement values, and by a contribution of RC columns,which at this stage of behaviour have not developed their entire strength yet.Hence, the latter contribution is significantly influenced by stiffness of RCelements, and not only by their strength.As already illustrated for the X direction, when E w , G w and τ cr increase,several effects are observed, including the decrease in r u , globally leading to alower value of R collapse ; this effect may or may not be counterbalanced by thehigher C s,max . Opposite to X direction, in the case of Y direction the effect ofdecrease in R collapse prevails over the increase in C s,max , leading to a lowerS ae,collapse (see Figure 4.3.2.12) and also to a lower PGA collapse (see Figure4.3.2.13). Vice versa when lower values of infill mechanical characteristics areconsidered.The influence of remaining parameter is quite similar to X direction.

Chapter IV – Numerical investigation of seismic capacity of RC buildings with infills 2492.52S ae(T eff) [g]1.510.500 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16Top displacement in Y direction [m]Figure 4.3.2.12. Pushover and IN2 curves in terms of S ae (T eff ) for Models #6, #1 and #7: Lower,Median and Upper values for infill mechanical characteristics (Uniformly Infilled frame – Ydirection)0.80.70.60.5PGA [g]0.40.30.20.100 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16Top displacement in Y direction [m]Figure 4.3.2.13. IN2 curves in terms of PGA for Models #6, #1 and #7: Lower, Median andUpper values for infill mechanical characteristics (Uniformly Infilled frame – Y direction)

250 Chapter IV – Numerical investigation of seismic capacity of RC buildings with infillsSensitivity analysisGwfcVariablethyfythuUpper valueLower value-60 -40 -20 0 20 40 60Change in PGA at last infill maximum (%)Figure 4.3.2.14. Results of sensitivity analysis for DL LS (Uniformly Infilled frame – Ydirection)As far as PGA capacity at last infill maximum is concerned, opposite toPGA capacity at collapse, a beneficial effect of the increase in E w , G w and τ cr isobserved; as a matter of fact, see Figure 4.3.2.12, the beneficial effect of ahigher strength (higher value of C s,max ) on the capacity – in terms of S ae (T eff ) –is more important when the ductility capacity is in a lower range of values (e.g.,DL limit state). If the ductility capacity is, on average, higher (e.g., NC limitstate), the detrimental effect of a more brittle behaviour (lower value of r u ) onthe corresponding capacity – expressed as S ae (T eff ) – tends to prevail. This trendis reflected by the decrease in the slope of IN2 curves when the infillmechanical characteristics assume upper values.Based on these observations, when E w , G w and τ cr decrease a lower PGAcapacity at last infill maximum is expected. Nevertheless, due to the fullcorrelation assumed between the infill mechanical characteristics, in theadopted model a lower strength and a lower secant-to-maximum stiffness areobserved at the same time, resulting in a higher displacement capacity at thisLimit State. This effect partially counterbalances the detrimental effect of lower

Chapter IV – Numerical investigation of seismic capacity of RC buildings with infills 251initial stiffness and strength, leading to a only slightly lower PGA capacity atlast infill maximum.Remaining parameters do not have a significant influence on the PGAcapacity at last infill maximum.Comparison between X and Y directionsIf a comparison is carried out between the seismic capacity in X and Ydirections for Model #1 (see Figures 4.3.2.15 and 4.3.2.16) it is observed howthe displacement capacity does not change significantly and the beneficial effectof a higher strength, both maximum (C s,max ) and residual (C s,min ), leads tohigher PGA capacities in X direction, both at collapse and last infill maximum.The higher strength in X direction compared with Y direction is due (i) to thelarger amount of infill panels in X direction and (ii) to the orientation of columnelements, which, following the parallel plane frame configuration, provide ahigher strength in X direction.2.52S ae(T eff) [g]1.510.500 0.02 0.04 0.06 0.08 0.1 0.12 0.14Top displacement [m]Figure 4.3.2.15. Pushover and IN2 curves in terms of S ae (T eff ) for Model #1 in X and Ydirections (Uniformly Infilled frame)

252 Chapter IV – Numerical investigation of seismic capacity of RC buildings with infills0.90.80.70.6PGA [g]0.50.40.30.20.100 0.02 0.04 0.06 0.08 0.1 0.12 0.14Top displacement [m]Figure 4.3.2.16. IN2 curves in terms of PGA for Model #1 in X and Y directions (UniformlyInfilled frame)

Chapter IV – Numerical investigation of seismic capacity of RC buildings with infills 253ModelNo.ModifiedVariableStoreyValue T el ∆ lim ∆ coll T eff µ s C s,max C s,min r u µ lim µ coll R lim R coll S ae,lim S ae,coll PGA lim PGA coll involved incollapse∆ PGA,NC ∆ PGA,lim1 - - 0.13 0.01 0.14 0.16 3.04 0.73 0.29 0.39 2.21 23.26 1.33 2.97 0.97 2.17 0.38 0.80 1 - -2 f cµ-1.7σ 0.13 0.01 0.11 0.16 2.89 0.70 0.26 0.37 2.23 18.74 1.34 2.62 0.94 1.84 0.37 0.69 1 -14.4 -2.53 " µ+1.7σ 0.13 0.01 0.17 0.16 2.94 0.76 0.30 0.40 2.15 27.21 1.31 3.19 0.99 2.42 0.39 0.90 1 12.3 2.54 f yµ-1.7σ 0.13 0.01 0.14 0.16 3.00 0.73 0.27 0.37 2.21 23.29 1.33 2.88 0.97 2.10 0.38 0.78 1 -3.1 0.25 " µ+1.7σ 0.13 0.01 0.14 0.16 3.04 0.73 0.30 0.41 2.20 23.28 1.33 3.08 0.97 2.24 0.38 0.83 1 3.4 -0.26 G wµ-1.7σ 0.16 0.02 0.16 0.20 3.44 0.57 0.23 0.41 2.41 20.95 1.50 3.74 0.85 2.13 0.34 0.79 2 -2.2 -10.87 " µ+1.7σ 0.10 0.01 0.14 0.13 2.57 1.00 0.29 0.29 2.21 25.46 1.25 2.01 1.26 2.02 0.52 0.85 1 6.0 35.78 θ yµ-1.7σ 0.13 0.01 0.14 0.16 3.05 0.73 0.29 0.39 2.20 23.19 1.33 2.97 0.97 2.17 0.38 0.80 1 0.0 0.19 " µ+1.7σ 0.13 0.01 0.14 0.16 3.02 0.73 0.29 0.39 2.21 23.38 1.33 2.98 0.97 2.17 0.38 0.80 1 0.1 -0.210 θ uµ-1.7σ 0.13 0.01 0.07 0.16 3.04 0.73 0.29 0.39 2.21 12.21 1.33 2.25 0.97 1.64 0.38 0.62 1 -23.0 0.011 " µ+1.7σ 0.13 0.01 0.27 0.16 3.04 0.73 0.29 0.39 2.21 44.82 1.33 4.17 0.97 3.04 0.38 1.15 1 42.6 0.0Table 4.3.2.1. Results of pushover and IN2 analyses on the Uniformly Infilled frame in X directionModelNo.ModifiedVariableStoreyValue T el ∆ lim ∆ coll T eff µ s C s,max C s,min r u µ lim µ coll R lim R coll S ae,lim S ae,coll PGA lim PGA coll involved incollapse∆ PGA,NC ∆ PGA,lim1 - - 0.17 0.02 0.15 0.22 2.81 0.44 0.20 0.45 2.20 22.29 1.48 4.39 0.65 1.94 0.27 0.72 2 - -2 f cµ-1.7σ 0.18 0.01 0.11 0.22 2.94 0.43 0.21 0.48 2.23 16.81 1.49 3.87 0.64 1.65 0.26 0.62 1 -13.4 -2.33 " µ+1.7σ 0.17 0.02 0.18 0.22 3.04 0.45 0.21 0.46 3.04 26.71 1.77 4.95 0.79 2.22 0.32 0.82 2 13.2 19.84 f yµ-1.7σ 0.17 0.02 0.15 0.22 2.86 0.44 0.19 0.42 2.19 22.26 1.48 4.25 0.65 1.88 0.27 0.70 2 -2.8 0.05 " µ+1.7σ 0.17 0.02 0.15 0.22 2.80 0.44 0.21 0.48 2.21 22.44 1.48 4.57 0.65 2.01 0.27 0.75 2 3.4 0.06 G wµ-1.7σ 0.22 0.02 0.16 0.27 3.63 0.33 0.20 0.59 2.86 21.08 1.91 6.31 0.63 2.08 0.26 0.77 2 6.8 -3.17 " µ+1.7σ 0.14 0.01 0.14 0.18 2.56 0.61 0.22 0.37 2.15 22.93 1.35 3.09 0.82 1.88 0.33 0.70 1 -2.8 23.68 θ yµ-1.7σ 0.17 0.02 0.15 0.22 2.83 0.44 0.20 0.45 2.26 22.33 1.50 4.40 0.66 1.94 0.27 0.72 2 0.2 1.49 " µ+1.7σ 0.17 0.02 0.15 0.22 2.80 0.44 0.20 0.45 2.20 22.30 1.48 4.40 0.65 1.94 0.27 0.72 2 -0.1 0.010 θ uµ-1.7σ 0.17 0.02 0.08 0.22 2.81 0.44 0.20 0.44 2.20 12.05 1.48 3.09 0.65 1.36 0.27 0.52 2 -27.5 0.011 " µ+1.7σ 0.17 0.02 0.29 0.22 2.81 0.44 0.20 0.45 2.20 42.27 1.48 6.59 0.65 2.90 0.27 1.04 2 44.9 0.0Table 4.3.2.2. Results of pushover and IN2 analyses on the Uniformly Infilled frame in Y direction

254 Chapter IV – Numerical investigation of seismic capacity of RC buildings with infills4.3.2.2 Pilotis frameX direction2.52S ae(T eff) [g]1.510.500 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18Top displacement in X direction [m]Figure 4.3.2.17. Pushover and IN2 curves for Model #1 (Pilotis frame – X direction)Figure 4.3.2.18. Deformed shape and element damage for Model #1 at NC (Pilotis frame – Xdirection)

Chapter IV – Numerical investigation of seismic capacity of RC buildings with infills 255Sensitivity analysisthufcVariableGwfythyUpper valueLower value-60 -40 -20 0 20 40 60Change in PGA at collapse (%)Figure 4.3.2.19. Results of sensitivity analysis for NC LS (Pilotis frame – X direction)Pushover and IN2 curves for Model #1 in X direction are reported in Figure4.3.2.17. Results of sensitivity analysis for NC and DL Limit States are reportedin Figures 4.3.2.19 and 4.3.2.22, respectively.The building collapses under a soft-storey mechanism at the 1 st storey,where infills are not present, in all cases.Similar to previous cases, the sensitivity analysis shows that θ u has thehighest influence on the PGA at collapse through ∆ collapse , that is, throughµ collapse , directly influencing S ae,collapse (see Figure 4.3.2.20) and, hence,PGA collapse (see Figure 4.3.2.21).f c also influences the collapse capacity through the value of θ u , as alreadyillustrated.The beneficial effect of the increase in E w , G w and τ cr is due to fact that inhis case the distribution of lateral forces is closer to a uniform distribution (thisis reflected by the decrease in the modal participation factor Γ), leading to ahigher initial stiffness of the pushover curve, resulting in lower values of T effand S dy , whereas the displacement capacity ∆ collapse does not change

256 Chapter IV – Numerical investigation of seismic capacity of RC buildings with infillssignificantly and, hence, µ collapse increases. Given practically equal the strengthC s,max , in R-µ-T relationships, as already illustrated, the latter (beneficial) effectprevails over the former (detrimental) effect leading to higher values ofS ae,collapse and PGA collapse .An increase in f y leads to a higher C s,max , but also to higher values of S dy andT eff . Given practically equal the displacement capacity ∆ collapse , µ collapse decreasesand this effect prevails over the beneficial increase in C s,max , leading to lowervalues of S ae,collapse and PGA collapse . Vice versa if f y decreases.The rotation at yielding θ y has no significant influence on PGA capacity atcollapse.

Chapter IV – Numerical investigation of seismic capacity of RC buildings with infills 25743.53S ae(T eff) [g]2.521.510.500 0.05 0.1 0.15 0.2 0.25 0.3 0.35Top displacement in X direction [m]Figure 4.3.2.20. Pushover and IN2 curves in terms of S ae (T eff ) for Models #10, #1 and #11:Lower, Median and Upper values for θ u (Pilotis frame – X direction)1.41.21PGA [g]0.80.60.40.200 0.05 0.1 0.15 0.2 0.25 0.3 0.35Top displacement in X direction [m]Figure 4.3.2.21. IN2 curves in terms of PGA for Models #10, #1 and #11: Lower, Median andUpper values for θ u (Pilotis frame – X direction)

258 Chapter IV – Numerical investigation of seismic capacity of RC buildings with infillsSensitivity analysisfcfyVariableGwthythuUpper valueLower value-60 -40 -20 0 20 40 60Change in PGA at first RC yielding (%)Figure 4.3.2.22. Results of sensitivity analysis for DL LS (Pilotis frame – X direction)When f c decreases, both S dy and ∆ fRCy increase, but the former effectprevails on the latter, leading to a lower value of µ fRCy and, hence, of R fRCy .Moreover, the detrimental effect of a decrease in f c on S ae,fRCy is also given bythe decrease in C s,max . Vice versa when f c increases.Opposite to the case of f c , when f y decreases both S dy and ∆ fRCy decrease, butthe former effect prevails on the latter, leading to a higher value of µ fRCy and,hence, of R fRCy . Nevertheless, the detrimental effect of the decrease in C s,maxprevails. Vice versa when f y increases.Contrary to expectations, an increase in θ y does not have a great beneficialinfluence on S ae,fRCy and, hence, on PGA fRCy . This is due to the fact that whenθ y increases, the displacement capacity ∆ fRCy increases, but S dy increases too,leading to a not much different value of µ fRCy and, hence, of R fRCy .An increase in E w , G w and τ cr , as already illustrated, leads to a higher initialstiffness of the pushover curve, resulting in lower values of S dy but also of∆ fRCy . These two effects counterbalance each other, globally leading to nosignificant change in µ fRCy and, hence, in R fRCy . When E w , G w and τ cr decrease,

Chapter IV – Numerical investigation of seismic capacity of RC buildings with infills 259both S dy and ∆ fRCy increase, but the former effect prevails on the latter, leadingto a lower value of µ fRCy and, hence, of R fRCy .Y direction1.41.21S ae(T eff) [g]0.80.60.40.200 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16Top displacement in Y direction [m]Figure 4.3.2.23. Pushover and IN2 curves for Model #1 (Pilotis frame – Y direction)Figure 4.3.2.24. Deformed shape and element damage for Model #1 at NC (Pilotis frame – Ydirection)

260 Chapter IV – Numerical investigation of seismic capacity of RC buildings with infillsSensitivity analysisthufcVariablefyGwthyUpper valueLower value-60 -40 -20 0 20 40 60Change in PGA at collapse (%)Figure 4.3.2.25. Results of sensitivity analysis for NC LS (Pilotis frame – Y direction)Pushover and IN2 curves for Model #1 in Y direction are reported in Figure4.3.2.23. Results of sensitivity analysis for NC and DL Limit States are reportedin Figures 4.3.2.25 and 4.3.2.26, respectively.Also in this direction, the building always collapses under a soft-storeymechanism at the 1 st storey, where infills are not present.The same considerations made for X direction can be reported for allparameters, except infill mechanical characteristics since in this direction theirinfluence – which was already not particularly significant in X direction – isabsolutely negligible, due to the lower number of infill panels in Y direction.

Chapter IV – Numerical investigation of seismic capacity of RC buildings with infills 261Sensitivity analysisfyfcVariablethyGwthuUpper valueLower value-60 -40 -20 0 20 40 60Change in PGA at first RC yielding (%)Figure 4.3.2.26. Results of sensitivity analysis for DL LS (Pilotis frame – Y direction)From a qualitative standpoint, analyzed parameters influence the PGAcapacity at first RC yielding by the same way in Y direction, compared with Xdirection. Again, the only exception is for infill mechanical characteristics,whose influence on the seismic behaviour in Y direction is absolutelynegligible.

262 Chapter IV – Numerical investigation of seismic capacity of RC buildings with infillsComparison between X and Y directionsIf a comparison is carried out between the seismic capacity in X and Ydirections for Model #1 (see Figures 4.3.2.27 and 4.3.2.28) it is observed howthe displacement capacity at collapse does not change significantly and thebeneficial effect of the higher strength in X direction compared with Ydirection, due to the orientation of column elements – which, following theparallel plane frame configuration, provide a higher strength in X direction –leads to a higher S ae,collapse and also to a higher PGA collapse in X direction. Thedifference between the values of S ae,collapse in X and Y directions is higher thanthe difference between the values of PGA collapse , due to the difference in T effbetween the two directions.As far as first RC yielding is concerned, column orientation leads to a lowerdisplacement capacity in X direction compared with Y direction; nevertheless,beneficial effect of the higher strength in X direction leads to a higher seismiccapacity in terms of S ae also at this Limit State. Again, due to the difference inT eff between the two directions, the difference between the values of S ae,fRCy inX and Y directions is higher than the difference between the values of PGA fRCy .2.52S ae(T eff) [g]1.510.500 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18Top displacement [m]Figure 4.3.2.27. Pushover and IN2 curves in terms of S ae (T eff ) for Model #1 in X and Ydirections (Pilotis frame)

Chapter IV – Numerical investigation of seismic capacity of RC buildings with infills 2630.90.80.70.6PGA [g]0.50.40.30.20.100 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18Top displacement [m]Figure 4.3.2.28. IN2 curves in terms of PGA for Model #1 in X and Y directions (Pilotis frame)

264 Chapter IV – Numerical investigation of seismic capacity of RC buildings with infillsModelNo.ModifiedVariableStoreyValue T el ∆ fRCy ∆ coll T eff C s,max µ fRCy µ coll R fRCy R coll S ae,fRCy S ae,coll PGA fRCy PGA coll involved incollapse∆ PGA,NC ∆ PGA,fRCy1 - - 0.39 0.02 0.14 0.49 0.24 1.12 9.15 1.12 9.11 0.27 2.22 0.16 0.82 1 - -2 f c µ-1.7σ 0.46 0.02 0.11 0.57 0.22 1.01 5.83 1.01 5.83 0.22 1.30 0.15 0.61 1 -25.7 -4.33 " µ+1.7σ 0.35 0.02 0.17 0.43 0.26 1.33 13.92 1.33 11.52 0.34 2.96 0.17 1.06 1 30.0 7.04 f yµ-1.7σ 0.38 0.02 0.14 0.48 0.23 1.15 10.14 1.15 9.83 0.27 2.28 0.15 0.84 1 2.1 -4.55 " µ+1.7σ 0.40 0.02 0.14 0.52 0.26 1.05 7.89 1.05 7.89 0.27 2.04 0.16 0.79 1 -3.4 3.26 G wµ-1.7σ 0.39 0.02 0.14 0.52 0.24 1.02 8.18 1.02 8.18 0.25 2.00 0.15 0.78 1 -4.6 -3.97 " µ+1.7σ 0.38 0.02 0.14 0.48 0.24 1.16 9.58 1.16 9.35 0.28 2.28 0.16 0.84 1 2.3 1.48 θ y µ-1.7σ 0.38 0.02 0.14 0.50 0.24 1.06 8.86 1.06 8.86 0.26 2.16 0.15 0.81 1 -1.3 -3.49 " µ+1.7σ 0.39 0.02 0.14 0.50 0.24 1.12 8.79 1.12 8.79 0.27 2.15 0.16 0.81 1 -1.5 1.410 θ uµ-1.7σ 0.39 0.02 0.07 0.49 0.24 1.12 4.71 1.12 4.71 0.27 1.15 0.16 0.49 1 -39.6 0.011 " µ+1.7σ 0.39 0.02 0.27 0.49 0.24 1.12 17.80 1.12 15.92 0.27 3.88 0.16 1.36 1 66.6 0.0Table 4.3.2.3. Results of pushover and IN2 analyses on the Pilotis frame in X directionModelNo.ModifiedVariableStoreyValue T el ∆ fRCy ∆ coll T eff C s,max µ fRCy µ coll R fRCy R coll S ae,fRCy S ae,coll PGA fRCy PGA coll involved incollapse∆ PGA,NC ∆ PGA,fRCy1 - - 0.54 0.02 0.14 0.68 0.19 0.98 6.18 0.99 6.18 0.18 1.15 0.15 0.63 1 - -2 f c µ-1.7σ 0.61 0.02 0.11 0.77 0.17 0.89 3.94 0.91 3.94 0.16 0.68 0.15 0.47 1 -25.8 -2.33 " µ+1.7σ 0.49 0.02 0.17 0.61 0.20 1.10 8.90 1.10 8.90 0.21 1.74 0.16 0.80 1 26.1 4.44 f yµ-1.7σ 0.53 0.02 0.14 0.65 0.18 1.04 7.17 1.04 7.17 0.18 1.26 0.14 0.66 1 3.5 -4.35 " µ+1.7σ 0.55 0.02 0.14 0.71 0.20 0.94 5.38 0.95 5.38 0.19 1.07 0.16 0.62 1 -2.8 5.96 G wµ-1.7σ 0.55 0.02 0.14 0.69 0.19 0.96 6.03 0.97 6.03 0.18 1.13 0.15 0.63 1 -0.6 -0.37 " µ+1.7σ 0.54 0.02 0.14 0.69 0.19 0.95 6.05 0.96 6.05 0.18 1.13 0.15 0.63 1 -0.4 -1.18 θ y µ-1.7σ 0.54 0.02 0.14 0.68 0.19 0.97 6.24 0.98 6.24 0.18 1.16 0.15 0.64 1 0.4 -1.39 " µ+1.7σ 0.55 0.02 0.14 0.68 0.19 1.01 6.14 1.01 6.14 0.19 1.15 0.15 0.63 1 -0.2 2.410 θ uµ-1.7σ 0.54 0.02 0.07 0.68 0.19 0.98 3.19 0.99 3.19 0.18 0.60 0.15 0.38 1 -39.4 0.011 " µ+1.7σ 0.54 0.02 0.27 0.68 0.19 0.98 11.99 0.99 11.99 0.18 2.24 0.15 1.05 1 65.5 0.0Table 4.3.2.4. Results of pushover and IN2 analyses on the Pilotis frame in Y direction

