98269174 calibration of force reduction

8/22/2019 98269174 Calibration of Force Reduction

1/36

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

CALIBRATION OF FORCE REDUCTION FACTORS OF RC BUILDINGSA. M. Mwafya; A. S. Elnashaiba Department of Civil and Environmental Engineering, Imperial College, London SW7 2BU, UK b Civil

and Environmental Engineering Department, University of Illinois at Urbana-Champaign, Urbana, IL61801-2397, USA [email protected]

To cite this Article Mwafy, A. M. and Elnashai, A. S.(2002) 'CALIBRATION OF FORCE REDUCTION FACTORS OF RCBUILDINGS', Journal of Earthquake Engineering, 6: 2, 239 273

To link to this Article: DOI: 10.1080/13632460209350416URL: http://dx.doi.org/10.1080/13632460209350416

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/10.1080/13632460209350416http://www.informaworld.com/terms-and-conditions-of-access.pdfhttp://www.informaworld.com/terms-and-conditions-of-access.pdfhttp://dx.doi.org/10.1080/13632460209350416http://www.informaworld.com/smpp/title~content=t741771161


2/36

Journal of Ear thquake Engineering, Vol. 6, No. 2 (2002) 234-273@ Imperial College Press

CALIBRATION OF FORCE REDUCTION FACTORS OFRC BUILDINGS

A. M. MWAFYDeparhent of Civil and Environmental Enginewing,

Imperial College, Imperial College Road, London SW 7 ZBU, UKA. S . ELNASHAI'

Civil and Environmental Engineering Department,University of Illinois a t Urbana-Champaign, Urbana, IL 61801-2397,USA

aeInashOuic.eduReceived 10 May 2001Revised 20 June 2001Accepted 17 July 2001

A comprehensive study is undertaken to assess and calibrate t he force reduction factors(R) adopted in modern seismic codes. Refinedexpressions are employed t o calculate theR factors "supply" for 12 buildings of various character istics represent a wide range ofmedium-rise RC buildings. The "supply" values are then compared with the "designnand "demand" recommended in t h e literature. A comprehensive range of response cri-teria at the member and storey levels, including shear as a failure criterion, alongsidea detailed modelling approach and an extensively verified analytical tool are utilised. Arigorous technique is employed to evaluate R factors, including inelastic pushover andincremental dynamic collapse analyses employing eight natural and artificial records.In the light of the information obtained from more than 1500 inelastic analyses, it isconcluded that including shear and vertical motion in assessment and calculations of Rfactors is necessary. Force reduction factors adopted by the design code (Eurocode 8) areover-conservative and can be safely increased, particularly for regular frame structuresdesigned to lower PGA and higher ductility levels.Keywords: Force reduction factor; ductility; overstrength; shear assessment; verticalmotion; RC buildings.

1. IntroductionThe conventional approach of reducing the seismic forces using a single reductionfactor to arrive at the design force level is widely utilised in seismic codes. Force-based design procedures, which include a hal check on deformations, are likelyto remain as the primary seismic design method for some time since other designalternatives are still in the development phase. Hence, the need for reliable cali-bration of force reduction factors, which have a central role in conventional designmethods, is a pressing objective.'Corresponding author.


3/36

240 A. M. Mwafy 13A . S.EInashaiDespite the fact that the force reduction factor serves the same function in

all seismic codes, it is denoted different terms and assigned different numericalvalues. The force reduction factor is expressed in the form of the behaviour factor(q) in Eurocode 8 [EC8, 19941, the response modification factor (R)n the UScodes and guidelines [Uniform Building Code "UBCn, 1997; NEHRP Provisions"FEMA 273", 19971, the force modification factor (R ) in the National BuildingCode of Canada [NBCC, 19951, the structure displacement ductility factor ( p ) andstructural performance factor (S,) in the New Zealand Loading Standard [NZS,19921 and the ductility factor (l/D,) in the Japanese Building Standard Law W E ,19921. In the present study, the term "force reduction factor (R)" is adopted sinceit precisely describes the main function of this parameter in reducing elastic seismicforces to the force level used in design.

As mentioned above, the numerical values of the force reduction factor arenotably varied between seismic codes. For instance, the EC8 behaviour factor rangesbetween 1.5 and 5.0 for RC hame structures, whilst for the same systems theresponse modification factor of the US codes may be as high as 8.0. ECSdesignedbuildings are therefore assigned higher force levels than those imposed by US codes.This implies that buildings designed for the requirements of the US codes will bemore economical or more vulnerable than similar buildings designed according toEC8 [ATG lS, 19951. However, the difference between the reliability of buildingsdesigned to different seismic codes cannot be assessed based on the force levelsused in the design only. Taking into consideration different partial safety factorsmay reduce the difference between the quantities and the parameters adopted inseismic codes and account should be taken of LLcapacityn,ot just udemand".

The commentary of th e NEHRP provisions FEM A 274,19971 confirms that thevalues of force reduction factor are empirical. Since no supporting investigations arereported in modem seismic codes, it is likely that its values are based on judgment,experience and observed performance of buildings during past earthquakes. Seismiccodes rely on ductile response and unquantilied levels of overstrength of structuresto justify the reduction in seismic forces via the R factor. Hence, The accurate eval-uation of force reduction factors and investigation of the interrelationships betweenthe parameters influencing it are essential elements of seismic design according tocodes.

Previous studies [Miranda and Bertero, 1994; Vidic et d., 994; Borzi andElnashai, 2000] have mainly focused on evaluation of the force reduction factor"demand", particularly the ductility-dependent component of the force reductionfactor. A review of the studies carried out prior to 1994 can be found in Mirandaand Bertero [1994].Few studies [e.g. Elnashai and Broderick, 1996 for compositeand steel frames] were carried out to estimate the force reduction factor "supply"of buildings. However, these studies were either performed on a limited number ofbuildings designed to old versions of seismic codes using a simplified modelling andprocedure, or concerned structures other than RC buildings.


4/36

Cdabration of Force Reduction Factors of RC Buildings 241In the present study, refined definitions are employed to evaluate the R factors

"supply" of medium-rise RC buildings, aiming to assess the accuracy of the valuesadopted in modern seismic codes. Since calibration of R factors should be based on arepresentative sample of adequately designed buildings, twelve structures varying incharacteristics are employed here. Different design ground accelerations, ductilitylevels and vertical regularity are taken into consideration to cover a reasonablerange of contemporary RC buildings. A rigorous technique is employed to evaluatethe R factors. This includes inelastic static pushover and incremental dynamiccollapse analyses employing a diverse range of ground motions. Th e latter approachinvolves successive scaling and applying of each of the employed records followedby assessment of the response using a comprehensive range of performance criteria.This enables identifying and comparing the ground motion intensities correspondingto different limit states. Special attention is also given to investigating the effect ofshear modelling and employing the vertical ground motion in analysis.

2. Definitions and ProcedureIt is now accepted that the force reduction factor accounts for the inherent ductility,overstrength and damping of structures. Early definitions of the force reduction fac-tor proposed in the mid-1980s suggested subdividing R into the three componentsmentioned above. Thus,

where R, is the ductility reduction factor, ad s the overstrength factor and REis th e damping factor. The effect of damping is generally included in the ductilityreduction factor (R,). The factor considered in Eq. (1) was included only toaccount for response reduction provided by supplemental viscous damping devices[ATC-19, 19951, hence it could be excluded horn Eq. (1). Another term was intro-duced by ATC-34 [I9951 o account for redundancy (RR).his factor is intended toquantify the improved reliability of seismic framing systems that use multiple lineof vertical seismic framing in each principle direction of a building. The R factor istherefore given by:

Moreover, the overstrength and redundancy are considered as one component, ashas been adopted by many investigators including some of the ATC researchers[e.g. Freeman, 19901. This is because the overstrength parameter implicitly ac-counts for redundancy through redistribution of actions; which leads to higheroverstrength. The force reduction factor can be therefore defined as the productof the ductility reduction factor (R,) and the overstrength factor (ad), s shownin Fig. 1.Thus,


5/36

242 A . M.Mwafy EJ A. S. Elnashai

Fig. .I . Relationship between force reduction factor (R), overstrength ( ad ) ,uctility reductionfactor (R*)nd diplacement ductility factor (p) .

