Displacement Spectra

7/28/2019 Displacement Spectra

1/33

PLEASE SCROLL DOWN FOR ARTICLE

This article was downloaded by: [University of Illinois]

On: 19 July 2010

Access details: Access Details: [subscription number 917353191]

Publisher Taylor & Francis

Informa Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer House, 37-

41 Mortimer Street, London W1T 3JH, UK

Journal of Earthquake EngineeringPublication details, including instructions for authors and subscription information:http://www.informaworld.com/smpp/title~content=t741771161

DISPLACEMENT SPECTRA FOR SEISMIC DESIGNJulian J. Bommera; Amr S. Elnashaiaa Department of Civil and Environmental Engineering, Imperial College of Science, Technology &

Medicine, London SW7 2BU, UK

To cite this Article Bommer, Julian J. and Elnashai, Amr S.(1999) 'DISPLACEMENT SPECTRA FOR SEISMIC DESIGN',Journal of Earthquake Engineering, 3: 1, 1 32

To link to this Article: DOI: 10.1080/13632469909350338URL: http://dx.doi.org/10.1080/13632469909350338

Full terms and conditions of use: http://www.informaworld.com/terms-and-conditions-of-access.pdf

This article may be used for research, teaching and private study purposes. Any substantial orsystematic reproduction, re-distribution, re-selling, loan or sub-licensing, systematic supply ordistribution in any form to anyone is expressly forbidden.

The publisher does not give any warranty express or implied or make any representation that the contentswill be complete or accurate or up to date. The accuracy of any instructions, formulae and drug dosesshould be independently verified with primary sources. The publisher shall not be liable for any loss,actions, claims, proceedings, demand or costs or damages whatsoever or howsoever caused arising directly

or indirectly in connection with or arising out of the use of this material.
http://www.informaworld.com/smpp/title~content=t741771161http://dx.doi.org/10.1080/13632469909350338http://www.informaworld.com/terms-and-conditions-of-access.pdfhttp://www.informaworld.com/terms-and-conditions-of-access.pdfhttp://dx.doi.org/10.1080/13632469909350338http://www.informaworld.com/smpp/title~content=t741771161


2/33

Journal of Earthquake Engineering, Vol. 3, No. 1 (1999) 1-32@ Imperial College Press

DISPLACEMENT SPECTRA FOR SEISMIC DESIGN

JULIAN J. BOMMER and AMR S. ELNASHAIDepartment of Civil and Envimrnentat Engineering, Imperial College of Science,

Technology & Medicine, London S 7 2B U, UK aReceived 17 August 1998

Revised 27 September 1998Accepted 5 October 1998

Displacement-based seismic design and assessment of structures require t h e reiiable def-inition of displacement spectra for a wide range of periods and damping levels. T h edisplacement spectra derived from acceleration spectra in existing seismic codes do notprovide a suitable answer and there are no existing frequency-dependent attenuat ionrelationships derived specifically for t h i s purpose. Using a carefully processed da taset ofEuropean strong motion records, attenuation relationships have been derived for hori-zontal displacement response spectral ordinates. The results have been simplified intoa parametric form that allows th e straightforward construction of displacement designspectra for rock, stiff soil and soft soil sites a t distances of up to 50 km from earthquakeswith magnitudes' between 5.5 and 7.5, for six damping levels and up to response peri-ods of 3.0 seconds. Results from recent studies linking levels of ductility to equivalentdamping, using a complex hysteretic model and th e same strong motion databank, arealso reported.Keywords: displacement-based design, displacement spectra, attenuation relationships,substitute structure.

I . Preamble1.1. Force- based and displacement-based se ismic des i gnConventional seismic design, as employed in codes of practice, is entirely force-based, with a final check on structural displacements. The reasons for this situationare more historical than scientific. Force-based design is suited t o design for ac-tions that are permanently applied and where members are designed to resist theeffects of these actions at levels of stress constrained by their force resistance at th eplastic limit. The deformations corresponding to the plastic member capacity arenot normally excessive, and evaluating them is not an onerous task. Since seismicdesign was developed as an extension to primary load design, it followed the sameprocedure, noting though that inelastic deformations may be utilised to absorbquantifiable levels of energy, eading to reduction in the forces for which structuresare'designed. This led to the creation of the response modification (or behaviour)factor; this all-embracing parameter purports to account for over-strength, ductility,energy absorption and dissipation as well as th e structural capacity to re-distribute


3/33

2 J . J . Bommer & A. S. ELnashai

actions from inelastic highly stressed regions to other less stressed locations in thestructure. Problems of evaluating behaviour factors that are generally applicableto various structural systems, materials, configurations and input motions are welldocumented and the inherent weakness in code-specified factors is widely accepted.In force-based design, he primary input to.theprocess is a set of forces, with acheck on the level of deformation corresponding to the attainment of values of be-haviour factors equal to or higher than the design value. In contrast, displacement-based design inverts the process. Here, the primary design quantity is a targetdisplacement. If the level of damping of an equivalent linear (substitute) system isknown, corresponding to the target displacement, then the period of vibration of therequired structure may be readily available from a displacement spectrum. Armedwith the knowledge of the required period of vibration, the designer can dimensionthe structure with the stiffness, strength and ductility that ensure the realisationof the target displacement. Moreover, control of the equivalent damping, throughinelastic deformations, is availed of. This process replaces the 'elastic accelerationspectrum' and its derivatives with the 'displacement spectrum' as the centre-pieceof the design process. Since damage of structures subjected to earthquakes is cer-tainly expressed in deformations (strains at fibres, curvatures at sections, rotationsat members and drift a t storey levels), displacement-based approaches are concep-tually more appealing.

The origins of displacement-based design may be traced to work published asearly as the 1960s,where comments on the displacements of inelastic systems andtheir relationship to their elastic counterparts were made [e.g., Muto e t al., 1960,as reported by Moehle, 19921.However, it was he work of Sozen and his associatestha t developed the concept of a substitute structure [e.g., Gulkan and Sozen, 1974;Shibata and Sozen, 19761.The substitute structure is a single degree of freedomelastic system, the characteristics of which represent the inelastic system (Fig. 1).

% s , 6Fig. 1. Characteristics of substitute sructwe.


4/33

Dijplacenaent Spectm or Seismic Design 3The secant stiffness K, s that at the deformational limit s ta te (LS) under consider-ation, and may be used to evaluate an equivalent period T,.The hysteretic energyabsorption characteristics of the substitute structure may be accounted for by eval-uating the level of viscous damping that results in the same response displacementamplitude as that of the inelastic system. The concept of substitute structure there-fore enables the use of an elastic displacement spectrum in design, while availing ofthe displacement capacity of an inelastic system.

