Engineering Structures 29 (2

amn

e M

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fore 2

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carried out. The beamcolumn hierarchy of resistance rules are applied both according to the old (1994) and the new (2003) version of EC8: the

large differences are discussed. The results of two different computer programs are compared, SAP2000 and CANNY99. A suite of 7 earthquakes(each with both the horizontal components), fully satisfying the EC8 provisions, are used as input of non-linear dynamic analyses.

The results show that the 3 methods of analyses provided by EC8 for new buildings respect a correct hierarchy in terms of safety, i.e. thesimpler the analysis is the safer is the result returned: the building designed according to elastic analyses is verified by both non-linear static anddynamic analyses and displacements and total chord rotations demanded by non-linear static methodology are larger than those demanded bynon-linear dynamic one.c 2007 Elsevier Ltd. All rights reserved.Keywords: Dynamic analysis; Non-linear analysis; Natural records; Seismic design; Eurocode 8; Capacity design

1. Introduction

The modern seismic codes, such as EC8 [1] and IBC [2],allow the designer to use different analysis methodologies, inparticular: (1) lateral force and (2) multi-modal elastic onesand (3) static and (4) dynamic non-linear ones. Their levelof reliability decreases from (4) to (1) and, consequently, thesafety margin with respect to the same limit state shouldincrease according to the same order.

This has not yet been clearly shown, at least in terms ofmethodologies strictly fulfilling the EC8 provisions. A largeamount of comparisons have been performed by Fajfar [3,4]both on plane and space models with the main goal to validatethe N2 method [5], i.e. the non-linear static procedure assumedby EC8. But the analysis methodologies Fajfar compared do not

code constraints; this is particularly important if the distancewith respect to the ultimate limit state of a structure analysedby non-linear dynamic procedure is to be determined andcompared to the one obtained by other analysis methodologies.

In the paper the results of elastic, non-linear static andnon-linear dynamic analyses are reported and commented; theanalysed structure, a four-storey r/c frame building, completelyfulfils the EC8 design provisions, along with the adopted suiteof accelerograms, which was recently published [6].

The results shown herein are, for sake of brevity, limited to asingle structure, but they are confirmed by analyses performedon other r/c frame buildings, with different, also irregular,geometry, designed according to the same level of seismicaction.Comparison between non-linear dynEC8 and elastic and no

Gennaro Magliulo, GiuseppDepartment of Structural Analysis and Design, Universit

Received 27 October 2006; received in revisedAvailable onlin

Abstract

The paper deals with the topic of analyses performed according to mlinear static and non-linear dynamic analyses of a multi-storey r/c framesatisfy in detail all the EC8 provisions and, above all, the suitesof accelerograms used for dynamic analyses do not satisfy the

Corresponding author. Tel.: +39 0817683656; fax: +39 0817683491.E-mail addresses: gmagliul@unina.it (G. Magliulo), gmaddalo@unina.it

(G. Maddaloni), cosenza@unina.it (E. Cosenza).

0141-0296/$ - see front matter c 2007 Elsevier Ltd. All rights reserved.doi:10.1016/j.engstruct.2007.01.027007) 28932900www.elsevier.com/locate/engstruct

ic analysis performed according to-linear static analyses

addaloni, Edoardo Cosenza

f Naples Federico II, via Claudio 21, 80125 Naples, Italy

m 29 January 2007; accepted 30 January 20071 March 2007

ern code provisions, in particular Eurocode 8 (EC8) rules. Elastic, non-ilding designed according to Eurocode 2 (EC2) and EC8 provisions are2. Geometry of the building and elastic analysis

2.1. Geometry

The geometry of the building is reported in Fig. 1; it is a four-storey r/c frame building. The bottom interstorey height is equalto 4 m, while at the other levels it is equal to 3.2 m; at the first

ing

th

positions, indicated in the following with respect to the initialposition: dx @(1.25,inf @(0, 0.68).

In order to take the cis assigned to be one-haone; the column stiffnes3 modes of such a modand 0.495 s (rot.), whiluncracked structure are0.417 s (rot.).