A proper calibration of the R factor can be undertaken by evaluating the twocomponents contributing to it. These can be obtained from the force-displacementrelationship of the struc ture, which can be determined either experimentally or an-alytically. Since the experimental evaluation of the R factor for a broad range ofstructures and a realistic suite of excitations is extremely costly, the only alterna-tive left is inelastic analysis methods. The capacity envelope of a structure can beobtained from inelastic pushover analysis, subject to the constraints of this tech-nique [Mwafy and Elnashai, 20011. For structures that exhibit a period > 0.5 s, theductility reduction factor (R , ) may be taken equal to.the displacement ductilityfactor ( p ) . The latter approximation follows the equal displacement assumptionproposed by Newmark and Hall [1982].n this assumption, which is applicable to awide range of structures and adopted in many seismic design codes, the maximumdisplacements are considered comparable for elastic and elasto-plastic systems. Mul-tiplying the ductility factor ( p ) and the overstrength factor ( R d ) results in the forcereduction factor (R).

The aforementioned procedure is simple to apply and requires relatively lesscomputational effort compared with other alternatives since only inelastic staticpushover analysis is needed to obtain p and pd . However, it has the drawback ofignoring completely the ground motion dependence of the force reduction factor.Despite this clear deficiency in this approach, it has been employed by other in-vestigators [e.g. Balendra e t al.,19991.An alternative that has emerged recently isadaptive pushover that accounts for spectral amplification and period elongation


6/36

Calibmtion of Force Reduction Factors of RC Buildings 243[Elnashai, 20001.Whereas preliminary results have shown that this developmentopens a whole range of possibilities for the inelastic pushover metbod [Mwafy, 20011,it is not fully established yet.The R factor in all seismic codes serves to reduce the elastic base shear (V,)to the design base shear levet (Vd). or instance, EC8 defines the force reductionfactor (behaviour factor q) as the ratio of elastic seismic forces with 5% viscousdamping to minimum forces used in design. The elastic and the design forces areobtained from the elastic acceleration spectrum of the site (Sa )el and the spectrumused in design (So)'", respectively. Thus,

where (S,)eiand (So)'"are the spectral acceleration ordinates corresponding tothe predominant period of the structure. Collapse is normally anticipated underthe effect of an earthquake having a spectrum higher than the elastic spectrum,particularly at the period considered. Therefore, the following definition may beemployed to evaluate an ultimate value of the force reduction factor for a particularstructure under a specific accelerogram:

K , d y = (~o):'/(sa)j" (5)where the subscripts L ' ~ " and "dy" refer to collapse and design yield (the yield levelassumed in design), respectively. Moreover, the structure is mainly designed forforces consistent with its yield limit state. Consequently, Elnashai and Broderick[I9961 have employed a definition that utilises the spectral acceleration causingactual yield in the denominator, as given in the following equation:

where the subscript 'Lay" refers to actual yield. By assuming that the responsespectra of the design, yield and collapse earthquake have constant dynamic amplifi-cation (ratio of peak ground-teresponse acceleration), at least for the period rangeconsidered,Eqs. (5) and (6) can be rewritten as follows:

where ag collapse) , (design) and as (actual yield) are the peak ground accelerationsof the collapse, design and yield earthquake, respectively. ag desisn yield) is the de-sign PGA divided by the force reduction factor employed in design (&ode). Thedifference between a, (design yield) and a, ( is that the former is the yieldintensity assumed in the design, whilst the latter is the PGA a t first indication ofactual yield.Both definitions given in Eqs. (7) and (8) relate the intensity of loading at col-lapse to the elastic seismic forces. Equation (7 ) adopts the assumption tha t yieldingwill occur at the design ground acceieration divided by &ode. This definition isstraightforwardand less computationally demanding because only the PGA of the


7/36

earthquake that causes collapse is required. It is more appropriate for assessing ex-isting force reduction factors since it checks the validity of the design by examiningthe capability of-the structure to resist greater seismic forces than those implied bythe design. However, the definition of has the shortcoming of not accountingfor the dissimilarity between the design spectrum and the spectral acceleration ofthe ground motion at yield plnashai and Broderick, 19961.Even though a set of ar-tificially generated ground motions compatible with the elastic response spectrumof the code are utilised to calculate the disparity still exists, as shown inFig. 2(a). In this figure, the spectrum of an artificial record is scded t o the designPGA divided by (the yield assumed in the design) and compared with thedesign spectrum. I t is clear that synthetic records are not compatible with the de-sign spectrum in the short period range and in the period range beyond the cornerperiod (T,).This is because the code decreases'the force reduction factors in theshort period range as a result of the limited capability of structures in this rangeto develop inelastic deformation. EC8 is a h onservative for long period struc-tures; hence Kodealues are decreased in this range. This leads to a decrease inthe steepness of the inelastic spectrum beyond the corner period.

On the other hand, structures designed to modern seismic codes usually exhibita considerable level of overstrength [Elnashai and Mwafy, 20011. This leads to asignhcant dierence between the PGA causing first global yield (a, (,t,,~ yield))and the yield intensity implied by the design (a, (d,,i, = design PGA/%,de).It is observed in many cases investigated in the present study that the accelerationspectrum of the record causing yield (s,): is even higher than both the design(S,)'" and the elastic spectra of the code (&)"I, as shown in Fig. Z(b). Clearly,the reserve strength results in delaying the yield to -thi s high level of ground mo-tion. Since the PGA corresponding to yield is more sensitive to the level of over-strength compared with the PGA that causes collapse, it is expected that thedefinition of R , , will underestimate the force reduction factor, particularly forbuildings exhibiting high overstrength. It is clear that the definition of & which

Fig. 2. Evaluation of the force reduction factor for a 12-storey regular frame building using anartificial record comp atible with th e code spectrum: (a ) definition of R < , J ~ ;b) definition of &.ay.


8/36

Calibmtion of Force Reduction Factors of RC Buildings 245

Fig. 3. Comparison between th e ductility reduction factor ( R p )and th e definition of (&)

represents the inherent force reduction factor of a struc ture of no known designhistory, is more suitable when recommending R factors for ideal systems. For prac-tically designed and detailed buildings, this definition should be rnodfied to accountfor overstrength. It is also important to note that there is a clear similarity betweenthe dehi tion of&,, and the ductility-dependent component of the force reductionfactor (Rp= V,/V,), as shown from Fig. 3. This emphasises the need to modifyEq. (8) by adding the overstrength factor (ad= actual-to-design strength) to h&.The suggested modification is given by:

The latter modification allows for reserving characteristics of the original definitionof a,, in terms of the ground motion dependence of a, ~,o~~a,,,~ and a, (actual yield).This gives some advantages RLay for over &,dy, which ignores this dependencein its denominator. The main shortcomings of the expression of Eq. (9) are itsdemanding computations and being based on the assumption of constant dynamicamplification. However, it is an effectiveway of evaluating the force reduction factorof a particular structure subjected to a specific earthquake. It is also noteworthythat in another study, Salvitti and Elnashai [I9961have concluded that the forcereduction factors calculated using Eq . (8) are not significantly influenced by theelongation in the period and the dynamic amplification effect.

Other methods and alternative definitions may be suggested to predict the forcereduction factors. However, it is beyond the scope of the current study to reviewand discuss all these approaches. Only the two definitions given in Eqs. (7) and(9 ) are adopted here for evaluation th is important factor using inelastic pushoverand incremental collapse analysis. Pushover analysis is employed to evaluate th eglobal yield limit sta te, structural capacity and overstrength. The extensive dynamiccollapse analysis is performed by progressively scaling and applying each of theemployed set of accelerogram, starting from a relative low intensity, typically the


9/36

Perform ioelasricp w b v c ranalysis i c c e (righrward andleftward)up w a high drift Limitto achicvc yield in all critical

Dynamic +sir ourpvtRun thc staric pushover

global pafonnancc. formatimlmal a d lobal rw o f = lmdcr Ihc

Fig. 4. Performed analysis procedure for each building-input ground mo tion combination.

design intensity divided by the Rcode(ag(designield)), nd terminatkg with theintensity at which all yield and collapse definitions are achieved. This rigoroustechnique allows evaluating the performance of the struc ture at different levels ofexcitations. Hence, the peak ground accelerations causing yield and collapse canbe identified according to the performance criteria adopted here. Between 15 to20 analyses are performed for each structure- input combination to identify theresponse at different limit states. The procedure is surnmarised in Fig. 4.