Various contributions were made towards the development of displacement-based seismic design since the early work mentioned above. However, it was inthe 1990s that formal proposals were made to implement the emerging ideas into adesign procedure, the earliest of which is that by Moehle and his co-workers [e.g., Qiand Moehle, 1991; Moehle, 19921.A complete and workable procedure for seismicdesign of structures that sets aside forces and relies entirely on displacement as theprimary design quantity is that proposed by Kowalsky et at. [I9951 or single de-gree of freedom systems (such as bridge piers). A concurrent paper on multi-degreeof freedom systems is due to Calvi and Kingsley [1995]. he steps comprising thedesign process for SDOF ystems, for simplicity, are given below:

(i) A target displacement for the structure is selected, based on the type of struc-ture and the governing limit states.

(ii) Knowing the yield and ultimate (or some other limit sta te) displacement, andthe material and structural system as well as the characteristics of site andexpected. earthquake, a value of equivalent damping is determined.

(iii) Displacement spectra representative of the seismwtectonic environment areconsulted, the input to which are the target displacement and the equivalentdamping. The output is an effective period of vibration.

(iv) The structure is dimensioned to give an effective period, taking into account re-duced stiffness consistent with th e level of deformation, equal to that obtainedfrom the displacement spectra.

(v) If the effective period is not sufficiently close to the required period, return to'step (ii) above and repeat until convergence.

It is clear from the above that whereas displacement-based design is certainly thelogical framework for seismic design, since the primary source of seismic energy dis-sipation is inelastic deformations, it imposes new requirements for verifiable design,as described below. I t is important, however, to note that the procedure outlinedabove is by no means he only framework for the application of displacement-baseddesign. Alternatives exist [e.g. Fajfar, 19981,where a proposal is made to developinelastic capacity spectra for use in displacement-based design. The capacity spec-trum approach, proposed by Reeman et 01. [1975], omprises a plot of accelera-tion spectral response versus its displacement counterpart. The load-deformationcunre of the structure under consideration, obtained from ppsh-over analysis, isthen super-posed on the combined force-versus-displacement response spectrum,


5/33

4 J. J . Bommer & A. S. Elntlshatto establish the point of supply-demand balance. This approach was extended by

. Fajfar [I9981by plotting inelastic force-versus-displacement spectra instead of theelastic approach used by F'reeman et al. [1975].1.2. Requirements for displacement-based assessment and designPrimarily, accu rate, representative and parametrically described displacement spec-t r a are essential ingredients th at are hith erto unavailable. Indeed, conversion of codeacceleration spectra to displacement spectra immediately emphasises this point,since th e ensuing spectral shape is rathe r unrealistic in mos t cases, as shown n sub-sequent sections of this work. The underlying reason is tha t accelerat ion spec tra areno t as sensitive to digitisation errors as their displacement counterparts. Followingth e derivation of a su i te of acceleration spec tra with a range of properties, withoutdue consideration for th e equally imp ortant range of properties of th e displacementrecords, smoothed acceleration spectra are derived for code application. Whereasnear-field records of small magnitude events may have high ground accelerations,rendering them eligible for inclusion in regression studies of acceleration attenua-tion, they are characteristically weak from a displacements point of view. Hence,a well-balanced catalogue for acceleration studies may be totally unbalanced fordisplacement purposes. It is therefore not surprising that idealised, perfectly valid,acceleration spectra give rise to completely unrealistic displacement spectra. Thefinal outcome is that whilst sketching an acceleration spectrum given the groundacceleration and corner periods is straightforward, there is n o analogous approachfor displacement spectra. The application of displacement-based design thereforehinges on developing attenuation relationships specifically for displacements fromdat ase ts selected for this purpose.The second essential requirement for application of displacement-based seismicdesign, within the framework outlined in detail in Sec. 1.1, is the derivation ofverifiable relationships between inelasticity and equivalent damping. This requiresinvestigating comprehensively the various characteristics of both s t ruc tura l sys-tems and input motion. For the former, hysteretic response models w i t h varioushardening-softening characteristics are required, whilst for the lat ter , ensembles ofstrong motion w ith an acceptable spread in magnitude, distan ce and si te conditionare required.1.3. Scope of workIn this study, the displacement spectra obtained horn code acceleration spectr a arebriefly examined, -with part icular a t tention to the spectra roomEC8. Following this,displacement spec tra obtained born frequency-dependent attenuation relationshipsare explored and t h e European datase t is used to investigate the effects of obta inin gspectra using pseudo-spectral conversions.

The derivation of new attenuation equations for the prediction of displace-ment spectra ordinates in Europe is approached in tw o stages. The first s t ep is


6/33

Displacement Spectna fo r Seismic Desagn 5an exploration of the period ranges within which the spectral ordinates may beconsidered reliable. In the second stage, a reduced data set of European s t rong mo-tion records, individually processed t o obt ain the m ost reliable information possible,is assembled and new regression analyses are run. The spectra obtained horn thenew attenuation equations are evaluated and conclusions are drawn regarding th ebest methods through which to ob tain displacement spe ctra for design. Finally, sim-plified sp ectral sh apes in a linearised form are derived and shown to be completelydescribed by a limited num ber of parameters. The proposed shapes and values aresuited to codified seismic design of new st ruc tur es and assessment of existing ones.

To complement the above linearised spectra, simple relationships relating in-elastic energy 'dissipation throu gh ductile response and equivalent damping, fromthe work of Borzi et 01. [I9981 are reported. These relationships have been de -rived using the same dataset alluded t o above, after applying the sam e procedurefor individual record filtering and correction. This completes the requirement ofapplication of displacement-based seismic design and assessment.

1.4. Response periods of duct i l e st ructuresIt is instructive to relate ranges of equivalent periods used to describe displacemen tspe ctra to a ctual response periods of structures. As discussed above, the pertinentperiods in a displacement-based seismic design scenario are the secant periods atthe target l imit state displacement of th e su bstitute stru cture (Fig. I), as opposedto cracked or uncracked periods referred to in force-based design.