The building is desig2 [9] and 8 [1], by modspectrum soil B type 1type A ground, ag = 0.code [10], is considereto the High Ductility C

MRb (2.2)

Eq. (2.1) and

MScnding moments at thehe application of thecoefficient (2.2) can

oment of resistance ifinations; indeed somesed by a low columngive a high value of0), sx @(1.25, 0), sup @(0, 0.68),

racking into account, the beam stiffnesslf of the corresponding uncracked beams is not reduced. The periods of the firstel are: 0.571 s (X dir.), 0.526 s (Y dir.)e the periods of the first 3 modes of the: 0.485 s (X dir.), 0.462 s (Y dir.) and

ned according to Eurocodes 0 [7], 1 [8],al response spectrum analysis. A designwith a design ground acceleration on35g, taken from the Italian new seismic

= Rd MScwhere Rd = 1.3 is the coefficient ofis the sum of the column design betop and at the bottom of the node. Tbeamcolumn capacity design by thelead to overestimating the column mit is computed for all the design combcombinations, even though characteribending moment at the node, cancoefficient .

3. Non-linear model2894 G. Magliulo et al. / Engineer

Fig. 1. Geometry of

storey the dimensions of the sections of all the columns are 4065 cm2, of all the beams are 40 60 cm2, at the second storeysuch dimensions are respectively 4060 cm2 and 4055 cm2,at the third 40 55 cm2 and 40 50 cm2, while at the top levelthey are 4050 cm2 both for column and beam sections. A lowvariation of the element dimensions between adjacent floors isassigned in order to favour the structures vertical regularity,while column dimensions are kept larger than beam ones inorder to take into account the capacity design. The stairs aresustained by non-horizontal beams, except at the first flight,which is connected to the foundation on one side and to thebeam at middle height of the first storey on the other side, inorder to avoid concentrations of shear at the bottom half storey.

2.2. Elastic analysis

Beams and columns are modelled as massless onedimensional finite elements; the mass is concentrated in thefloor levels, assumed rigid in their own planes; consequentlythe structure is characterised by 3 DOFs for each floor. Fromthe 1st to the 4th floor the masses are respectively 419 t,396 t, 385 t and 361 t, while the polar moment of inertia iscomputed considering a uniform mass distribution on the floorarea, equal to 16.4 25.4 m2. As imposed by the code, a 5%accidental eccentricity is considered; consequently 4 modelsare analysed with the centre of mass placed in 4 differentd. The design is performed accordinglass rules, a behaviour factor equal toStructures 29 (2007) 28932900

e analysed building.

5.85 is computed, also considering that the frame is regular inelevation.

Concrete characteristic cubic strength equal to fck =30 N/mm2 and steel characteristic yielding strength equal tofyk = 450 N/mm2 are adopted.The orthogonal effects are considered by the 30% rule: 8

combinations for each of the 4 models are computed.It is to be noted that the dimensions of the frame elements

reported above are assigned also in order to satisfy the damagelimitation requirement, in particular the limitation for buildingshaving non-structural elements of brittle materials attached tothe structure.

As provided by the code, all nodes of the frame structure,unless the top floor ones and those at foundations, satisfy thedesign condition:

MRc 1.3

MRb (2.1)

where

MRc and

MRb are the sum of design valuesof moments of resistance of respectively the columns andthe beams framing the joint; this is satisfied along both theorthogonal directions and considering both signs of seismicaction.

In order to satisfy such condition, some seismic codes, suchas the new Italian one [10] and the previous version of EC8[11], impose to multiply the design value of the column bendingmoment at the node by a coefficient computed as:Non-linear analyses are performed by means of 2 computerprograms, SAP2000 [12] and CANNY99 [13]. Non-linearity

ruc

-C

is computed according to EC8 [1] equivalent lateral force pro-base shear. The bi-linear capacity curve is also presentedalong with capacity and demand points: mec indicates thecedure taking into account the vertical regularity of the struc-ture. The yielding and the ultimate rotations are evaluated asprovided by EC8 [14] equations (A.10b) and (A.1) respectively,where the already cited medium values are assigned to concretemaximum ( fc) and steel yielding ( fy) strength.

