Evaluation of Egyptian Seismic Code Implications and System Configuration Effects

8/13/2019 Evaluation of Egyptian Seismic Code Implications and System Configuration Effects

1/13

Engineering Structures 32 (2010) 23942406

Contents lists available atScienceDirect

Engineering Structures

journal homepage:www.elsevier.com/locate/engstruct

Assessment of RC moment frame buildings in moderate seismic zones:Evaluation of Egyptian seismic code implications and systemconfiguration effects

S.S.F. Mehanny a,, H.A. El Howary b

a Structural Engineering Department, Cairo University, Egyptb Structural Engineer, DAR Al-Handasah, Cairo, Egypt

a r t i c l e i n f o

Article history:

Received 4 November 2009

Received in revised form

21 February 2010

Accepted 4 April 2010

Available online 7 May 2010

Keywords:

RC moment framesDuctile

Moderate seismic zones

Codes

Response modification factors

a b s t r a c t

Building code restrictive seismic design provisions and building systems type and configuration haveremarkable implications on seismic performance of reinforced concrete moment framed structures.Seismic assessment of ductile versions of low- to mid-rise moment frames located in moderate seismiczones is carried out through comparative trial designs of two (4- and 8-story) buildings adoptingboth space and perimeter framed approaches. Code-compliant designs, as well as a proposed modifiedcode design relaxing design drift demands for the investigated buildings, are examined to test theireffectiveness and reliability. Fragility curves for the frames are generated corresponding to various code-specified performance levels. Code preset lower or upper bounds on either design acceleration or drift,respectively, that would control the final design are also addressed along with their implications, ifimposed, on the frames seismic performance. The trial design study demonstrates that built-in staticoverstrength is generally larger for space frames than for perimeter frames, whereas the force reductionattributable to inelastic dynamic responsediffersfrom one frame type to the otherfor various investigated

heights and for different target performance levels. Nonetheless, all trial designs are shown to meet theminimum performance implied by building codeprovisions but withvaryingmargins. However,the studysuggests that more consistent reliability for designed structures can be achieved by disaggregating theforce reduction factorinto its static and dynamic parts and that code default valuesof this factor forsomebuilding types would be better reduced for a more reliable performance.

2010 Elsevier Ltd. All rights reserved.

1. Introduction

Performance-Based Design (PBD) is now widely recognizedas the pre-eminent seismic design methodology for structures.The advent of PBD methodologies now requires that engineersdevelop code-compliant structures that also achieve specific

performance objectives. Accordingly, it is necessary to developefficient designs with predictable seismic response. To this day,the seismic designs of most general and some complex buildingstructures are performed with Force-Based Design (FBD) method.This method is conceptually straightforward and thus appealing,but relies heavily upon unique, semi-empirical, force reductionfactors and displacement equivalences for a selected lateral forceresisting structural system. These factors are largely based onconsensus opinion of code committees. The FBD methodology may

Corresponding author. Tel.: +20 12 444 8008.E-mail addresses:[email protected],

[email protected](S.S.F. Mehanny).

yield life-safe designs in most cases; however, its ability to deliverdesigns that achieve specific performance objectives remains inquestion. These issues of life safety and predictable response areaddressed in this paper through an investigation of a modern-dayFBD code.

Earlier efforts in this direction include but are not limited

to the work by Mehanny et al. [1] and Rivera et al. [2]. Theformer [1] was mainly geared towards calculating estimates offorce modification and displacement amplification factors (R andCd , respectively, known asR and Rd in ECP 201 [3], and q and qdin EC8[4]) for composite RCS and Steel moment frames designedas per US standards (e.g., [5,6]), and comparing them to theircorresponding values specified in the adopted design codes inorder to assess how such provisions were successful to deliversafe, reliable and economic designs. On the other hand, therecent work by Rivera et al. [2] focused on trying to furnish ananswer to the question that naturally arises: Are FBD provisionsof modern seismic codes compatible with PBD objectives?. Theytherefore investigated the predictability of response and marginof safety of trial designs of regular medium ductility RC moment

0141-0296/$ see front matter 2010 Elsevier Ltd. All rights reserved.doi:10.1016/j.engstruct.2010.04.014
http://www.elsevier.com/locate/engstructhttp://www.elsevier.com/locate/engstructmailto:[email protected]:[email protected]:[email protected]://dx.doi.org/10.1016/j.engstruct.2010.04.014http://dx.doi.org/10.1016/j.engstruct.2010.04.014mailto:[email protected]:[email protected]://www.elsevier.com/locate/engstructhttp://www.elsevier.com/locate/engstruct


2/13

S.S.F. Mehanny, H.A. El Howary / Engineering Structures 32 (2010) 23942406 2395

framed structures designed according to [4]. Their assessmentwas performed by comparing the design displacements and forcesfor these frames to those obtained from nonlinear time historyanalysis.

The current paper is an additional effort along the same frontierlooking into semi-empirically based key factors R and Rd usedfor FBD procedures. The research focuses though on investigatingonly low- to mid-rise ductile RC moment resisting frames locatedin moderate seismic zones (0.25 g), and further studying theimplications that the frames configuration (perimeter versusspace frames) may have on theoverall response.Seismic provisionsof interest for this study are the emerging Egyptian seismicprovisions [3] thatare largely compatiblewith EC8 maindirections.The ultimate goal is to evaluate the current code-specified R andRdfactors, and to eventually improve the reliability of constructedfacilities designed using FBD methodologies.