Chapter IV – Numerical investigation of seismic capacity of RC buildings with infills 2654.3.2.3 Bare frameX direction0.70.60.5S ae(T eff) [g]0.40.30.20.100 0.05 0.1 0.15 0.2 0.25Top displacement in X direction [m]Figure 4.3.2.29. Pushover and IN2 curves for Model #1 (Bare frame – X direction)Figure 4.3.2.30. Deformed shape and element damage for Model #1 at NC (Bare frame – Xdirection)

266 Chapter IV – Numerical investigation of seismic capacity of RC buildings with infillsSensitivity analysisthuVariablefcfythyUpper valueLower value-60 -40 -20 0 20 40 60Change in PGA at collapse (%)Figure 4.3.2.31. Results of sensitivity analysis for NC LS (Bare frame – X direction)Pushover and IN2 curves for Model #1 in X direction are reported in Figure4.3.2.29. Results of sensitivity analysis for NC and DL Limit States are reportedin Figures 4.3.2.31 and 4.3.2.32, respectively.The building collapses under a soft-storey mechanism at the 3 rd storey in allcases. The formation of a soft-storey mechanism also without the presence ofinfill panels is likely to occur in such a building, which has not been designedfor seismic loads and, obviously, does not comply with Capacity Designprinciples such as weak beam/strong column condition. In the Uniformlyinfilled frame the soft-storey mechanism occurs at one storey at the bottom (1 stor 2 nd storey), thus confirming the well-known phenomenon of concentration ofdisplacement demand in bottom storeys in this kind of structures, due to themore uniform distribution of strength along the height, whereas in the Bareframe this mechanism occurs at the 3 rd storey, where a decrease in columndimension (and strength) is observed, due to the Gravity Load Designprocedure.

Chapter IV – Numerical investigation of seismic capacity of RC buildings with infills 267Again, the sensitivity analysis shows that θ u has the highest influence on thePGA at collapse through ∆ collapse , that is, through µ collapse , directly influencingS ae,collapse and, hence, PGA collapse .Similarly, f c also influences the collapse capacity through the value of θ u , asalready illustrated.When f y increases, the displacement capacity ∆ collapse does not changesignificantly, but S dy increases, thus leading to a reduction in µ collapse .Nevertheless, this effect is counterbalanced by the increase in C s,max , resultingin no significant change in S ae,collapse and PGA collapse . Vice versa if f y decreases.The rotation at yielding θ y has no significant influence on PGA capacity atcollapse.Sensitivity analysisfyVariablefcthythuUpper valueLower value-60 -40 -20 0 20 40 60Change in PGA at first RC yielding (%)Figure 4.3.2.32. Results of sensitivity analysis for DL LS (Bare frame – X direction)When f y decreases both S dy and ∆ fRCy decrease, but (contrary to the Pilotisframe) the latter effect prevails on the former, leading to a lower value of µ fRCyand, hence, of R fRCy . Moreover, the decrease in C s,max leads to a further decreasein S ae,fRCy and PGA fRCy . Vice versa when f y increases.

268 Chapter IV – Numerical investigation of seismic capacity of RC buildings with infillsFor the same reasons illustrated for the Pilotis frame, when f c decreases alower value of S ae,fRCy is observed. Nevertheless, the increase in T effcounterbalances this effect, leading to a slightly higher capacity in terms ofPGA. Vice versa when f c increases.Again, an increase in θ y does not have a great beneficial influence on S ae,fRCyand, hence, on PGA fRCy , for the same reasons above illustrated for the Pilotisframe: when θ y increases, the displacement capacity ∆ fRCy increases, but S dyincreases too, leading to a not much different value of µ fRCy and, hence, ofR fRCy .As expected, θ u has no significant influence on PGA capacity at this LimitState.Y direction0.40.350.3S ae(T eff) [g]0.250.20.150.10.0500 0.1 0.2 0.3 0.4 0.5 0.6 0.7Top displacement in Y direction [m]Figure 4.3.2.33. Pushover and IN2 curves for Model #1 (Bare frame – Y direction)

Chapter IV – Numerical investigation of seismic capacity of RC buildings with infills 269Figure 4.3.2.34. Deformed shape and element damage for Model #1 at NC (Bare frame – Ydirection)Sensitivity analysisthuVariablefcfythyUpper valueLower value-60 -40 -20 0 20 40 60Change in PGA at collapse (%)Figure 4.3.2.35. Results of sensitivity analysis for NC LS (Bare frame – Y direction)Pushover and IN2 curves for Model #1 in Y direction are reported in Figure4.3.2.33. Results of sensitivity analysis for NC and DL Limit States are reported

270 Chapter IV – Numerical investigation of seismic capacity of RC buildings with infillsin Figures 4.3.2.35 and 4.3.2.36, respectively.In this direction, the building always collapses under a global mechanism atinvolving all the four storeys. This collapse mechanism is certainly stronglyinfluenced by the structural configuration, where beams in transversal directionare present only in external frames. A strong difference with the Uniformlyinfilled and the Pilotis frame, where the presence of infill panels forces thecollapse mechanism to develop only in one storey (at the bottom), is noted.As far as the influence of single variables is concerned, the main influenceof displacement capacity through θ u and, indirectly, through f c is observedagain.The decrease in f y leads to a lower value of S dy , whereas the displacementcapacity ∆ collapse does not change significantly, thus leading to a higher µ collapseand, hence, to a higher R collapse . However, this effect is counterbalanced by alower C s,max , thus leading to a only slightly higher PGA collapse .Sensitivity analysisfyVariablefcthythuUpper valueLower value-60 -40 -20 0 20 40 60Change in PGA at first RC yielding (%)Figure 4.3.2.36. Results of sensitivity analysis for DL LS (Bare frame – Y direction)Similar to PGA capacity at collapse, it is observed that the decrease in f yleads to a lower value of S dy , whereas the displacement capacity ∆ fRCy also

Chapter IV – Numerical investigation of seismic capacity of RC buildings with infills 271decreases but in a lower measure, thus leading to a higher µ fRCy and, hence, to ahigher R fRCy . However, this effect is counterbalanced by a lower C s,max , thusleading to a only slightly higher PGA fRCy .As far as θ y is concerned, it is observed again that when θ y increases, thedisplacement capacity ∆ fRCy increases, but S dy increases too, thuscounterbalancing the former effect. Vice versa when θ y decreases.For the same reasons, also f c has a negligible influence on PGA capacity atfirst RC yielding.Comparison between X and Y directionsIf a comparison is carried out between the seismic capacity in X and Ydirections for Model #1 (see Figures 4.3.2.37 and 4.3.2.38) a clear difference isobserved in the lateral response of the building: the column-sway storeymechanism in X direction leads to a higher strength but also to a lowerductility, whereas the opposite happens in Y direction, where a globalmechanism occurs. Globally, S ae,collapse in Y direction is lower than in Xdirection, since – due to the higher deformability (higher value of S dy ) – in Ydirection the ductility capacity µ collapse is not as higher (compared with the Xdirection) as the displacement capacity ∆ collapse . Hence, the lower strength is noteffectively counterbalanced by the higher ductility capacity.Nevertheless, due to the difference in T eff between the two directions, interms of PGA a higher capacity is observed in Y direction.As far as first RC yielding is concerned, a similar displacement capacity isobserved, but the higher value of S dy and, above all, the lower strength, lead to alower S ae,fRCy in Y direction. Due to the difference in T eff , this differencedecreases in terms of PGA, but, however, a higher PGA fRCy is observed in Xdirection.

272 Chapter IV – Numerical investigation of seismic capacity of RC buildings with infills0.70.60.5S ae(T eff) [g]0.40.30.20.100 0.1 0.2 0.3 0.4 0.5 0.6 0.7Top displacement [m]Figure 4.3.2.37. Pushover and IN2 curves in terms of S ae (T eff ) for Model #1 in X and Ydirections (Bare frame)0.70.60.5PGA [g]0.40.30.20.100 0.1 0.2 0.3 0.4 0.5 0.6 0.7Top displacement [m]Figure 4.3.2.38. IN2 curves in terms of PGA for Model #1 in X and Y directions (Bare frame)

Chapter IV – Numerical investigation of seismic capacity of RC buildings with infills 273ModelNo.ModifiedVariableStoreyValue T el ∆ fRCy ∆ coll T eff C s,max µ fRCy µ coll R fRCy R coll S ae,fRCy S ae,coll PGA fRCy PGA coll involved incollapse∆ PGA,NC ∆ PGA,fRCy1 - - 0.76 0.06 0.22 1.01 0.20 0.95 3.33 0.95 3.33 0.19 0.68 0.22 0.57 3 - -2 f c µ-1.7σ 0.99 0.08 0.20 1.18 0.19 0.89 2.38 0.90 2.38 0.17 0.46 0.23 0.48 3 -16.3 3.63 " µ+1.7σ 0.67 0.05 0.24 0.85 0.21 1.03 4.80 1.03 4.80 0.22 1.02 0.21 0.68 3 19.8 -4.14 f yµ-1.7σ 0.74 0.05 0.22 1.00 0.19 0.81 3.54 0.82 3.54 0.16 0.68 0.18 0.57 3 -0.4 -16.55 " µ+1.7σ 0.78 0.08 0.22 1.04 0.22 1.04 3.00 1.04 3.00 0.23 0.65 0.25 0.57 3 -0.8 16.16 θ y µ-1.7σ 0.75 0.06 0.22 1.00 0.20 0.94 3.37 0.95 3.37 0.19 0.69 0.22 0.57 3 0.2 -1.57 " µ+1.7σ 0.77 0.07 0.22 1.02 0.20 0.95 3.24 0.96 3.24 0.20 0.66 0.22 0.57 3 -0.6 1.88 θ uµ-1.7σ 0.76 0.06 0.15 1.01 0.20 0.95 2.22 0.95 2.22 0.19 0.45 0.22 0.42 3 -26.5 0.09 " µ+1.7σ 0.76 0.06 0.36 1.01 0.20 0.95 5.50 0.95 5.50 0.19 1.12 0.22 0.84 3 46.3 0.0Table 4.3.2.5. Results of pushover and IN2 analyses on the Bare frame in X directionModelNo.ModifiedVariableStoreyValue T el ∆ fRCy ∆ coll T eff C s,max µ fRCy µ coll R fRCy R coll S ae,fRCy S ae,coll PGA fRCy PGA coll involved incollapse∆ PGA,NC ∆ PGA,fRCy1 - - 1.35 0.08 0.56 2.10 0.09 0.61 4.34 0.71 4.34 0.06 0.40 0.16 0.66 1+2+3+4 - -2 f c µ-1.7σ 1.57 0.09 0.45 2.36 0.09 0.57 2.84 0.64 2.84 0.06 0.25 0.16 0.51 1+2+3+4 -23.3 2.53 " µ+1.7σ 1.19 0.07 0.67 1.85 0.09 0.70 6.45 0.79 6.45 0.07 0.60 0.16 0.83 1+2+3+4 25.5 1.54 f yµ-1.7σ 1.32 0.07 0.57 2.02 0.08 0.64 5.13 0.74 5.13 0.06 0.43 0.15 0.69 1+2+3+4 3.9 -6.55 " µ+1.7σ 1.38 0.09 0.55 2.14 0.10 0.61 3.75 0.69 3.75 0.07 0.37 0.17 0.64 1+2+3+4 -3.0 7.46 θ y µ-1.7σ 1.34 0.08 0.56 2.07 0.09 0.62 4.44 0.71 4.44 0.06 0.40 0.16 0.67 1+2+3+4 0.9 -0.87 " µ+1.7σ 1.36 0.08 0.56 2.12 0.09 0.62 4.22 0.71 4.22 0.06 0.38 0.16 0.65 1+2+3+4 -1.2 1.58 θ uµ-1.7σ 1.35 0.08 0.26 2.10 0.09 0.61 2.01 0.71 2.01 0.06 0.18 0.16 0.37 1+2+3+4 -44.3 0.09 " µ+1.7σ 1.35 0.08 1.14 2.10 0.09 0.61 8.80 0.71 8.80 0.06 0.80 0.16 1.13 1+2+3+4 71.1 0.0Table 4.3.2.6. Results of pushover and IN2 analyses on the Bare frame in Y direction

274 Chapter IV – Numerical investigation of seismic capacity of RC buildings with infills4.3.3. Comparison between different infill configurationsIn this Section, the influence of different infill configurations on the seismiccapacity of the case study building is evaluated. To this aim, the IN2 curves arecompared (always referring to Model #1, where a median value is consideredfor all the variables). The comparison is carried out in both directions. Hence,vulnerability curves are evaluated, through the application of a ResponseSurface Method.4.3.3.1 Comparison between different infill configurations: IN2 curvesX directionA first comparison can be carried out between the IN2 curves in terms ofS ae (T eff ) for Uniformly infilled, Pilotis and Bare frame.Actually, the MDOF displacement capacity at Collapse is almost coincidentbetween the Uniformly infilled and the Pilotis frame since the collapsemechanism involve in both cases RC columns at the 1 st storey; nevertheless, alower displacement capacity of the equivalent SDOF is observed in Figure4.3.3.1, due to the lower modal participation factor Γ for the Pilotis frame. Thedisplacement capacity of the Bare frame is the highest one since in this framethe collapse mechanism involves the columns at the 3 rd storey, which arecharacterized by a lower axial load and, hence, by a higher ductility. The highbase shear capacity of the Uniformly infilled frame leads to much higher valuesof S ae for relatively low displacement values (e.g., DL Limit State). As theductility increases, the detrimental effect given by the increase in the slope ofthe IN2 curve, due to the drop of strength represented through the parameter r u ,prevails over the higher base shear and, at NC Limit State, the S ae capacity ofthe Uniformly infilled frame is lower compared with the corresponding capacityof the Pilotis frame. The higher displacement capacity of the Bare frame iscounterbalanced by its lower strength but, above all, by the lower stiffness ofthe pushover curve, resulting in lower S ae capacity at both Limit States,compared with other frames.

Chapter IV – Numerical investigation of seismic capacity of RC buildings with infills 2752.52S ae (T eff ) [g]1.510.500 0.05 0.1 0.15 0.2 0.25Top displacement in X direction [m]Figure 4.3.3.1. Pushover and IN2 curves in terms of S ae (T eff ) for Model #1 in X direction(Uniformly infilled, Pilotis and Bare frame)Nevertheless, in order to compare the seismic capacity of different frames, itis more correct to plot the IN2 curves in terms of PGA since this can beconsidered as a common measure of seismic intensity, whereas it is notappropriate to compare the seismic capacity in terms of spectral acceleration ifthe periods of the various frames are significantly different.It can be observed that the relative ratios between the seismic capacities ofthe Uniformly infilled and the Pilotis frame do not change significantly if PGAis considered instead of S ae (T eff ) (see Figure 4.3.3.2), because in both cases theperiod T eff is lower than T C , hence the spectral acceleration is on the constantbranch of the spectrum. Therefore, when PGA is considered instead of S ae (T eff ),the only (slight) change in the relative ratios between the seismic capacities ofthe frames is due to the little change in F 0 with the different PGA. A severechange, instead, is observed if the seismic capacity of the Bare frame isconsidered in terms of PGA. In this case, due to the relatively high period T eff ,the evaluation of the seismic capacity significantly changes: the PGA capacityat NC Limit States remains the lowest, compared with Uniformly infilled and

276 Chapter IV – Numerical investigation of seismic capacity of RC buildings with infillsBare frames, but anyhow the relative distance between the seismic capacity ofthe Bare frame and of remaining frames significantly decreases. Moreover, atDL Limit State the PGA capacity of the Bare frame is higher, compared withthe capacity of the Pilotis frame.0.90.80.70.6PGA [g]0.50.40.30.20.100 0.05 0.1 0.15 0.2 0.25Top displacement in X direction [m]Figure 4.3.3.2. IN2 curves in terms of PGA for Model #1 in X direction (Uniformly infilled,Pilotis and Bare frame)In conclusion, the better seismic performance at DL Limit State is shown bythe Uniformly infilled frame, due to the high contribution of infill elements interms of stiffness and strength, whereas at NC Limit State the betterperformance is shown by the Pilotis frame since for higher values of ductilitythe detrimental effect due to the brittle behaviour of infills counterbalancestheir strength contribution. At NC Limit State the Bare frame shows the worstbehaviour. Nevertheless, it is to be noted that in this frame the collapsemechanism, even without infills, is an unfavourable soft-storey mechanism, asmay happen in existing buildings not designed according to modern principlessuch as weak beam/strong column condition.