The hysteretic model is Takeda type, even though inCANNY99 the pinching effect is also taken into account anda small value of the unloading stiffness is assigned, i.e. in eachcycle it is reduced by 50% with respect to the previous one;a less degrading model is assumed for columns with respectto beams: in CP7 model [13] for beams the value of all the 3coefficients , and is always 0.5, while for columns is

mechanism of the structure, ULS (Ultimate Limit State)the attainment in at least one plastic hinge of any elementof the rotation value 3/4 u and t.ULS the demandcorresponding to the elastic design acceleration spectrum soilB type 1, ag = 0.35g, computed, as prescribed by EC8[1], at the target point of N2 method [5]; u is the totalchord rotation capacity computed according to EC8 empiricalformula (A.1) [14]. Results presented in Fig. 3 regard modelssup pushed along positive X direction and sx pushedalong positive Y direction; the other 6 curves are not shownbecause models inf and dx provide very similar results toG. Magliulo et al. / Engineering St

Fig. 2. Pushover curves along longitudinal (left) and transversal (right) dir.: SAPlegend, the reader is referred to the web version of this article.)

regards flexural rotations, while all the other deformations areassumed linear. Both beams and columns are characterised bylumped plasticity models; in the latter case for each sectiontwo independent non-linear springs are assigned, one foreach orthogonal direction. No axial forcebending momentinteraction is considered at the plastic hinge.

Bending moment springs are characterised by tri-linearskeleton curve, defined by cracking and yielding moment andcorresponding rotations; the post-yielding rotation is assumedequal to zero. Such moments and the corresponding curvaturesare computed considering a parabolarectangle diagram forconcrete under compression, characterised by maximum andultimate strength equal to the medium value for concrete 30/37according to EC2 [9], i.e. 38 N/mm2; a strain value at theend of the parabola equal to 0.2% and an ultimate strainequal to 0.35% are assigned. The concrete Young modulus andits maximum tensile strength are also computed according toEC2. An elasticperfectly plastic steel stressstrain diagramis considered, characterised by a maximum strength equal to530 N/mm2, computed as mean of tests on more than 200 barsmade by steel called FeB44K performed at the Laboratory ofthe Department of Scienza delle Costruzioni of University ofNaples Federico II. A steel maximum strain equal to 1% and aYoung modulus equal to 200 000 N/mm2 are assigned.

The cracking rotation is computed multiplying the corre-sponding curvature by Lv/3, where Lv is the shear span, i.e. thebending moment/shear ratio, evaluated at the end section wherethe plastic hinge is located; such internal forces result from con-sidering the building loaded by horizontal forces, whose shapechanged and assumed equal to 1.0 [15].tures 29 (2007) 28932900 2895

ANNY comparison. (For interpretation of the references to colour in this figure

4. Non-linear static analysis

Non-linear static analyses are performed according to EC8,considering a force distribution proportional for each of the2 orthogonal directions to first modal shape in the relativedirection by mass distribution. The first 2 modes of thebuilding are translational and the square root of the ratio oftorsional stiffness to lateral stiffness in each of the 2 orthogonaldirections is larger than the radius of gyration of floor massin plan (see equation (4.1b) in EC8 [1]); consequently thestructure is torsionally stiff and the application of a particularprocedure for the estimation of the torsional effects is notnecessary.

Eight pushovers are performed, 2 opposite signs for 4different positions of the centre of mass.

In Fig. 2 a comparison between pushover curves madeby SAP2000 (black line) and CANNY99 (red line) alonglongitudinal (X) direction (left side of the figure) of themodel inf and transversal (Y ) direction of the model dxis shown; the curves are reported in terms of top centre of massdisplacement divided by the total height of the structure alongthe horizontal axis of the diagram and base shear divided by thebuilding seismic weight along the vertical axis. The 2 computerprograms give coincident curves along X direction, and almostcoincident along Y direction, confirming the reliability ofnumerical results; all the results shown in the following areobtained by CANNY99.