Since measurements of the periods of vibration of RC structures a t maximumductility (close to failure) has not been undertaken, two sources of information inthis respect are utilised. Firstly, detailed analysis of multi-storey RC buildings hasbeen undertaken by Elnashai et al. [I9961 nd Mwafy [1998]. he st ruc tur al ideali-s a t ons employed in the above studie s included stress-st rain ch aracteris at on of theconcrete and steel ma terials using the most advanced models available. T h e frameswere analysed at the design, twice the design and the collapse ground accelera-tion, and a number of local and global limit states were monitored. In particular,the collapse analysis sheds light on the effective period of vibration that may beemployed in a displacement-based approach, since the response of the s t ruc turesw as fundam ental m ode-dominated. Of th e three stru ctural configurations consid-ered (regular frame, irregular fram e, core-frame), th e irregular frame was selectedfor the purposes of this paper, due to its longer response period. There is a to ta lof four stru ctur es with this configuration, designed for pairs of ductility class (DC)and ground acceleration (PGA). The DC-PGA airs considered are DCL-0.15g,DCM-O.lSg, DCM-O.3g and DCH-0.3g, where L, M and H refer to low, mediumand high respectively. The s t ruc ture is eight storeys and four bays in the groundfloor, with eight bays above, hence th e irregularity.

T h e calculated elastic fundam ental periods of the four structure s wried between0.67 a n d 0.72 seconds, whilst th e first harmonic was in the range of 0.2 seconds.


7/33

R o m push-over analysis, the stiffness of the buildings at the point of first yield (incolumns) varied between 35 and 45 kN/mm, corresponding to a displacement ofbetween 130 and 150 mm.The push-over values for the secant stihess at maxi-mum displacement (drift limit) varied between 14 and 22 kN/mm (about 40% ofthe secant stiffness at first yield). Fourier analysis of the acceleration response wasundertaken a t various levels of input. Prior to yield, the structures had dominantresponse periods of 1.1-1.2 seconds. At yield, these were 1.3-1.4 seconds, whilst atcollapse the fundamental periods were 1.5-2.0 seconds, with the shorter period ob-served for DCL-0.15g and longer value for DCH-0.3g. Considering the yield periodshorn inelastic dynamic response alongside the secant stiffness values at yield andcollapse from push-over analysis, the secant periods a t collapse (not available fromanalysis) are in the range 2.0-2.2 seconds (1 58 times yield period, as a consequenceof the secant stiffness at collapse being 40% of that a t yield). This correlates wellwith the measured periods at twice the design acceleration given above, noting tha tfor three structures the collapse acceleration was close to twice the design value.

Similar observations were made for the other two structures, with the core-frame system exhibiting lower drift at collapse (triggered by local criteria) andhence shorter periods. Therefore, a wide range of low to medium rise RC'buildingshave effective periods (at maximum ductility) below 3.0 seconds. High rise RCstructures will not necessarily have higher displacement response. This is becausethey will exhibit higher mode response, thus reducing the amplitude of maximumdisplacement. Moreover, drift limits will govern the design; thus they are likely tohave wall systems that will also delimit their displacements.

The response of structures hit by the Northridge earthquake of 17January 1995was studied by Naeim [1997]. elow are short notes on some of the characteris-tics and response of the buildings alongside analysis of their response periods, asdetermined from discrete Fourier transforms of the acceleration response:

(i) A 10-storey RC wall structure located about 20 km from the source, andfounded on alluvium, was subjected to 0.34 g ground acceleration. T h e o bserved response period was about 0.6 seconds. This is typical of stiff RC wallstructures.' (ii) A 6-storey steel moment framewith concrete caissons founded on alluvium andlocated about 20 k m from the source exhibited a dominant response periodof 1.4 seconds when subjected to a ground acceleration of 0.13 g. Had theacceleration been higher, it is likely that this period would have been above2.0 seconds.

(iii) A 20-storey RC structure (frame n one direction, walls in the orthogonaldirection) was subjected to a ground acceleration of 0.32 g,measured a t 19 kmfrom the source. T h e fundamental period was 2.5 seconds whilst the secondmode period was 0.8 seconds.

(iv) A Fstorey RC moment hame structure founded on piles in al luvium and 1ecated at 7 irm horn the source was subjected to a ground acceleration of


8/33

DispLucement Spectm fo r Seismic Design 7

about 0.49 g. The fundamental period of the structure~was .2 seconds,with ahigher amplitude at 1.4seconds.This structurewas heavily damaged with mostcolumns on the fourth floor failing in shear. The periods measured thereforerepresent highly inelastic response,probably near the deformation capacity ofthe structure.

Rorn the above brief treatment, it is reasonable to conclude that the periodrange for derivation of robust displacement spectra up to 3.0 seconds covers themajority of cases for RC and steel buildings. It would also be sufficient for a widerange of RC bridges. However, ong span bridges and bridges with isolated decksmay require spectra extending to periods longer than 3.0 seconds.2. Displacement Spectra from Seismic Design CodesThe determination of the shape and amplitude of the displacement design spectrais the objective of this paper. It is known that the spectral ordinates for all damping

0 0.5 1 1.5 2 2.5 3 3.5 4Period (sec)

0 0.5 1 1.5 2 2.5 3 3.5 4Period (sec)

Fig. 2. Acceleration (top) and displacement (bottom) spectra New Zealand Code (19921 forhighest hazard / ord inq importance.


9/33

levels increase with period from zero to some maximum value and then descend toconverge at the value of the peak ground displacement (PGD) at long periods.

The most simple and straightforward solution is to convert the accelerationspectra (SA) from seismic design codes using the pseudwpectral relationship:

2PSD = SA [$Iwhere T is the response period. The displacement spectra obtained in this way from22 seismic codes from around the world [IAEE, 1992;Paz, 19941have been examinedand in nearly all cases th e PSD ordinates increase indefinitely with period, eitherlinearly, as in the case of the codes of Japan and New Zealand (Fig. 2 ) , or even

. parabolically, as in the case of the USA code (Fig. 3). It is clear therefore thatnone of these spectra are suitable for use in displacement-based design withoutmodificatiori.

.--- Intermediate Soil

Period (sec)

Period (scc)Fig. 3. Acceleration (top) and displacement (bottom) spectra. UBC [1992] for highest hazardand ordinary importance.


10/33

Displacement Spectra f i r Seismic Design 9

Period (sec)

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5Period (sec)

Fig. 4. Acceleration (top) and displacement (bottom) spectra. French Code [1990] for highesthazard and ordinary importance.

The two exceptions to this trend of continuously increasing ordinates are th ecodes from France (Fig. 4) and Romania (Fig. 5). The PSD spectra obtained byconversion of the SA spectra in EC8 are similar in shape to those obtained fromthe French code except that for all three site classes the plateau begins at a periodof 3.0 seconds.