Four Code-Compliant-Design (CCD) versions of RC ductilemoment resisting frame buildings (4-, and 8-story, adoptingperimeter and space frames configurations) are developed usingECP 201-FBD provisions.Using nonlinear analyses involving inelas-tic static pushover analysis and incremental dynamic time historyanalysis under a suite of 20 multi-level scaled records, static and

dynamic contributions to inelastic force reduction are identifiedand compared to code/regulations-specifiedassumptions. Fragilitycurves for the frames are also developed corresponding to variousuniversally code-specified performance levels encompassing, forexample, Immediate Occupancy (IO), Life Safety (LS) and CollapsePrevention (CP) as identified by FEMA 356 [7]. Generated informa-tion facilitates retrieving relevant actual inherentR andRd factorsand comparing them to code pre-specified values adopted earlierin theFBD process. A Modified Code Design(MCD)procedure relax-ing design drift demands for the investigated buildings (and henceovercoming a specific deficiency in the current requirementsof theECP 201 seismic provisions as will be demonstrated in what fol-lows) is proposed in the current research and is further examinedto test its effectiveness and reliability.

2. Outlines and specifics of the seismic design procedures

The main design requirements specified in [3] are the no-collapse and the damage limitation requirements. Satisfyingtheno-collapse requirement depends mainly on the strength of thedesigned elements to resistall expected stress resultantsthat occurdueto theseismic actions. Designseismic actions correspond tothereference seismic hazard associated with a reference probabilityof exceedance of 10% in 50 yrs (or a reference return periodof 475 yrs). In a complementary step, and in line with EC8regulations[4], the structure shall be also checked to withstanda seismic action having a larger probability of occurrence (minorearthquake) than the design seismic action associated with the

no-collapse requirement, without occurrence of damage tostructural and non-structural elements. Such seismic action is usedto verify the damage limitation requirement. It has a probabilityof exceedance of 10% in 10 yrs (or a return period of 95 yrs) andis almost equal to half of the design seismic action for the no-collapse limit state taking into account the importance factor ofthe building. As per code, the damage limitation requirement issatisfied if the interstory drifts are limited to a given fraction ofthe story height depending on the type and fixation form of thenon-structural elements. The interstory drift associated with thedesign seismic action for the no-collapse limit state has thusto be first reduced to take into account the lower return periodof the seismic action associated with the damage limitationrequirement. Implicit in the use of this reduction is the assumption

that the response spectrum of the seismic action for the no-collapse requirement has the same shape as the spectrum of

the seismic action for damage limitation requirement (i.e., thelatter is a scaled down replica of the former). For buildingsinvestigated herein, this reduction factor, , istaken equal to2.0 [3]and the interstory drift limit is set to 0.5% associated with non-structural elements of brittle materials that are attached to thestructure. It is worth pointing herein that in other similar seismicprovisions commonly adopted worldwide especially in the USpractice (such as in[5,8,9]), instead of performing the drift checksfor a minor earthquake with a larger probability of occurrence(10% in 10 yrs) than the design level earthquake used for strengthchecks (i.e., the 10% in 50 yrs event), and accordingly reducing theinterstory drift limit or capacity (e.g.,0.5%), they ratherperform thedrift (and strength) check(s) for one same design level earthquakeof 10% in 50 yrs but with a magnified interstory drift limit. Thismagnified limit is roughly equal to the limit set by Eurocode (as aratio of the story height) times the factor mentioned above. Inother words, even though different codes apparently approach thesame task from different perspectives, they are basically more-or-less heading towards the same target.

Note that, furthermore, in order to avoid excessively low designacceleration values (and hence potentially non-conservativedesigns in terms of lateral strength/resistance) for medium- to

long-period structures that may arise from inaccurate modeling,and again similar to Eurocode directions in that concern, ECP 201is imposing a constant minimum design acceleration of 0 .2ag.Such enforced lower bound sometimes introduces too muchconservatism into the design which will be examined in the courseof this research.

Two seismic design scenarios are performed in this paper onfour case study buildings. The buildings consist of 4- and 8-storymoment framed ductile RC structures adopting either space orperimeter frames systems. The two seismic design procedures aredepicted below:1. Code-Compliant Design (CCD):

It is a design procedure where (1) no-collapse in termsof satisfying strength of different structural elements consideringsecond-order effects and (2) damage limitation in termsof satisfying code interstory drift limits under reduced hazard requirements are jointly satisfied.Code Design Response Spectrum(DRS) modified by the response modification factor, R, as shown inFig. 1(a) and featuring the constant acceleration lower bound of0.2agis adopted.2. Modified Code Design (MCD):