In Fig. 3 the results of 2 of the 8 performed pushoversare shown in terms of adimensionalised top displacement vsmodels sup and sx respectively and two pushovers withopposite sign provide almost coincident curves. The capacity

ing

of

demand parameters evaluated at target points are computed

Both the horizontal components of a set of 7 earthquakes(Table 1), i.e.dynamic analysto the selectionEC8 provisionsacceleration valushould not be squestion; in theT1 is the fundamwhere the acceldamping elasticshould be less thdamping elasticfrom at least 7 n

ign value of the

records used,line), the EC8e curve whosenes (black thinale the recordsnly one recordnoted that the

e design of the

f the accelero-14 natural records, are used for non-lineares whose results are shown herein; accordingprocedure presented in [6], they satisfy the: the mean of zero period spectral responsees (calculated from individual time histories)maller than the value of ag S for the site inrange of periods between 0.2T1 and 2T1, whereental period of the structure, in the directionerogram is applied, no value of the mean 5%spectrum, calculated from all time historiesan 90% of the corresponding value of the 5%response spectrum; if the response is obtained

of response quantities should be used as the desaction effect Ed in relevant verifications.

Fig. 4 shows the elastic spectrum of the 14along with the average spectrum (red thickelastic design spectrum (black thick line) and thordinates are equal to 90% of such spectrum oline); SF indicates the value of factors used to scfor the purpose to matching code spectrum: ois scaled by a low SF equal to 1.08. It is to bematched code spectrum is the one used for thbuilding analysed, assigning q = 1.

According to the direction of registration oby the Square Root of Sum of Squares rule (SRSS)resulting in 16 combinations; the maximum values obtainedby such combinations, considering the results at t.ULS,are compared to results of elastic and non-linear dynamicanalyses. The results are provided in terms of top centre ofmass displacements and demand/capacity ratio of total chordrotation computed at beam and column ends.

5. Step by step non-linear dynamic analysis Fig. 4. Spectra of the records used for non-linear analyses, their average andEC8 spectrum. (For interpretation of the references to colour in this figurelegend, the reader is referred to the web version of this article.)2896 G. Magliulo et al. / Engineer

Fig. 3. Capacity curves

Table 1Earthquakes used for non-linear dynamic analyses

Earthquake code Earthquake name

000187 Northern and central Iran000196 Montenegro000199 Montenegro000230 Montenegro (aftershock)000291 Campano lucano006263 South Iceland006334 South Iceland (aftershock)

curves computed forcing the structure along Y direction show acertain slope and the attainment of u precedes the mechanismpoint, evidencing a less ductile behaviour with respect to theorthogonal direction; this is due to the presence along suchdirection of the inclined beams supporting the stairs. TheUltimate Limit State is always verified, i.e. the demand is lowerthan the capacity.

According to EC8 provisions, the orthogonal effects ofon-linear time histories analyses, the averageStructures 29 (2007) 28932900

models sup and sx.

Earthquake country Date

Iran 16/09/1978Yugoslavia 15/04/1979Yugoslavia 15/04/1979Yugoslavia 24/05/1979Italy 23/11/1980Iceland 17/06/2000Iceland 21/06/2000grams, a direction, X or Y , is given to the two components of

2897

Table 2Top cent

Analysis

NLSANLDA(aNLDA(aNLDA (

each eaearthquof therection

Asdisplacchord rthe 4 mof theis consand the maximum of the 7 maximum results; the maximum

nd the+ SD)e onlyhile asresultse otherable 2namicNLDAr statice plus

)) and,ximum

ility inlumnseneraletweenmum).

The row representing the demand due to NLDA (average) is

effect on the 4 models is always considered.

6. Comparisons between the analysis results

Non-linear dynamic analyses are compared to non-linearstatic ones in terms of maximum displacement and rotationalductility demand and such demand is compared to capacity atthe Ultimate Limit State, which is equal to 3/4 u as alreadywritten.

In Table 2, X and Y top centre of mass displacements arelisted: NLSA indicates the maximum values obtained by the 16SRSS combinations of the results of non-linear static analysesat t.ULS, i.e. the demand corresponding to the elastic designacceleration spectrum soil B type 1, ag = 0.35g; NLDA(average) means that the average among the maximum resultsFig. 5. Comparison in terms of beam and column maximum rotational dshorter than the row representing the demand for NLSA, andshorter than the row representing the capacity at the UltimateLimit State: this means that globally the demand due to NLDA(average) is lower than the demand due to NLSA,both less thanthe capacity at the Ultimate Limit State (attainment of 3/4 u).