Chapter IV – Numerical investigation of seismic capacity of RC buildings with infills 277Y directionIn Y direction, different considerations can be made if the seismic capacityof Uniformly infilled and Pilotis frames are compared, see Figure 4.3.3.3. In theformer case, the soft-storey collapse mechanism takes place at the 2 nd storey,where RC columns are characterized by a slightly higher deformation capacitycompared with the 1 st storey, where the soft-storey collapse mechanism takesplace in the Pilotis frame. Hence, the detrimental effect (in terms of SDOFdisplacement capacity) of higher modal participation factor for the Uniformlyinfilled frame is partially counterbalanced. Moreover, in this direction thehigher strength provided by the Uniformly infilled frame counterbalances thedetrimental effect given by the increase in the slope of the IN2 curve, due to thedrop of strength, thus leading to a higher capacity, in terms of S ae (T eff ), at bothLimit States. If the Bare frame is considered, it is noted how the global collapsemechanism provides a significantly higher ductility, compared with otherframes, but also a significantly lower strength, globally resulting in a lowercapacity, in terms of S ae (T eff ), at both Limit States.21.81.61.4S ae (T eff ) [g]1.210.80.60.40.200 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5Top displacement in Y direction [m]Figure 4.3.3.3. Pushover and IN2 curves in terms of S ae (T eff ) for Model #1 in Y direction(Uniformly infilled, Pilotis and Bare frame)

278 Chapter IV – Numerical investigation of seismic capacity of RC buildings with infillsIf the seismic capacity is assessed in terms of PGA, see Figure 4.3.3.4,different effects are observed: first, the relative distance between seismiccapacity of Uniformly infilled and Pilotis frames decreases, especially at NCLimit State, mainly because in this case T eff is lower than T C for the Uniformlyinfilled frame and higher than T C for the Pilotis. Therefore, when PGA isconsidered instead of S ae , seismic capacities of these frames become muchcloser to each other.For the same reason, the assessment of the seismic capacities of the Bareframe, which is characterized by a much higher value of T eff , significantlychanges if PGA is considered instead of S ae (T eff ), showing a seismic capacityhigher than the Pilotis frame at both Limit States.0.80.70.60.5PGA [g]0.40.30.20.100 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5Top displacement in Y direction [m]Figure 4.3.3.4. IN2 curves in terms of PGA for Model #1 in Y direction (Uniformly infilled,Pilotis and Bare frame)It is observed how, in Y direction, opposite to X direction, the seismicperformance of the Bare frame at NC Limit State is better compared with thePilotis frame and very closer to the Uniformly infilled frame. This is abeneficial consequence of the higher ductility provided by the global collapsemechanism observed in the Bare frame in this direction. At DL Limit State, the

Chapter IV – Numerical investigation of seismic capacity of RC buildings with infills 279beneficial influence of the higher stiffness and strength provided by infills leadsto a higher PGA for this kind of frame.Summary of remarksNumerical results confirm how the presence of infills provides a beneficialincrease in stiffness and strength which may or may not be counterbalanced bythe detrimental effect due to the sudden loss of strength, which leads to anincrease in displacement demand when a certain threshold of seismic intensityis exceeded. The latter effect is expressed in the adopted R-µ-T relationships(Dolšek and Fajfar, 2004a) by the coefficient r u , and is reflected in thedecreasing slope of IN2 curves with r u decreasing.Compared with the Bare frame, in the Uniformly infilled frame thebeneficial influence of the increase in stiffness and strength prevails over thedetrimental influence of the brittle behaviour, both in X and Y direction.The detrimental effect of an irregular distribution of infills – leading, asexpected, to a localization of inelastic displacement demand at the bottom barestorey – is evident in Y direction, where the displacement capacity of the Bareframe is significantly higher, due to the formation of a favourable globalcollapse mechanism. On the contrary, in X direction, where the formation of anunfavourable column-sway storey mechanism is observed also in the Bareframe, the detrimental effect of an irregular distribution of infills is notobserved. These observations confirm how the evaluation of the infill influenceon seismic behaviour cannot be independent of the evaluation of the seismicbehaviour shown by the bare structure.4.3.3.2 Comparison between different infill configurations: fragility curvesEvaluation of fragility curves: methodologyIn this paragraph, the methodology used for the evaluation of fragilitycurves for the case study structure is illustrated.A fragility curve represents a relationship between a seismic intensity

280 Chapter IV – Numerical investigation of seismic capacity of RC buildings with infillsparameter and the corresponding probability of exceedance of a given damagethreshold (typically represented by a displacement capacity).The PGA capacity – for a certain Limit State – is defined as the PGAcorresponding to the demand spectrum under which the displacement demandis equal to the displacement capacity for that Limit State. PGA capacity for acertain Limit State is represented by the ordinate of the IN2 curve (expressed interms of PGA) corresponding to the displacement capacity of the equivalentSDOF system at that Limit State. Hence, if the seismic intensity is given by aPGA higher than the PGA capacity, the threshold displacement capacity for thatLimit State is exceeded, and vice versa.If PGA capacity is “observed” in a population of buildings, according to afrequentistic approach the cumulative frequency distribution of theseobservations provides the fragility curve (based on PGA seismic intensitymeasure) for that population of buildings and for that Limit State, based on thedefinitions themselves of fragility curve and PGA capacity.Given a defined building, some variables – which are input parameters forthe determination of the PGA capacity – can be defined as Random Variables,in order to investigate the influence of the uncertainty in the determination ofsuch Variables on the seismic capacity of the structure. Hence, ProbabilityDensity Functions describing the expected values and the correspondingvariability for each one of these Variables can be defined. According to asimulation technique, for instance, a number of samplings for these Variablescan be carried out. In this way, a population of buildings is generated, each onecorresponding to a different set of values of the defined Random Variables. IfPGA capacity, at a given Limit State, is calculated for all the generatedbuildings, the cumulative frequency distribution of the obtained values providesthe fragility curve for the building at that Limit State.In this study, the Monte Carlo simulation technique is used, and sampling ofRandom Variables is executed through the Latin Hypercube Sampling (LHS)technique. However, it would be too computationally demanding to carry out aSPO analysis (for calculating the PGA capacity) for each sample of the chosen

Chapter IV – Numerical investigation of seismic capacity of RC buildings with infills 281Random Variables. Hence, a Response Surface Method (RSM) is applied (Pintoet al., 2004), briefly described in the following.In RSM, a scalar output variable y is assumed as depending on k inputvariables x i . The relationship between the output variable and the inputvariables can be set in the form of a polynomial function of second order:k k k∑ ∑∑ (4.3.3.1)y = β + β x + β x x + ε0 i i ij i ji= 1 i= 1 j≥iwhere x i are the k input variables, β 0 , β i and β ij are the coefficients to bedetermined and ε is the error term. Hence, the mean model corresponding toEq. (4.3.3.1) isk k k k21 k= β0+ βi i+ βii i+ βij i ji= 1 i= 1 i= 1 j≥i( )∑ ∑ ∑∑ (4.3.3.2)y x ,..., x x x x xIf k input variables x i are considered, β coefficients are in the number ofp = 1+ 2k + k( k − 1 ) / 2 .In order to estimate the β coefficients, some experiments have to be carried out.An experiment is defined as an observation (or measurement) of the outputvariable as response to some values of the assumed input variables x i . Theresults of n experiments can be written as⎡β0⎤⎢...⎥⎢ ⎥2⎢i( 1 ... xi... xi... xix j...β ⎥⎡ y)1 ⎤⎡⎤1 ⎡ε1⎤⎢ ......⎥⎢ ⎥ ⎢... ⎢⎥⎥ ⎢...⎥⎢ ⎥= ⎢⎥ + =⎢β⎥ ⎢ ⎥2ii⎢⎢⎥⎣y ⎥n ⎦ ⎢( 1 ... xi... xi... xix j...)⎢ ⎥ ⎢ε⎥n⎣ n⎥⎦ ⎣ ⎦ ⎢ ... ⎥⎢β⎥ij⎢ ⎥⎢⎣... ⎥⎦= Zβ + ε(4.3.3.3)where Z is the n × p design matrix, collecting the n row vectors corresponding

282 Chapter IV – Numerical investigation of seismic capacity of RC buildings with infillsto the n experiments, and β is the p× 1 column vector collecting the βcoefficients to be determined. In each of the n row vectors of Z (one for eachexperiment) the so-called explanatory functions are collected. The explanatoryfunctions are the functions of the x i variables shown in Eq. (4.3.3.2).After carrying out n experiments, an estimate of β coefficients, representedby the p× 1 column vector b, can be obtained through the Ordinary LeastSquares method as1−1Tb = Z Z Z⎢...T( )⎡ y ⎤⎥⎢ ⎥⎢⎣y ⎥n ⎦(4.3.3.4)Now the Response Surface is defined, and m estimates of y can be obtainedthrough the RSM, as a function of m row vectors containing the explanatoryfunctions corresponding to the m chosen sets of values for the input variablesx i :2( 1 ... xi... xi... xix j...)⎡ y1⎤⎡⎤1⎢...⎥⎢⎥⎢ ⎥ = ⎢ ... ⎥ b⎢⎢y2⎥⎣ ⎥m ⎦ ⎢( 1 ... xi... xi... xix j...⎣) ⎥m ⎦(4.3.3.5)Hence, in order to estimate the second-order polynomial relationshipsbetween y and the input variables, n experiments have to be designed. To thisaim, the Central Composite Design (CCD) (Pinto et al., 2004) is used. Thismethod is intermediate between the two-level and the three-level factorialdesigns. Considering that two levels (low and high) are chosen for each of the kinput variables x i , symmetrically located above and below an intermediatevalue, in a two-level factorial design experiments are performed for all the 2 kpossible combinations of low and high values. In a three-level factorial design,aimed at the determination of a full quadratic form, experiments are performedfor all the 3 k possible combinations that also include the intermediate value foreach variable. CCD consists of adding to a two-level factorial design furtherpoints, located at the centre and at two other points along each of the variables

Chapter IV – Numerical investigation of seismic capacity of RC buildings with infills 283axes (Star points), see Figure 4.3.3.5.Figure 4.3.3.5. Component portions of Central Composite Design of experiments for 3 variables(Pinto et al., 2004)Once thekn = 1+ 2k + 2 CCD-based experiments have been carried out, theb vector – including p = 1+ 2k + k( k − 1 ) / 2 parameters – can be estimated.Moreover, the scatter between the observed values of y from the nexperiments and the corresponding values that would be estimated on theResponse Surface can be calculated, representing the residual r u . Hence, thevariance of the error termthe fit, can be estimated assn2 2ε= ⋅ run p u=12σε, providing an indication about the reliability of1∑ (4.3.3.6)−In our case, RSM is applied considering the PGA capacity as scalar outputvariable (y) and assuming as input variables different material characteristicsand capacity parameters influencing the seismic capacity. Hence, in order toevaluate fragility curves, the Monte Carlo simulation technique is applied. Tothis aim, m sets of samplings of the considered input variables are carried out,according to the Probability Density Functions respectively assumed. Samplingis executed according to the LHS technique (McKay et al., 1979), assuming a

284 Chapter IV – Numerical investigation of seismic capacity of RC buildings with infills“median” sampling scheme (Vorechovsky and Novak, 2009). For each of the msets of sampled values, the corresponding value of the output variable (PGAcapacity) is estimated through RSM (see Eq. 4.3.3.5). Hence, fragility curvesare obtained as cumulative frequency distributions of the PGA capacity.Evaluation of fragility curves: analysis of resultsThe above illustrated methodology for the evaluation of fragility curves isapplied to the case study building. In our case, the scalar output variable y is thePGA capacity for the Limit State of interest and the input variables are theRandom Variables selected in Section 4.3.1 (see Table 4.3.1.1), alreadyconsidered for the sensitivity analysis. In particular, in order to apply the aboveillustrated procedure, the considered input variables are represented by theRandom Variables normalized to their median values:Variable Median Value Distribution CoVf̂ c1 Lognormal 0.31f̂ y1 Lognormal 0.08G w1 Lognormal 0.30θ ̂ y1.015 Lognormal 0.331θ ̂ u0.995 Lognormal 0.409Table 4.3.3.1. Random Variables assumed to evaluate fragility curvesWhen designing the experiments to be carried out, CCD is applied asshown. In our case, the intermediate values are represented by the medianvalues. The Cube points are at a distance of 1 time the standard deviation fromthe median values, whereas the position of the Star points is assumed at adistance of 1.7 times the standard deviation from the centre of design (Liel etal., 2009). Each experiment is represented by a SPO analysis.Hence, the Center point corresponds to Model #1, as defined in Section4.3.1. These results, together with the results of the SPO analyses carried out

Chapter IV – Numerical investigation of seismic capacity of RC buildings with infills 285with the sets of values corresponding to Star points (Models #2 to #11 – in thenumber of 2× 5 – for buildings with infills, i.e. Uniformly infilled and Pilotisframes, and Models #2 to #9 – in the number of 2× 4 – for buildings withoutinfills, i.e. Bare frame), have been illustrated in the sensitivity analysis.Therefore, SPO analyses with the sets of values corresponding to Cubepoints, in the number of 2 5 or 2 4 , are carried out now. Results are not reportedherein in detail for the sake of brevity.Hence, the number of experiments adds to5n = 1+ 2⋅ 5 + 2 = 43 or4n = 1+ 2⋅ 4 + 2 = 25 analyses for each building, in each direction. These dataallow to estimate, according to Eq. 4.3.3.4, the 3× 2× 2 = 12 b vectors for PGAcapacity in Uniformly infilled, Pilotis and Bare frames, in X and Y directionsand at DL and NC Limit States, respectively. Each b vector includes theestimates of p = 1+ 2⋅ 5+ 5⋅( 5− 1 ) / 2 = 21 or ( )p = 1+ 2⋅ 4 + 4⋅ 4 − 1 / 2 = 15 βcoefficients.Variance of the error term (Eq. 4.3.3.6) is checked for all the 12 obtainedResponse Surfaces; maximum value is 2.9⋅ 10 −4 for Pilotis frame in X directionat NC Limit State, thus highlighting an acceptable scatter between the values ofPGA capacity obtained from the n experiments and the corresponding values onResponse Surfaces.Subsequently, a LHS of the k=5 considered Random Variables is carriedout, thus obtaining m sets of values of these variables. In particular, m=1000samplings are executed. The m× k obtained sampling matrix is used to estimate– through RSM – the corresponding m values of PGA capacity, by applying Eq.4.3.3.5. This procedure is carried out 12 times, each time with a different bvector (note that the same sampling matrix is always used; obviously in Bareframe only 4 of the 5 columns of the matrix are used). The correspondingcumulative frequency distributions of the obtained PGA capacity valuesrepresent the 12 fragility curves for Uniformly infilled, Pilotis and Bare frames,in X and Y directions and at DL and NC Limit States. Results are illustrated inthe following.

286 Chapter IV – Numerical investigation of seismic capacity of RC buildings with infillsThe comparison between the median values of the fragility curves reportedherein has been actually already carried out through the previously reportedobservations, when comparing the seismic capacities of Uniformly infilled,Pilotis and Bare frame referring to Model #1. From a qualitative standpoint, theslope of the fragility curves – representing the variability associated with theseismic capacity – depends on the amount of variation in PGA capacity with thevariation in each Random Variable, shown in the sensitivity analysis. Lowerthis amount, lower the change in PGA capacity with the change in RandomVariables, less sensitive the PGA capacity to the modelled uncertainties, steeperthe fragility curve (as typically happens, for instance, at DL Limit State).1NC Limit State - X directionP f0.90.80.70.60.50.40.30.2Uniformly infilled0.1PilotisBare00 0.5 1 1.5 2 2.5PGA [g]Figure 4.3.3.6. Fragility curves at Near Collapse Limit State in X direction

Chapter IV – Numerical investigation of seismic capacity of RC buildings with infills 2871DL Limit State - X directionP f0.90.80.70.60.50.40.30.2Uniformly infilled0.1PilotisBare00 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1PGA [g]Figure 4.3.3.7. Fragility curves at Damage Limitation Limit State in X directionIf fragility curves at NC Limit State in X direction are observed (see Figure4.3.3.6), a quite close median seismic capacity is noted between Uniformlyinfilled and Pilotis frame, whereas the Bare frame results as the morevulnerable. Nevertheless, the relatively low slope of the fragility curve for thePilotis frame reflects the particularly high influence of the uncertainty in θ u onthe seismic capacity of this frame (compare Figure 4.3.2.3 with Figures 4.3.2.19and 4.3.2.31).Fragility curves at DL Limit State in X direction (see Figure 4.3.3.7)highlight the beneficial effect of uniformly distributed infills on the seismiccapacity at this Limit State, that is, for relatively low seismic demand.Moreover, it is observed how in this case the detrimental effect of localizationin displacement demand leads to a lower capacity of the Pilotis frame,compared with the remaining ones.

288 Chapter IV – Numerical investigation of seismic capacity of RC buildings with infills1NC Limit State - Y directionP f0.90.80.70.60.50.40.30.2Uniformly infilled0.1PilotisBare00 0.5 1 1.5 2 2.5PGA [g]Figure 4.3.3.8. Fragility curves at Near Collapse Limit State in Y directionIn Y direction the fragility curves at NC Limit State (see Figure 4.3.3.8)highlight that the best seismic performance is provided by the Uniformlyinfilled frame, whereas the worst one is provided by the Pilotis frame.Moreover, it is noted how the seismic capacity of the Uniformly infilled frameis also less affected by dispersion compared with other frames.

Chapter IV – Numerical investigation of seismic capacity of RC buildings with infills 2891DL Limit State - Y directionP f0.90.80.70.60.50.40.30.2Uniformly infilled0.1PilotisBare00 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1PGA [g]Figure 4.3.3.9. Fragility curves at Damage Limitation Limit State in Y directionFinally, also in Y direction the beneficial effect of the increase in stiffnessand strength provided by uniformly distributed infills on the seismic capacity atDL Limit State is clearly shown (see Figure 4.3.3.9).4.3.4. Comparison with simplified models based on Shear Type assumptionThe observation of failure modes carried out in Section 4.3.2 hashighlighted the importance of storey collapse mechanisms when evaluating theseismic capacity of existing RC buildings. In particular, frames with infills arelikely to collapse under such a kind of mechanism, as already pointed out inliterature (see Section 4.2).In this Section, in view of the proposal of a simplified method for theassessment of seismic capacity of existing RC buildings (see Chapter V), theidentical set of analyses previously illustrated is carried out on structuralmodels where the top and the bottom ends of each column have been restrainedagainst rotation (Shear Type models). Obviously, the only possible collapsemechanism in these models is a column-sway storey mechanism.

290 Chapter IV – Numerical investigation of seismic capacity of RC buildings with infillsThe approximation of a seismic capacity assessment based on thisassumption is investigated through the comparison with the results evaluated on“exact” models and already illustrated in Section 4.3.2.4.3.4.1 Uniformly infilled frameX direction1Uniformly infilled frame - X directionP f0.90.80.70.60.50.40.30.2DL - "exact"DL - Shear Type0.1NC - "exact"NC - Shear Type00 0.5 1 1.5 2 2.5PGA [g]Figure 4.3.4.1. Comparison between the fragility curves evaluated on “exact” and Shear Typemodels (Uniformly infilled frame – X direction)It is to be noted that if “exact” models are considered, the Uniformly infilledframe in X direction collapses under a soft-storey mechanism at the 1 st storey inall cases except when a lower value is assumed for infill mechanicalcharacteristics; in this case there is a soft-storey mechanism at the 2 nd storey.On the contrary, if Shear Type models are considered the frame alwayscollapses under a soft-storey mechanism at the 1 st storey.The reasons for this difference can be understood looking at the evolution ofthe damage in the frame that collapses under a soft-storey mechanism at the 2 nd

Chapter IV – Numerical investigation of seismic capacity of RC buildings with infills 291storey, different from others (“exact” model, lower value of infill mechanicalcharacteristics). In uniformly infilled RC frames the soft-storey collapsemechanism generally takes place at the storey the maximum strength in infillsis attained first. Nevertheless, in some cases the evolution of damage isdifferent. For instance, in the considered case, as the top displacementincreases:1. the displacement corresponding to maximum infill strength is overcomein all infill elements at 1 st storey;2. the displacement corresponding to maximum infill strength is overcomein all infill elements at 2 nd storey;3. first RC column yields at 2 nd storey;4. soft-storey collapse mechanism activates at 2 nd storey.This kind of “redistribution“ of displacement demand from the 1 st to the 2 ndstorey can take place if rotation at the ends of the columns is not retained, henceshear force contribution of these elements, step by step, is not directly andexclusively related to the interstorey displacement, as happens in the ShearType model.However, more importantly, given equal the input material and capacitycharacteristics, a slight overestimation of the seismic capacity is noted whenShear Type models are used. As a matter of fact, if two corresponding modelsare considered, one “exact” and one Shear Type, in the Shear Type model thedisplacement capacity does not change significantly, but the base shear capacityis slightly higher (due to the higher contribution of RC columns to themaximum base shear C s,max , due to their higher stiffness since rotation isretained at both ends). Moreover, the increase in stiffness also leads to abeneficial slight decrease in S dy , given practically equal the displacementcapacity ∆ collapse . Hence, a slightly higher seismic capacity is obtained.Nevertheless, on the whole a very good agreement is observed between thetwo models, at both Limit States.

292 Chapter IV – Numerical investigation of seismic capacity of RC buildings with infillsY direction1Uniformly infilled frame - Y directionP f0.90.80.70.60.50.40.30.2DL - "exact"DL - Shear Type0.1NC - "exact"NC - Shear Type00 0.5 1 1.5 2 2.5PGA [g]Figure 4.3.4.2. Comparison between the fragility curves evaluated on “exact” and Shear Typemodels (Uniformly infilled frame – Y direction)In Y direction a very good agreement is observed, too. In the “exact” model,the building collapses under a soft-storey mechanism at the 2 nd storey in allcases except when a lower value is assumed for f c and when an upper value isassumed for infill mechanical characteristics (in these cases the storey involvedby the collapse mechanism is the 1 st one) whereas in the Shear Type model thebuilding always collapses under a soft-storey mechanism at the 1 st storey. Thereasons for this difference have been previously described.As above illustrated, at NC Limit State in Shear Type models a slightoverestimation of the seismic capacity is observed, even if the collapsemechanism takes place at the same storey compared with the “exact” model. Inthis case, the fact that the collapse mechanism activate at the 1 st storey insteadof the 2 nd one exalts this effect of decrease in displacement capacity butincrease in base shear capacity, thus leading to a slightly higher overestimationof seismic capacity, compared with the X direction.