3. Ingredients of the Analytical Study3.1. BuildingsTwelve structures varying in characteristics are employed in the current studyas representatives of medium-rise RC buildings. The structures are split into thethree groups shown in Table 1. Four buildings designed to different ductility andPGA combinations are employed in each group. This is aimed to compare between


10/36

Calibmtion of Force Reduction Factors of RC Buildings 24 7Table 1. Characteristics of the buildings considered.

Structure No. of storeys and Design Design Design ElasticGroup reference structural system ductility PGA (g) force red. period (sec)factorIF-HO3O

1 IF-MOJOIF-M015IF-LO15RF-H030

2 RF-M030*-MOl5RF-LO15FW-HO30

3 FW-MOB0FW-M015FW-LO15

High&storey irregular Mec hm

frame MediumLowHigh

12-storey regular bkdiumframe Medium

LowHigh

&storey regular Mdi umfram+wall Medium

Low

structures designed according to capacity design set of rules but for different groundaccelerations and for the same ground acceleration but different capacity designrules, The buildings were designed and detailed in accordance with EC8 [1994],asa typical modern seismic design code applicable to more than one country withvarious levels of seismicity, soil conditions and construction practice. TabIe 1 showsthe elastic force reduction factors used in the design and the observed elastic fun-damental period ''Tel,ti,"obtained from elastic free vibration analyses. Live loadsand loading from floor finishes and partitions are 2.0 kN/m2. All buildings areassumed to be founded on medium soil type "B" of EC8 (firm). A characteristiccylinder strength of 25 N/mrn2 for concrete and yield strength of 500 N/mm2 forsteel are utilised. More information regarding member cross- section sizes and rein-forcements are given elsewhere [Fardis, 19941. The geometric characteristics of thebuildings are illustrated in Fig. 5.

3.2. Analytical modellingThe structural analysis program ADAPTIC [Izzuddin and Elnashai,1989) s utilisedto perform the inelastic analyses. The program has been developed for the inelasticanalysis of two- and three-dimensional structures under static and dynamic load-ing, taking into account the effects of both geometric nonlinearities and materialinelasticity. ADAPTIC has the feature of representing the spread of inelasticityw i t h the member cross-section and along the member length through utilisingthe fibre approach. Further information regarding the program and its validationcan be found elsewhere [e.g. Elnashai and Elghazouli, 1993; Elnashai and Izzuddin,1993; Martinez-Rueda and Elnashai, 19971.


11/36

g. 5. Plan and sectional elevation of the buildings: (a) group I "eight-storey irregular framebuildingsn; (b) group 2 "12-storey regular frame buildingsn; (c ) group 3 "eight-storey regularframe-wall buildingsn.

Refined analytical models are utilised for the 12 buildings investigated here.Detailed description of this approach is given elsewhere [Mwafy, 2001; Elnashaiand Mwafy, 2001). Only the main features of the adopted modelling technique aresummarised below:

Two-dimensional representation is selected in the light of the symmetry of thebuildings and the limited si@cance of torsional effects. Internal and externallateral force resisting systems are combined by means of an overlay approach, asshown in Fig. 6 for the frame-wall structural system.The analyses are conducted along one horizontal direction onIy (global X-axis orgroup 1 and 2, and Z-axis for group 3). This is justified by the fact that criticalresponse criteria were expected to occur earlier in those directions.

0 Horizontal and vertical structural members are modelled using three cubic elasto-plastic elements, where the lengths of the elements are determined accordingto the distribution of longitudinal and transverse reinforcements. Shear springelements are introduced to represent the shear s t ih ess of the beam-column con-nection, as shown in Fig. 6(d). In the frame-wall structures, th e core wall on eachside of the coupling beams is modelled as a "wide-column". The elements arelocated at the centroid of the core U-shaped cross-section and connected withthe end of beams a t each storey level using rigid arms, as shown in Fig. 6(c).


12/36

Caiibmtion oJ Force Reduction Factors of RC Buddings 249

Rigid/- elements 7

(a) Internal s t r u c h l ~vstem 0 ) lan of the frame-wall Ic) 2-D modellinp of central cores m c d ystem

" I_-dp-=-- 1 - 1 L - fikeCbl' I.-----_-----------le)Overfy technicwe considered JO Decompositionofbeam T-section into fibres

Fig. 6. Modelling of frame-wall structures.

The concrete is represented using a uniaxial constant confinement concretemodel [Martinez-Rueda and Elnashai, 1997).The advanced multisurface plastic-ity model [Elnashaiand Izzuddin, 19931 is utilised for modelling he reinforcementbars.

3.3. Input ground motionsInelastic dynamic analysis is performed using eight input excitations. Four 10-second duration artificially-generated records compatible wi th the EC8 responsespectrum for medium soil class (firm) were selected for comparison and calibrationwith the design. Furthermore, two natural earthquakes were selected in terms of


13/36

250 A . M.Mwafy B A. S. ElnashaiTable 2. Ground motions used in time-history analysis.

Earthquake and station Date M s PGA ('I V /N NO. of inputHoriz. Vert. excitationsKobe (Japan), 17/01/95 7.20 0.276 0.431 1.56 2Kobe UniversityLorna Prieta (USA), 18/10/89 7.17 0.319 0.349 1.09 2Saratoga "Aloha Ave."Artificial Records, 4Art-recl to Art-rec4

the site-to-source distance and the V / H ratio and applied with and without thevertical component of ground motion (four input combinations). This is motivatedby the desire to investigate the effect of the vertical ground motion on buildingssituated in the vicinity of active faults, which may be significant as concluded inprevious studies [e.g. Papazoglou and Elnashai, 19961. For the sake of brevity, onlybrief results are presented herein illustrating the significance of this effect on theR factors. Complete results of this investigation are given elsewhere [blwafy, 20011.Characteristics of the selected records are given in Table 2. '

Employing a reliable method to scale the selected records is significant sincethe assessment methodology requires successive scaling of the records. A refinednormalisation approach is adopted in here, where all records are scaled to possessequal velocity spectrum intensity in the period range considered, whilst the designcode elastic spectrum is taken as a reference. For instance, when the input accelero-grams are scaled to a PGA of 0.309, he scaliig factors ensure that the velocityspectral areas of th e scaled records equal to the area under the velocity spectrumof th e code anchored to a PGA of 0.30g. herefore, the term "intensity" or "PGA"quoted thereafter is not of the original or scaled records but rather multiples of thedesign ground acceleration. Advantages of this approach were discussed by Mwafy[2001].

3.4. Performance parametersBased on the approach adopted in the present study to evaluate the R factors, anumber of response criteria are needed to d e b he yield and collapse limit states.Two yield and six failure criteria are utilised here. These are classified into twogroups, iocal and global criteria. Local yield is defined when the s train in the maintensile reinforcement exceeds the yield strain of steel. The global yield limit state isdefined as the yield displacement of the elasto-plastic idealisation of the real system.On the other hand, two failure criteria on the member level are utilised: exceedingthe ultimate curvature (4, = (E,, + ~ , ) / d ) r shear strength. The latter is eval-uated for structural members using a realistic ductility- and axial force-sensitive


14/36

Calibmtion of Force Redtictima Fuctws of RC Buildings 25 1shear strength approach capable of providing an experimentally verifiable estimateof shear supply in RC members [Priestley e t al.,1994).To allow for effective cornpar-ison with the design, the shear strength model of the design code is also employedafter eliminating safety factors. The adopted globaj failure criteria are: an upperlimit of the interstorey drift (ID) ratio equal to 3%, formation of a column hingingmechanism, a drop in the overall lateral resistance by more than 10%and an upperlimit of the stability index (0 = ID x storey gravity load/storey shear) equal to0.3. The adopted performance criteria are implemented in a post-processing pro-gram to directly monitor capacities and demands of shear and curvature and applythe performance parameters during the time history analysis. Further informationregarding t.he ingredients of the rigorous analytical study can be found elsewhere[Mwafy, 2001; Mwafy and Elnashai, 2001; Elnashai and Mwafy, 0011.