In Figs. 6 and 7 demand/capacity ratios in terms of totalchord rotations at beam (black numbers) and column (rednumbers) end sections of frames X1 and Y1 respectively arepresented; for sake of brevity the other frames are not shown,but, obviously, the reported conclusions concern the wholebuilding. In the case of NLSA and NLDA (average) the ratiosare always lower than one; consequently it is confirmed thatthe building designed according to EC8 provisions by elasticmodal response spectrum analysis at the Ultimate Limit Stateis verified at the same limit state according to both non-G. Magliulo et al. / Engineering Structures 29 (2007) 28932900

re of mass X and Y direction displacements

UX (m) UY (m)

0.189 0.181verage) 0.142 0.138v+SD) 0.247 0.216maximum) 0.345 0.273

rthquake; the analyses are performed applying, for eachake, the X component along the longitudinal directionbuilding and the Y component along the orthogonal di-.for non-linear static analyses top centre of massements and demand/capacity ratio in terms of totalotation at beam and column ends are shown. For each ofodels obtained moving the centre of mass, the average7 maximum results obtained applying the 7 earthquakesidered along with the average plus the standard deviation

of the 7 non-linear dynamic analyses is considered amaximum among the 4 models is reported; as NLDA(avthe average plus the standard deviation instead of thaverage of the 7 results for each model is considered, wNLDA (maximum) the maximum among the maximumof the 7 non-linear dynamic analyses is taken and, as in th2 cases, the maximum of the 4 models is presented. Tshows that the displacements obtained by non-linear dyanalyses, averaged, according to EC8, on 7 earthquakes ((average)), are lower than the ones obtained by non-lineaanalyses (NLSA). This does not happen when the averagthe standard deviation is considered (NLDA(av + SDwith a large scatter, when the maximum of the 7 madisplacements is computed (NLDA (maximum)).

In Fig. 5 both the available and the demanded ductterms of total chord rotation at each end of beams and coare reported as coloured points: the figure provides a gcomparison for beams and columns in both directions bcapacity, NLSA, NLDA (average) and NLDA (maxiuctility between NLDA (average and maximum), NLSA and capacity.

ng

ilit

linear static and dynamic analysis performed according to EC8. Table 3

Furthermore, also in terms of ductility demand, as alreadynoted in terms of displacements, NLDA (average) provideslower values with respect to NLSA; consequently results showthat safety levels associated to different analyses performedaccording to EC8 are correlated to their accuracy, i.e. the designof elastic analysis, the simplest, is more conservative withrespect to safety verification made by non-linear static analysis,which is more conservative with respect to non-linear dynamicanalysis, which is the most complicated.

On the contrary, in the case of NLDA(av + SD), fewsections, which do not belong to the two presented frames,show a ductility demand in terms of total chord rotation whichoverpass the capacity; this happens at many sections if resultsgiven by NLDA (maximum) are observed. The variation isobviously due, as shown in Fig. 4, by the variability of theintensity of the seismic input: the variation coefficient, i.e. thestandard deviation/mean ratio, of ductility demand averagedon all element ends is equal to 0.665, while its maximumvalue is 2.35. Lower values can be obtained considering themaximum variation coefficients of the top centre of massdisplacement among the 4 models: 0.76 along X direction, 0.60along Y direction. An evident consequence of the large standarddeviation is, as already noted, that the evaluation of the safetylevel on the base of maximum of the maximum effect of each ofthe 7 earthquakes can lead to opposite conclusions with respectto considering the average of maximum effects.