Another limitation of current code spectra for direct use in displacement-bseddesign is the fact that spectra are required for a wide range of damping values.Although some codes present spectra for three or four damping ratios, such as theIndian and Portuguese codes, most present only one elastic spectrum which usuallycorresponds, implicitly or explicitly, to a damping ratio of 5,% of critical. Manycodes incorporate other damping values implicitly into the behaviour factors, thus


11/33

Period (sec)

0 0.5 1.5 2 2.5 3Period (sec)

Fig. 5. Acceleration (top)and displacement (bottom)spectra. Romanian Code [1991]or highesthazard and ordinary importance.

making it impossible to obtain elastic spectra for damping values other than 5%.The French and Spanish codes both include the following equation to obtain acorrection factor for different damping ratios c:

In the French code the maximum value of the damping ratio is limited to 30%. InEC8 the correction factor is defined by the equation:

q =,/I2 + t (2.3)

Ln EC8 the minimum permissible value of r ) is 0.7, which means that the largestdamping ratio that can be accommodated is 12.3%.


12/33

Displacement Spectra for Seismic Design 11A final point worthy of mention on the EC8 spectra is that the code. provides a

formula for the prediction of the PGD s a function of the effective peak accelerationa,. This implies that for any damping ratio higher than 9%, -the displacementspectra actually has o rise from the long-period plateau to converge with the PGD,which would not be expected.

It is clear from the foregoing that none of th e current code spectra are suitablefor use in displacement-based seismic design. The PSD from the Romanian code,which corresponds to the particular and special tectonics of that country, is onlydefined for a damping ratio of 5%. The EC8 spectra are currently limited to toonarrow a range of damping ratios and do not converge at longer periods. The PSDfrom the French code for different damping levels also remain parallel at longerperiods and do not converge to PGD, although these seem to be the most suitableof the existing spectra. Therefore, there is clearly scope to explore more suitablecriteria to define the shape and amplitude of displacement response spectra foranalysis, design and assessment.

3. Displacement Spectra from Attenuation RelationshipsThe first frequency-dependent attenuation relationships for response spectral ordi-nates were published by Johnson [I9731 nd a large number of equations have sinceappeared in the technical literature. The majority of the available equations em-ploy the pseudo-velocity response (PSV) s the predicted variable although thereare also a number of attenuation relationships for acceleration response (SA) ordi-nates. To date there have been no equations published in the technical literaturefor the estimation of relative displacement (SD) response spectral ordinates, butsince PSV s actually determined directly from SD, relationships for the predictionof PSV could be considered suitable for the prediction of SD ordinates.

Displacement response spectra can be determined from predicted values of SAthrough Eq. ( 2 4 , although this is an approximation. In order to explore the relia-bility of PSD rdinates obtained in this way, n experiment was performed to obtainpredictions of SD directly and from conversion of SA ordinates. The attenuation re-lationships derived for the prediction of SA ordinates in Europe and adjacent areasby Arnbraseys e t al. (19961were used to construct PSD spectra for different corn-binations of magnitude, source-to-site distance and site conditions. The dataset ofaccelerograrns used to derive these relationships were then employed, exactly as pro-cessed for the SA regressions, to generate 5% damped SD spectral ordinates. Then,using the same attenuation model as for SA, regressions were performed directlyon SD and the new equations used to construct displacement response spectra forthe same-combinationsof magnitude, distance and site classification [Chlimintzas,19971. The comparisons (Fig. ) show that the displacement spectra obtained inboth ways are very similar, only deviating at periods greater than 1.3 seconds andat very short source-tesite distances; in these cases, the PSD ordinates calculatedby conversion of SA ordinates slightly overestimate the SD values.


13/33

12 J . J . Bommer & A. S.Elnashai

In view of this observation, it could be argued that existing attenuation relation-ships for response spectral ordinates, whether PSV or SA, could be employed to pre-dict displacement spectra to be used in design. The displacement sp ect ra predicted-in this way by a wide range of attenuation relationships have been explored an d

0 0 -5 1 1.5 2Period (sec)

0 0.5 f 1.5 2Period (sec)

0 0.5 1 1.5 2. Period (sec)

Soil Site

Period (sec)

Period (sec)

0 0.5 1 1.5 2Period (sec)

Fig. 6(a) Displacement spectra for MS= 6 from acceleration spectra (solid) and direct displace-ments (dashed).


14/33

Displacement Spectnt for Seismic Design 13

0.5 1 1.5Period (sec)

0 0.5 1 1.5 2Period (sec)

0 0.5 1 1.5 2Period (sec)

0 0.5 1 1.5 2Period (sec)

0 0.5 I 1.5 2Period (sec)

0 0.5 1 1.5 2Period (sec)

Fig. 6(b) Displacement spectra for 1\3,= 7 from acceleration spectra (solid) and direct displacements (dashed).

compared [Bommer et d.,9981.Direct comparison amongst attenuationequationsis always difficult because of different definitions of the independentvariables (mag-nitude, distance and site classification)and different treatment of the two horizontalcomponents of each accelerogram [Ambraseys and Bornmer, 19951.Nonetheless, itcan be observed that the predicted spectral shapes are generally much more realistic


15/33

than those obtained from the code spectra. However, the various equations exhibitvery different levels of influence of magnitude, distance and soil classification.

A Limitation on the use of current attenuation relationships forspectral ordinatesto provide the input for displacement-based design is the fact that the majority ofthe available equations only provide spectral ordinates for 5% damping. A notableexception to this are the equations presented by Boore et al . 11993, 19941 whichpredict spectral ordinates for damping ratios of2, 5, 10 and 20%. However, theseequations only predict spectral ordinates at response periods up to 2.0 seconds.Mohammadioun [I9943 also reports regressions on ordinates of PSV for dampinglevels of 0, 2, 5, 10 and 20% up to periods of 5.0 seconds, ut the coefficients for theequations, which are a function of magnitude and distance only, are not presented.Hence, here is a need to explore the development of attenuation relations for SDordinates for a range of damping levels and also for a s wide a period range aspossible.