4. Analytical ResultsInelastic sta tic pushover and incremental dynamic analyses up to collapse are car-ried out on the 12 buildings investigated here. In total, over 1500 inelastic dynamicanalyses were performed to calculate the force reduction factors. However, for thesake of brevity only a summary of these extensive results is presented in subsequentdiscussion in the form of average results for the artificial and natural records (withand without the vertical ground motion).

4.1. Results at yieldA summary of the average intensities at which local and global yield are observedfrom dynamic analysis is shown in Table 3. First indication of member yieldingis observed at different locations for the three groups of buildings. In the firstgroup, the severance at the ground storey of some intermediate columns causes earlyyielding in those columns. For the dual structures, first yield is observed in beamsfollowed by a plastic hinge at the base of the core. Unlike the latter two groups,first yield in vertical members of the 12-storey buildings is observed relatively latecompared with the first beam yielding. In many cases, it was necessary to applyhigher PGA than that causing global yield to achieve yielding in column. This isdue to the regularity of this structural system and th e rigorous capacity designprovisions imposed by the design code.

For two buildings designed to the same PGA, yield occurs at a lower level ofexcitation for the structure designed to higher R factor (higher ductility level).This is confirmed in all cases when applying the gIobal yield criterion. When thelocal yield criterion is employed, the aforementioned observation is also applied onthe first and the third group of buildings where equal cross-section dimensions wereused for the' pairs of buildings designed to the same PGA. For the second group, the


15/36

Te3Smmayogoaeaoayedmisae

aauyed

aauyed

aauy~eld)~ned

ned

aauyed

O

eh

Ree

aed

(

(H+V

"Wdadgyed

rod)

L

G

L

G

LG

Id

G'

Sa

Dy

'Aaohacaed

b

afonuaemrdhzaeh

cmp

ssoeyus

=Aaonuaedhzaavccmp

saeae

dadgyed=dgRc

*Aaoeightgomoo

L&G:L

goyedneeepvy

Sa&D

O

eheueomsacph

anemeadmiccaaysepvy


16/36

Calibration of Force Reduction Factors of RC Buildings 253

depth of RF-HO3O beams is 65 cm compared with 60 cm for RF-MO30 beams. Theincrease in the depth of RF-H030 beams, which was made to fulfil local ductilityrequirements of the design code, causes delaying the first member yielding.The values of as(desisn yield) (design PGA/KOde) nd the average observed I*car and global yield intensities for the eight ground motions divided by ag(designyield) are also shown in Table 3. The latter. yield)/aS(design yield)) is theratio between the averagePGA hat causes actual yieldand the intensity at whichyield is implied in the design. In all cases, this ratio exceeds 2.0, reflecting the highoverstrength exhibited by the buildings. It is clear that the first member yieldingis observed at high intensity leveIs compared with ag(design It k also note-worthy that the overall structural response generally remains elastic even slightlybeyond the &st indication of member yielding due to the insigruficance of one plas-tic hinge, as shown from Figs. 7. The latter figure depicts the sequence of hingeformation of the irregular frame group of buildings obtained from pushover analysisat the global yield limit state. The above supports the need for the modificationof adding the overstrength factor (ad) o the definition of force reduction factorsuggested in Eq. (9). It also reinforces the conclusion of Elnashai and Mwafy (20011

Fig. 7. Progress in plastic hinge formation at global yield limi t state for th e first group of build-ings: (a) IF-H030 (top dkp.= 277 mm, top drift ratio= 1.09%); (b) IF-MO3O (top disp. = 289 mm,top drift ratio = 1.13%); c ) IF-MOl5 (top disp. = 21 5 mm, top drift ratio = 0.84%); d) IF-LO15(top disp. = 263 mm, top drift ratio = 1.03%).


17/36

2% A. M. Mwafy # A . S. Ellurshai

regarding the high overstrength of buildings designed to modern seismic codes andthe conservatism of the minimum nd factor of 2.0 suggested for low and mid-risebuildings.The overstrength factors ( Q d ) evaluated by Elnashai and hlwafy [ZOO11 forthe 12 buildings using inelastic pushover and incremental dynamic collapse anal-yses are presented in Table 3. It is clear from the comparison between averageag(actuaiield)-t~-ag(designield) ratios and overstrength factors that employing Rdin the definition of the force reduction factor proposed in Eq. (9) is conservative(ag(actual ield)/~g(designyield) > ad) . owever, in the third group of buildings theag(actua~ield)-to-ag(designield) ratios are lower than the R d factors evaluated fromdynamic collapse analyses. This is mainly due to the sensitivity of wall structuresto higher mode effects, which significantly amplify the base shear during time-history analysis. This represents one of the differences between static pushoverand dynamic analysis results, as concluded by Mwafy and Elnashai (20011. Hence,higher overstrength is evaluated from dynamic collapse analysis compared withstat ic pushover analysis. To be on the conservative side in evaluation of the R fac-tors, the fld factors calculated from static pushover analyses are utilised with theyield intensities determined from the local criterion, whilst the Rd factors evaluatedfrom dynamic collapse analyses are employed with the intensities obtained usingthe global criterion.

The distribution of plastic hinges and sequence of hinge formation a t the globalyield shown in Fig. 7 shed light on the suitability of the local yield criterion forevaluation of the R factors, which are mainly overall parameters. Several plastichinges are formed at the global yield limit sta te, which clearly represents the actualyield of the structure. The aforementioned observation may not be applicable to thelocal collapse criteria since member failure may practically cause partial structuralcollapse. It was therefore decided to categorise the force reduction factors calculatedin the present study according to the following classification:

Factors evaluated from local response criteria (yield and collapse).Factors evaluated based on the global performance criteria.Factors calculated from first indication of yield and collapse (local or global).

4.2. Results at collapseThe extensive range of collapse parameters explained earlier (two local and fourglobal criteria) is employed to assess the ground accelerations that cause memberor structure failure. It should be mentioned that some of these criteria, particularlymany of those defining the global collapse limit state, have not been observed up to ahigh level of PGA. No formation of a column sidesway mechanism has been observedup to a high drift limit, which reflects the success of capacity design provisions inprotecting vertical members. This is clear in Fig. 8 from the distribution of plastichinges at the interstorey drift collapse for the irregular buildings, which has theweakest lateral force resisting system.


18/36

Calibration of Force Reduction Factors of RC Buildings 253

Fig. 8. Distribution of plastic hinges at the interstorey d rift collapse limit sta te (ID= 3%) forthe first group of buildings: (a) IF-H030 (top disp.= 532 mm); (b) IF-M030 (t op disp.= 552 mm);(c) IF-MO15 (to p disp. = 476 mm); (d) IF-LO15 (top disp. = 516 mm).

1 -111 Art-rccl -2] Kobe (H ) - 31Lorna Rieta ( H ) 1Storey

Fig. 9. Maximum interstorey drift (ID) and stability coefficient (8) or a sample building fromeach group at ID collapse (results of three records from eight ground motions employed).

The capacity envelopes of the 12 buildings obtained from static as well as fromincremental dynamic analysis are given elsewhere [Mwafy and Elnashai, 2001). Itwas observed that no significant reduction in the lateral capacity of the 12 build-ings was recorded. Moreover, the observed values of the stability coefficient (9)


19/36

Te4Goaeaoacamsae

b

"c

aca

*

~

Aa

Ree

aed

nedH

ned(+V)

aaadg

LhLcG

LshLcG

IhLcG

LhLcG

IFH IFM IFM IFLOS

RHO

RMO

RM

RLO

FW-HO

FWM

FW-M

FW-LO

-

-

-

aAaohacaed

bafohnuaedhzaeh

cm

ssoeyus

Caohnuaedhzaavccm

saeae

dafoeggomo

LhLshaue

LcLcuhnauenceecvuedydm>uy

Ggoaueneoed>3%

INa

aueouoovnwyoaueoagoca

BddehPGAepnoovoaue

IacncehPGasu

yovoaue


20/36

Calibration of Force Reduct iun Factors of RC Buildings 257up to the interstorey drift collapse were well below the limiting value adopted here(0.3). Sample results of the calculated values of B at the ZD collapse are presentedhereafter (Fig. 9). The foregoing observations are noted in all structures consideredand under all ground motions employed. Therefore, the interstorey drift (ID) cri-terion is practically the controlling global collapse parameter tha t was utilised toevaluate the R factors.