It is a modified (more relaxed) seismic design procedurethrough ignoring the code pre-specified constant accelerationlower bound when checking drift demands. This concept is notuncommon in well established international seismic design pro-visions (e.g.[5,8,9]). In other words, checking drift is carried outfor a scaled down version of the code acceleration Elastic ResponseSpectrum (ERS) associated with 10% in 50 yrs hazard as shown inFig. 1(a) by directly dividing its ordinates by the R factor, as well

as by a reduction factor = 2.0 [3]accounting for the lower re-turn period(corresponding to a 10% in 10 yrshazard) of theseismicaction associated with the code damage limitation requirement,then magnifying it back by a displacement behavior factor, Rd, ap-proximately equal to 0.7R [3]. The resulting Modified Elastic Re-sponse Spectrum, MERS [=ERS(1/)(Rd/R)]used forcheckingdrift and developed in the context of this step is shown inFig. 1(a)for comparison purposes. This proposed step entirely discards anyeffect on seismic design drift demands that may arise from thelower bound of 0.2agon the design acceleration specified by codeand reflected into the code DRS. However, the no-collapse re-quirement is still verified for the code acceleration DRS with thelower bound on the design acceleration. MCD procedure, despitebeing a code non-compliant design procedure, is promoted herein

since it provides potentially economic versions of the case studybuildings yet without risking safety as will be demonstrated later.


3/13

2396 S.S.F. Mehanny, H.A. El Howary / Engineering Structures 32 (2010) 23942406

(a) Acceleration response spectra as per ECP 201. (b) Displacement spectra.

Fig. 1. ECP 201 elastic and design acceleration response spectra and interpretation of design spectral displacement curves with and without an upper bound limit on

displacement.

3. Egyptian code (ECP 201) versus Eurocode (EC 8) seismic

design provisions

It is worth noting that ECP 201 is more liberal than EC8 inselecting the R factor that is set to a value of 7 in the former for

ductile RC moment resisting frames. EC8 assumes instead a valueof 5.85 for the behavior,q, factor (equivalent to ECP 201R-factor).This value of 5.85 that accounts for energy dissipation capacityas per Eurocode wording is calculated for a multi-story multi-baymoment resisting frame system pertaining to the high ductilityclass (DCH). On the other hand, both codes rely on linear analysisto estimate the actual expected displacement, ds, induced by thedesign seismic action at a given point within the structure throughthe following simplified expression:

ds = Rdde (1)

where de is the displacement of the same point as determinedby a linear analysis based on the design response spectrum(DRS); and Rd is a displacement behavior factor. Rd (or qd

in [4]) is approximately assumed by the Eurocode equal to R(or more precisely q) in line with the commonly recognizedequal displacement rule, whereas ECP 201 is assigning to Rd areduced value of 0.7R. Such reduction could be justified by thelarge (relaxed) value ofR (=7) assumed to determine the designbase shear used throughout the strength design of the frames.The validity and effectiveness of these values to mimic actualresponse will be assessed in what follows when retrieved relyingon pushover nonlinear inelastic static analyses and incrementaldynamic analyses performed in the current research.

Another point to highlight is the reason for promoting the MCDprocedure introduced in this work as a potentially useful andcorrectivemodification to ECP 201 seismic design provisions. MCDprocedure, outlined in the previous section, draws its threshold

from the note spelled out in[4] stating that the value ofds doesnot need to be larger than the value derived from the elasticspectrum. The fundamental role of this note for buildings withrelatively medium to long periods is to avoid the effect of the 0.2aglower bound enforced in the code acceleration DRS that producesincreasingly larger spectral displacements compared to the case ofsimply adopting the ERS [2], which is physically not possible. Forillustration purposes, one may refer to Fig. 1(b) showing the trendsof the spectral displacement, SD, curves and their interpretation forthe following two cases. The first is if this limit on ds is equallyimposed in ECP 201 as in EC8; this is equivalent to applying Eq.(2)below while computing SD,DRS (that is the spectral displacementbased on the code acceleration DRS corresponding to the 10% in50 yrs hazard, Sa,DRS) but with the limitation that the resulting

value should not exceed SD,ERS calculated based merely on thecode acceleration ERS (also associated with the 10% in 50 yrs

hazard) as per Eq.(3).Applying this upper bound, or limitation, ismore-or-less compatible for medium- to long-period structures with the MCD procedure promoted in this paper since the latterdirectly adopts the code acceleration ERS or more precisely itsmodified version MERS (instead of theDRS) forchecking drift and

accordingly ignores the 0.2aglower bound as previously stated.Conversely, the second curve shown in Fig. 1(b) refers to thesituation when this limit on dsis instead ignored; this is equivalentto likewise applying Eq.(2)to calculate the spectral displacementbut overlooking the upper bound value of SD,ERS as is currentlythe case in [3]. This results in unbounded, and hence unrealistic,values for the spectral displacements for medium- to long-periodstructures. Note that Eq. (2)is equivalent to simply stating thatRd/R 1.