4. Displacement Spectra of European 'strong Motion RecordsIn order to derive attenuation relationships for the prediction of response spectrafor use in displacement-based design, it. is necessary to compile a dataset of high-quality accelerograms for which the associated source, path and site parametersare uniformly and accurately determined. High quality accelerograms, in this con-text, are those with a high signal-to-noise ratio, particularly at long periods, whichmeans that it would be preferable to employ recordings from digital accelerographs[Tolis and Faccioli, 19991.However, the number of available digital accelerograms isrelatively low and hence even though these data may provide more accurate valuesfor the spectral ordinates, it would be difficult to find correlations between theseordinates and the parameters characterising the earthquake source, the travel pathand the recording site. The lack of digital accelerograrns is particularly apparentfor Europe and adjacent regions, where the majority of available accelerograms arefrom SMA-1 and other analogue instruments. However, source, path and site pa-rameters have been uniformly determined for the European strongmotion databaseand presented by Ambraseys et al. [1996]. or this study, it was decided t o makeuse of this dataset, taking the independent parameters directly from the publishedpaper bu t re-examining the strong motion accelerogams in order to obtain th emost suitable processing.The dataset presented by Ambraseys e t d. [1996]consists of 422 triaxialaccelerograrns generated by 157shallow earthquakes with sufface wave magnitudeMs etween 4.0 and 7.9. The source-to-distance used in that study is the short-est horizontal distance to the surface projection of the fault rupture, althoughwhenever this value cannot be determined, mainly for smaller earthquakes, theepicentral distance is used. The recording site geology is classified according theaverage shear wave veiocity over the upper 30 rn [Boore et d , 19933.Sites forwhich V' is greater than 750 m/s are classified as rock (R) and sites for which V, is


16/33

Dtsplacement Spectra for Seismic Design 15less than 360 m/s are classified as soft (S); intermediate sites are classified as stiffsoil (A).

Two additional accelerograms were incorporated into the dataset, the first ofwhich was the record from the temporary Gemona station of the Ms .1 Riuli(Italy) earthquake of 15 September 1976. According to RoveUi et ol. (19911 thestationwas ocated on massive Mesozoic limestones, suggesting that the appropriateclassification would be rock (R). However, information from a borehole 100 m fromthe recording site confirms that the correct classification would be stiff soil (A)[S. Tolis, personal communication, 19973. The source distance for this record has

5 5.5 6 6.5 7 7.5 8Magnitude(Ms)

5 5 .5 6 6.5 7 7.5 8Magnitude (Ms)

5 5 .5 6 6.5 7 7.5 8Magnitude (Ms)Fig. 7. Magnitudedistance distribution of dataset w.r.t. to site classes R (top), A (middle) andS (bottom),


17/33

16 J . J . Bommer 0 A . S. Elnashai

been estimated as 6 km.The second new accelerogram to be incorporated into thedataset was the recording of the Ms .1 Aegion (Greece) earthquake of 15 June1995 obtained a t the Telecornmunicat ions Building in ~ e ~ i o n .his recording site,at a distance of 10km from the source, has been classified as soft soil (S) according .to Ambraseys et al. [1996].

In view of the fact t h a t this study is particularly focused on the long-periodresponse spectrum and t h a t small magnitude earthquakes do not produce signif-icant long-period radiation, it was decided to impose a lower magnitude limit tothe dataset . T he removal of weak (low amplitude) records from the dataset, in or-der to obtain better signal-to-noise ratios, would not be acceptable since it wouldintroduce a bias into the data, but the removal of all the earthquakes with magni-tude below the chosen lower limit of Ms .5 does partially achieve this objective.The reduced dataset consisted of 189 accelerogams, but a further six accelero-grams were eliminated since they were only available a s filtered by other agencies,and hence could not be included in the uniform processing of the records. The fi-nal dataset thus consisted of 183 accelerograms from 43 shallow earthquakes. Forthree of the recording stations, each of which contributed only one record, thesite classification is unknown. For the remaining 180 accelerograms t h e distribu-t ion amongst the three site classifications R:A:S as percentages is 25:s :%, whichcompares favourably to the distribution of the original dataset of Ambraseys eta[. 119961 which is 26:54:20. The distribution of the dataset in magnitude-distancespace is shown in Fig.7.In the study by Ambraseys et al. [I9961 ll of the accelerograrns were processedusing an elliptical filter with a lower cut-off frequency of 0.20 Hz. A number of thestronger accelerograms from the reduced dataset were processed with a straightbaseline and also filtered with cut-of i at periods of 15, 10,7 and 5 seconds (frequen-cies of 0.067, 0.10, 0.143 and 0.20 Hz) and both the acceleration and displacementspectra generated. As can be seen from Fig. 8, the processing usually has very littleeffect on the acceleration spectra and then only at periods of about 4.0 seconds andgreater. Indeed, for SA ordinates up to 2.0 seconds, it would seem that filtering isnot actually necessary. However, the SD ordinates show a very high sensitivity tothe applied filter at long periods. In general, the SD spectra are almost identicalfor periods up to 2 seconds, regardless of the processing, but beyond 3 seconds thedivergence can be very considerable. Since the long-period response ordinates a re ofparticular interest, it is clear tha t special attention must be given to the processingof each record.

It is difficult to establish a single optimum filter for the digitised accelerogramsbecause the variation of signal- o- noise ratios is very large. An interesting exampleare the recordings from Procisa Nuova of an aftershock of the Irpinia (southernItaly) earthquakeof November 1980: the ground shaking at the site was recordedsimultaneously on an analogue SMA-1 accelerograph and a digital DSA-1 accelero-graph. T h e SMA - 1 record was digitised both automatically +nd manually. TheDSA-1 recording was filtered with a cut-off a t 5 seconds (up to 3 seconds he SD


18/33

Displacement Spectm far Seismic Dtsign 17ordinates are almost unchanged by the filter limits) and th e corresponding spectrumwas assumed to be free of noise. It was found that an almost identical displacementspectrum could be obtained horn the automatically digitised SMA-1 ecord if itwas filtered with a cut-off at 2.4 seconds. For the manually digitised record it wasnot possible to obtain a displacement spectrum that matched that of the DSA-1record beyond a period of about 0.6 seconds. However, these recordings were gen-erated by a very small earthquake with very weak long-period radiation: for thestronger records in the dataset, digitised in a similar fashion, the absolute noiselevel is probably similar bu t the signal-to-noise ratio would be considerably better.

-..-.. 5 sec cutoff-.-.- 7 sec cutoff*.....*.... I0 sec cutoff- - - -

15 sec cutoff- aseline only1 10

Period (sec)

0 3 6 9 12 15Period (sec)

Fig. 8(a) Acceleration and displacement spectra for th e Tabas [I9781 earthquake (5% damping)with different filtering and correction.


19/33

18 J . J . Bommer & A . S. Elnashai

1Period (sec)

-..-.. 5 scc cutoff7 scc cutoff

......*.... 10 sec cutoff---- 15 sec cutoff- aseline only

Period (sec)Fig. 8(b) Acceleration and displacement spectra for th e Corinth [I9811earthquake (5% damping)with different filtering and correction.