The two member failure criteria (ultimate curvature ductility and shear ca-pacity) are also employed here since they are observed within a practical level ofexcitation, particularly the ultimate curvature ductility. As explained above, theshear suppIy-demand ratio is monitored during dynamic analysis by employing twoshear strength mode!s, Priestley e t aL (19941and the design code IEC2, 19941. Allsafety factors were elimhated from the code shear model to be consistent with theassessment objective of this investigation. However, shear failure under relativelylow levels of PGA is frequently recorded when employing this model, confirming theover-conservatism of shear strength predicted using code approaches. Hence, it wasdecided to exclude this model from calculations of the force reduction factors. Thecollapse intensities from the shear criterion shown in Table 4 a re therefore thoseobtained from applying Priestley e t al. (1994) shear strength model only.

The ground accelerations that cause first collapse,as shown in Table 4, confirmthe importance of including shear as a failure criterion in assessment studies. Inframe structures, it is observed that the most susceptible buildings to shear failureare those designed to ductility level "Low". For those buildings, shear failure is thecontrolling criterion that defines local collapse intensities. This is because capacitydesign rules are not required by ECS when designing for this level of ductility. Onlysome provisions are applied to enhance the ductility of columns. EC8 does notalso impose supplementary provisions to those specified in EC2 for shear designor for maximum stirrups spacing in critical regions of beams designed to ductilitylevel L L L ~ ~ " .herefore, these beams are vulnerable to shear failure. A sample ofshear assessment results are presented hereafter, whilst complete results of thiscomprehensive investigation are presented in Mwafy [2001].

For buildings designed to higher levels of ductility, member shear failure is ob-served at high PGA levels. Hence, ground motions that cause shear failure are onlypresented in Table 4 when this type of failure is observed a t or before collapse fromboth the ultimate curvature and the ID criteria. Indeed, the structure at this limitshould experience extensive damage since it would undergo two types of collapse(local and global), hence shear failure will not be a controlling parameter. Threedifferent values of collapse ground acceleration (a,~,,ll,,,,~) are therefore shown inTable 4 for each building-ground motion combination (based on two local and oneglobal criteria). The first observed local failure is only utilised in calculations of Rfactors, in addition to the intensity at global collapse. The intensity levels at firstlocal failure (ultimate curvature or shear) are shown in bold in Table 4.


21/36

258 A. M. Mwafy # A. S.ElnashaiIt is clear for moment resisting frames that critical concrete strains are exceeded

slightly before the global ID collapse limit. For the hybrid structures, the interstoreydrift collapse is attained well after the critical concrete strain, confirming the effi-ciency of this structural system in controlling deformations. As shown in Tabie 4for the third group, ID collapse is observed for the 0.309 pair at about four timesthe design PGA, and at about six times the design PGA for the 0.159 pair. It isclear that local failure criteria are more critical for this type of construction thanglobal parameters due to the concentration of demands at wall base and in couplingbeams.

The average ag~,,ll,,,,~-to-ag~desi~~atio for the eight input ground motions arealso shown in Table 4. This ratio reflects the average margin of safety exhibitedby each building under the effect of the eight ground motions. It is clear thatthe margin of safety increases with the decrease in the design PGA, reflectingthe higher contribution of gravity Ioads. The balance between gravity and seismicdesign scenarios is the main parameter controlling this margin. It is also observedwith few exceptions, mainly in the irregular frame buildings, that the safety marginincreases with decreasing the ductility level. This implies that the stringent capacitydesign rules imposed on structures designed to higher ductility levels do not balanceadopting higher force reduction factors. This also suggests that buildings designedfor lower PGA and detailed for lower ductility levels are more reliable comparedwith those with higher ductility and designed for comparatively higher PGA.4.3. Sample time-history collapse analysis resultsTo allow comparisons between the seismic response of the investigated buildingdesign on the member and structure leveIs, sample dynamic analysis results arepresented in Figs. 9 to 11. The results are shown for a sample buildings and ac-celerograms from those employed in the present study. Further results are givenelsewhere [Mwafy, 20011.4 .3 .1 . Global collapseFigure 9 shows the distribution of the maximum observed hterstorey drift at theglobal collapse limit state for a sample building from each group when subjectedto one artificial record and two natural ground motions employing the longitudinalcomponent. The recorded m w u m tability coefficients (8) at the same limit stateare also shown. The observed values of 0, which place a further limitat ion on P -Aeffects, are well below the limiting value adopted here (0 < 0.3). This implies thatsecond order effects are not significant up to this high level of PGA.The levels of excitation that cause ID collapse are varied a s shown hornTables 4. It is clear in Fig. 9 that each building-input combination is a distinctcase, where the ID limit state is observed at different storey levels. For the irregularframe buildings, the maximum ID is likely to occur in the ground storey due to itsincreased height compared with other storeys and .the severance of four columns.


22/36

CoIibmtion of Force Reduction Factors of RC Buildings 259For the second group, ID collapse occurs in the intermediate storeys, highlight-ing the contribution of higher modes. It is also observed that the distribution ofthe maximum ID along the height is more uniform for hybrid structures comparedwith frame buildings. This emphasises the efficiency of dual structural systems inreducing lateral deformations.4.3 .2 . Local collapse - maximum curvature ductilityFigure 10 illustrates the distribution of the maximum curvature ductility demand(CDD) in horizontal and vertical structural members for a sample building horneach of the three groups. This is presented at an excitation level equal to twicethe design PGA to simplify the comparison between structural systems and in-put ground motions. Due to the rigorous capacity design provisions imposed byEC8, critical concrete strains are mainly attained in beams under the eight inputground motions. For vertical members, maximum CDDs are observed at the groundstorey with the exception of the cu$-off columns in the irregular buildings, where- rt-recl -Kobe (H) -Lorna Pricta (H)

'

1 .

0 .,

Storcy

(a) ExternalpiTlystem1 2 S 4 S 6 I Z 3 ~ 6 1 2 1 1 6Fig. 10. Maximum curvature ductility demand (CDD) for a sample building from each group attwice the design PGA (0.609) results of three records from eight ground motions employed).


23/36

260 A. M. Mwafy El A. S. Elwhai

high demands are observed at the second and the eighth storeys [Fig. 10(b)J. Theadvantage of regular structural systems is clear from the distribution of CDDs inRF-H030 in comparison with IF-H030, where energy is mainly dissipated in beamsof the regular structure. The comparison also point towards the need for possibleimprovements in EC8 o protect cut-off columns in irregular structures. In the dualstructural system, high demand is generated in the central core (walls and couplingbeams), contrary to the frame buildings where demands are distributed betweenexternal and internal lateral force resisting systems. This confirms that couplingbeams and walls provide the primary source of energy dissipation in hamewal l

.structures and support the special provisions imposed by the code on the design ofthese members.

The sample buildings presented in Fig. 10 are those designed to high ductllitylevel in each group. For this level of ductility, the minimum conventional curvature

SF. upply :- EC2)- Riutley el al.)-

o i i isl ime (ref)

(b) RF-LOIS

-F- M F -

SF. upply :- EO)- Priculyn aL)m -i!

Fig. 11. Results at first observed member shear failure in frame buildings designed to ductil-ity level "Low" for a sample records from the eight ground motions utilised here: (a ) IF-L015;(b) RF-LOIS.