SD,DRS= RdSa,DRS(T/2)2 SD,ERS (2)

SD,ERS = Sa,ERS(T/2)2. (3)

From another perspective, one maytherefore consider the MCDprocedure introduced in the previous section as directly usingthe ERS corresponding to the 10% in 10 yrs hazard (obtained byreducing the code acceleration ERS associated with the design-basis earthquake of 10% in 50 yrs hazard by a factor of 2 asillustrated above) while estimating design drift demands. Suchcalculated drift is yet to be further reduced by a factor of 0.7 [ 3]inorder to get the actual expected displacement, ds, induced by thedesign seismic action. As such the Equal Displacement Rule (EDR)is notactivated (conversely to [4]) andthe estimation of actualdriftishence still along the samebase lineof[3]. Notethat the notionforreducing the displacement factor,Rd, as adopted in [3]is likewisefollowed by other world-widely recognized seismic provisions andstandards such as [5,9] setting this factor equal to approximately0.69(=[Cd = 5.5]/[R = 8]) times R for RC special (i.e., ductile)moment resisting frames. Although ECP 201 [3]draws most of its

background from EC8[4], it may nevertheless have set Rd = 0.7R(and thus notliterally following theEDR adopted by EC8provisionsthat simply setqd = q) to counter-account for the larger value ofR = 7 used a priori for the design of ductile RC moment framesversus the smaller value ofq = 5.85 set by EC8 for the seismicdesign of the same type of frames. Among the major objectives ofthis paper is therefore to assess the effect that such upper boundnote statedin [4] (or, the proposed MCD procedure) regarding driftestimation may have on the reliability/safety versus economy ofductile RC momentframes of eitherthe space or theperimeter typewhen located in moderate seismic zones.

4. Case study building design

The case study building (see structural plan in Fig. 2) is de-veloped according to the general layout of a theme structure


4/13


24000

6000

6000

6000

6000

24000

6000600060006000

24000

Fig. 2. Layout (plan) of the case study buildings case of PFB (dimensions shown

are in millimeters).

proposed for this research work. It is designed as a 4- and8-story building in moderate seismic region according to appro-priate portions of relevant codes and standards[3,10]. RC ductileframed designs are developed first employing a space frame con-figuration where thelateral systemconsists of five moment framesin each direction. Another framed design is then developed usinga perimeter frame approach as common, for example, in the USpractice [11] where only perimeter frames constitute the lateralresisting system.

A typical floor height of 3 m is adopted whereas the ground

floor is 5 m high. Buildings layout is essentially bi-symmetricin plan, square in shape with a typical bay width of 6 m inboth directions, and is representative of benchmark typical officebuildings in current practice in Egypt. For gravity load design,dead loads include the self-weight of the structure, a typicalfloor cover of 1.5 kN/m2 and partition (wall) loads intensityof 1.5 kN/m3 including plastering and assuming typical wallsthickness of 250 mm. A live load of 5.0 kN/m2 is also considered.On the other hand, for seismic design purposes, a total seismicmass including self-weight and floor cover plus 50% of live loadis considered. The seismic design has been carried out assuming asoil type B as per[3,4] referring to dense/stiff soil, an importancefactor of 1.0 and a seismic zone 5 (as per Egyptian zoning system)with a design ground acceleration, ag, of 0.25 g associated with the

code reference probability of exceedance of 10% in 50 yrs. CodeaccelerationERS type 1 is adopted [3]knownastype2in [4]andis shown inFig. 1(a) for the case study buildings. For comparisonpurposes, also shown inFig. 1(a) is the code DRS used for elasticanalysis of the buildings after introducing a lateral force reductionfactorRof 7.

A solid slab is used at all floors with a designed constantthickness of 140 mm. All columns and beams dimensions andreinforcement are as shown in Tables 1 and 2. Reinforcingsteel used has a minimum guaranteed (i.e., nominal) yieldstrength of 360 MPa, and concrete has a minimum specifiedcube characteristic strength in compression of 30 MPa. For designpurposes using FBD methodology and linear elastic analysis,cracked members properties are adopted as per recommendations

in [3]; 70% of the gross inertia is used for columns while 50%of the gross inertia is used for beams. Furthermore, the current

trial designs have considered the first interior frame in the SpaceFrame Building (SFB) configuration (i.e., the one adjacent to theedge frame) believed to be the vulnerable frame of interest worthto be studied when only a two-dimensional analysis of a singlerepresentative critical frame is sought for this space framebuilding.This decision wastaken dueto thelarger tributarygravityloads and seismic mass of this selected interior frame relative tothe edge one residing along the perimeter of the building, alongwith an associated larger contribution from the design accidentaleccentricity relative to the most inner frame located on the axis ofsymmetry of the buildings footprint with basically no eccentricityeffects. As a result, and as per the recommendations in [3] (similarto requirements set in[4]) for the design for minimum accidentaleccentricity, the design base shear for this selected frame has beenincreased by 15%, while the design base shear for the perimeterframe in the Perimeter Frame Building (PFB) configuration alsoinvestigated in this research has been increased by 30%. Suchfactor will add to the intrinsic (actual) overstrength of the variousmoment frames considered herein but with different magnitudesand effects thereof as will be highlighted in what follows.

All case study moment frames designed satisfy the minimumstrength, stiffness (drift), and strong columnweak beam require-

ments specified in [3]. Members (columns and beams) sizes inboth CCD and MCD procedures were controlled nearly exclusivelyby drift requirements whereas only the design of the 4-story SFBframe has been marginally controlled by the strength require-ments undergravity loadsfundamental ultimate combination. Thisresulted in having the 4-story MCD-SFB frame a replica of the4-story CCD-SFB frame. Calculated fundamental period of vibration(and second lateral mode period) along with the associated modalmass ratiosrelativeto thetotalconsidered seismic mass forall casestudy framesare given in Table 3 forboth CCDand MCDproceduresfor future relevance in the seismic assessment study.