One possibility for identifying the optimum filter cutsff for an accelerogam isfrom the Fourier spectra of the record and the fixed trace, but the latter is notavailable for the majority of the records. The procedure adopted for this dtudy wassimply to ater each record starting with a cut-offat 10 seconds and then inspectthe velocity and displacement timehistories found by double integration.The ong-period cut-off was then successively decreased until the velocity and displacementtime-histories appeared to be physically reasonable and further decreases in thefdter cut-off did not significantly enhance them. Some exampleof the filtered time-histories and their associated displacement response spectra are shown n Fig. 9.


20/33

Displacement Spectm. far Seismic 'Design 19

0 ' 5 10 15 20Time (sec)

0 3 6 9 12 15Period (sec)Fig. 9(a) Filtered t me-histor ies and displacement spectrum for record ITSOL (dotted line showsfilter cutoff).


21/33

20 J . J . Bommer 0 A . S. Elnashai

0.30.20.10-0.1-0.2-0.3

0 10 15 20 25 30Time (sec)

3020100

-10-20-30

0 5 10 15 20 25 30Time (sec)

ISTime (sec)

6 9Period (sec)

Fig. 9(b) Filtered timehistories and displacement spectrum for recordKALlT (dotted line showsfilter cutoff).


22/33

Dtsplacement Spectrn for Seismic Design 21

0 5 10 15 20 25 30 35 40Time (sec)80400

-40-80

0 5 10 I 5 20 25 30 35 40Time (sec)

10 IS 20 25 30 35 40Time (sec)

3 6 9 12Period (sec)Fig. 9(c) Filtered time-histories and displacement spectrum for record TABAL (dotted line showsfilter cutoff).


23/33

5. European Attenuation Relationships for DisplacementResponse Spectra

Regression analyses were performed on the horizontal displacement spectral ordi-nates for damping ratios of 5, 10, 15,20 , 25 and 30% of critical. The regressionmodel used for SD ordinates (cm) was the same as that employed by Ambraseyset ol. I19961 for acceleration spectral ordinates:

where

d is the source-to-site distance in km, cr is the standard deviation, and P is a variablethat takes a value of 0 for mean values of SD and 1 for 84-percentile values. Sa is adummy variable that takes a value of 1 for stiffsoil (A) ites and 0 or rock (R) andsoft soil (S) sites; Ss is defined in the same way for soft soil sites. The coefficientsCl, 2, 4,Ca, s and ho are determined by regression analysis, performed inthree stages [Ambraseys et al., 19961.The term in C3 orresponding to inelasticattenuation was constrained to zero in all cases, since, as in t h e case of accelerationresponse spectra, it was found tha t the distribution of the dataset did not permit thesimultaneous determination of inelastic and geometric attenuation. In some casesthe value of C4 was slightly less than -1.0 which sensu strictu is not physicallyadmissible but is acceptable since this term is accounting for both mechanisms ofenergy dissipation.

At each period the larger spectra1 ordinate from the two horizontal componentsof each accelerogram was used as the dependent variable. Each component recordwas only used for regressions up to a period equal to 0.1 second less than thelong-period cut-off employed for that record. As a result, for periods greater than1.8 seconds there was a reduction in the number of data points available for eachregression, as illustrated in Fig. 10. At a response period of 3.0 seconds, the datasetwas reduced from 183 accelerograms t o 121. It was decided not to perform theregressions for periods longer than 3.0 seconds since the number of usable spectralordinates becomes in sf ic ient .

The regression coefficients for six damping levels and for periods between 0.05and 3.0 seconds are presented by Bommer et d.[1998]. he standard deviationsof the regressions are consistently lower than those found for SA ordinates by Am-braseys e t al. [l996], early always being less than 0.3 for log(SD). However, as aresult of the relatively small number of da ta points used to perform the regressions,there are fluctuations in the predicted spectra Smoother spectral shapes could beobtained by smoothing the values of each regression coefficient with respect to pe-riod using an appropriate technique. However, tw o important observationsare maderegarding the predicted displacement response spectra,which enable a more elegantpresentation: the first observation is that the fluctuations in the 30% damped re-sponse spectra are comiderably lower and hence these can be used to define the


24/33

Dicphcrmmt Spectm fo r ~ & i c Dwign 23

0 0.5 t 1.5 2 2.5 3 3.5 4Period (sec)

Number of records available fo r regression for each soil type at different periods.

average shape of the spectra; secondly, the apparent amplification of the averageresponse spectra for lower damping levels, with respect to the 30% damped spectra,appear to be approximately constant regardless of the magnitude, distance and siteclassification. These observations have been used to derive a simplified approachto constructing displacement response spectra for design, presented in the nextsection.Regression analysis was also performed on th e larger values of peak grounddisplacement (in cm) rom each record, using the same attenuation model as inEq. (5.I ) , resulting in the following equation:

where r is defined as in Eq. 5.2)' with a value of ho of 3.5. Although it is notpossible to make direct comparisons because of the use of different definitions fo rthe parameters, Eq. (5.3) predicts values of PGD very similar to those presentedby Bolt [I9961 or the near field, but attenuating more rapidly with distance.

. 6. Recommended Displacement Spectra for DesignFrom inspection of a large number of displacement response spectra for the sixspecified damping levels, particularly those for which the applied filter cut-off wasgreater than 5.0 seconds, it was concluded that a general, idealised format would beas shown in Fig. 11.The spectrum for each damping level is composed of six straightline segments defined by four control periods and their corresponding amplitude..


25/33

24 J . J . Bummer 0 A . S. Elnashai

Fig. 11. Lineariseddisplacement spectra for design.The amplitude corresponding to TE s the peak ground displacement. For thisstudy, only that part of the spectrum up to periods of 3.0 seconds is considered forreasons explained previously. The approach foliowed was first to obtain the controlc-ordinates for 30% damped spectra for a representative range of magnitude anddistance. These results are presented in Tables 1 and 2.

Table 1. Control periods for design spectraas func-tion of magnitude and sail type.

TA TBM, Rock Stiff Soft Rock Stiff Soft

'Actual control period probably slightly greaterthan 3.0 seconds.

Table 2. Control ordinates for design spectra asfunction of magnitude and soil type.


26/33

Displacement Spectm for Seismic Design 25Table 3. Distance factors Fd for spectral ordinates.

Table 4. Damping ratio factors F( for spectralordinates.

Inspection of the predicted spectral ordinates shows hat t h e shape of the spec-tra is strongly influenced by magnitude and site classification, bu t far less so bydistance. It was found that the decrease of the spectral ordinates with distance isreasonably constant across the period range and similar for all three site categories,hence simple reduction factors could de found. The 30% damped spectra for dis-tances up to 50 km from th e source can be obtained by simply multiplying theordinates by the appropriate factor Fd taken from Table 3.