Chapter IV – Numerical investigation of seismic capacity of RC buildings with infills 293ModelNo.ModifiedVariableStoreyValue T el ∆ lim ∆ coll T eff µ s C s,max C s,min r u µ lim µ coll R lim R coll S ae,lim S ae,coll PGA lim PGA coll involved incollapse∆ PGA,NC ∆ PGA,lim1 - - 0.12 0.01 0.14 0.15 3.13 0.75 0.28 0.38 2.29 26.36 1.33 2.88 0.99 2.16 0.39 0.84 1 - -2 f cµ-1.7σ 0.12 0.01 0.11 0.15 3.06 0.72 0.26 0.36 2.32 21.20 1.34 2.56 0.97 1.85 0.38 0.71 1 -15.1 -2.53 " µ+1.7σ 0.12 0.01 0.17 0.15 3.05 0.78 0.30 0.38 2.25 31.34 1.31 3.11 1.02 2.41 0.40 0.95 1 12.8 2.24 f yµ-1.7σ 0.12 0.01 0.14 0.15 3.06 0.75 0.27 0.36 2.30 26.50 1.33 2.78 1.00 2.09 0.39 0.81 1 -3.3 0.35 " µ+1.7σ 0.12 0.01 0.14 0.15 3.20 0.75 0.30 0.40 2.28 26.23 1.32 2.99 0.99 2.24 0.39 0.87 1 3.6 -0.36 G wµ-1.7σ 0.15 0.02 0.14 0.19 3.49 0.60 0.28 0.47 2.23 21.13 1.41 3.77 0.84 2.25 0.34 0.83 1 -1.7 -14.57 " µ+1.7σ 0.10 0.01 0.14 0.12 2.78 1.02 0.29 0.28 2.31 29.89 1.25 1.98 1.27 2.02 0.55 0.90 1 6.6 40.98 θ yµ-1.7σ 0.12 0.01 0.14 0.15 3.15 0.75 0.28 0.38 2.29 26.37 1.33 2.88 1.00 2.16 0.39 0.84 1 0.1 0.19 " µ+1.7σ 0.12 0.01 0.14 0.15 3.10 0.75 0.28 0.38 2.28 26.35 1.32 2.88 0.99 2.16 0.39 0.84 1 -0.2 -0.210 θ uµ-1.7σ 0.12 0.01 0.07 0.15 3.13 0.75 0.28 0.38 2.29 13.75 1.33 2.21 0.99 1.65 0.39 0.64 1 -24.4 0.011 " µ+1.7σ 0.12 0.01 0.27 0.15 3.13 0.75 0.28 0.38 2.29 50.98 1.33 4.01 0.99 3.01 0.39 1.19 1 41.4 0.0Table 4.3.4.1. Results of pushover and IN2 analyses on the Uniformly infilled frame (Shear Type model) in X directionModelNo.ModifiedVariableStoreyValue T el ∆ lim ∆ coll T eff µ s C s,max C s,min r u µ lim µ coll R lim R coll S ae,lim S ae,coll PGA lim PGA coll involved incollapse∆ PGA,NC ∆ PGA,lim1 - - 0.16 0.01 0.14 0.20 3.21 0.48 0.24 0.50 2.05 23.01 1.38 4.43 0.66 2.11 0.27 0.78 1 - -2 f cµ-1.7σ 0.17 0.01 0.11 0.20 3.15 0.45 0.22 0.49 2.12 18.35 1.41 3.86 0.64 1.75 0.26 0.66 1 -15.5 -2.33 " µ+1.7σ 0.16 0.01 0.17 0.20 3.06 0.50 0.25 0.50 1.99 27.42 1.36 4.85 0.67 2.40 0.27 0.88 1 12.9 2.24 f yµ-1.7σ 0.16 0.01 0.14 0.20 3.17 0.48 0.22 0.47 2.06 23.16 1.39 4.27 0.66 2.04 0.27 0.75 1 -3.1 0.45 " µ+1.7σ 0.16 0.01 0.14 0.20 3.23 0.47 0.25 0.53 2.04 22.83 1.38 4.60 0.66 2.18 0.27 0.80 1 3.2 -0.36 G wµ-1.7σ 0.20 0.01 0.14 0.25 4.08 0.38 0.23 0.61 1.99 18.88 1.46 5.56 0.56 2.12 0.23 0.78 1 0.7 -14.17 " µ+1.7σ 0.13 0.01 0.14 0.16 2.69 0.64 0.24 0.38 2.12 25.93 1.31 3.10 0.84 1.98 0.34 0.74 1 -5.5 25.18 θ yµ-1.7σ 0.16 0.01 0.14 0.20 3.24 0.48 0.24 0.50 2.05 22.97 1.38 4.42 0.66 2.11 0.27 0.78 1 0.0 0.29 " µ+1.7σ 0.16 0.01 0.14 0.20 3.16 0.47 0.24 0.50 2.05 23.06 1.39 4.44 0.66 2.11 0.27 0.78 1 -0.1 -0.210 θ uµ-1.7σ 0.16 0.01 0.07 0.20 3.21 0.48 0.24 0.50 2.05 12.07 1.38 3.08 0.66 1.46 0.27 0.56 1 -28.3 0.011 " µ+1.7σ 0.16 0.01 0.27 0.20 3.21 0.48 0.24 0.50 2.05 44.36 1.38 6.72 0.66 3.20 0.27 1.14 1 46.5 0.0Table 4.3.4.2. Results of pushover and IN2 analyses on the Uniformly infilled frame (Shear Type model) in Y direction

294 Chapter IV – Numerical investigation of seismic capacity of RC buildings with infills4.3.4.2 Pilotis frameX direction1Pilotis frame - X directionP f0.90.80.70.60.50.40.30.2DL - "exact"DL - Shear Type0.1NC - "exact"NC - Shear Type00 0.5 1 1.5 2 2.5PGA [g]Figure 4.3.4.3. Comparison between the fragility curves evaluated on “exact” and Shear Typemodels (Pilotis frame – X direction)In Pilotis frame, as expected, the collapse mechanism takes place at thebottom bare storey in all cases, both for the “exact” and Shear Type models.Moreover, practically no difference is observed in displacement and base shearcapacity between these models. The only difference is in the initial stiffness,consisting in a decrease in S dy for Shear Type models. This decrease isbeneficial at NC Limit State, leading to an overestimation of seismic capacity.Nevertheless, at DL Limit State, which in this case is defined as the firstyielding in RC elements, the higher stiffness leads to a decrease in thedisplacement capacity ∆ fRCy , too, thus counterbalancing the decrease in S dy andfinally leading to no appreciable difference in seismic capacity.

Chapter IV – Numerical investigation of seismic capacity of RC buildings with infills 295Y direction1Pilotis frame - Y directionP f0.90.80.70.60.50.40.30.2DL - "exact"DL - Shear Type0.1NC - "exact"NC - Shear Type00 0.5 1 1.5 2 2.5PGA [g]Figure 4.3.4.4. Comparison between the fragility curves evaluated on “exact” and Shear Typemodels (Pilotis frame – Y direction)In Y direction, very similar considerations can be made. Also in this case, asexpected, the frame always collapses under a soft-storey mechanism at thebottom bare storey, and an overestimation of seismic capacity is noted at NCLimit State when using Shear Type models, due to the beneficial influence ofthe higher initial stiffness.Also in this direction, at DL Limit State, the decrease in the displacementcapacity ∆ fRCy tends to counterbalance the decrease in S dy , thus leading to a verysimilar seismic capacity.

296 Chapter IV – Numerical investigation of seismic capacity of RC buildings with infillsModelNo.ModifiedVariableStoreyValue T el ∆ fRCy ∆ coll T eff C s,max µ fRCy µ coll R fRCy R coll S ae,fRCy S ae,coll PGA fRCy PGA coll involved incollapse∆ PGA,NC ∆ PGA,fRCy1 - - 0.35 0.02 0.14 0.46 0.24 1.22 10.37 1.22 9.65 0.30 2.35 0.16 0.86 1 - -2 f cµ-1.7σ 0.39 0.02 0.11 0.51 0.22 1.20 7.27 1.20 7.27 0.27 1.62 0.16 0.66 1 -23.5 -0.13 " µ+1.7σ 0.31 0.02 0.17 0.39 0.26 1.54 16.69 1.54 12.45 0.40 3.21 0.18 1.14 1 32.6 10.54 f yµ-1.7σ 0.34 0.02 0.14 0.44 0.23 1.28 11.80 1.28 10.52 0.30 2.43 0.16 0.89 1 3.1 -3.35 " µ+1.7σ 0.35 0.02 0.14 0.46 0.26 1.28 10.00 1.28 9.21 0.33 2.38 0.17 0.87 1 0.9 8.66 G wµ-1.7σ 0.35 0.02 0.14 0.44 0.24 1.34 11.22 1.34 9.93 0.33 2.43 0.17 0.89 1 2.9 4.57 " µ+1.7σ 0.34 0.02 0.14 0.46 0.24 1.25 10.75 1.25 9.85 0.31 2.40 0.16 0.88 1 1.8 1.48 θ yµ-1.7σ 0.34 0.02 0.14 0.44 0.24 1.32 11.51 1.32 10.11 0.32 2.47 0.17 0.90 1 4.4 2.79 " µ+1.7σ 0.35 0.02 0.14 0.46 0.24 1.25 10.22 1.25 9.58 0.30 2.34 0.17 0.86 1 -0.6 2.910 θ uµ-1.7σ 0.35 0.02 0.07 0.46 0.24 1.22 5.33 1.22 5.33 0.30 1.30 0.16 0.52 1 -40.0 0.011 " µ+1.7σ 0.35 0.02 0.27 0.46 0.24 1.22 20.21 1.22 16.81 0.30 4.10 0.16 1.43 1 66.1 0.0Table 4.3.4.3. Results of pushover and IN2 analyses on the Pilotis frame (Shear Type model) in X directionModelNo.ModifiedVariableStoreyValue T el ∆ fRCy ∆ coll T eff C s,max µ fRCy µ coll R fRCy R coll S ae,fRCy S ae,coll PGA fRCy PGA coll involved incollapse∆ PGA,NC ∆ PGA,fRCy1 - - 0.45 0.02 0.14 0.56 0.20 1.31 8.38 1.31 8.38 0.27 1.71 0.17 0.74 1 - -2 f cµ-1.7σ 0.50 0.02 0.11 0.65 0.19 1.11 5.01 1.11 5.01 0.21 0.95 0.16 0.53 1 -27.6 -6.83 " µ+1.7σ 0.41 0.02 0.17 0.51 0.21 1.42 11.65 1.42 11.65 0.30 2.49 0.18 0.91 1 24.4 3.34 f yµ-1.7σ 0.44 0.02 0.14 0.53 0.19 1.38 9.66 1.38 9.66 0.27 1.87 0.17 0.76 1 3.2 -4.35 " µ+1.7σ 0.46 0.02 0.14 0.59 0.22 1.21 7.00 1.21 7.00 0.26 1.52 0.18 0.70 1 -4.4 3.46 G wµ-1.7σ 0.45 0.02 0.14 0.58 0.20 1.23 7.69 1.23 7.69 0.25 1.58 0.17 0.71 1 -3.6 -2.57 " µ+1.7σ 0.44 0.02 0.14 0.58 0.20 1.21 7.80 1.21 7.80 0.25 1.59 0.17 0.72 1 -2.4 -3.78 θ yµ-1.7σ 0.44 0.02 0.14 0.57 0.20 1.24 8.08 1.24 8.08 0.25 1.65 0.17 0.72 1 -1.4 -3.39 " µ+1.7σ 0.45 0.02 0.14 0.56 0.20 1.32 8.16 1.32 8.16 0.27 1.67 0.18 0.73 1 -1.0 1.910 θ uµ-1.7σ 0.45 0.02 0.07 0.56 0.20 1.31 4.32 1.31 4.32 0.27 0.88 0.17 0.44 1 -39.5 0.011 " µ+1.7σ 0.45 0.02 0.27 0.56 0.20 1.31 16.30 1.31 16.30 0.27 3.33 0.17 1.22 1 65.6 0.0Table 4.3.4.4. Results of pushover and IN2 analyses on the Pilotis frame (Shear Type model) in Y direction

Chapter IV – Numerical investigation of seismic capacity of RC buildings with infills 2974.3.4.3 Bare frameX direction1Bare frame - X directionP f0.90.80.70.60.50.40.30.2DL - "exact"DL - Shear Type0.1NC - "exact"NC - Shear Type00 0.5 1 1.5 2 2.5PGA [g]Figure 4.3.4.5. Comparison between the fragility curves evaluated on “exact” and Shear Typemodels (Bare frame – X direction)The Bare frame in X direction always collapses under a column-sway storeymechanism at the 3 rd storey, both in “exact” and in Shear Type models. Hence,the only reason for the slight shift in PGA capacity at NC Limit State (whenShear Type models are used instead of “exact” ones) is the beneficial thedecrease in S dy again observed. Moreover, it is observed how the fragility curveevaluated on “exact” models is steeper. The reason for this slight difference canbe understood looking at the different influence of the change in randomvariables observed in the two kind of models (see Figure 4.3.4.6): PGAcapacity at NC in Shear Type models is slightly more sensitive to the variationof θ u and f c (which are the only parameters characterized by a significantinfluence) compared with the “exact” models. Hence, a higher variability inPGA capacity at NC in Shear Type models is expected, reflected by the

298 Chapter IV – Numerical investigation of seismic capacity of RC buildings with infillsdifferent slope of the fragility curve. At DL Limit State, instead, no appreciabledifference is observed.Sensitivity analysisSensitivity analysisthuthuVariablefcfyVariablefcfythyUpper valueLower value-60 -40 -20 0 20 40 60Change in PGA at collapse (%)thyUpper valueLower value-60 -40 -20 0 20 40 60Change in PGA at collapse (%)(a)(b)Figure 4.3.4.6. Comparison between the influence of random variables on the PGA capacity atNC LS in “exact” (a) and Shear Type (b) models (Bare frame – X direction)Y direction1Bare frame - Y directionP f0.90.80.70.60.50.40.30.2DL - "exact"DL - Shear Type0.1NC - "exact"NC - Shear Type00 0.5 1 1.5 2 2.5PGA [g]Figure 4.3.4.7. Comparison between the fragility curves evaluated on “exact” and Shear Typemodels (Bare frame – Y direction)

Chapter IV – Numerical investigation of seismic capacity of RC buildings with infills 299The most significant differences between the results obtained from “exact”and Shear Type models are observed for the Bare frame in Y direction.These differences are essentially due to the complete change in collapsemechanism: in “exact” models the frame collapses under a global mechanisminvolving all the four storeys; a reason for the formation of such a mechanismcan be certainly found in the absence of beams in internal frames along thisdirection. On the contrary, in Shear Type models only column-sway storeymechanism can take place. In particular, the collapsed storey is the 2 nd one in allcases except when a lower value of f c is considered; in this case, the collapsemechanism involves the 3 rd storey. This difference leads a much lower ductility,obviously, but also to a much higher base shear capacity in the Shear Typemodel. If IN2 in terms of S ae (T eff ) curves are compared (see Figure 4.3.4.8), asignificant overestimation of the seismic capacity in the Shear Type model,compared with the “exact” model, is observed. Nevertheless, the correct way tocompare seismic capacities is in terms of PGA (see Figure 4.3.4.9), and in thiscase the relative ratio between the seismic capacities significantly changes, dueto the high difference in T eff , thus highlighting that in Shear Type models thedetrimental effect of ductility decrease prevails, leading to an underestimationof the actual seismic capacity at NC Limit State.Moreover, it is observed how the fragility curve evaluated on Shear Typemodels is steeper. Again, the reason for this difference can be understoodlooking at the different influence of the change in random variables on the PGAcapacity (see Figure 4.3.4.10): PGA capacity at NC in Shear Type models isless sensitive to the variation of f c and, above all, of θ u , thus leading to a higherslope of the fragility curve.At DL Limit State, instead, the increase in stiffness and strength observed inthe Shear Type model prevails, leading to an overestimation of seismiccapacity.

300 Chapter IV – Numerical investigation of seismic capacity of RC buildings with infills0.90.80.70.6S ae (T eff ) [g]0.50.40.30.20.100 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5Top displacement in Y direction [m]Figure 4.3.4.8. Pushover and IN2 curves in terms of S ae (T eff ) for Model #1 in “exact” and ShearType models (Bare frame – Y direction)0.70.60.5PGA [g]0.40.30.20.100 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5Top displacement in Y direction [m]Figure 4.3.4.9. IN2 curves in terms of PGA for Model #1 in “exact” and Shear Type models(Bare frame – Y direction)

Chapter IV – Numerical investigation of seismic capacity of RC buildings with infills 301Sensitivity analysisSensitivity analysisthuthuVariablefcfyVariablefcfythyUpper valueLower value-60 -40 -20 0 20 40 60Change in PGA at collapse (%)thyUpper valueLower value-60 -40 -20 0 20 40 60Change in PGA at collapse (%)(a)(b)Figure 4.3.4.10. Comparison between the influence of random variables on the PGA capacity atNC LS in “exact” (a) and Shear Type (b) models (Bare frame – Y direction)

302 Chapter IV – Numerical investigation of seismic capacity of RC buildings with infillsModelNo.ModifiedVariableStoreyValue T el ∆ fRCy ∆ coll T eff C s,max µ fRCy µ coll R fRCy R coll S ae,fRCy S ae,coll PGA fRCy PGA coll involved incollapse∆ PGA,NC ∆ PGA,fRCy1 - - 0.59 0.05 0.19 0.75 0.20 1.39 5.02 1.39 5.02 0.28 1.02 0.23 0.62 3 - -2 f cµ-1.7σ 0.67 0.06 0.16 0.86 0.19 1.26 3.58 1.26 3.58 0.24 0.69 0.23 0.51 3 -18.0 -1.73 " µ+1.7σ 0.53 0.04 0.21 0.63 0.21 1.64 7.67 1.64 7.67 0.35 1.62 0.24 0.77 3 24.0 1.74 f y µ-1.7σ 0.58 0.05 0.18 0.71 0.19 1.49 5.86 1.49 5.86 0.29 1.13 0.22 0.64 3 3.0 -4.25 " µ+1.7σ 0.61 0.06 0.19 0.77 0.22 1.38 4.53 1.38 4.53 0.30 0.98 0.25 0.62 3 -0.7 7.16 θ yµ-1.7σ 0.59 0.05 0.19 0.74 0.20 1.41 5.14 1.41 5.14 0.29 1.05 0.23 0.63 3 0.8 -0.57 " µ+1.7σ 0.60 0.05 0.19 0.76 0.20 1.39 4.89 1.39 4.89 0.28 1.00 0.24 0.62 3 -0.7 1.58 θ u µ-1.7σ 0.59 0.05 0.11 0.75 0.20 1.39 3.03 1.39 3.03 0.28 0.62 0.23 0.43 3 -31.8 0.09 " µ+1.7σ 0.59 0.05 0.33 0.75 0.20 1.39 8.89 1.39 8.89 0.28 1.81 0.23 0.96 3 54.4 0.0Table 4.3.4.5. Results of pushover and IN2 analyses on the Bare frame (Shear Type model) in X directionModelNo.ModifiedVariableStoreyValue T el ∆ fRCy ∆ coll T eff C s,max µ fRCy µ coll R fRCy R coll S ae,fRCy S ae,coll PGA fRCy PGA coll involved incollapse∆ PGA,NC ∆ PGA,fRCy1 - - 0.67 0.07 0.20 0.88 0.21 1.31 3.80 1.31 3.80 0.28 0.81 0.26 0.59 2 - -2 f cµ-1.7σ 0.76 0.07 0.17 1.01 0.20 1.14 2.69 1.14 2.69 0.23 0.53 0.25 0.48 2 -18.9 -4.93 " µ+1.7σ 0.60 0.06 0.22 0.77 0.22 1.50 5.39 1.50 5.39 0.33 1.18 0.27 0.71 3 21.3 3.34 f y µ-1.7σ 0.65 0.06 0.19 0.86 0.20 1.32 4.13 1.32 4.13 0.26 0.83 0.25 0.59 2 -0.1 -5.75 " µ+1.7σ 0.69 0.08 0.20 0.91 0.23 1.27 3.43 1.27 3.43 0.29 0.77 0.28 0.58 2 -0.5 5.46 θ yµ-1.7σ 0.66 0.07 0.20 0.87 0.21 1.29 3.81 1.29 3.81 0.27 0.81 0.26 0.59 2 -0.2 -1.37 " µ+1.7σ 0.68 0.07 0.20 0.89 0.21 1.31 3.72 1.31 3.72 0.28 0.79 0.27 0.58 2 -0.4 1.68 θ u µ-1.7σ 0.67 0.07 0.13 0.88 0.21 1.31 2.45 1.31 2.45 0.28 0.52 0.26 0.42 2 -28.4 0.09 " µ+1.7σ 0.67 0.07 0.33 0.88 0.21 1.31 6.45 1.31 6.45 0.28 1.37 0.26 0.88 2 49.3 0.0Table 4.3.4.6. Results of pushover and IN2 analyses on the Bare frame (Shear Type model) in Y direction

Chapter IV – Numerical investigation of seismic capacity of RC buildings with infills 3034.3.4.4 Summary of remarksAs far as frames with infills are concerned (both Uniformly infilled andPilotis frame), a capacity assessment carried out with Shear Type models yieldsresults very close to the results obtained by means of “exact” models, except fora slight overestimation of seismic capacity due to the influence of the stiffnessincrease, whereas displacement and strength capacities are actually very closebetween the two types of models. The effectiveness of the Shear Typeapproximation (that only allows column-sway storey mechanisms) certainlyderives from the fact that also in “exact” models a column-sway storeymechanism always occurs.Results from the Bare frame highlight the possible limits of the Shear Typeapproximation. In longitudinal direction, where a column-sway storeymechanisms occurs also in the “exact” model (due to the absence of weakbeam/strong column condition), the comparison of results obtained according tothe two models points out a still acceptable agreement. In longitudinaldirection, where a global mechanism actually occurs in the “exact” model, theShear Type approximation yields less good results, as expected, at bothconsidered Limit States.Further research is needed in order to investigate the influence of otherparameter such as, for instance, the type of design or the number of storeys.However, especially for infilled buildings, the illustrated approach based onShear Type assumption may fit the needs of a seismic vulnerability assessmentat large scale, which certainly requires the adoption of simplifiedmethodologies characterized by a low computational demand (see Section5.2.4) and based on poor knowledge data (see Sections 5.2.1 and 5.2.2), thusrepresenting a good compromise between acceptable approximation andeffectiveness in assessing the seismic capacity.