Fig. 8 provides in the case of NLSA and NLDA (average) forframe Y1 demand/capacity ratios in terms of maximum chord

Displacements at frames X1Y1 intersection of top floor for different modelsby NLDA (average)

Model UX (m) UY (m) X (%) Y (%)

NLDAG 0.144 0.138 NLDASUP 0.138 0.138 4.2 0NLDAINF 0.148 0.140 +2.8 +1.5NLDASX 0.155 0.161 +7.6 +16.7NLDADX 0.141 0.115 2.1 16.7

Figs. 6 and 7. In such a way results are affected by the effectiveyield chord rotations, which depend on the idealization ofmoment rotation relationship. From a qualitative point of viewthese results are coincident with the corresponding ones shownin Fig. 7 and, consequently, their comments are confirmed.

All the performed analyses show that taking into accountthe accidental eccentricity the computational effort increasesby a factor equal to four; consequently, it is interesting toevaluate if the effect of such eccentricity is significant in termsof structural seismic response. In Table 3 the displacements ofthe top floor at the intersection of frames X1 and Y1 (Fig. 1)along X (UX) and Y (UY) directions resulting by NLDA(average) are reported for the models sup (NLDASUP),inf (NLDAINF), sx (NLDASX) and dx (NLDADX). Suchresults are compared to the corresponding ones obtained by themodel without accidental eccentricity (NLDAG); the variationsin terms of percentage are reported in columns X and Y.These variations, when the eccentricity along the larger side is2898 G. Magliulo et al. / Engineeri

Fig. 6. Frame X1: demand/capacity ratio in terms of maximum rotational ductlegend, the reader is referred to the web version of this article.)rotations instead of maximum chord rotational ductility as inStructures 29 (2007) 28932900

y at element ends. (For interpretation of the references to colour in this figureassigned, are not negligible (17%).

truFig. 7. Frame Y1: demand/capacity ratio in terms of maximum rotational ductility at element ends. (For interpretation of the references to colour in this figurelegend, the reader is referred to the web version of this article.)

Fig. 8. Frame Y1: demand/capacity ratio in terms of maximum rotations atelement ends.

7. Conclusions

A 4-storey, r/c frame building is designed according toEC8 provisions [1] by modal response spectrum analysisconsidering soil B type 1 with a design ground acceleration ontype A ground, a = 0.35g. Non-linear static and dynamic

characterised by a non-linear moment rotation relationshipwith a tri-linear skeleton curve and a Takeda like hystereticbehaviour which also takes into account the pinching effect.The input adopted for non-linear dynamic analysis is selected inorder to rigorously satisfy the EC8 provisions; this allows us torigorously compare for the same design spectrum the demandcomputed by non-linear dynamic analysis to the one associatedto elastic modal response spectrum analysis and to non-linearstatic analysis. A suite of 7 natural earthquakes is selected [6].

A large amount of results is obtained; herein, for sakeof brevity, they are reported only in terms of top centre ofmass displacement and rotational ductility at the element ends.The 5% accidental eccentricity is considered, consequently 4models are analysed. 28 non-linear dynamic analysis (7 4)are performed and the maximum effect of the 4 modelsis considered; for each model the average of 7 maximaobtained from 7 earthquakes (NLDA (average)), the averageplus standard deviation (NLDA(av+SD)) and the maximum ofthe maximum (NDLA(maximum)) are computed. The results ofelastic analysis are the maximum among the 32 combinationsdue to 8 combinations (the 30% rule is adopted) by 4 models,G. Magliulo et al. / Engineering Sganalyses are performed adopting a lumped plasticity model,ctures 29 (2007) 28932900 2899while the ones of non-linear static analysis (NLSA) are the

2900 G. Magliulo et al. / Engineering Structures 29 (2007) 28932900

maximum at the Ultimate Limit State of 16 results due to theSRSS rule (4 models by 4 different combinations).

All the results show that at Ultimate Limit State NLDA(average) provides lower effects with respect to NLSA and forboth of them the demand is lower than the capacity provided bythe code, corresponding to the attainment of 3/4 u in at leastone end of any element, whereu is the ultimate chord rotation[14]; this demonstrates that safety level associated to differentanalyses performed according to EC8 is correlated to theiraccuracy, i.e. the design of elastic analysis, the simplest, is moreconservative with respect to safety verification made by non-linear static analysis, which is more conservative with respectto non-linear dynamic analysis, which is the most complicated.