24/36

Cal ibm tion of Force Reduction Factors of RC Buildings 261

ductility factors (CCDF) equired by EC8 for columns and walls are 13 and 9.8,respectively. It is clear that the observed CDD values at twice the design intensityare well below the minimum supply imposed by the design code. The satisfactorysafety margin, expressed by the difference between the CCDF and the CDD values,at this high level of excitation highlights the robustness of vertical members designedto EC8.4.3.3. Lour1 collapse - ltimate shear strengthResults of the shear assessment investigation clearly confirm the si&cance of em-ploying this rigorous collapse parameter hassessment studies. I t is concluded thatthe shear failure criterion is the controlling parameter that define member failurefor frame buildings designed to ductility level "Low". Hence, ignoring this criterionin calculations of the force reduction factors will result in inaccurate prediction ofthese significant factors. Sample results of this investigation are presented in Fig. 11,where the shear supply-demand time-histories for two records are presented at theintensity levels that cause first indication of member shear failure.

5 . Evaluation of Force Reduction FactorsIt is shown in Sec. 2 that the force reduction factor "supplyJ' of a specific structuresubjected to a specific earthquake record can be evaluated according to Eqs. (7) and(9), which are used to calculate and RiSayrespectively. Tables 5 and 6 show asummary of the average force reduction factors evaluated using the set of artificialand natural records employed here. DesignR factors (&ode) and average supply-to-design ratios are also presented. For each structure investigated here, three valuesof the R factor are presented. These correspond to the R factors calculated using:the local yield and collapse intensities, global intensities and first observed yieldand collapse PGA regardless of the classification of the limit s ta te (being local orglobal).

Generally, the average supply-t~designvalues obtained when employing thedefinition of &,dy are higher than those of RL,dy. The definition of &,d, as-sumes that yield will occur at as(design yield) (Design PGA/&,d,), which implic-itly accounts for overstrength but ignores the ground motion dependence of theyield intensity. The definition of Rilaytakes this into consideration by employingthe actual yield intensity corrected by the overstrength factor (Rd). The ratio ofag(actud yield)/ag(design yield), which represents the overstrength assumed in the def-inition of &,dy, is generally higher than the actual overstrength Rd, as shown inTable 3. Therefore, average values of are higher than &,,.The evaluated R:,ay and factors show clearly the dependence of this fac-tor on the ground acceleration used in the analysis. This is exemplified by theRi,, values of the second group of buildings, as shown from Table 5. Differencesin excess of 100%afe observed between the factors calculated using the artificial


25/36

Te5A

ordoaoRafoardapomacea

Ra

R

A

oo

-

ard

K,a

A

ow

nrdH)

L

G

F

%,a

A

ow

nrdH+V

L

G

F

FW-H

722672

548654

58855.83

35

1

3

17

FWM

451045

446844

456645

26

1

9

1

FW-MO15

9

1296

538453

499149

26

2.593

2

FW-LO15

9

1395

457545

437743

17

3

4

3

Rca=a

P~auyed%

L

ceaaempodoccuaeRa

G:Gloceaa

d

FFro

dyedacaaempodoccuaeZ


26/36

Te6Av

ordof

R

foardapomacea

%,dY

%,d

'd

Re

Av

oo

Av

owo

Av

owo

Rd(a

ard

nrdH)

nrd(W+V)

R

&o

L

G

F

L

G

F

L

G

F

L

G

F

&,d

=

yed

G:Gloceaaud

L:L

ceaaempodoccuaeRCsd

FFro

dca

sempodoccuae&,d


27/36

264 A . M. Mwafy E4 A. S. EInahniaccelerograrns and those obtained when employing the natural earthquake records.The comparison between the two sets of accelerograms does not show any trend.,Thisemphasises the need to employ a diverse range of natural and code spectrum-compatible records if reliable estimation of force reduction factors is required.

It is clear in Tables 3 and 4 that yield and collapse may occur under lowerPGA when the structure is subjected to horizontal and vertical ground motion.This may lead to reduce the R factors "supply", leading to the adoption of higherseismic forces in design. The R factors "supply" for the 12 buildings investigatedhere are evaluated using the artificial and the natural records (with andwithout thevertical vibration), as shown in Tables 5 and 6; t is observed that both definitionsof R factors (q,,nd are influenced by the inclusion of vertical earthquakeload. Lncluding this effect in analysis does not give a clear trend in increasing ordecreasing the R factors "supply". However, the mean values of ET , , , and &,dy'are reduced by up to 18% and 15%, respectively. This confirms the significance of

, including vertical vibration in calculations of R factors.Force reduction factors evaluated using local yield and collapse criteria are con-trolled by the response of specific structural members, whilst those calculated usingglobal criteria reflect better the overall characteristics of the structures. The factorsobtained from the first indication of yield and collapse may be more worthy of con-sideration since they account for the h s t observed limit state, which may be moresigruficant than subsequently observed yield or collapse. For instance, early failurein a vertical structural member, which is not accounted for when utilising gbbalfailure criteria, is more significant compared with ID collapse occurs afterwards.Therefore, the force reduction factors "supplyn evaluated using the first indicationof yield and collapse are employed below to compare with the "design" and the"demand" values.

5 .1 . C o m p a r i s o n with th e de s i gn force r e d u c t io n f a c t o rThe calculated averageR factors "supply" are compared in Fig. 12 with the designforce reduction factor spectra. The latter are obtained by dividing the elastic bythe inelastic spectra of each of the 12 buildings, resulting in nine design spectra. Itis noteworthy that the two buildings designed to ductility level "Medium" in eachgroup share the same R-spectrum, hence nine design spectra are produced Eromthe 12 buildings investigated here. The results are classified'in Fig. 1 2 accordingto the ductility level (one plot for each of the three ductility 1eveI.s employed inthe design), hence three force reduction factor spectra corresponding to the threegroups of buildings are shown in each of the three plots.

The R;,, and &,+. actors are plotted at the inelastic period of the buildingsevaluated a t the design intensity levels. These periods are evaluated by Mwafy andElnashai [2001] slug Fourier analyses of the roof response time-histories obtainedfrom dynamic analysis (average of eight ground motions). Moreover, to highlightthe increase of the supply-to-design ratio due to period elongation, the calculated


28/36

Calabmtion of F m e Reduction Factom of RC Buildings 265

-.-.- R (IF-building) 13-"-.IKGqatT a 0 RC.& at T-)- - - - - R (RF-building) KG.,atT& 0 RG,,at T a(a) Ductility level 'High'buildings

-f

(b) Ductility level 'Medium'buildings

16= O I R

I 0 l ((c) Ductility level U w ' uildings

RF-LO 5

IF-MIS

Fig. 12. Force reduction factors "supply" versus the "designn: (a) ductility level "Highn build-ings (R factors are plotted at the elastic and at the inelastic periods]; (b ) ductility "Medium";(c ) ductility "Low".


29/36

266 A . M. wafy 4 A . S. E lno sh i

R factors for the high ductility level buildings ~ i ~ .2(a)] are plotted a t the elasticand inelastic period levels. It is clear that employing the inelastic periods in thecomparison leads to increasing the supply-tedesign force reduction factor ratiosshown in Tables 5 and 6.

High force reduction factors "supply" are observed for the sample buddings em-ployed here in comparison with the values adopted by the design code. This impliesthat the design R factors can be increased without adverse effects on structuralsafety. Th e satisfactory performance of the buildings at the design and twice thedesign intensities a well as the observed high ground accelerations that cause firstindication of collapse support this conclusion. It is aIso clear that buildingsdesignedto lower PGA have higher force reduction factors compared with their higher designground acceleration counterparts, as shown in Fig. 12(b). This confirms the needfor including the effect of the design PGA in the definition of used in seismiccodes to obtain more uniform safety margins for structures designed t o differentlevels of ground motions. This is strengthened by the observation shown earlierregarding the relatively high overstrength exhibited by the buildings designed t olower levels of ground motion.