304 Chapter IV – Numerical investigation of seismic capacity of RC buildings with infillsREFERENCES− Calvi G.M., Bolognini D., Penna A., 2004. Seismic Performance ofmasonry-infilled RC frames – Benefits of slight reinforcements. Invitedlecture to “Sísmica 2004 - 6º Congresso Nacional de Sismologia eEngenharia Sísmica”, Guimarães, Portugal, April 14-16.− CEN, 1995. European Standard ENV 1998-1-1/2/3. Eurocode 8: Designprovisions for earthquake resistance of structures – Part I: General rules.Technical Committee 250/SC8, Comité Européen de Normalisation,Brussels.− Circolare del Ministero dei Lavori Pubblici n. 617 del 2/2/2009. Istruzioniper l’applicazione delle “Nuove norme tecniche per le costruzioni” dicui al D.M. 14 gennaio 2008. G.U. n. 47 del 26/2/2009. (in Italian)− Cornell C.A., Jalayer F., Hamburger R.O., Foutch D.A., 2000.Probabilistic basis for 2000 SAC federal emergency managementagency steel moment frame guidelines. ASCE Journal of StructuralEngineering, 128(4), 526-533.− Crowley H., Colombi M., Borzi B., Faravelli M., Onida M., Lopez M.,Polli D., Meroni F., Pinho R., 2009. A comparison of seismic risk mapsfor Italy. Bulletin of Earthquake Engineering, 7(1), 149-190.− Decreto Ministeriale del 14/1/2008. Approvazione delle nuove normetecniche per le costruzioni. G.U. n. 29 del 4/2/2008. (in Italian)− Dymiotis C., Kappos A.J., Chryssanthopoulos M.K., 1999. Seismicreliability of RC frames with uncertain drift and member capacity.ASCE Journal of Structural Engineering, 125(9), 1038-1047.− Dymiotis C., Kappos A.J., Chryssanthopoulos M.K., 2001. Seismicreliability of masonry-infilled RC frames. ASCE Journal of StructuralEngineering, 127(3), 296-305.− Dolšek M., 2010. Development of computing environment for the seismicperformance assessment of reinforced concrete frames by using

Chapter IV – Numerical investigation of seismic capacity of RC buildings with infills 305simplified nonlinear models. Bulletin of Earthquake Engineering, 8(6),1309-1329.− Dolšek M., Fajfar P., 2000. On seismic behavior and mathematicalmodelling of infilled RC frame structures. Proceedings of the 12 thWorld Conference on Earthquake Engineering, Auckland, New Zealand,January 30-February 4. Paper No. 1632.− Dolšek M., Fajfar P., 2001. Soft storey effects in uniformly infilledreinforced concrete frames. Journal of Earthquake Engineering, 5(1), 1-12.− Dolšek M., Fajfar P., 2002. Mathematical modelling of an infilled RCframe structure based on the results of pseudo-dynamic tests.Earthquake Engineering and Structural Dynamics, 31(6), 1215-1230.− Dolšek M., Fajfar P., 2004a. Inelastic spectra for infilled reinforcedconcrete frames. Earthquake Engineering and Structural Dynamics.33(15), 1395-1416.− Dolšek M., Fajfar P., 2004b. IN2 - A simple alternative for IDA.Proceedings of the 13 th World Conference on Earthquake Engineering,Vancouver, B.C., Canada, August 1-6. Paper No. 3353.− Dolšek M., Fajfar P., 2005. Simplified non-linear seismic analysis ofinfilled reinforced concrete frames. Earthquake Engineering andStructural Dynamics, 34(1), 49-66.− Dolšek M., Fajfar P., 2008a. The effect of masonry infills on the seismicresponse of a four-storey reinforced concrete frame – a deterministicassessment. Engineering Structures, 30(7), 1991-2001.− Dolšek M., Fajfar P., 2008b. The effect of masonry infills on the seismicresponse of a four-storey reinforced concrete frame – a probabilisticassessment. Engineering Structures, 30(11), 3186-3192.− EERI, 2000. 1999 Kocaeli, Turkey earthquake reconnaissance report.Earthquake Spectra, 16(S1), 237-279.

306 Chapter IV – Numerical investigation of seismic capacity of RC buildings with infills− Fajfar P., 1999. Capacity spectrum method based on inelastic demandspectra. Earthquake Engineering and Structural Dynamics, 28(9), 979-993.− Fajfar P., Drobnič D., 1998. Nonlinear seismic analyses of the ELSAbuildings. Proceedings of the 11 th European Conference on EarthquakeEngineering, Paris, France, September 6-11.− Fardis M.N., 1997. Experimental and numerical investigations on theseismic response of RC infilled frames and recommendations for codeprovisions. Report ECOEST-PREC8 No. 6. Prenormative research insupport of Eurocode 8.− Fardis M.N., 2007. LESSLOSS – Risk mitigation for earthquakes andlandslides. Guidelines for displacement-based design of buildings andbridges. Report No. 5/2007, IUSS Press, Pavia, Italy.− Fardis M.N., Panagiotakos T.B., 1997a. Seismic design and response ofbare and masonry-infilled reinforced concrete buildings. Part I: barestructures. Journal of Earthquake Engineering, 1(1), 219-256.− Fardis M.N., Panagiotakos T.B., 1997b. Seismic design and response ofbare and masonry-infilled reinforced concrete buildings. Part II: infilledstructures. Journal of Earthquake Engineering, 1(3), 475-503.− INGV-DPC S1, 2007. Progetto S1. Proseguimento della assistenza alDPC per il completamento e la gestione della mappa di pericolositàsismica prevista dall'Ordinanza PCM 3274 e progettazione di ulteriorisviluppi. Istituto Nazionale di Geofisica e Vulcanologia – Dipartimentodella Protezione Civile, http://esse1.mi.ingv.it (in Italian)− Kappos A.J., Stylianidis K.C., Michailidis C.N., 1998. Analytical modelsfor brick masonry infilled R/C frames under lateral loading. Journal ofEarthquake Engineering, 2(1), 59-87.− Liel A.B., Haselton C.B., Deierlein G.G., Baker J.W., 2009. Incorporatingmodeling uncertainties in the assessment of seismic collapse risk ofbuildings. Structural Safety, 31(2), 197-211.

Chapter IV – Numerical investigation of seismic capacity of RC buildings with infills 307− Madan A., Hashmi A.K., 2008. Analytical prediction of the seismicperformance of masonry infilled reinforced concrete frames subjected tonear-field earthquakes. ASCE Journal of Structural Engineering, 134(9),1569-81.− McKay M.D., Conover W.J., Beckman R.J., 1979. A comparison of threemethods for selecting values of input variables in the analysis of outputfrom a computer code. Technometrics, 21(2), 239-245.− McKenna F., Fenves G.L., Scott M.H., 2004. OpenSees: Open System forEarthquake Engineering Simulation. Pacific Earthquake EngineeringResearch Center. University of California, Berkeley, California, USA.http://opensees.berkeley.edu− Negro P., Colombo A., 1997. Irregularities induced by nonstructuralmasonry panels in framed buildings. Engineering Structures, 19(7), 576-585.− Negro P., Verzeletti G., 1996. Effect of infills on the global behaviour ofR/C frames: energy considerations from pseudodynamic tests.Earthquake Engineering and Structural Dynamics, 25(8), 753-773.− Pinto P.E., Giannini R., Franchin P., 2004. Seismic reliability analysis ofstructures. IUSS Press, Pavia, Italy.− Pinto A.V., Verzeletti G., Molina J., Varum H., Coelho E., 2002. Pseudodynamictests on non-seismic resisting RC frames (infilled frame andinfill strengthened frame tests). Report EUR, EC, Joint Research Centre,Ispra, Italy.− Regio Decreto Legge n. 2229 del 16/11/1939. Norme per la esecuzionedelle opere in conglomerate cementizio semplice od armato. G.U. n. 92del 18/04/1940. (in Italian)− Rossetto T., Elnashai A., 2005. A new analytical procedure for thederivation of displacement-based vulnerability curves for populations ofRC structures. Engineering Structures, 7(3), 397-409.− Sattar S., Liel A.B., 2010. Seismic performance of reinforced concreteframe structures with and without masonry infill walls. 9 th U.S. National

308 Chapter IV – Numerical investigation of seismic capacity of RC buildings with infillsand 10 th Canadian Conference on Earthquake Engineering, Toronto,Canada, July 25-29.− Valiasis T.N., 1989. Experimental investigation of the behavior of RCframes infilled with masonry panels and subjected to cyclic horizontalload - Analytical modeling of the masonry panel. PhD thesis, AristotleUniversity of Thessaloniki, Greece. (in Greek)− Verderame G.M., Polese M, Mariniello C., Manfredi G., 2010a. Asimulated design procedure for the assessment of seismic capacity ofexisting reinforced concrete buildings. Advances in EngineeringSoftware, 41(2), 323-335.− Verderame G.M., Manfredi G., Frunzio G., 2001. Le proprietàmeccaniche dei calcestruzzi impiegati nelle strutture in cemento armatorealizzate negli anni ’60. Atti del X congresso nazionale ANIDIS‘‘L’ingegneria Sismica in Italia”, Potenza-Matera, Italy, September 9-13.(in Italian)− Verderame G.M., Ricci P., Manfredi G., 2010b. Statistical analysis ofmechanical characteristics of reinforcing bars in Italy between 1950 and1980, ACI Structural Journal. (in preparation)− Vorechovsky M., Novak D., 2009. Correlation control in small-sampleMonte Carlo type simulations I: A simulated annealing approach.Probabilistic Engineering Mechanics, 24(3), 452-462.

Chapter V – Simplified approach to the seismic vulnerability assessment of existing RC buildings: 309the case study of AvellinoChapter VSimplified approach to the seismic vulnerabilityassessment of existing reinforced concretebuildings: the case study of Avellino5.1 INTRODUCTIONSimplified methodologies for seismic vulnerability assessment of buildingstocks are of fundamental importance for the development of earthquake lossmodels. These models are needed to support the decision process in disasterprevention and emergency management, as far as seismic risk is concerned (seeChapter I). In this Chapter, a simplified method is presented for reinforcedconcrete buildings, employing a simulated design procedure to evaluate thebuilding structural characteristics based on few data such as number of storeys,global dimensions and type of design, and on the assumption of a Shear Typebehaviour to evaluate in closed form the non-linear static response. Theapproximation in the evaluation of seismic capacity due to a Shear Typeassumption has been illustrated in Section 4.3.4. Hence, the assessment of theseismic capacity is evaluated within the framework of the N2 method, leadingto the construction of fragility curves and, finally, to the evaluation of thefailure probability in given time windows and for given Limit States.The steps of the simplified procedure are described in detail in Section 5.2,

310 Chapter V – Simplified approach to the seismic vulnerability assessment of existing RC buildings:the case study of Avellinotogether with an example application.In Section 5.3, results from the field survey carried out on building stock ofthe Avellino city (southern Italy) within the SIMURAI project (2010) will bedescribed first, from the preparation of the survey form to the analysis ofcollected data. Then, the previously illustrated simplified approach to theseismic vulnerability assessment of RC buildings will be applied to such data,and obtained results will be illustrated.5.2 A SIMPLIFIED PROCEDURE FOR THE ASSESSMENT OFSEISMIC VULNERABILITY OF RC BUILDINGIn this Section, the step of the previously summarized procedure areillustrated in detail. The procedure described herein has been implemented inPOST (PushOver on Shear Type models), a software based on MATLAB®code, including a graphical interface. Some screenshots from this software willbe reported in next Sections.5.2.1. Definition of input dataThe first step of the procedure consists of the definition of input data. Thesedata include:- global geometrical parameters;- distribution of infill panels;- type of design and values of allowable stresses to be employed in thesimulated design procedure;- material characteristics;- data for the definition of seismic hazard.Considered buildings are rectangular in plan. Hence, the parameters neededto completely define the global building geometry include: number of storeys,plan dimensions in longitudinal (X) and transversal (Y) directions, number ofbays in X and Y, height of the bottom storey, height of upper storeys. Hence, a

Chapter V – Simplified approach to the seismic vulnerability assessment of existing RC buildings: 311the case study of Avellinopossible irregularity in interstorey height (often due to architectonic orfunctional reasons) is considered.The presence of infill panels can be defined according to three differentoptions: (i) Uniformly infilled building, (ii) Pilotis building or (iii) Barebuilding. The opening percentage can also be defined, both in bottom infillpanels (case i) and in upper infill panels (cases i and ii). If present, infill panelsare regularly distributed in plan in all the external frames in X and Y directions.The design can be defined as “gravitational” or “seismic”. If the design isseismic, the base shear coefficient prescribed by code (to be employed in thesimulated design procedure) is needed as input. Values of allowable stress forconcrete and steel are also defined. The details of the simulated designprocedure will be illustrated in Section 5.2.2.Material characteristics are defined, namely the concrete compressivestrength, the steel yield strength and the infill characteristics (if infill panels arepresent). The latter include the thickness of infill panels, the infill mechanicalcharacteristics (shear cracking strength, shear elastic modulus and Young’selastic modulus) and parameters α and β, respectively representing the ratiobetween post-capping degrading stiffness and elastic stiffness and the ratiobetween residual strength and maximum strength. Hence, the envelope of thelateral force displacement relationship of infill panels can be completelydefined, according to the adopted model (see Section 5.2.3). Values of infillmechanical characteristics from the Italian code (Circolare 617, 2009) areproposed as default values for different infill typologies.Finally, the data for the definition of seismic hazard are defined. Theprobabilistic seismic hazard assessment carried out for Italy (INGV-DPC S1,2007) is adopted. Hence, the location of the building is needed, defined by itsLongitude and Latitude. Stratigraphic (A to E) and topographic (T1 to T4)conditions are defined, according to the Italian code (DM 14/1/2008).Moreover, V N , C U and P VR are defined (representing the nominal life, theimportance coefficient (providing the reference period V R as V N·C U ) and theprobability of exceedance in the reference period, respectively) to obtain the

312 Chapter V – Simplified approach to the seismic vulnerability assessment of existing RC buildings:the case study of Avellinoelastic spectrum used for a single assessment of seismic demand (see Section5.2.5).Figure 5.2.1.1. Definition of input data in POST software5.2.2. Simulated design procedureThe simulated design procedure adopted herein (Verderame et al., 2010a) isbased on the compliance with past code prescriptions and design practices forItalian RC buildings. Hence, the allowable stresses method is followed.First, design loads are defined. As far as gravity loads are concerned, deadloads are evaluated from a load analysis, whereas live loads are evaluated frompast code prescriptions for ordinary structures (e.g., 2 kN/m 2 ). Lateral loads(evaluated if the selected type of design is “seismic”) are calculated based onthe assigned base shear coefficient (ratio between the design base shear and theweight of the structure). Typical values for this coefficient were, for instance,0.07 or 0.10, according to the category of the seismic zone (e.g., see Section2.5).Then, element dimensions are evaluated. To this aim, according to pastdesign practices, column area is determined as the ratio between the axial load

Chapter V – Simplified approach to the seismic vulnerability assessment of existing RC buildings: 313the case study of Avellino(evaluated referring to the area of influence of each column) and the allowablestress of concrete. In seismic design, the latter was typically multiplied by acoefficient γ lower than 1, roughly accounting for combined axial load andbending action acting on the column due to lateral loads (Pecce et al., 2004).Hence, γ was typically assumed equal to 1 in gravity load design. Coefficient γis given as an input for the simulated design procedure. The column section isthen determined from the calculated area, starting from a width equal to 30 cmand considering a maximum height of 70 cm. If the calculated area is higherthan ( 30× 70)cm 2 , column width is increased from 30 to 35 cm, and so on. Anupper approximation of 5 cm is considered for the determination of sectionheight. The beam width is given equal to 30 cm and the corresponding height iscalculated based on the maximum bending moment acting on the beam forgravity loads from slabs; this moment is calculated with a formulationaccounting in a simplified way for the element constraint scheme. Finally,column dimensions are checked to avoid cross-section variation higher than 10cm between two adjacent storeys.Once column and beam dimensions have been calculated, reinforcement incolumns is designed. Beam reinforcement is not designed since in the assumedShear Type model the behaviour of beam elements has not to be modelled (seeSection 5.2.3).As far as gravitational design is concerned, the design of columnreinforcement is based on the minimum amount of longitudinal reinforcementgeometric ratio prescribed by code (e.g., 0.8% of the minimum concrete areaaccording to RDL 2229 (1939), or 0.6% according to DM 3/3/1975)). Once theminimum area of reinforcement has been determined, a set of possible values ofbar diameter is considered and the combination of (even) number and diameterof bars providing the best upper approximation is chosen. Hence, bars aredistributed along the periphery of the section as uniformly as possible.In seismic design, storey shear forces are evaluated from lateral forces,which are calculated as a fraction of the weight of the structure, based on theassigned base shear coefficient. Hence, the distribution of the storey shear

314 Chapter V – Simplified approach to the seismic vulnerability assessment of existing RC buildings:the case study of Avellinoamong the columns of the storey is based on the ratio of inertia of the singlecolumn versus the sum of inertia of all the columns at the considered storey(Shear Type element model). The bending moment acting at the ends of eachcolumn is obtained multiplying the corresponding shear force by half of thecolumn height, according to the assumed Shear Type model; the axial load iscalculated from gravity loads, given by the sum of gravity loads and of afraction of live loads (30%), always based on the area of influence of thecolumn. Then, based on the assigned values of allowable stress for steel andconcrete, the reinforcement area is designed to provide a flexural strength(according to the allowable stresses method) not lower than the bendingmoment from design. Again, the combination of number and diameter of barsproviding the best upper approximation is chosen, provided at least two barsper layer. The described procedure is carried out in both directions. Hence, thetotal amount of longitudinal reinforcement is compared with the minimumamount prescribed by the considered code; the maximum between these valuesis assumed.Transverse reinforcement in columns is designed too. In gravitationaldesign, a minimum amount of transverse reinforcement is provided, based oncode prescriptions. For instance, according to (RDL 2229/1939) stirrup spacingin columns had to be determined as the minimum value between (i) half of theminimum section dimension and (ii) ten times the diameter of longitudinalreinforcement, whereas according to (DM 40/1975) it was determined as theminimum value between (i) 25 cm and (ii) fifteen times the minimum diameterof longitudinal reinforcement. In seismic design, transverse reinforcement isdesigned to resist the shear force due to lateral forces, calculated as previouslyillustrated. It is to be noted that in several old technical codes a so-called“threshold-based” design method for transverse reinforcement was proposed(see Section 2.3): a value of allowable tangential stress was assumed (e.g., τ c0 )and, if the design stress did not exceed this value, only a minimum amount oftransverse reinforcement was prescribed. Hence, in the simulated designprocedure τ c0 is evaluated, depending on the allowable concrete stress, and is