The next stage was to establish the amplification factors to be applied to thecontrol ordinates in order to obtain the displacement spectra for damping levelsfrom 5 to 25 % of critical. These factors FE are presented in Table 4. Therefore,using the values presented in Tables 1-4, and interpolating where necessary, it is a

0 0.5 1 1.5 2 2.5 3Period (sec)

Fig. 12. Derived vs. h e a r d displacement spectra (rock, Ms 6, d = 15 km).


27/33

26 J . J . Bommer & A. S . Elnashoi

W I " I " ' I " ' I " " I " " I " I, O 0.5 1 1S 2 2.5 3Period (sec)

Fig. 13. Derived vs. Iinearised displacement spectra (stiff soil M, = 6 , d = 15 km).

1.5 2Period (sec)

Fig. 14 . Derived vs. liaearised displacement spectra (soft soil Ms= 6, d = 15 km).


28/33

Lhplacemmt Spectm for Seismic Design 27

Period (sec)Fig. 15. Derived vs. linearised displacement spectra (rock M, = 7, d = 15 km).

0.5 1 1.5 2 2.5 3Period (sec)

Fig. 16. Derived vs. linearised dispIacement spectra (stiff sail , M,= 7 , d = 15 km).


29/33

28 J . J . Bommer & A . S. Elncrshai

Period (sec)Fig. 17 . Derived vs. linearised displacement spectra (soft soil, 1LI, = 7, d = 15 km).

simple matter to construct design displacement spectra for rock, stiff soil and softsoil sites for magnitudes between 5.5 and 7.5 and distances up to 50 km.

Figures 12-17 compare the spectra obtained from the attenuation relationships,smoothed by successive passes of a a-9-a ' unning average, with the design spectrafor the corresponding situations. In some cases, particularly at short distances, thedesign spectra are conservative at long periods for the lower damping ratios, butthe approximation is generally very good.

One limitation of these design spectra is that they are defined only up to pe-riods of 3.0 seconds, although as it has been shown this covers the majority ofapplications. Certain assumptions can be made in order to extrapolate the spectrato longer periods knowing that the ordinates for all six damping levels will con-verge to the value of PGD predicted by Eq. (5.3) at long periods. Inspection of th espectra born the records filtered at longer cut-ofs suggests that the spectra willgenerally converge, even for large magnitudes and soft soil, at periods no greaterthan 8-9 seconds. For smaller magnitudes and stiffersites it is reasonable to assumeconvergence between 5 and 6 seconds.

7. * ~ u c t i l i t ~ - ~ a m ~ i n ~elationships and Residual InelasticDisplacements

The dataset used above was employed in a study by Boni et al. [1998], longsidethe same attenuation model described above. Two tructural response models were


30/33

Displacement Spectm for Seismic Design 29employed in e ~ l u a t i n g onstant ductility spectra for all records. These were anelastic perfectly plastic (EPP) nd a hysteretic model (HHS). The latter is basedon the model implemented by Lee [I9981 or representation of shear behaviour ofRC bridge. piers. Whereas convergence to a target ductility was always achievedfor the EPP model, this was not the case for the HHS representation. However,the maximum percentage of divergent solutions was 3% for elastic perfectly plasticbehaviour, and dropped to 0.8% for hardening response (post-peak load stiffness of10% of the yield stiffness). For softening response, lack of convergencewas observedin 5%-8% of cases for p = 3, increasing to 12%-30% for p = 4. All non-convergingpoints were eliminated from the regression analysis. Table 5 summarises the medianvalues of equivalent damping for various ductility levels for both models employed.

The equivalent damping values given in Table 5 are recommended for use withthe elastic response spectra of Sec. 5 of this paper, for periods of up to 3.0 seconds.Borzi e t al. (19981utilised a procedure based on spectral intensities to evaluatemedian damping ratios for longer period structures. The resulting values are onthe whole lower than those given above. If a more accurate period-dependent valueof equivalent damping is sought, the complete set of attenuation relationships aregiven in Borzi et al. [1998].Nil entries in Table 5 indicate that structures withhighly degrading response ( K 3 = -20% and -30%K,) would not have ductilitycapacity of four or more.

The design procedure based on displacement results in a structure with stiffness,strength and ductility characteristics that satisfy the requirements of the displace-ment spectrum used. It is important to note that th e solution is not unique, andother structural systems with different response characteristics may also satisfy thedesign premise. Due to the asymmetric nature of natural earthquake records, thereis a possibility that the structure will have a residual irrecoverable inelastic dis-placement. This issue was studied by Boni et al. [I9981 or subsets of the strongmotion records mentioned above. It was observed that for magnitude six at a dis-tance of 10 km on soft ground, the residual displacement of a degrading system(K3 -20%Ky) is 18%, 32%.and 43%of the maximum displacement for ductilityfactors 2, 3 and 4, respectively. This observation may lead to the requirement toincrease the strength of the structure, to reduce the ductility demand hence theresidual displacement. For non-degrading systems, his issue is of significantly less

Table 5. Equivalent damping ratios for substitute struc-ture [Borzi et d ,19981.

p = 2 p = 3 p = 4 p = 6


31/33

importance for the earthquake magnitude studied. Further comprehensive work isneeded using degrading systems before a final proposal is made.

8. Discussion and ConclusionsIn this study, attenuation equations for displacement response spectra ordinatesin Europe have been derived. Although the attenuation relationships can be useddirectly to construct displacement spectra for design, a simple parametric presen-tation has been formulated. Taking ust six d u e s from Tables 1-4, displacementdesign spectra can be constructed for all sites (except exceptionally soft soils) forth e range of magnitudes and distances of greatest engineering interest. These spec-tra cover response periods up to 3 seconds and damping ratios between 5%and 30%of critical, which covers the majority of engineering applications of displacement-based seismic design and assessment. To complete the requirements of the designprocedure, recent work on deriving attenuation relationships for inelastic displace-ment response and its relationship with the damped elastic response of substitutestructures is briefly reported. Finally, the issue of irrecoverable displacements ofductile structures is mentioned, and approximate limits are given for the medianvalue of residual displacement as a percentage of maximum response displacement.

The simplified design spectra and ductility-damping relationships are recom-mended for use in displacement-based design. The spectra can be extrapolated 'beyond 3 seconds, using the attenuation relationship for PGD, with caution. Asmore digital accelerograms in Europe become available, such as those from the1997 Umbria-Marche earthquakes in Italy, it will be possible to extend th e atten-uation relationships, and hence the design spectra, to longer periods, applicablemainly to special structures.