5.2. Comparison with force mduction factor "demand"It is interesting to compare the force reduction factors "supply" and the "demand"values suggested in several previous studies [e.g. Miranda and Bertero, 1994; Vidicet uL, 1994; Borzi and Elnashai, 20001. Based on a group of 124 ground motionsrecorded on different types of soil conditions, Miranda and Bertero [1994] havesuggested the following expression for the force reduction factors:

1where @ = 1+ 2--exp[ -2(ln~- ;)'] forallur ivnsite s. (11)12T-pT 5TBorzi and Elnashai [2000] have employed the large dataset of Imperial College toderive force reduction factor spectra using 365 records of magnitude M, 2 5.5.It is noteworthy that the majority of the studies reported in the literature arebased on bilinear non-degrading SDOF systems with zero or positive strain hard-ening [Krawinkler and Seneviratna, 19981. The study of Borzi and Elnashai [2000]employed two.hysteretic models, includinga more advanced hysteretic hardening-softening model [Ozcebe and Saatcioglu, 19891, to derive trilinear force reductionfactor spectra. The R factors "demand" suggested in the two studies of Mirandaand Bertero [1994] and Borzi and Elnashai (20001 are employed in the comparisonwith the "supply" evaluated in the current study. It is important to note that theforce reduction factor "demand" represents only the ductility-dependent componentof R, whilst overstrength is not accounted for.


30/36

Calibmtion of Fo r ce Reduction Factors of RC Buildings 267

1 4 1(a) Ducriliry level 'High' buildings

m lR I (b) Ductility level 'Medium' uildings

10, R I (c) Ductility level 'Low' buildings 1

- - =4.---.*-.--*-

Time sec)0 I 10.0 0.5 IO I .5 2.0 2.5

Fig. 13. Force reduction factors "supply" versus th e "demand" suggested by Miranda and Bertero[I9941 nd Borzi and Elnashai [2000]:a) ductility level "Highn buildings; (b) ductility "Medium";(c) ductility "Low" .


31/36

Table 7. Observed overall displacement ductility Usupply" (p = A,,/A,,).Group -HO3O bddings -M030 buildings -1M015 buildings -Ml5 bdd i ngsIF- 1.92 1.91 2.21 1.96RF- 2.10 1.98 2.62 2.29FW- 2.61 2.27 3.11 2.83

Figure 13 shows this comparison, where the 12 buildings are classified againaccording to their ductility. The demand spectra are shown for different ductilitylevels. Although the 12 buildings investigated here were designed to three levels ofductility (High, Medium and Low), the difference between their actual displacementductility ( p = A,,/A,) is not significant, as shown from Table 7. The maximumand the yield top displacements (A,, and A,) are evaluated from pushover anal-yses using an inverted triangular load. It is seen that the displacement ductilityfactors (ductility supply) of the 1 2 buildings range between 1.9 and-3.1.Maximumvalues are observed for the FW-builclmgs, whilst minimum factors are noted forthe IF-group. The efficiency of the walls is reducing interstorey drift in the dual .structures leads to relatively high A,, at first indication of interstorey drift col-lapse compared with A,, hence p is higher for this group of buildings. For framestructures, the twelve-storey buildings have higher ductility factors compared withthe eight-storey group of structures. For the same group of buildings, the effect ofthe design ductility on the overall displacement ductility factor is insignificant. Theabove suggests employing the demand spectra of ductility level 2 and 3 only in thecomparison with the R factors "suppIy".

Notwithstanding comparisons of the force reduction factors "supply" with thecode-adopted factors are more sigd ican t, from the design point of view, than com-parisons of the "supply" with the "demand". The latter can provide codidencein decisions taken to mod^ the R factors of the code. Considering the demandspectra of ductility 2 and 3, it is clear from Fig. 13 that the force reduction factor"supplyn is higher than the "demand" in all cases. This confirms the conservatismof the R factors employed in the design of the 12 buildings.

Figure 13 also reveals a number of interesting features. It is observed that thebuildings designed to higher ductility levels exhibit the highest margins of safety.This is clear when comparing the supply-to-demand ratio for buildings designedto the same PGA but for different ductility leveIs. The latter observation is notclearly noted in the comparison of the force reduction factor L'supply" with thedesign. Some other observations are common between the two comparisons shownin Figs. 12 and 13. It is confirmed that frame structures have higher safety marginsthan frame-wall buildings. The latter observation is not noticed in the buildingsdesigned to ductility level "Low" ,a s shown from Figs. 12(c) and l3(c). This s dueto vulnerability of beams of frame buildings designed to ductility level "Low" toshear failure, as concluded above. For frame structures, the regular buildings exhibit


32/36

Cdi bm t i on of Fone Reduction Factors of RC Buildings 269higher supply-to-demand ratio compared with the irregular s truc tura l system. Thetrend shown in Fig. 13(b) for buildings designed to the same level of ductility butfor difTerent ground motions also reinforces the conclusion drawn above regardinghigher safety margins of buildings designed to lower PGA levels and the need toinclude the design PGA in the definition of R factors.

5.3. ~u&e,stedmodification to the code R FactorsThe lowest observed supply-to-design force reduction factors are those recorded forthe dual structures designed to higher PGA levels (FW-HO3O and FW-MO30). Theresults obtained from the more conservative definition of R:,, show thatfactors may be increased by 70%. It should be noted that the concentration ofdemands at the wall base and coupling beams compared with perimeter framesrepresents a drawback of this structural system. Moreover, Elnashai and Mwafy[2001] investigated the possibility of predicting the inelastic period of buildings usingeffective flexural stiffness in eigenvalue analysis. It was concluded that reductionin the stiffness of the walls would result in considerable softening in the overallstructural response. Due to the sensitivity and dependence of dual systems on wallsas the main lateral force resisting element, it is recommended to apply relativelylower increase to Godehan that observed here. An increase in &ode between 10-20% is suggested. The force reduction factors of dual structures designed to lowerIeveIs of PGA may be increased hrther.

In contrast with the latter structural system; strength, stiffness and ductilityin frame buildings are uniformly distributed between different lateral force resist-ing elements. Hence, their &ode values may be safely increased according to thevalues observed here. However, for those designed to lower levels of ductility, par-ticularly irregular frames, it is recommended first to improve the shear strength ofbeams and cut-off vertical members. It is also important to note that due to theestablished firm relationship between the force reduction factor and overstrength[Elnashai and Mwafy, 20011, the suggested increase in &ode values should not becoupled with major modifications in the code provisions that may lead to a reduc-tion in overstrength. Indeed, increasing the design R factors will cause a reductionin overstrength, hence it should be performed gradually and assessment of ensuingstructures should be rigorously carried out. For regular frame buildings designed tomedium and high ductility levels, an increase between 30-40% may be applied.

It may be argued that the conclusion drawn above regarding the available pos-sibilities to increase the force reduction factors of EC8 s subject to the modellingassumptions, ground motions and adopted performance criteria. However, the o bserved high force reduction factors "supply" compared with the values adoptedby the code show clearly the over-conservatism of the code and the possibility ofincreasinghe.he recommended increase to EC8 force reduction factors is s u pported by the fact that other major seismic design codes such as the US codesadopt higher R factors. For instance, the upper limit of R adopted by the NEHRP


33/36

270 A . M. Mwafy 8 . S. Elnashai

provisions (FEMA 273, 19971 is 60% higher than that of EC8. This lends weightto feasibility of the modifications suggested here. F d y , t should be noted thatEC8 values were also obtained from analysis, but using less rigorous analysis andassessment approaches.