Chapter V – Simplified approach to the seismic vulnerability assessment of existing RC buildings: 315the case study of Avellinocompared with the shear stress demand τ. Then, ifevaluated assA ⋅σ ⋅0.9dτ > τc0, the stirrup spacing issw s,adm= (5.2.2.1)Vwhere A sw is the unit transverse reinforcement area, σ s,adm is the allowable steelstress, d is the column effective depth and V is the shear force. Stirrup diameteris given as an input.5.2.3. Characterization of nonlinear responseBased on the assumed Shear Type model, the lateral response of thestructure under a given distribution of lateral forces can be completelydetermined based on the interstorey shear-displacement relationships at eachstorey. Hence, the nonlinear response of column and infill elements has to bedetermined.The nonlinear behaviour of each column element is characterized as aT( ∆ ) relationship evaluated from the corresponding ( )consistent with the Shear Type assumption (see Figure 5.2.3.1).M θ relationship,TM∆hθL V =h/2MTMomentdistributionFigure 5.2.3.1. Shear type assumptionThe moment-rotation envelope M( θ ) is calculated assuming a shear span

316 Chapter V – Simplified approach to the seismic vulnerability assessment of existing RC buildings:the case study of Avellinoequal to half of the column height (L V = h/2). A tri-linear envelope for M( θ ) isassumed, with three characteristic points: cracking, yielding and ultimatecondition. Behaviour is linear elastic up to cracking and perfectly-plastic afteryielding.Moment and rotation at cracking are evaluated as:Mcr⎛ N ⎞ B⋅H= ⎜ − fct+ ⎟⋅⎝ B⋅H ⎠ 62(5.2.3.1)M hEI 6crθcr= ⋅ (5.2.3.2)where f ct is the concrete strength in tension, N is the axial load acting on thecolumn, B and H are width and height of the column section (in the considereddirection), EI is the gross flexural inertia of the section and h is the columnheight.Moment (M y ) and section curvature at yielding are calculated in closed formby means of the first principles-based simplified formulations proposed in(Fardis, 2007 – Section 2.2.1.3, Eqs. 2.12 to 2.18). Hence, rotations at yielding(θ y ) and ultimate (θ u ) are evaluated through Eqs. 2.20a and 3.27a, respectively,from the same study. The type of reinforcement is given as input, too; if smoothbars are present, no reduction for the lack of seismic detailing is applied, seeSection 2.2.2.The relationship between the displacement ∆ and the shear T for eachcolumn is evaluated from the relationship between the rotation θ and themoment M, based on the following relationship:( )M θ ⋅2T( ∆ ) = T( θ⋅ h)= (5.2.3.3)hShear strength is also calculated for each column, according to the modelproposed by (Biskinis et al., 2004), also adopted in EC8-part 3 (CEN, 2005)(see Section 2.3). In this model, a degradation of the shear strength with the

Chapter V – Simplified approach to the seismic vulnerability assessment of existing RC buildings: 317the case study of Avellinoductility demand is modelled. In particular, a coefficientrepresenting the plastic part of ductility demand.The initial shear strengthcalculated, the latter attained forplµ∆is adopted,VR,maxand the residual shear strength VR,minareµ = 5 , that is, for ∆ = ( 1+ 5) ⋅ ∆y. Hence, it ispl∆possible to determine if column behaviour is controlled by flexure, by shearflexureinteraction or by shear (see Section 2.3). In second and third cases, adisplacement is determined on the T − ∆ envelope (post- or pre-yielding,respectively) corresponding to shear failure, thus representing a furthercharacteristic envelope point.Lateral force-displacement relationships for infill panels are evaluated fromthe model proposed by Panagiotakos and Fardis (see Section 3.2.4), based onpreviously defined data (panel thickness, infill mechanical characteristics andmodel parameters α and β) and evaluating clear dimensions of the panelconsidering section dimensions of surrounding beams and columns. Theinfluence of openings is taken into account through a coefficient linearlydependent on the opening ratio A openings /A panel , based on the experimentalresults reported in (Kakaletsis and Karayannis, 2009):⎛ Aλopenings= max 0;1−1.8⋅⎜⎝ Aopeningspanel⎞⎟⎠(5.2.3.4)Hence, envelope forces in the load-displacement relationship of the panel aremultiplied by λ openings .At each storey, the relationship between the interstorey displacement andthe corresponding interstorey shear is evaluated considering all the RC columnsand the infill elements (if present) acting in parallel. To this aim, displacementvalues corresponding to characteristic points of lateral force-displacementenvelopes of RC columns and infill elements are sorted in a vector; then, foreach of these displacement values the corresponding shear forces provided byeach element are evaluated and summed. In this way, a multi-linear storey

318 Chapter V – Simplified approach to the seismic vulnerability assessment of existing RC buildings:the case study of Avellinoshear-displacement relationship is obtained.The illustrated procedure is carried out in both building directions.5.2.4. Calculation of pushover curveOnce the interstorey shear-displacement relationship at each storey has beendefined, the base shear-top displacement relationship representing the lateralresponse of the Shear Type building model – under a given distribution oflateral forces – can be evaluated through a closed-form procedure.First, the fundamental period of vibration and the corresponding lateraldisplacement shape are evaluated by means of an eigenvalue analysis. To thisaim, mass and stiffness matrices of the Shear Type model are easilyconstructed; elastic stiffness at each storey is calculated as the ratio betweenforce and displacement values corresponding to the first point of the multilinearenvelope representing the interstorey shear-displacement relationship.Hence, a linear, uniform or 1 st mode lateral displacement shape is chosenand the corresponding lateral load shape is determined.Once the shape of the applied distribution of lateral forces is given, theshape of the corresponding distribution of interstorey shear demand can bedetermined, too. A normalized distribution of interstorey shear demand isassumed and the ratios between such demand forces and the correspondinginterstorey shear strengths (i.e., maximum force values of the interstorey sheardisplacementrelationships) are calculated. Hence, the storey characterized bythe maximum value of this ratio will be the first (and only) to reach itsmaximum resistance (with increasing lateral displacement). Hence, if infillelements are present at that storey, leading to a degrading post-peak behaviourof the interstorey shear-displacement relationship, that storey will also be thefirst (and only) to start to degrade, thus controlling the softening behaviour ofthe structural response. Moreover, the peak of resistance of the pushover curvecan be calculated from the interstorey shear resistance of the same storey, basedon the constant ratio between the interstorey shear at that storey and the baseshear. As a matter of fact, due to the constant shape of the lateral force

Chapter V – Simplified approach to the seismic vulnerability assessment of existing RC buildings: 319the case study of Avellinodistribution, such a ratio can be calculated at each storey and remains constantat each step of the pushover curve.Therefore, the pushover curve can be evaluated by means of a forcecontrolledprocedure up to the peak, and by means of a displacement-controlledprocedure after the peak. In the latter phase, the evaluation of the response isbased on the interstorey shear-displacement relationship of the storey where thecollapse mechanism has taken place. At each step, the top displacement iscalculated as the sum of the interstorey displacement at each storey, evaluatedas a function of the corresponding interstorey shear demand, whereas the baseshear is given by the sum of lateral applied forces. If the storey where thecollapse mechanism takes place is characterized by a softening post-peakbehaviour, during the post-peak phase in the remaining N-1 storeys (where N isthe number of storeys) the interstorey shear will decrease starting from a prepeakpoint of the interstorey shear-displacement relationship; hence, thecorresponding displacement will decrease, too, following an unloading branch.An unloading stiffness equal to the elastic stiffness is assumed. Figure 5.2.4.1reports a schematic representation of the described procedure.Following this procedure, the pushover curve can be completely determinedin both directions.

320 Chapter V – Simplified approach to the seismic vulnerability assessment of existing RC buildings:the case study of AvellinoPushovercurveLateral forcedistribution∆ topDeformedshapeInterstorey sheardistributionInterstoreyshear-displacementrelationshipsV base∆ topV base∆ topV base∆ topV base∆ topV base∆ topV baseFigure 5.2.4.1. Schematic representation of pushover analysis procedure on Shear Type models

Chapter V – Simplified approach to the seismic vulnerability assessment of existing RC buildings: 321the case study of Avellino5.2.5. Seismic assessmentOnce the pushover curve has been determined, a multi- or bi-linearization iscarried out, according to the same procedure illustrated in Section 4.3.1.Figure 5.2.5.1. Seismic safety assessment in POST softwareHence, characteristic parameters of the equivalent SDOF system aredetermined. The displacement capacity is evaluated for different Limit States:Damage Limitation, Severe Damage and Near Collapse. Damage Limitation isdefined as corresponding to the displacement when the last infill starts todegrade or when yielding occurs in the first RC column, whereas SevereDamage and Near Collapse respectively correspond to the displacements when0.75×θuandθuoccur in the first RC column. Then, based on assigned data(namely site coordinates, soil conditions, reference period and probability ofexceedance of the seismic demand) the elastic demand spectrum is evaluated.Hence, N2 method is applied and the inelastic displacement demand under thisspectrum is calculated through different R-µ-T relationships, according to thedegrading or non-degrading behaviour of the equivalent SDOF system (seeSection 4.3.1). In this way, a seismic safety assessment can be carried out by

322 Chapter V – Simplified approach to the seismic vulnerability assessment of existing RC buildings:the case study of Avellinocalculating the displacement Demand/Capacity ratio for each Limit State.5.2.6. Evaluation of fragility curvesThe methodology for the evaluation of fragility curves from values of PGAcapacity “observed” in a population of buildings has been described in Section4.3.3.2. Nevertheless, in Section 4.3.3.2 a Response Surface Method (RSM) hasbeen applied since it would have been too computationally demanding to carryout a SPO analysis for each set of the sampled Random Variables. On thecontrary, in the described software the evaluation of a pushover curve(including the simulated design procedure and the characterization of nonlinearresponse) starting from the input data requires a reasonable time (typicallybetween 0.5 and 1.0 seconds on a “standard” Personal Computer). Hence, PGAcapacity (at the three considered Limit States) is explicitly calculated for eachbuilding of the generated population, without using any RSM.This procedure is applied in the described software assuming as RandomVariables the same Variables described in Section 4.3.3.1. Moreover, theinelastic displacement demand evaluated from R-µ-T relationships is assumedas Random Variable, too. The estimate of the uncertainty in the evaluation ofthe inelastic displacement demand (in a spectral assessment method) derivesfrom the record-to-record variability observed in the results of the nonlineardynamic analyses carried out on SDOF systems (with several records) to obtainsuch R-µ-T relationships. Hence, when the inelastic displacement demand istreated as a Random Variable, the value of inelastic displacement demandcalculated by means of the given R-µ-T relationship is assumed as medianvalue, and the corresponding variability has to be modelled; in this procedure, aCoefficient of Variation (CoV) equal to 0.70 is assumed (Dolšek and Fajfar,2004 – Sections 5 and 9).It is to be noted that in Section 4.3 the uncertainty in inelastic displacementdemand associated with the employed R-µ-T relationships has not beenincluded among considered Random Variables. As a matter of fact, thisuncertainty does influence the assessment of seismic capacity (modifying the

Chapter V – Simplified approach to the seismic vulnerability assessment of existing RC buildings: 323the case study of Avellinoslope of fragility curves) but there was no need to consider this uncertaintywhen carrying out a relative comparison (rather than a proper estimate)between the seismic capacities obtained through different models (in particularbetween “exact” and Shear Type models). As a matter of fact, this uncertaintywould have affected in the same way the assessment of seismic capacity in thedifferent considered models, thus not influencing the relative comparisonbetween them. If two mechanical models of the same building provide the samecapacity curve then the results provided by a seismic assessments carried outaccording to these two models would be equal to each other, the uncertainty ininelastic displacement demand considered or not.It is worth noting that, actually, further parameters may be also consideredas Random Variables, such as the input data for the simulated design procedure,global dimensions or building mass. Nevertheless, in the illustrated procedureuncertainty is considered also in seismic assessment, whereas a deterministicknowledge of the structural model (i.e., element dimensions, reinforcement,etc.) is postulated (Rossetto and Elnashai, 2005; Polese et al., 2008; Verderameet al., 2010a).Once the Random Variables have been defined, their sampling is carried outaccording to the Latin Hypercube Sampling (LHS) technique (McKay et al.,1979), adopting the “median”, “random” or “mean” sampling scheme(Vorechovsky and Novak, 2009). Hence, the number of samplings and thesampling scheme have to be defined in this phase.Subsequently, PGA capacity at the three defined Limit States is evaluatedfor each one of the generated buildings. To this aim, the same procedureillustrated in Section 4.3.1 is applied. First, the “ductility capacity” on theequivalent SDOF system is evaluated, corresponding to the displacement forwhich that Limit State is exceeded. Hence, the R-µ-T relationship is “backapplied”,calculating the R value corresponding to the determined ductilitycapacity, the period of the equivalent SDOF system T already evaluated. Then,the elastic spectral acceleration is obtained as the product between R and theacceleration capacity (C s,max ) of the equivalent SDOF system. Given the elastic

324 Chapter V – Simplified approach to the seismic vulnerability assessment of existing RC buildings:the case study of Avellinospectral acceleration at a certain period, the corresponding PGA is univocallydetermined, based on the demand spectra defined in (INGV-DPC S1, 2007)(also extrapolating seismic intensity parameters out of the given range, ifnecessary). As already highlighted in Section 4.3.1, a double iterative procedureis required to evaluate the PGA capacity since (i) the spectral shape changeswith the seismic intensity and (ii) some parameters are input parameters for theR-µ-T relationship but also depends on the results obtained from thisrelationship. In this procedure, assigned stratigraphic and topographicconditions are considered; hence, the obtained value of PGA capacity alreadyaccounts for these conditions. In other words, capacity is expressed in terms ofPGA on horizontal stiff soil.Once this procedure has been carried out for all the generated buildings, thefragility curve is obtained as cumulative frequency distribution of the PGAcapacity, for the three considered Limit States and in both directions.Figure 5.2.6.1. Evaluation of fragility curves in POST software

Chapter V – Simplified approach to the seismic vulnerability assessment of existing RC buildings: 325the case study of Avellino5.2.7. Calculation of failure probabilityThe failure probability (P f ) of a structural system characterized by aresistance R under a seismic load S can be evaluated as+∞P = ∫ f S F S dS(5.2.7.1)( ) ( )f S R0where f ( )SS is the Probability Density Function (PDF) of the seismic intensityparameter and F ( )RS is the probability that the resistance R is lower than alevel S of seismic intensity. Hence, F ( )RS is represented by a fragility curve(see Section 4.3.3.2), whereas the PDF of the seismic intensity S – in a giventime window – is obtained from seismic hazard studies.In particular, based on the seismic hazard data provided in (INGV-DPC S1,2007) for the Italian territory, if the coordinates of the site of interest are given,PGA values corresponding to different return periods (T R ) can be determined.Hence, given a PGA value, the corresponding T R (PGA) can be calculated.Finally, given a time window (V R ), the exceeding probability of the same PGAis given by the Poisson process:VR( )P PGA 1 e −VRTR( PGA)= − (5.2.7.2)In the procedure described herein, PGA is assumed as seismic intensityparameter S, F ( )RS is represented by the calculated fragility curves (assuminga linear interpolation between subsequent values of PGA) and f ( )represented by PV R( PGA ) .SS isHence, the failure probability Pfis calculated through Eq. 5.2.7.1, by meansof a numerical integration based on Simpson quadrature.Pfis calculated (for the assigned time window V R ) for the three consideredLimit States and in both directions.

326 Chapter V – Simplified approach to the seismic vulnerability assessment of existing RC buildings:the case study of Avellino5.2.8 Example applicationsIn this Section, the procedure described in detail in Section 5.2 is applied todifferent case study building, varying main parameters such as the number ofstoreys, the surface area, the infill configuration and the age of construction, thelatter through material characteristics and type of design (gravitational orseismic). Hence, seismic safety assessment for a given seismic intensity andevaluation of fragility curves is carried out.First, seismic capacities of an Uniformly infilled frame are evaluatedconsidering different numbers of storeys (3, 5 and 7) and two differentsimulated design procedures: for gravity loads only and for gravity and seismicloads. In the latter case, a base shear coefficient (i.e., ratio between design baseshear and building weight) equal to 0.10 is assumed. The building has five baysin longitudinal direction and three bays in transversal direction. Interstoreyheight is equal to 3.0 m (at all storeys, including the first one) and bay length isequal to 4.5 m.Infill panels are assumed to be 20 cm thick, with the followingcharacteristics: shear elastic modulus equal to 1240 MPa, Young’s elasticmodulus equal to (10/3×1240) MPa and shear cracking stress equal to 0.33MPa (see Section 4.3.1). Parameters α and β (see Section 5.2.1) are given equalto 0.03 and 0.01, respectively.A concrete compressive strength f c =25 MPa is assumed (Verderame et al.,2001). In simulated design procedure, the cubic compressive strength for theconcrete is assumed equal to 25 MPa, thus leading (RDL 2229/1939, DM3/3/1975) to an allowable concrete compressive stress equal to 6.0 and 8.5 MPafor axial load and axial load combined with bending, respectively. In order todetermine column dimensions, the allowable stress of concrete for axial load ismultiplied by a coefficient equal to 0.7 in seismic design, whereas it is notreduced in gravity load design.The reinforcement is assumed as smooth; hence, no reduction for the lack ofseismic detailing is applied, see Section 2.2.2. Steel yield strength f y is assumedequal to 369.7 MPa and to 426.9 MPa for the gravity load designed and the

Chapter V – Simplified approach to the seismic vulnerability assessment of existing RC buildings: 327the case study of Avellinoseismic load designed building, representing Aq50 and FeB32 steel typologies,the most widely spread in Italy during 1960s and 1970s, respectively(Verderame et al., 2010b). In simulated design procedure, allowable stress forsteel is assumed equal to 160 MPa for both typologies (Circolare 1472, 1957;DM 30/5/1972).As far as seismic input is concerned, soil type C and 2 nd topographiccategory are assumed (DM 14/1/2008).Seismic safety assessment is carried with an input elastic spectrumcorresponding to a 5 % probability of exceedance in a time window of 50 years.For the sake of brevity, only results in transversal direction are reported.Uniformly infilled frameMain equivalent parameters of the equivalent SDOF systems are reported inTable 5.2.8.1. As expected, an increase in T eff with the number of storeys isobserved; nevertheless, due to the considerable contribution of infills (whosecharacteristics are equal for all the analyzed buildings) both in terms of stiffnessand strength, T eff values of Gravity Load Designed (GLD) and Seismic LoadDesigned (SLD) buildings are quite closer.For both GLD and SLD buildings the storey collapse takes place at the 1 ststorey for 3- and 5-storey buildings and at the 2 nd storey for 7-storey buildings.The base shear strength of the RC frame alone can be observed looking atthe residual base shear C s,min , corresponding to the range of behaviour wheninfills are failed, thus practically not contributing to the lateral strength of thebuilding (infill residual resistance is assumed equal to 1 % of the maximumresistance). First, it is to be noted that C s,min in SLD buildings is more than 2times higher than the base shear coefficient used in simulated design (= 0.10).This considerable overstrength, compared with the design prescription, ismainly due to the difference between the material strength values used in designand in assessment (e.g., between the steel allowable stress σ s,adm = 160 MPaused in simulated design procedure and the median value of steel yield strengthf y = 426.9 MPa used in capacity assessment), but also to the conservatism in

328 Chapter V – Simplified approach to the seismic vulnerability assessment of existing RC buildings:the case study of Avellinodesign (e.g., the upper approximation used when determining the number anddiameter of bars corresponding to a certain amount of longitudinalreinforcement). The importance in the use of a simulated design procedure alsolies in the capability to account for such effects, which, for instance, can bemodelled only very approximately (e.g., Giovinazzi, 2005), or are not modelledat all (e.g., Grant et al., 2006), when code prescription-based methods are usedto assess the seismic capacity of existing RC buildings.As expected, C s,min in GLD buildings is quite lower compared with the SLDbuildings. For this kind of buildings, which have not been designed to resistseismic forces, a simulated design procedure may be considered as the mosteffective and reliable alternative to evaluate their seismic capacity.As far as C s,max is concerned, it is observed how this coefficient decreaseswith the number of storeys. This was an expected result since, with the numberof storeys increasing, the base shear strength of the building (not normalized toits effective mass) increases, whereas the contribution of infills to lateralstrength remains constant since, obviously, the characteristics of these elementsdo not change with the increasing height, opposite to RC column elements (inlower storeys) that show an increasing lateral strength. This is true both in SLDbuildings (where the increase in the strength of RC elements is clearly due tothe increase in the design shear demand with increasing mass) and in GLDbuildings, where, although not designed to resist any lateral load, RC columnsat lower storeys show an increase in section dimensions with the number ofstoreys, due to the increasing design axial load. Hence, given a certain amountof minimum prescribed longitudinal reinforcement ratio, these elements alsoshow an increase in lateral strength.Hence, the specific contribution of infills to the overall lateral strengthdecreases (e.g., Fardis and Panagiotakos, 1997), thus leading to a lower C s,max .The change in collapsed storey (from 1 st to 2 nd one for 7-storey buildings)may also be explained according to this phenomenon of relative decrease ininfill contribution to the lateral strength (see Section 4.3.2.1).The increase in T eff and the decrease in C s,max are the main reasons for the