From design data reported in Tables 1 and 2, it may be observedthat CCD procedure constantly results in heavier mid-rise framescompared to the MCD procedure (1.43 times heavier for 8S-PFB

and 1.2 times for 8S-SFB). This is a straight outcome of relaxingdesign drift demands for the proposed MCD technique. This ratiois however reduced for investigated low-rise frames scoring onlya value of 1.12 for 4S-PFB and a straight 1.0 for 4S-SFB (literallyspeaking CCD and MCD result in exactly the same frame forthe 4S-SFB building). From another perspective, PFB frames areconsistently heavier than their equivalent SFB frames irrespectiveof the adopted design technique (CCD versus MCD), especially forlow-rise buildings investigated herein. For example, 4S-CCD-PFBand 4S-MCD-PFB frames are 1.35 and 1.2 times heavier than4S-CCD-SFB and 4S-MCD-SFB frames, respectively. This could beinferred from the relevant larger lateral seismic mass assigned tothe perimeter frames compared to the equivalent space framesfor a particular building configuration. This ratio is reduced to

only 1.2 for mid-rise 8S-CCD buildings. It is further noted thoughthat 8S-MCD-PFB frame (as designed) has almost same overallweight relative to the 8S-MCD-SFB frame. Moreover, referring toTable 3,and in harmony with the observations made above in thisparagraph, it may be noted that MCD technique furnishes framesthat are fairly more flexible (i.e., having longer period of vibration)than their equivalent CCD frames. In addition, whether adoptingthe CCD or the MCD procedure, PFB frames consistently featurelonger periods than their equivalent SFB frames for both low- andmid-rise buildings investigated herein.

5. Selected ground motion records

A binof 20ground motions is selected forthe seismic evaluation

study presented in this paper. The 20 records pertain to thelarge database of records gathered in [12] and are originally


5/13


Table 1

Sizes and reinforcement of structural members of CCD case study moment frame sa.

Building type Outer columns Inner columns Beams

Story # Size (mm) Reinf. Story # Size (mm) Reinf. Story # Size (mm) Reinf.

4S-PFB 14 600 600 1220 12 400 1100 720 14 300 1000 425

34 400 1000 620

4S-SFB

14 400 400 1216 12 700 700 1620 14 250 800 42034 600 600 1220

8S-PFB

18 500 500 1216 13 500 1500 825 14 300 1100 62546 500 1400 725 58 250 900 62078 400 1300 525

8S-SFB

18 500 500 1216 13 800 800 2020 14 250 1000 52046 700 700 1620 58 250 900 42078 600 600 1220

a Reinforcement shown in tables for all columns with a square cross-section represents the total number of re-bars to be distributed equally along the 4 sides, while that

for columns with a rectangular cross-section represents the number of main re-bars per each of the two opposite shorter sides of the cross-section, i.e., in the direction

resisting the bending moment in the frame direction; additionalsecondaryre-bars are placed along the longer sides. Reinforcement given for beams represents the number

of re-bars used per each side (top and bottom) of the beams cross-section. Beams have symmetric reinforcement to accommodate expected reversible bending momentsduring seismic events.

Table 2

Sizes and reinforcement of structural members of MCD case study moment frame sa.

Building type Outer columns Inner columns Beams

Story # Size (mm) Reinf. Story # Size (mm) Reinf. Story # Size (mm) Reinf.

4S-PFB 14 600 600 1220 12 400 900 620 14 300 900 720

34 400 800 6204S-SFB A replica of the 4S-CCD-SFB moment resisting frame

8S-PFB

18 500 500 1216 13 400 1100 820 14 300 1000 82046 300 900 716 58 250 700 72078 300 600 516

8S-SFB

18 500 500 1216 13 800 800 2420 14 250 800 72046 600 600 1620 58 250 700 62078 400 400 1216

a Reinforcement shown in tables for all columns with a square cross-section represents the total number of re-bars to be distributed equally along the 4 sides, while that

for columns with a rectangular cross-section represents the number of main re-bars per each of the two opposite shorter sides of the cross-section, i.e., in the direction

resisting the bending moment in the frame direction; additionalsecondaryre-bars are placed along the longer sides. Reinforcement given for beams represents the number

of re-bars used per each side (top and bottom) of the beams cross-section. Beams have symmetric reinforcement to accommodate expected reversible bending moments

during seismic events.

Table 3

Period and associated modal mass ratio for fundamental and second mode ofvibration for case study moment frames from modal analysis.