AcknowledgementsThe authors are indebted to a number of people who have assisted with differentaspects of the development of this work. Thanks are due to Professor D. apasta-matiou of the National Technical University of Athens, for supplying the accelero-gram from Aegion, and Professor E. Faccioli and Dr. S. Tolis of the Politecnico diMilano, for supplying the Gemona accelerogram. Dr. Tolis also went to consider-able length to determine the site characteristics for the Gemona record. The workon residual displacements was motivated by earlier work carried out by ProfessorK. Kawashima of Tokyo Institute of Technology and discussed with one of the au-thors in April 1998.

A t Impenal College, George Chlimintias undertook the painstaking task ofprocessing the strong motion accelerograms and also in performing the regressions together with Dohyung Lee.Dr. K. Simpson provided very considerable as-sistance with accessing the data and performing the regression analyses. PetrosKonstantakos, Stephen Scott, Alejandro Mar tha and Barbara Boni assisted with


32/33

Dasplacement Spectra for Seismic Design 31parts of the analysis and th e preparation of a number of illustrations and spectralplots. The auth ors would also like to acknowledge he important contributionmadeby Professor N. N. Ambraseys in the form of re-evaluated source,path and siteparameters for the European strong motion dataset, and Dr. S.K. Sarma for use ofhis regressionprogram.

This work is supported financially by the European Union project InnovativeConcepts for the Seismic Design of New and Existing Structures (ICONS).

ReferencesAmbraseys, N. N., Simpson, K. A. and Bommer, J. J. (19961 "Prediction of horizontal

response spectra in Europe," Earthq. Engrg. Stnrct. Dyns. 25, 371-400.Ambraseys, N. N. and Bommer, J. J. [1995] 'Attenuation relations for use in Europe:

A n overview," in Eumpean Seismic Design Pmctice: Reseatch and Applications, ed.A. S. Elnashai (Bakema, Rotterdam), pp. 67-74.Bolt, B. A. [I9961 "From earthquake acceleration to seismic displacement," The Fzfth

Mallet-Milne Lectun (Wiley).Bommer, J. J., Elnashai,A. S.,Chlimintzas, G.0. nd Lee,D. (19981 Review and devel-

opment of response spectra for displacement-based design " ESEE Research ReportNo. 98-3, Imperial College, London.

Boore, D. M., Joyner,W. B.and Fumal, T. E. (19931 "Estimation of response spectra and, peak accelerations from western North American earthquakes: A n interim report ,"US Geological Survey Upen-File Report 93-509.

Boore, D. M., Joyner, W. B. and FurnaI, T. E. [I9943 "Estimation of response spectra andpeak accelerations from western North American earthquakes: A n interim report,"US Geologicd Survey Open-File Report 94- 27.

Boni, B., lnashai, A. S., Faccioli, E.,Calvi, G.M. and Bommer, J. J. (19981 "lnelasticspectra and ductility-damping relationships for displacement-based seismic design"ESEE Research Report No. 98-4, Joint Imperial College-Politecnico di Milano, Impe-rial College, London.Calvi, G . M. and Kingsley, G. R. [I9951 "Displacement-based seismic design of multi-

degree-of-freedom bridge structures," Earthq. Engrg. U Struct. Dyns. 24, 1247-1266.Chlimintzas, G.0. I9971 "Selection of response spectra for displacement- based seismic

design," M.Sc. Dissertation, Imperial College, London.Elnashai,A. S., Sdvitti, L. M. and Broderick, B. M. [I9961UAssessmentof EC8 behaviour

factors for RC, teel and composite frames," Eleventh World Conference on Earth-quake Engineering, June 23-27, Acapulco, Paper No. 2050.Fajfar, P. 19981 uCapacity spectrum method based on inelastic demand spectra," IKPIRReport EE3/98, 1nst tute of Structurd Engineering,University of Ljubljana.Freeman,S. A., Nicoletti, J.P. andwell,J. V. 119751 ttEvaluationof existing buildings or

seismic risk- case study of Puget Sound NavalShipyard,Bremerton,Washington,"First U. . Confeence on Earthquake Engmeering.Gulkan, P. and Sozen, M. 19741 "Inelastic response of reinforced concrete structures toearthquake rnotion~,'~CI Journal 71,604-6 0.IAEE [I9921 nternational Association for Earthquake Engineering,Earthquake Ruis tantRegulations: A World List - 992,Tokyo, Japan.

Johnson, R. A. (19733 "A n earthquake-spectrum prediction technique," Bull. Seis. Soc.Am. 63, 2551274.


33/33

Kowalski, M. J., Priestley, M. J. N. and MacRae, G.A. [I9951 L'Displacement-basedde-sign of RC bridge columns in seismic regions," Earthq. Engq. & struct. Dyns. 24,1623-1643.

Lee,D. I9981 "Seismic analysis of RC bridge piers using an axial load-sensitive hystereticmodel," Ph.D. transfer report, Imperial College, London, UK.

Moehle, J. P. [I9921 "Displacement-based design of RC structures subjected to earth-quakes," Earthq. Spectm 8(3 ) , 403-428.Mohammadioun, G. [I9941 "Calculation of site-adapted reference spectra from the statis-tical analysis of an extensive strong motion databank," Tenth European Conferenceo n Earthquake Engineering, Vienna, 1,pp. 177-181.Mwafy, A.M. I9981 "Seismic performance of RC buildings under multi-axial earthquakeloading," Ph.D. transfer report, Imperial College, London, UK.

Naeim, F., [I9971 %stnuaented buildings information system; January 17, 1994Northridge, California, earthquake," CD-ROM, ohn' A. Martin and Associates, LosAngeles (for CDMG-SMIP),USA.

Paz, M. ed.) I9941 International Handbook of Ear thpoke Engineering (Chapman&Hall).Qi, X. and Moehle, J. P. (19911 "Displacement design approach for reinforced concrete

structures subjected to earthquakes," Report No. UCB/ERC-91/02, niversity ofCalifornia at Berkeley, January, 186 pp.Rovelli,A., Cocco, M., Console, R.,Alessandrini, B. and Mazza, S. 1991j "Ground motion

waveforms and source spectral scaling from close-distanceaccelerograms in a compres-sional regime area (Friuli, Northeastern Italy)," Bull. Seis. Soc. Am. 81, 7-80.

Shibata, A. and Sozen, M. 119761 "Substitutestructure method for seismic design in RC,"J . Stnrct. Div. ASCE 102, -18.

Tolis, S. and Faccioli, E. (19991 "Displacement design spectra," J . Earthq. Engrg. 3(1),107-125.

Displacement Spectra

Documents

Transcript of Displacement Spectra