Chapter V – Simplified approach to the seismic vulnerability assessment of existing RC buildings: 329the case study of Avellinodecrease in seismic capacity with the number of storeys, observed in bothbuilding typologies and for all the considered Limit States, see Table 5.2.8.2.As far as displacement Demand to Capacity ratios for the assigned seismicinput are concerned, similar trends are observed, see Table 5.2.8.3.Nevertheless, at DL Limit State in GLD buildings a decrease in this ratio isobserved with the number of storeys, thus interestingly highlighting howdifferent approaches to the evaluation of the Demand to Capacity ratio (e.g.,based on PGA rather than displacement values) may yield slightly differentresults.ΓT eff C s,max C s,minTΓeff C s,max C s,min[sec] [g] [g][sec] [g] [g]N=3 1.22 0.15 0.53 0.14 1.22 0.15 0.56 0.24N=5 1.25 0.24 0.38 0.17 1.26 0.24 0.43 0.28N=7 1.27 0.31 0.31 0.17 1.28 0.34 0.39 0.28GLDSLDTable 5.2.8.1. Main equivalent SDOF parameters (Uniformly infilled buildings – X direction)DL SD CO DL SD CON=3 0.18 0.36 0.45 0.19 0.56 0.64N=5 0.13 0.32 0.40 0.13 0.46 0.53N=7 0.12 0.28 0.35 0.11 0.38 0.48GLDSLDTable 5.2.8.2. PGA capacities (expressed in g) (Uniformly infilled buildings – X direction)DL SD CO DL SD CON=3 5.17 0.42 0.32 1.84 0.17 0.13N=5 4.15 0.69 0.53 3.02 0.48 0.37N=7 3.66 0.86 0.67 3.40 0.62 0.50GLDSLDTable 5.2.8.3. Displacement Demand to Capacity ratios for a seismic input characterized by a5% probability of exceedance in 50 years (Uniformly infilled buildings – X direction)

330 Chapter V – Simplified approach to the seismic vulnerability assessment of existing RC buildings:the case study of AvellinoN=310.90.80.70.60.50.4capacity curveidealized capacity curveelastic demand spectruminelastic demand spectrumdemandDL capacitySD capacityCO capacity10.90.80.70.60.50.40.30.20.10.30.20.100 50 100 150 200 250 300 35000 50 100 150 200 250 300 35010.90.80.70.610.90.80.70.6N=50.50.40.50.40.30.20.100 50 100 150 200 250 300 3500.30.20.100 50 100 150 200 250 300 35010.90.80.70.610.90.80.70.6N=70.50.40.50.40.30.20.100 50 100 150 200 250 300 3500.30.20.100 50 100 150 200 250 300 350GLDSLDFigure 5.2.8.1. Seismic assessment for a seismic input characterized by a 5% probability ofexceedance in 50 years (PGA = 0.2495 g) (Uniformly infilled buildings – X direction)

Chapter V – Simplified approach to the seismic vulnerability assessment of existing RC buildings: 331the case study of AvellinoBy means of the described software, fragility curves can be obtained too(see Section 5.2.6). In the following, such results are shown for curvesevaluated with 100 samplings of the considered Random Variables, see Figure5.2.8.2.Failure probabilities in 50 years are also calculated, showing the increase invulnerability with the number of storeys and, as expected, the highervulnerability of GLD buildings compared with SLD buildings.Nevertheless, the differences between these two building typologies aresignificantly lower at DL Limit State, compared with SD or NC. As a matter offact, at DL Limit State the infill contribution has a relatively higher weight (seeSection 4.3.2.1), thus reducing the differences between vulnerability of GLDand SLD buildings.DL SD CO DL SD CON=3 0.0129 0.0030 0.0023 0.0106 0.0014 0.0001N=5 0.0209 0.0050 0.0037 0.0189 0.0028 0.0019N=7 0.0247 0.0064 0.0047 0.0247 0.0043 0.0032GLDSLDTable 5.2.8.4. Failure probabilities in 50 years (Uniformly infilled buildings – X direction)

332 Chapter V – Simplified approach to the seismic vulnerability assessment of existing RC buildings:the case study of Avellino10.90.80.70.610.90.80.70.6N=3P f0.50.4P f0.50.40.30.2DL0.1SDNC00 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8PGA [g]0.30.20.100 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8PGA [g]10.90.80.70.610.90.80.70.6N=5P f0.50.4P f0.50.40.30.20.100 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8PGA [g]0.30.20.100 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8PGA [g]10.90.80.70.610.90.80.70.6N=7P f0.50.4P f0.50.40.30.20.10.30.20.100 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8PGA [g]00 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8PGA [g]GLDSLDFigure 5.2.8.2. Fragility curves (Uniformly infilled buildings – X direction)

Chapter V – Simplified approach to the seismic vulnerability assessment of existing RC buildings: 333the case study of AvellinoPilotis frameThe same analyses are now carried out on Pilotis buildings, in order toinvestigate the influence of a different arrangement of infill elements on theseismic capacity. As expected, in all cases the collapse mechanism takes placein the bottom bare storey. Hence, the lateral response of the building may bedirectly interpreted based on the behaviour of 1 st storey RC columns.From a qualitative standpoint, two opposite effects influence the effectiveperiod T eff , counterbalancing each other.On a side, of course, the effective mass increases with the number ofstoreys; in Pilotis buildings, due to peculiar stiffness distribution, the modalparticipation factor is closer to 1 (and the effective mass is closer to the totalbuilding mass) compared with other building typologies. Nevertheless, thiseffect is much more pronounced for lower number of storeys, when thedimension of RC columns is smaller and, hence, the presence of infills in upperstoreys has a relatively higher weight in the lateral stiffness distribution,compared with buildings with higher number of storeys. Hence, effective massincreases approximately less than linearly with the number of storeys.On the other side, with increasing number of storeys the strength and thestiffness of 1 st storey RC columns increase too. In SLD buildings, this isdirectly related to the design seismic shear demand in these elements, whichincreases linearly with the number of storeys, thus leading to an approximatelylinear increase of the base shear strength (except for design approximations). InGLD buildings, the interpretation of the increase in strength and the stiffness of1 st storey RC columns is not so straightforward; however, column section areadepends on the design axial load, which increases linearly with the number ofstoreys. As column section area increases, stiffness and strength increase too,obviously.On the whole, the latter effect tends to prevail on the former, thus leading toa decrease in T eff with the number of storeys.Nevertheless, the displacement capacity of 1 st storey columns also decreaseswith the number of storeys.

334 Chapter V – Simplified approach to the seismic vulnerability assessment of existing RC buildings:the case study of AvellinoFinally, the sum of these effects leads to a not clear tendency of seismiccapacity with the number of storeys, for both building typologies, whereas if arelative comparison is carried out between different building typologies, thehigher strength and stiffness shown by SLD buildings clearly leads to higherseismic capacities, as expected.T effΓC s,maxTΓeff C s,max[sec] [g][sec] [g]N=3 1.02 0.67 0.13 1.04 0.57 0.22N=5 1.09 0.59 0.15 1.14 0.48 0.24N=7 1.17 0.53 0.18 1.24 0.43 0.26GLDSLDTable 5.2.8.5. Main equivalent SDOF parameters (Pilotis buildings – X direction)DL SD CO DL SD CON=3 0.06 0.29 0.42 0.07 0.32 0.48N=5 0.06 0.26 0.36 0.07 0.32 0.48N=7 0.06 0.25 0.35 0.08 0.33 0.48GLDSLDTable 5.2.8.6. PGA capacities (expressed in g) (Pilotis buildings – X direction)DL SD CO DL SD CON=3 4.20 0.88 0.66 3.74 0.80 0.60N=5 4.76 0.98 0.73 3.80 0.79 0.60N=7 4.58 0.99 0.74 3.50 0.78 0.59GLDSLDTable 5.2.8.7. Displacement Demand to Capacity ratios for a seismic input characterized by a5% probability of exceedance in 50 years (Pilotis buildings – X direction)

Chapter V – Simplified approach to the seismic vulnerability assessment of existing RC buildings: 335the case study of AvellinoN=310.90.80.70.60.50.4capacity curveidealized capacity curveelastic demand spectruminelastic demand spectrumdemandDL capacitySD capacityCO capacity10.90.80.70.60.50.40.30.20.10.30.20.100 50 100 150 200 250 300 35000 50 100 150 200 250 300 35010.90.80.70.610.90.80.70.6N=50.50.40.50.40.30.20.100 50 100 150 200 250 300 3500.30.20.100 50 100 150 200 250 300 35010.90.80.70.610.90.80.70.6N=70.50.40.50.40.30.20.100 50 100 150 200 250 300 3500.30.20.100 50 100 150 200 250 300 350GLDSLDFigure 5.2.8.3. Seismic assessment for a seismic input characterized by a 5% probability ofexceedance in 50 years (PGA = 0.2495 g) (Pilotis buildings – X direction)

336 Chapter V – Simplified approach to the seismic vulnerability assessment of existing RC buildings:the case study of AvellinoFragility curves and the corresponding failure probabilities are evaluatedalso for Pilots buildings. Again, seismic performance do not changesignificantly with the number of storeys, whereas the failure probability of SLDbuildings is systematically lower compared with GLD buildings. Mostimportantly, a clear increase in failure probability, compared with thepreviously illustrated Uniformly infilled typology, is shown. As expected, thedetrimental effects of such an irregular infill distribution can be directlyobserved, for all the considered Limit States, in terms of failure probability.DL SD CO DL SD CON=3 0.0456 0.0100 0.0065 0.0414 0.0093 0.0060N=5 0.0494 0.0113 0.0073 0.0418 0.0086 0.0056N=7 0.0480 0.0113 0.0076 0.0380 0.0077 0.0049GLDSLDTable 5.2.8.8. Failure probabilities in 50 years (Pilotis buildings – X direction)

Chapter V – Simplified approach to the seismic vulnerability assessment of existing RC buildings: 337the case study of Avellino10.90.80.70.610.90.80.70.6N=3P f0.50.4P f0.50.40.30.2DL0.1SDNC00 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8PGA [g]0.30.20.100 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8PGA [g]10.90.80.70.610.90.80.70.6N=5P f0.50.4P f0.50.40.30.20.100 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8PGA [g]0.30.20.100 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8PGA [g]10.90.80.70.610.90.80.70.6N=7P f0.50.4P f0.50.40.30.20.10.30.20.100 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8PGA [g]00 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8PGA [g]GLDSLDFigure 5.2.8.4. Fragility curves (Uniformly infilled buildings – X direction)

338 Chapter V – Simplified approach to the seismic vulnerability assessment of existing RC buildings:the case study of Avellino5.3 URBAN SCALE VULNERABILITY ASSESSMENT: THE CASESTUDY OF AVELLINOAvellino is a city of the Campania region, in southern Italy, with more than55.000 people. It is in a high seismic area, and it was struck by the catastrophicIrpinia earthquake (M w = 6.9) on November 23 rd , 1980.The Italian Ministry of Education, University and Research has funded the“SIMURAI – Strumenti Integrati per il MUlti Risk Assessment territoriale inambienti urbani antropizzatI” (Integrated instruments for large scale multi riskassessment in urban anthropic environment) research project aimed at carryingout a case study multi risk assessment at urban scale on the Avellino city. As faras the seismic risk is concerned, building stock data have been collectedthrough a detailed field survey, aimed at a large scale vulnerability assessment.In this Section, this field survey will be described first, from the preparation ofthe survey form to the analysis of collected data (Section 5.3.1). Then, thepreviously illustrated simplified approach to the seismic vulnerabilityassessment of RC buildings (see Section 5.2) will be applied to such data.Results will be illustrated in Section 5.3.2, showing the trend of estimatedfailure probability, at different performance levels, among the analyzed buildingpopulation.5.3.1 Data collection and field survey resultsIn this Section, the form prepared to carry out the field survey on buildingstock is presented first. Hence, the analysis of collected data is presented,particularly focused on RC buildings.5.3.1.1 Survey formPrepared survey form (Figures 5.3.1.7 to 5.3.1.10) was sub-divided indifferent sections:

Chapter V – Simplified approach to the seismic vulnerability assessment of existing RC buildings: 339the case study of Avellino- Section 1 – Building identificationIn this section, data for the identification of the building were reported,consisting of the address, the assigned ID code and data concerning theexecution of the survey, i.e. the date and the survey team (each survey teamwas made up of two or three persons) and also the ID code of thephotographic image taken during the survey. In preparation of the survey, anID was assigned to each building identified through aerial photographs.Moreover, the survey was planned based on “census cells” determinedaccording to ISTAT (Istituto Nazionale di Statistica, National Institute ofStatistics) data. Census cells are the basic territory units considered byISTAT when carrying out a census survey. Figure 5.3.1.1 reports a detail ofan aerial view where census cells are delimited by coloured lines and IDspre-assigned to each building shape are reported.Figure 5.3.1.1. Census cells and building IDsMoreover, the building position was identified as “isolated” or“adjacent” to other buildings. In the latter case, the position of the buildingwith respect to the adjacent ones was reported (namely as internal, external

340 Chapter V – Simplified approach to the seismic vulnerability assessment of existing RC buildings:the case study of Avellinoor corner). It is to be noted that in many cases a single ID had been preassignedto a single “shape” that, actually, was composed of differentadjacent buildings. In these cases, different structural units were “generated”from a single pre-identified building (see Figures 5.3.1.2 and 5.3.1.3).Figure 5.3.1.2. Aerial view of a group of adjacent buildings (Virtual Earth©)Figure 5.3.1.3. Ground detail view of the buildings reported in Figure 5.3.1.2: separationbetween single structural units is highlighted with the red dashed lineA schematic representation of building plan view with the measureddimensions was reported, too.

Chapter V – Simplified approach to the seismic vulnerability assessment of existing RC buildings: 341the case study of Avellino- Section 2 – Building descriptionIn section 2 main data necessary for describing the building werereported, i.e. the number of storeys (above and below the ground level), theaverage surface area, the age of construction and the main destination use.The latter may represent an useful data in view of a loos estimationprocedure.- Section 3 – Building morphologySection 3 reported a detailed representation of morphologic buildingcharacteristics. Hence, the plan shape was identified first, referring to sixmain typologies (see Figure 5.3.1.4).(a)(b)(c)(d)Figure 5.3.1.4. Aerial view of example L- (a), T- (b), C- (c) or sawtooth- (d) shaped buildings(Virtual Earth©)

342 Chapter V – Simplified approach to the seismic vulnerability assessment of existing RC buildings:the case study of AvellinoThen, height dimensions were reported, also considering the possiblepresence of a mansard storey, the partial height above the ground level ofthe storey placed below the ground level (if present) and a possibledifference between the 1 st storey height and the upper storey height, oftendue to architectonic or functionality requirements. Finally, data about theregularity in elevation were reported, including the number of storeyscharacterized by a reduction in surface area (if present), see Figure 5.3.1.5,and the ground slope.H 1H maxH maxH minFigure 5.3.1.5. Irregularity in elevation characterized by a decrease in surface area (see section4 of the survey form, Figure 5.3.1.9)- Section 4 – Structural typologySection 4 reported the identification of the structural typology, namelyreinforced concrete, masonry, steel or mixed typology. In the case ofreinforced concrete, a further indication was provided, aimed at identifyingthe specific structural system, i.e. frame, shear wall or dual system.- Section 5 – InfillsSection 5 collected data about infill distribution. In particular, thearrangement of infill panels at the bottom storey was described by reportingthe type of distribution – regular infilling (infill panels present in each bay,see Figure 5.3.1.6a), irregular infilling (infill panels present only in a

Chapter V – Simplified approach to the seismic vulnerability assessment of existing RC buildings: 343the case study of Avellinospecified proportion of the side length), pilotis (no infill panel, see Figure5.3.1.6b) or partial infilling (infill panels with a height lower than the heightof adjacent columns) – and the respective number of sides characterized bysuch type of distribution. Infill typology was also reported. In particular,survey teams had to identify the type of material (i.e., hollow clay, solidclay, tuff or concrete bricks) and the number of layers composing the infillpanels (one or two). Nevertheless, these characteristics often were not easyat all to be determined, for instance, due to the presence of the plaster.(a)(b)Figure 5.3.1.6. Examples of regular (a) and pilotis (b) infill distributions- Section 6 – BaysIn section 6 the number of bays per each side (according to the planshape) was reported.- Section 7 – Stairs presence and positionSection 7 reported the number and the position (central or lateral) ofstaircases per each side of the building.

344 Chapter V – Simplified approach to the seismic vulnerability assessment of existing RC buildings:the case study of AvellinoFigure 5.3.1.7. Field survey form (1/4)

Chapter V – Simplified approach to the seismic vulnerability assessment of existing RC buildings: 345the case study of AvellinoFigure 5.3.1.8. Field survey form (2/4)

346 Chapter V – Simplified approach to the seismic vulnerability assessment of existing RC buildings:the case study of AvellinoFigure 5.3.1.9. Field survey form (3/4)

Chapter V – Simplified approach to the seismic vulnerability assessment of existing RC buildings: 347the case study of AvellinoFigure 5.3.1.10. Field survey form (4/4)It is to be noted that some of the illustrated sections (e.g., infill description)specifically fit reinforced concrete structural typology.The illustrated survey form includes the main parameters – among the onesthat can be reasonably collected during a field survey – that may have asignificant influence on building seismic capacity, addressing a particularattention to specific potential sources of seismic vulnerability. Some of theseparameters may not have a direct and immediate usefulness for the firstassessment procedures carried out. Nevertheless, based on damage observationfrom past earthquakes and also on engineering judgement, the importance ofcollecting information about all the above described parameters wasrecognized, also considering the precious opportunity represented by such afield survey campaign.5.3.1.2 Analysis of building stock dataIn the following, main collected data about building stock characteristics areillustrated.On the whole, 1327 buildings were surveyed. Among these, 1058 were RCbuildings and 265 were masonry buildings. Steel and mixed buildings werepresent in negligible percentages (only 4 buildings out of 1327), see Figure5.3.1.11.

348 Chapter V – Simplified approach to the seismic vulnerability assessment of existing RC buildings:the case study of Avellino90%80%70%60%50%40%30%20%10%0%RC Masonry Steel MixedFigure 5.3.1.11. Structural typology of surveyed buildingsAs far as the age of construction is concerned, in 254 buildings (almost 20%of the population) it was not determined. However, it is clearly observed how alarge part of masonry building stock was constructed at the beginning of the20 th century or before, or early after World War II, see Figure 5.3.1.12. Theperiod characterized by the highest growth of RC building stock is around1970s and 1980s, see Figure 5.3.1.13. It is noted that a quite large part of theRC building stock was constructed after the 1980 earthquake. Pre- and post-82buildings respectively represent about the 56 and 44 % of the RC buildingpopulation whose age of construction was determined.50%40%30%20%10%0%pre-191919-4546-6162-7172-8182-9192-9798-01post-2002Figure 5.3.1.12. Age of construction of masonry buildingsnr

Chapter V – Simplified approach to the seismic vulnerability assessment of existing RC buildings: 349the case study of Avellino50%40%30%20%10%0%pre-191919-4546-6162-7172-8182-9192-9798-01post-2002Figure 5.3.1.13. Age of construction of RC buildingsnrThe spatial distribution of the age of construction of surveyed buildings isreported in Figure 5.3.1.14: the presence of rather homogeneous areas isobserved; in particular, pre-1919 masonry buildings are concentrated in thecentral-eastern area corresponding to the old centre of the city, whereas 1960sand 1970s buildings are mainly located along East-West axis and in Northernarea, respectively. More recent buildings are present also in the central cityarea, due to post-1980 earthquake reconstruction; this is shown in Figure5.3.1.15, where pre- and post-1981 buildings are reported.