Building type Fundamental mode of

vibration

Second mode of vibration

Period (s) Modal mass

ratio (%)

Period (s) Modal mass

ratio (%)

Moment frames as per CCD procedure

4S-CCD-PFB 1.01 92.9 0.31 5.8

4S-CCD-SFB 0.83 92.9 0.24 5.9

8S-CCD-PFB 1.52 81.2 0.54 12.9

8S-CCD-SFB 1.37 86.9 0.49 9.4

Moment frames as per MCD procedure

4S-MCD-PFB 1.22 93.5 0.38 5.4

4S-MCD-SFB 0.83 92.9 0.24 5.9

8S-MCD-PFB 2.01 80.6 0.80 14.6

8S-MCD-SFB 1.65 82.6 0.63 11.2

extracted from the PEER (Pacific Earthquake Engineering Center)Strong Motion Database (PEER Strong Motion Catalog). The groundmotions represented by the records are characteristic of non-near-fault motions recorded in California. They all have magnitudesMwless than 6.5 and have been identified by the PEER database asSmall Magnitude (SM) records. Furthermore, the selected recordsconsidered hereinfeature a distance R to thefaultthatis largerthan30 km, and are hence recognized by the PEER database as LargeDistance (LR) records. In brief, this bin of records has been referredto by the PEER as a Small Magnitude Large Distance (SMLR) bin.All twenty ground motions were recorded on NEHRP soil types C

or D (stiff soil or soft rock) sites. These records were extensivelyused in several earlier studies related to building structures

1.0

0.8

0.6

0.4

0.2

0.00.0 0.5 1.0 1.5 2.0 2.5 3.0

Period, T [sec]

Sa

[g]

Fig. 3. Elastic acceleration response spectra for the 20 SMLR unscaled selected

records5% damping.

[1214] aswell asto bridges [15]. For specific details of the recordsincluding earthquake names, sensor location, magnitude, distance,soil type, faulting mechanism, and peak waveform ordinates, onemaybe referred to [12]. For completeness, Fig.3 shows accelerationresponse spectra curves for these 20 selected unscaled records.

6. Analytical models for case study moment resisting frames

In order to perform inelastic nonlinear static pushover anddynamic time history analyses, computer models of the as-designed buildings are required. The structural analysis platformOPENSEES [16] is used to determine structural response of thecase study moment resisting frames. Among the main features ofthe analytical models adopted in this research are (1) the use ofnominal (minimum specified) material property values rather thanexpected ones; (2) confined concrete response as per the uni-axial

KentScottPark model with degraded linear unloading/reloadingstiffness according to the early work of Karsan and Jirsa [17]


6/13


with no tensile strength, and using confined concrete parametersas illustrated in [18]; (3) steel reinforcement uni-axial bilinearmaterial model with kinematic strain hardening; and (4) hystereticbehavior in the form of distributed plasticity integrated alongthe length of two-dimensional beamcolumn elements using afiber-element model available in OPENSEES library. For more datarelated to these issues, the reader may be referred to[16,19].

Beam-column element with a displacement-based formula-tion is adopted to model both beams and columns of thetwo-dimensional moment resisting frames studied herein. P(i.e., second-order geometric) transformation is activated.Displacement-based elements assume cubic displacement shapefunctions and present distributed plasticity. Such formulation thusapproximates the displacement field within the element. In orderfor this type of element to capture the concentration of plastifica-tion (and consequentlyhigh curvaturegradients at plastic hinge lo-cations), a relatively fine discretization of beamcolumn membersshould be maintained. Good results are expected for elements sizeapproximately equals to the length of plastic hinge. Displacement-based elements are typically used in Finite Elements applications.After carrying out a sensitivity analysis, it has been found thatthe most convenient, reliable and fairly accurate discretization of

beams and columns of the case study moment resisting frames isachieved through using 10 displacement-based elements to modelboth beams and columns with 5 sections per each element and atleast 15 fibers per section depending on each cross-section dimen-sions [19]. This number of elements (and sections per element)captures a reasonable balance between computational issues atone hand and convergence and accuracy of calculated demandsof interest (maximum displacements) at the other hand. Further-more, such fairly dense discretization automatically capturesPin addition toPeffects.

Rayleigh mass and stiffness proportional damping is adopted inthe current study. A damping ratio of 5% has been assigned to thefirst two modes of vibration for all case study frames. It could benoted fromTable 3that modal mass ratios associated with these

two selected modes constitute an overall value that is fairly above90% of the total seismic mass for each investigated frame.

A dummy column (commonly known by a leaning column)is introduced in all PFB frames to account for P effects fromthe tributary gravity loads carried by the non-seismically designedinterior gravity-only columns in this building configuration. Theleaning column technique is based on introducing a set of leaningcolumns connected to the main perimeter frame using rigid links.These rigid links have a moment release condition at their ends.The main function of these rigid links is to push the leaningcolumns with the same lateral sway value of the PFB frame underconsideration at the different floor levels. The leaning columnsthemselves have negligibleinertia along with a large axial stiffness.

7. Static inelastic displacement-controlled pushover analysis

Displacement-controlled inelastic pushover analyses with ge-ometric nonlinearity (P effects) are conducted on two-dimensional base line models for the case study frames usingOPENSEES. Pushover analysis consists of first applying the dis-tributed gravity load (full dead loads and 50% of the design liveload) to the structure and then applying incremental displace-ments to the top of the frame with a given pre-specified distri-bution as per [3] at different floor levels until reaching a giventarget displacement. Note that for the frames of the PFBs, a leaningcolumn as introduced above is modeled in the two-dimensionalpushover analysis to account for the interior gravity columns ofthe PFB that are not part of the lateral resisting system. The per-

centage of the design base shear for each of the case study framesis plotted versus the Roof Drift Ratio (RDR) defined as the lateral

Table 4

Summary of pushover analysis results and static built-in overstrength factors.