6. ConclusionsRigorous approaches were adopted to calibrate t+e force reduction factors recom-mended by modern seismic codes. A wide range of RC buildings and extensiveperformance criteria including shear have been utilised. Inelastic pushover and s erim of timehistory analyses up to collapse have been undertaken. Eight naturaland artificial records scaled to different levels of velocity spectrum intensity havebeen employed. The effect of the vertical pound motion on the force reductionfactors has been also investigated. The following conclusions, which are applicableto a large class of RC building, are drawn based on this investigation:

The importance of including shear as a failure criterion and vertical ground m etion in seismic assessment and calculations of the force reduction factors is provenin this study. For frame buildings designed to low levels of ductility, the shearfailure criterion is the controlling parameter that defines the intensity of groundmotion at first indication of member failure. The vulnerability of beams designedto low ductility to thi s type of failure is a serious issue. In several cases, verticalground motion reduces the PGA that causes yield or collapse. It also reducesthe mean values of the force reduction factors by up to la%, leading to higherseismic design forces.Although dual structural systems are efficient in eliminating the lateral drift, theadvantages of utilising structural systems with more uniform st&ess distributionare confirmed here. The relatively high energy dissipated in the coupling beamsand the wall base, their vulnerability to shear failure and the lowest R factorsupply-tsdesign ratio obtained for this structural system reinforce this conclu-sion. Ln regular frame structures, plastic hinges and critical concrete strains occurin beams earlier than columns and the demand tends to be distributed uniformlybetween different lateral force resisting systems.. mongst other global collapse criteria, the interstorey drift is the collapse param-eter that controls the response of buildings designed to modern seismic codes.For moment resisting frames, the critical concrete strain is generally exceededmarginally before the global ID collapse, reflecting the importance of utilisingboth criteria in assessment. Due to the efficiency of the lateral force resistingsystem of hybrid structures in controlling deformations, the ID collapse criterionis attained at notably high intensity levels. Member ductility criterion is morecritical for this type of structural system.High supply-to-design force reduction factors utilising refined definitions of Rare observed for all buildings investigated here. This implies that R factors canbe increased without adverse effects on structural safety. The satisfactory safety


34/36

Calibmtion of Forte Reduction F actors of RC Building3 271margins observed at the design and twice the design intensities and the highground motions required to achieve collapse confirm the reliability of the buildingsand support increasing Z& factors. Buildings designed to higher ductility levelsand lower PGA exhibit higher R factors. This implies that th e effect of the designPGA should be incorporated in the expression of f i n d e similar to the inclusionof the effect of ductility.

0 The lowest force reduction factors are observed in frame-wall buildings, whichindicate a possibility to increase &ode by up to 70%.However, applying relativelylower increase than th at observed here is recommended due to the sensitivity anddependence of this structural system on walls. Regular frame buildings designedto ductili ty class "High" and "Medium" exhibit the highest force reduction factors"supply", hence their kOdeaIues may be safely increased further. For framestructures designed to low ductility levels, particularly irregular systems, shearstrength and ductility of beams and cut-off vertical elements should be enhancedand a more modest increase in the force reduction factors than those suggestedfor regular frame buildings designed to higher levels of ductility is recommended.The established firm relationship between the force reduction and the over-strength factors suggests applying a gradual increase in &,de factors and rigorousassessment of the performance of buildings designed accordingly. It is suggestedto increase factors initially by 10-20% for hybrid struc tures and by 3 W 0 %for regular frame systems designed to medium and high ductility levels.Whereas significant increase in R factors is recommended above, the suggestedmargins remain adequately conservative. Adoption of the above proposals would

render EC8 a more economic code, without jeopardising the reliability and safetyof the ensuing buildings.

ReferencesApplied Technology Coyncil (ATC) [I9951 L'Structural esponse modification factors," Rep.No. ATC-19, Redwood City, California.Applied Technology Council (ATC) (19951 "A critical review of current approaches toearthquake resistant design," Rep. No. ATC-34, Redwood City, California.Associate Committee on the National Building Code, 1995, "National Building Code ofCanada (NBCC)," National Research Council of Canada, Ottawa, Ontario.Balendra, T., Tan, K. and Kong, S. (19991 'Vulnerability of reinforced concrete frames

in low seismic region, when designed according to BS 8110," Earthq. Engrg. Struct.Dyna. 28(11), 1361-1381.Borzi, B. and Elnashai, A. S. [2000] Refined force reduction factors for seismic design,"Engq. Struct. 22(10), 1244-1260.Elnashai, A. S. and Elghazouli, A. Y. [I9931 [[Performanceof composite steel/concretemembers under earthquake loading, Part I: Analytical model," Earthq. Engq. Struct.Dyn. 22(4), 315-345.

Elnashai,A. S. and Izzuddin, B. A. [I9931 "Modelling of material non-linearities in steelstructures subjected to transient dynamic loading," EarUlq. Engrg. Struct. Dyn. 22,509-532.


35/36

Elnashai, A. S. and Broderick, B. M. [I9961 "Seismic response of composite frames- I.Calculation of behaviour factors," E m . Struct. l8 (9), 707-723.

Elnashai, A. S. (2000) "Advanced Inelastic Static (Pushover) Analysis for Seismic Designand Assessment," The Gemye Penelis Symposium, niversity of Thessaloniki, Greece.Elnashai, A. S. and Mwafy, A . M. (20011 "Overstrength and force reduction factors ofmulti-storey RC buildings,"accepted for publication in The Structural Design of TallBuildings, March 2001.

~urocode [I9941 "Design of concrete structures. Part 1," CEN (Comite Europeen deNormalisation), European P res tan dar d ENV 1998-1-1, Bruxelles.

Eurocode 8 [I9941 "Design provisions for earthquake resistance of structures . Part 1-1,1-2,and 1-3," CEN (Cormte Europeen de Normalisation), European Pre-standard ENV1998-1-1, 1-2, and 1-3, Bruxelles.

Fardis, M. N. [I9941 "Analysis and Design of 26 Reinforced Concrete Buildings Accordingto Eurocodes 2 & 8,"Configuration -3, 5 and 6, Report on Prenormative Research inSupport of Eurocode 8.

Federal Emergency Management Agency (FEMA) [I9971 "NEHRP provisions for the seis-mic rehabilitation of buildings," Rep. FEMA 273 (Guidelines) and 274 (Commentary),Washington, D. CReeman, S. A. (19901 "On the correlation of code forces to earthquake demands," P r eceedings 4th U.S.-JapanWorkshop on Improvement of Building Structural Designand Construction Practices, ATC-153 Report, Applied Technology Council, Red-wood City, California.

IAEE (19921 "Earthquake resistant regulations, a world list," International Associationfor Earthquake Engineering, Tokyo, Japan.

Izzuddin, B. A. and Ehashai, A. S. [I9891 "ADAPTIC- A program for static anddynamic analysis of structures by adaptive mesh refinement, user manual," ESEEReport 8917, Imperial College, London, UK .

Krawinkler, H. and Seneviratna, G.D.P.K.I9981 "Pros and cons of a pushover analysisof seismic performance evaluation," Engfg. Struct. 20(4-6), 452464.

Martinez-Rueda, J. E. and Elnashai, A. S. (19971 "Confined concrete model under cyclicload," Mat. SCruct. 30(197), 13S147.

Miranda, E. and Bertero, V. V. [I9941 "Evaluation of strength reduction factors forearthquakeresistant design," Earthq. Spectra 10(2), 357-379.Mwafy, A. M. [2001] "Seismic performance of codedesigned RC buildings," PhD Thesis,

Imperial CoUege, London, UK.Mwafy, A. M. and Elnashai, A. S. [2001] "Static pushover versus dynamic collapse analysis

of RC buildings," Engrg. Struct. 23(5), 407-424.Newmark, N. M. and Hall, W. J. [1982] "Earthquake spectra and design," Earthq. Engrg.Res. Institute, BerkeIey, California.

Ozcebe, G. and Saatcioglu, M. [l989] "Hysteretic Shear Model for reinforced ConcreteMembers," J. Struct. Engrg. ASCE 1 1 5 , 133-148.

Papazoglou, A. J. and Elnashai,A. S. [I9961 "Analytical and field evidence of the dam-aging effect of vertical earthquake ground motion," Earthq. Engrg. Struct. Dyn. 25,1109-1137.

Priestley, M. J. N., Verma, R.and Xiao, Y. (19941 "Seismic shear strength of reinforcedconcrete columns," ASCE 120(8) , pp. 2310-2329.

Salvitti, L. M. and Elnashai, A. S. [I9961 "Evaluation of Behaviour Factors for RC Build-ings by Nonlinear Dynamic Analysis," Proceedings 11 WCEE ,Acapulco, Mexico.


36/36

Calibrntion of Fone Reduction Factors of RC Buildings 373Standards New Zealand [1992] "General st ructural design an d design loadings for build-

ings," NZS'4203:1992, Standards New Zealand, Wellington.Uniform building code [I9971 International Conference of Building officials, Whittier,

California.Vidic, T., Fajfar, P. and Fischinger, M. 19941 'Consistent inelastic design spectra:

Strength and displacement," Earthq. Engrg. Struct. Dyn. 23(2), 507-521.

98269174 calibration of force reduction

Documents