350 Chapter V – Simplified approach to the seismic vulnerability assessment of existing RC buildings:the case study of AvellinoFigure 5.3.2.14. Age of construction of surveyed buildingspre-19191919-451946-611962-711972-811982-911992-971998-2001post-2002ns

Chapter V – Simplified approach to the seismic vulnerability assessment of existing RC buildings: 351the case study of AvellinoFigure 5.3.2.15. Pre- and post-1981 surveyed buildingspre-1981post-1981ns

352 Chapter V – Simplified approach to the seismic vulnerability assessment of existing RC buildings:the case study of Avellino70%60%50%40%30%20%10%0%RectangularL-shapedT-shapedC-shapedZ-shapedFigure 5.3.1.16. Plan morphology of RC buildingssawtooth-shapedIf data about building morphology of RC buildings are observed, see Figure5.3.1.16, it can be noted that the Rectangular buildings, in the number of 693,represent about 67% of the entire RC building stock. In Section 6.3 theproposed simplified methodology for seismic vulnerability assessment of RCbuildings (see Chapter V) will be applied to this group of buildings; hence,further data analyses will be focused on this typology.

Chapter V – Simplified approach to the seismic vulnerability assessment of existing RC buildings: 353the case study of Avellino10%9%8%

354 Chapter V – Simplified approach to the seismic vulnerability assessment of existing RC buildings:the case study of Avellino30%25%20%15%10%5%0%Lx/Ly>4.5Figure 5.3.1.18. Ratio between plan dimensions of rectangular RC buildingsBay length (see Figure 5.3.1.19) essentially ranges between 3 and 6.5 m, andthe most common values are around 3.5 ÷ 5.5 m.30%25%20%15%10%5%0%lb>7Figure 5.3.1.19. Bay length in rectangular RC buildingsInterstorey height at 1 st storey, as expected, is characterized by highervalues, on average, and also by a higher dispersion compared with upperstoreys, see Figure 5.3.1.20 and 5.3.1.21. In particular, in large part of thesurveyed buildings the interstorey height at upper storeys is between 3 and 3.5m.

Chapter V – Simplified approach to the seismic vulnerability assessment of existing RC buildings: 355the case study of Avellino90%80%70%60%50%40%30%20%10%0%h1

356 Chapter V – Simplified approach to the seismic vulnerability assessment of existing RC buildings:the case study of Avellinopercentage corresponds to Pilotis buildings.25%20%15%10%5%0%%op=00

Chapter V – Simplified approach to the seismic vulnerability assessment of existing RC buildings: 357the case study of Avellino- number of bays in X direction:- number of bays in Y direction;- interstorey height of the 1 st storey;- interstorey height of upper storeys;- infill average opening percentage at the 1 st storey (see Figure 5.3.1.20);- age of construction.Based on the age of construction, the following parameters weredetermined, as shown in Table 5.3.2.1:- Type of designAvellino was classified as seismic for the first time in 1981 (DM7/3/1981), following the 1980 Irpinia earthquake. It was in II seismiccategory, i.e., a seismic intensity parameter S = 9 was assumed. Hence,design base shear (see Section 2.5.2) was defined asS − 2F = C⋅ W = ⋅ W = 0.07 ⋅ W(5.3.2.1)100where W was the building weight. Therefore, a seismic (S) simulated designprocedure (see Section 5.2.2) was carried out according to such prescriptionfor building whose age of construction was determined as following 1981(see section 2 of the survey form, Figure 5.3.1.8).Vice versa, for older buildings a simulated design procedure based ongravity loads only (G) was carried out. It is noted that in some cases (about20% of surveyed buildings) the age of construction was not determined. Inthese cases, a weighted average of the ages of construction of otherbuildings in the same census cell was calculated and this value was assumedalso for the building of interest.- Allowable stressesValues of allowable stresses for steel and concrete employed in thesimulated design procedure were also determined according to the age ofconstruction. As far as concrete is concerned, a cubic compressive strength

358 Chapter V – Simplified approach to the seismic vulnerability assessment of existing RC buildings:the case study of Avellinoequal to 25 MPa was assumed in all cases, from which the allowableconcrete stress for bending and for axial load combined with bending werecalculated according to code formulations. Moreover, the concreteallowable stress used to determine column dimensions in the simulateddesign procedure was multiplied by a coefficient equal to 0.7 in the case ofseismic design ((Pecce et al., 2004), see Section 5.2.2). Allowable steelstress (σ s,adm ) was calculated as the weighted average of the valuescorresponding to different steel typologies in time window corresponding tothe surveyed age of construction, depending on the frequency of occurrenceof each typology in this time window, according to the data reported in astatistical analysis of mechanical and typological characteristics ofreinforcing steel used in Italy between 1950 and 1980 (Verderame et al.,2010b). For ages of construction above or below these limits, valuescorresponding to the most widely spread steel typologies in 1950 and 1980were adopted, respectively.- ReinforcementReinforcing steel typology (smooth or ribbed bars) was also determinedas the most frequent typology in the time window corresponding to thesurveyed age of construction, according to the data reported in (Verderameet al., 2010b).- Steel and concrete material characteristicsConcrete compressive strength (f c ) was assumed equal to 25 MPa foreach age of construction. The Coefficient of Variation (CoV) for thisvariable was assumed equal to 31% up to 1981. The assumption of thesevalues was based on (Verderame et al., 2001). In the following years, a CoVequal to 25% was assumed, reflecting the improve in the reliability ofconcrete preparation. As far as steel yield strength (f y ) and the related CoVare concerned, again, average values from the data reported in (Verderameet al., 2010b) are used. Also in this case, for ages of construction before

Chapter V – Simplified approach to the seismic vulnerability assessment of existing RC buildings: 359the case study of Avellino1950 or after 1980 the values corresponding to the most widely spread steeltypologies in these two years were adopted, respectively.Age Design Reinforcementσ s,adm f y CoV f c CoV[MPa] [MPa] [%] [MPa] [%]pre-1919 G smooth 140 325 20 25 311919-45 G smooth 140 325 20 25 311946-61 G smooth 173 336 22 25 311962-71 G smooth 203 399 18 25 311972-81 G ribbed 208 451 13 25 311982-91 S ribbed 240 466 11 25 251992-97 S ribbed 240 466 11 25 251998-01 S ribbed 240 466 11 25 25post-2002 S ribbed 240 466 11 25 25Table 5.3.2.1. Summary of data used in simulated design and in assessment depending on theage of constructionTopographic (category T1 to T4) and stratigraphic (soil type A to E) data,according to the code classification (DM 14/1/2008), were needed in order todetermine the characteristics of seismic input spectra. Such characteristics weremade available and georeferenced in SIMURAI project. Topographic category,according to code definition, was determined depending on ground slope,which was evaluated from a Digital Terrain Model (DTM), see Figures 5.3.2.1and 5.3.2.2. Soil type was determined from microzonation data, see Figure5.3.2.3. Census cells are also reported in Figures 5.3.2.2 and 5.3.2.3.Hence, to each building a topographic category and a soil type wereassociated. Among all the 693 considered buildings, 484 were located on soiltype E, 200 on soil type B and 8 on soil type C, while 587 were in topographiccategory T1, 94 in T2 and 12 in T4.

360 Chapter V – Simplified approach to the seismic vulnerability assessment of existing RC buildings:the case study of AvellinoFigure 5.3.2.1. Digital Terrain Model of Avellino city

Chapter V – Simplified approach to the seismic vulnerability assessment of existing RC buildings: 361the case study of AvellinoÜT1T2T40 250500 1 000 1 500 2 000MetersFigure 5.3.2.2. Distribution of topographic characteristics

362 Chapter V – Simplified approach to the seismic vulnerability assessment of existing RC buildings:the case study of AvellinoÜABCE0 250500 1 000 1 500 2 000MetersFigure 5.3.2.3. Distribution of stratigraphic characteristicsOpening percentage in upper storey infills was assumed equal to 20%,which can be considered as representative, on average, of window presence(Bal et al., 2007).

Chapter V – Simplified approach to the seismic vulnerability assessment of existing RC buildings: 363the case study of AvellinoInfill typology, actually, was not surveyed in a large part of cases, and aquite high uncertainty anyhow affected this parameter also in the case when thisinformation was available. Hence, it was assumed to consider hollow clay brickpanels in all cases, and the material characteristics were derived from codeprescriptions (Circolare 617, 2009) assuming central values of the proposedranges, i.e. a shear elastic modulus equal to 1350 MPa, a Young’s elasticmodulus equal to 4500 MPa and a shear cracking strength equal to 0.35 MPa.Both parameters α and β (see Section 5.2.3) were assumed equal to 0.05.5.3.2.2 Analysis of resultsResults of seismic vulnerability assessment on RC building stock arereported in this Section. Vulnerability curves for different building classes willbe shown first; then, the expected failure probability P f in a reference timewindow of 1 year will be illustrated. In particular, the attention will be focusedon Damage Limitation and Near Collapse Limit States.It is to be noted that the methodology for evaluating vulnerability curves inlongitudinal or transversal direction has been previously described (Section5.2.6), whereas in this Section, for each building and for each Limit State, asingle vulnerability curve is evaluated independent of the direction; to this aim,for each of the N samplings =1000 sets of samplings, the corresponding PGAcapacity is evaluated as the minimum value between longitudinal andtransversal directions. Hence, the vulnerability curve of the building,independent of the direction, is obtained as the cumulative frequencydistribution of these PGA capacity values. Failure probabilities at DL and NCLimit States are calculated for each building, according to the proceduredescribed in Section 5.2.7, based on the corresponding vulnerability curvesobtained according to this procedure and the seismic hazard described by thePGA exceeding probability in 1 year, obtained from (INGV-DPC S1, 2007) forthe site of interest (Lon.: 14.793, Lat.: 40.915), see Figure 5.3.2.4.

364 Chapter V – Simplified approach to the seismic vulnerability assessment of existing RC buildings:the case study of Avellino10.90.8Exceeding probability in 1 year0.70.60.50.40.30.20.100 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2PGA [g]Figure 5.3.2.4. Seismic hazard for Avellino city (Lon.: 14.793, Lat.: 40.915), according to(INGV-DPC S1, 2007)Fragility curves will be illustrated in the following not referring to singlebuildings, but to population of buildings. A fragility curve for a population ofbuildings is evaluated as the cumulative frequency distribution of PGA capacityvalues obtained for all buildings in the population; the number of these valuesis equal to Nsamplings × Nbuildings, where N samplings (=1000) is the number of analysescarried out for each building and N buildings is the number of buildings in theconsidered population.Figures 5.3.2.5 and 5.3.2.6 report fragility curves at NC and DL LimitStates, respectively, for buildings from 1 to 8 storeys. An increase in seismicvulnerability with the number of storeys is clearly observed in both cases. AtDL Limit State, in particular, fragility curves for buildings with more than 3storeys are very close to each other.

Chapter V – Simplified approach to the seismic vulnerability assessment of existing RC buildings: 365the case study of AvellinoP f10.90.80.70.60.50.40.30.20.1N storeys= 1N storeys= 2N storeys= 3N storeys= 4N storeys= 5N storeys= 6N storeys= 7N storeys= 800 0.5 1 1.5 2 2.5 3PGA [g]Figure 5.3.2.5. Fragility curves at NC Limit State for different number of storeysP f10.90.80.70.60.50.40.30.20.1N storeys= 1N storeys= 2N storeys= 3N storeys= 4N storeys= 5N storeys= 6N storeys= 7N storeys= 800 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1PGA [g]Figure 5.3.2.6. Fragility curves at DL Limit State for different number of storeys

366 Chapter V – Simplified approach to the seismic vulnerability assessment of existing RC buildings:the case study of AvellinoThe influence of the age of construction can be observed by reporting thefragility curves, at both DL and NC Limit States, of pre-1981 and post-1981buildings. As a matter of fact, the major change represented by the introductionof seismic load prescriptions took place in 1981. As an example, Figures5.3.2.7 and 5.3.2.8 report fragility curves for pre-1981 (i.e., gravity loaddesigned) and post-1981 (i.e., seismic load designed) five-storey buildings. Asexpected, a lower seismic vulnerability is observed in post-1981 buildings, atboth Limit States.P f10.90.80.70.60.50.40.30.20.1DL - GDL - S00 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2PGA [g]Figure 5.3.2.7. Fragility curves at DL Limit State for pre-1981 (gravity load designed - G) andpost-1981 (seismic load designed - S) five-storey buildings

Chapter V – Simplified approach to the seismic vulnerability assessment of existing RC buildings: 367the case study of AvellinoP f10.90.80.70.60.50.40.30.20.1NC - GNC - S00 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2PGA [g]Figure 5.3.2.8. Fragility curves at NC Limit State for pre-1981 (gravity load designed - G) andpost-1981 (seismic load designed - S) five-storey buildings

368 Chapter V – Simplified approach to the seismic vulnerability assessment of existing RC buildings:the case study of AvellinoSeismic vulnerability of analyzed buildings can be also observed in terms ofannual failure probability, at both Limit States. First, evaluated failureprobability at NC Limit State can be reported as a function of the number ofstoreys (see Figure 5.3.2.9). Mean values of P f are reported as red squares. Asexpected, a clear trend is observed, showing the higher vulnerability of tallerbuildings (see Section 5.2.8).5.00E-044.00E-04P f,NC3.00E-042.00E-041.00E-040.00E+00N storeys0 2 4 6 8 10 12Figure 5.3.2.9. Annual failure probability at NC Limit State depending on the number of storeysFailure probability at DL Limit State is reported in Figure 5.3.2.10. Onaverage, these probabilities are lower by an order of magnitude with respect tothe corresponding probabilities at NC. Also in this case, as expected, the failureprobability increases with the number of storeys; nevertheless, this increase isnot as uniform as for NC Limit State, rather highlighting a sudden increasewhen the number of storeys changes from the range of values N storeys ≤ 3 toN storeys ≥ 4.

Chapter V – Simplified approach to the seismic vulnerability assessment of existing RC buildings: 369the case study of Avellino5.00E-034.00E-03P f,DL3.00E-032.00E-031.00E-030.00E+00N storeys0 2 4 6 8 10 12Figure 5.3.2.10. Annual failure probability at DL Limit State depending on the number ofstoreysFigures 5.3.2.11 and 5.3.2.12 report mean failure probabilities at DL andNC Limit State in pre- and post-1981 buildings. If a relative comparison iscarried out for equal values of N storeys , a higher failure probability in pre-1981buildings, as expected, can be observed, particularly at NC Limit State.More clear observations can be made if a comparison is carried outassuming the same stratigraphic and topographic conditions for all thecompared buildings. In particular, soil type E and T1 topographic category areassumed, representing the most common conditions. Moreover, the comparisonis carried out between buildings built during 1972-81 and 1982-91 decades,right before and after the introduction of seismic load prescriptions. Three- toeight-storey buildings are observed, including the large part of the buildingstock. In this case, the decrease in failure probability due to the introduction ofseismic prescriptions can be more clearly observed. In particular, this differenceis more pronounced at NC Limit State. However, most clear is the dependenceon the number of storeys.

370 Chapter V – Simplified approach to the seismic vulnerability assessment of existing RC buildings:the case study of Avellino3.00E-033.00E-042.50E-032.50E-042.00E-032.00E-041.50E-031.00E-035.00E-040.00E+00pre-1981post-19811234567 81.50E-041.00E-045.00E-050.00E+00pre-1981post-19811234567 8(a)(b)Figure 5.3.2.11. Comparison between annual failure probabilities at DL (a) and NC (b) LimitStates in pre- and post-1981 buildings3.00E-033.00E-042.50E-032.50E-042.00E-032.00E-041.50E-031.50E-041.00E-03781.00E-04785.00E-04565.00E-05560.00E+0040.00E+00472-8182-91372-8182-913(a)(b)Figure 5.3.2.12. Comparison between annual failure probabilities at DL (a) and NC (b) LimitStates in 1972-81 and 1982-91 buildings (soil type E and topographic category T1)

Chapter V – Simplified approach to the seismic vulnerability assessment of existing RC buildings: 371the case study of AvellinoThe influence of infills on the seismic vulnerability can be observed lookingat the trends of failure probability with the percentage of infill openings at thebottom storey, for the same buildings reported in Figures 5.3.2.13 and 5.3.2.14.At both Limit States, the detrimental effect of a decrease in the amount ofinfills at this storey is clearly reflected by the increase in failure probability.4.00E-03P f,DL3.00E-032.00E-031.00E-030.00E+00infill openingpercentage0 20 40 60 80 100Figure 5.3.2.13. Annual failure probability at DL Limit State depending on the infill openingpercentage at the bottom storey (soil type E and topographic category T1)4.00E-04P f,NC3.00E-042.00E-041.00E-040.00E+00infill openingpercentage0 20 40 60 80 100Figure 5.3.2.14. Annual failure probability at NC Limit State depending on the infill openingpercentage at the bottom storey (soil type E and topographic category T1)

372 Chapter V – Simplified approach to the seismic vulnerability assessment of existing RC buildings:the case study of AvellinoSeismic vulnerability can also be analyzed by observing the spatialdistribution of main considered parameters and of failure probability at DL andNC Limit States. In particular, the spatial distribution can be referred to singlecensus cells reporting corresponding average values among buildings.Figures 5.3.2.13 to 5.3.2.15 report the average number of storeys, theaverage age of construction (pre- and post-1981 buildings) and the mostwidespread soil type per census cell, respectively. It can be noted that highervalues of the average number of storeys are generally observed close to the citycentre, while, as far as the age of construction is concerned, no homogeneousareas can be clearly identified, probably due to the post-1980 earthquakereconstruction. Soil types B and E are most widely spread in Western andCentral-Eastern areas, respectively.Figures 5.3.2.16 and 5.3.2.17 report the average annual failure probability atDL and NC Limit States per census cell; generally higher values are observed incentral and North-Western areas, at both Limit States. In addition to the numberof storeys and the age of construction, which have been previously discussed, aclear influence of the difference in seismic hazard due to a different soil typecan be recognized, see Figure 5.3.2.15, leading, as expected, to higher failureprobabilities, on average, for buildings located on soil type E.

Chapter V – Simplified approach to the seismic vulnerability assessment of existing RC buildings: 373the case study of AvellinoFigure 5.3.2.13. Average number of storeys of rectangular RC buildings per census cell7

374 Chapter V – Simplified approach to the seismic vulnerability assessment of existing RC buildings:the case study of Avellinopre-1981post-1981Figure 5.3.2.14. Average age of construction of rectangular RC buildings per census cell

Chapter V – Simplified approach to the seismic vulnerability assessment of existing RC buildings: 375the case study of AvellinoFigure 5.3.2.15. Most widespread soil type for rectangular RC buildings per census cellBCE

376 Chapter V – Simplified approach to the seismic vulnerability assessment of existing RC buildings:the case study of Avellino1.5e-004 - 8.7e-0048.8e-004 - 1.5e-0031.6e-003 - 2.0e-0032.1e-003 - 2.4e-0032.5e-003 - 3.3e-003Figure 5.3.2.16. Average annual failure probability of rectangular RC buildings at DL per census cell

Chapter V – Simplified approach to the seismic vulnerability assessment of existing RC buildings: 377the case study of Avellino1.3e-005 - 8.4e-0058.5e-005 - 1.5e-0041.6e-004 - 1.8e-0041.9e-004 - 2.2e-0042.3e-004 - 2.9e-004Figure 5.3.2.17. Average annual failure probability of rectangular RC buildings at NC per census cell

378 Chapter V – Simplified approach to the seismic vulnerability assessment of existing RC buildings:the case study of Avellino5.4 FUTURE RESEARCHThe proposed approach – based on a simulated design procedure and on asimplified modelling of the structural response through the Shear Typeassumption – can provide a large scale seismic vulnerability assessment of RCbuildings based on relatively poor input data, also taking into account importantparameters such as the presence of infill elements and the age of construction.However, further developments are foreseen; for instance, assessmentmethodologies more advanced than the spectral method, such as nonlineardynamic analyses, may be employed on such simplified models, which presentthe advantage of a high reduction in computational demand (e.g., Mollaioli etal., 2009).The illustrated procedure should also be integrated with a reliable estimateof the influence of brittle failure mechanisms – also due to local interactionmechanisms between structural and non-structural elements – on the seismicvulnerability. Moreover, other parameters such as the irregularity in plan and/orin elevation should be taken into account. As a matter of fact, post-earthquakeobserved damage often demonstrated how a reliable seismic vulnerabilityassessment cannot disregard these factors.

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