Building type o T o = o T IDRmaxat RDR = 2%


4S-CCD-PFB 2.54 1.30 3.30 0.042

4S-CCD-SFB 3.28 1.15 3.77 0.053

8S-CCD-PFB 1.88 1.30 2.44 0.027

8S-CCD-SFB 2.29 1.15 2.63 0.069


4S-MCD-PFB 1.93 1.30 2.51 0.0474S-MCD-SFB 3.28 1.15 3.77 0.053

8S-MCD-PFB 1.16 1.30 1.51 0.082

8S-MCD-SFB 2.30 1.15 2.65 0.032

drift at the top of the frame divided by the frame total height.The maximum value scored by this percentage simply defines theso-called static actual built-in overstrength,o, for each frame asdesigned.Fig. 4(a) gives this relationship for 4- and 8-story SFBand PFB frames designed according to the CCD approach. Fig. 4(b)shows thesame relationshipfor thefour MCDcase study framesforcomparison purposes. Note that in order to properlyrecover baseshear from column shear forces when performing displacement-

controlled lateral analysis withPeffects included, a correctiontechnique is introduced through a post-processing step[20]. It en-tails reducing at each displacement step in the analysis thesum of shearing forces retrieved in the columns by the summationof the horizontal components of the axial loads in these columns.This total horizontal component at the base of the frame is simplygenerally computed by summing the product of the recorded axialforces by the corresponding rotation (small angles approximation)for each column. This rotation is basically obtained by dividing theinterstory lateral drift by the story height. SFBs are generally stifferand less sensitive to P effects in their pre-peak performancecompared to PFBs since the gravity loads are tributary directly tothe lateral resisting system and not through gravity-only interiorcolumns that are non-seismically designed. On the other hand, the

descending branch in the base shearRDR curves (Fig. 4)is thoughgenerally steeper for the SFBs relative to same height PFBs for bothCCD and MCD approaches. This is mainly due to deeper, and hencemore efficient, column sections (in the direction resisting bendingmoments resulting from lateral loading) for the latter, and accord-ingly more detrimental and accelerated post-peak strength dete-rioration for the former due to increasing Peffects associatedwith further lateral pushing of the frames. A summary ofo val-ues for all case study frames is given in Table 4.Reported also inTable 4are maximum Interstory Drift Ratios(IDRmax)recorded atan RDR of 2%.

As a result of having same design base shear for strength cal-culations in both CCD and MCD procedures in conjunction withthe adoption of larger cross sections for the CCD frames to satisfy

restrictive code interstory drift requirements as previously men-tioned, the MCD approach usually yields more flexible (and furtherless strong) frames than these developed using the CCD approach.It may be also generally observed that the actual intrinsic staticoverstrength,o, for space frames is usually larger than that forperimeter frames as expected by intuition; this is mainly the re-sult of the significant effect of considerable gravity loads mobi-lizing more detrimental Peffects for the case of the perimeterframes (captured through the leaning column technique), thus re-sulting in a considerable loss in their lateral capacity relative to thespace frames of same height. This is as well a proof of the strengthdominance in the design, and hence the lateral capacity, of thespace frames compared to the perimeter frames for which drift re-quirements are more importantly controlling the seismic lateral

design. Furthermore, it has been noted that when following theproposed MCD procedure,o, of the 8-story PFB largely decreased


7/13


(a) CCD frames. (b) MCD frames.

Fig. 4. Static inelastic displacement-controlled pushover analysis results for case study frames.

from 1.88 to 1.16 dueto thereduced cross sections dimensions, andthereafter the magnified tortuous effects of the P phenomenon.However, on the other hand, o for 8S-SFB remains almost con-stant for both CCD and MCD approaches. Such observation shows

the relatively lowerPeffects on the lateral capacity of the SFBscompared to the PFBs for these mid-rise RC frames designed formoderate seismic regions, and further reinforces the fact that suchproposed relaxed design technique (MCD) does not penalize thebuilt-in overstrength(i.e.,the strength reserve) forthe SFBs. On theother hand, as shown inTable 4,the inherent static overstrengthremarkably increases with decreasing number of stories for thespace frame construction when following the same design proce-dure (i.e., either CCD or MCD), while it increases less sharply forperimeter frames. This observation is justified since it could beagain directly related to the decrease in the role of the Peffectsfor low-rise buildings along with the gravity dominance in designrelative to lateral drift demands. It is finally worth keeping in mindthat thedesignof almostall frames(except 4S-CCD- andMCD-SFB)is controlled by drift limitations and not by strength requirements.

Another general observation to report is that whenever IDRmaxscores a large value at large RDR, and the associated significantnonlinear demand is localized in a single story, this story is usuallythe ground floor. On the other hand, when the large nonlineardemandis distributed among twoor more stories fora given frame,IDRmax associated with a fairly large RDR is much lower than itsvalue forthe case of localizednonlinear demand. An example couldbe extracted fromTable 4;IDRmaxat 2% RDR scores a considerablylower value of 0.032 for 8S-MCD-SFB relative to the value of 0.069scored for the 8S-CCD-SFB. The latter value is concentrated atthe ground floor with other stories scoring much lower values,while the value of 0.032 for 8S-MCD-SFB is almost constant for thefirst three stories. It is though worth reporting that occasionallyunexpected differences in response could be attributed to humanfactor involving some minor changes in design decisions madethroughout the design process.