On the contrary, at few sections in the case of NLDA(av +SD) and at many sections in the case of NLDA (maximum)the Ultimate Limit State is not verified, i.e. the demand interms of maximum chord rotation surpasses the capacity. This

References

[1] CEN. Eurocode 8: Design of structures for earthquake resistance Part1: General rules, seismic actions and rules for buildings. Final draft. prEN1998-1. Brussels; 2003.

[2] International Building Code. Falls Church (VA): International CodeCouncil; 2000.

[3] Fajfar P, Magliulo G, Marusic D, Perus I. Simplified non-linear analysisof asymmetric buildings. In: De Stefano M, Rutenberg A, editors.Proceedings of the 3rd European workshop on the seismic behaviour ofirregular and complex structures. 2002.

[4] Fajfar P, Marusic D, Perus I. Torsional effects in the push-over basedseismic analyses of buildings. Journal of Earthquake Engineering 2000;9(6):83154.

[5] Fajfar P. A non linear analysis method for performance-based seismicdesign. Earthquake Spectra 2000;16(3):57392.

[6] Iervolino I, Maddaloni G, Cosenza E. Unscaled real record sets compliantwith Eurocode 8. In: First European conference on earthquake engineeringand seismology. 2006.is due to quite large variation of results due to differentaccelerograms, also shown by standard deviation/mean ratio ofresults. Consequently it can be stated that the evaluation of thesafety level on the base of maximum of the maximum effect ofeach of the 7 earthquakes can lead to opposite conclusions withrespect to considering the average of the maximum effects.

Finally, considering the increment of computation effortdue to accidental eccentricity, its effect on structural seismicresponse is evaluated: it is not negligible.

The results shown in this paper are confirmed by analysesperformed on other r/c frame buildings, characterised bydifferent, also irregular, geometry and designed according to thesame level of seismic action, which, for sake of brevity, are notreported herein; consequently conclusions are limited on thistype of buildings.

Acknowledgment

This research has been partially funded by ItalianDepartment of Civil Protection in the frame of the nationalproject ReLUIS.[7] CEN. Eurocode 0: Basis of structural design. EN 1990. Brussels; 2002.[8] CEN. Eurocode 1: Actions on structures Part 1-1: General actions-

Densities, self weight, imposed loads for buildings. EN 1991-1-1.Brussels; 2002.

[9] CEN. Eurocode 2: Design of concrete structures Part 1-1: General rulesand rules for buildings. EN 1992-1-1. Brussels; 2004.

[10] PCM. Ordinanza n.3431. Ulteriori modifiche ed integrazioni allordinanzadel Presidente del Consiglio dei Ministri n. 3274 del 20 marzo 2003,recante Primi elementi in materia di criteri generali per la classificazionesismica del territorio nazionale e di normative tecniche per le costruzioniin zona sismica. Rome; 2003 [in Italian].

[11] CEN. Eurocode 8: Design provisions for earthquake resistance ofstructures. ENV 1998-1-2 General rules for buildings. Brussels; 1994.

[12] CSI Computer & Structures Inc. SAP2000. Linear and nonlinear staticand dynamic analysis of three-dimensional structures. Berkeley (CA):Computer & Structures, Inc.; 2004.

[13] Li KN. CANNY99. Three-dimensional nonlinear dynamic structuralanalysis computer program package. In: Technical and users manual.Canny Consultants Pte Ltd; 1996.

[14] CEN. Eurocode 8: Design of structures for earthquake resistance Part3: Assessment and retrofitting for buildings. Draft No 7. prEN 1998-3.Brussels; 2004.

[15] Faella G, Kilar V, Magliulo G. Symmetric 3D r/c buildings subjectedto bi-directional input ground motion. In: 12th world conference onearthquake engineering. 2000.

Comparison between non-linear dynamic analysis performed according to EC8 and elastic and non-linear static analysesIntroductionGeometry of the building and elastic analysisGeometryElastic analysis

Non-linear modelNon-linear static analysisStep by step non-linear dynamic analysisComparisons between the analysis resultsConclusionsAcknowledgmentReferences