Results of the pushover analysis presented above for studiedperimeter and space frames are in line with other recent pub-lished data in [21,22] where low- and mid-rise RC moment framedbuildings have been thoroughly investigated. In addition, simi-lar to results highlighted in[23]where low-rise 3-story one-way(i.e., perimeter) and two-way (i.e., space) steel frames have beenstudied, the current research shows that space frames are stiffer(regarding the elastic stiffness) andstrongerthan their equivalentperimeter frames(Fig. 4). Moreover, Tagawa et al. [23]further re-ported a calculated factor referred to by DCF giving the first storyDrift Concentration Factor that is defined as the first story drift an-gle divided by the roof drift angle. Similar factor analogous to DCFcould be computed from results given in the current paper by di-

viding the IDRmax(reported in last column ofTable 4) by the corre-sponding Roof Drift Ratio of 0.02 (i.e., 2% RDR), and similar trend to

what has been reported in [23] is then observed. In brief, this quo-tient forthe space framesis consistentlylarger than forthe perime-ter frames at this RDR, except for the mid-rise8-story MCD frame.

A point that could be of some importance to justify many of

the results presented herein is that the ratio of gravity to lateraltributary area for the space frame in a SFB is 1.0 while this ratiois much smaller (=0.25) for the perimeter frame in a PFB. Inthe latter configuration, the gravity load of half of the building ismobilizingP effects placing extra demands on this perimeterframe (captured through the leaning column technique).

Generally speaking, results of pushover analyses presentedin this paper reflect the following sources of overstrength:(1) minimum stiffness (drift) criteria, (2) structural redundancy,(3) strong-columnweak-beam criterion, among other sourcescommonly identified in the literature and recognized by seismicprovisions worldwide. In addition to reportedovalues in Table 4,there is an inherent overstrength factor included in the designbase shear calculation in this research. This factor is attributedto the accidental torsion specified by the code as has beenpreviously pointed out in the literature [1]. Accordingly, the actualoverstrength of the frames is higher than the values previouslypresented. Updated (i.e.,adjusted)overstrength value,o , for eachcase study frame is determined as the product ofo and T andis also presented inTable 4.Tsimply refers to the overstrengthintroduced by the accidental torsion. This updated o is theactual overstrength and is the one affecting the response sinceall assessment static pushover and time history analyses hereinare based on a two-dimensional configuration (with no torsionaleffects). This adjustment approach is therefore necessary so thatthe actual R-values, as defined by thecode, canbe extractedrelyingon the time history results presented in what follows. Note thatTtakes different values for SFBs and PFBs since, in the currentresearch, the first interior frame is the one considered for the

former while the perimeter frame is the one investigated for thelatter as mentioned earlier. This will further contribute to the finalconclusions made in this research.

8. Incremental dynamicanalysis, targetperformancelevels and

fragility curves

Seismic performance is further assessed through nonlinear timehistory analyses using the set of 20 SMLR acceleration recordspresented above. For multi-level seismic hazard analyses, it isassumed that the acceleration component of the records canbe linearly scaled based on the spectral acceleration computedat the fundamental period of the structure, Sa(T1). Shomeand Cornell [24] have demonstrated that, compared to other

approaches, scaling based on Sa(T1) will reduce the record-to-record dispersion in the response data and will not bias the results


8/13


especially when the response of interest is the IDR. The spectralaccelerations of the scaled earthquake records, Sa(T1), can berelated to the maximum interstory drift ratio,IDRmax, depicting thepeak response from corresponding time history analyses providingwhat is referred to in the literature as Incremented DynamicAnalysis (IDA) curves [25].

Fragility Curves (FC) constitute a representation of the rela-tionship between (a) the probability of a set of Performance Lev-els (PL), or limit states, being reached or exceeded at a prescribedsystem demand and (b) the system demand itself. For a conven-tional performance-based seismic analysis, the system demandsare typically represented by (or, are corresponding to) variousground motion severities or Intensity Measures (IM). A recentlypromoted efficient IM is typically represented by the spectral ac-celeration at the fundamental period of the structure, Sa(T1) aspreviously highlighted. On the other hand, the structural perfor-mance limit states of interest can vary from Immediate Occupancy(IO), to Life Safety (LS), to Collapse Prevention (CP) as per FEMA356 definitions [7], and even up to complete failure of the struc-ture. PLs are generally represented in the literature by a givenEngineering DemandParameter (EDP).The EDPadoptedin thecur-rent study is a semi-global parameter given by IDRmax. The fragility

function is basically thus giving the probability that a particu-lar PL is exceeded (reflected by recorded IDRmax exceeding a pre-specified IDRtarget set by specialized seismic provisions as will beclarified in what follows) conditioned on Sa(T1)(simply referredto byP[IDRmax IDRtarget|Sa(T1)]). Characterized by a lognormaldistribution, fragility curves developed in this paper represent acumulative distribution function defined by the median IM corre-

sponding to exceeding a given PL, Sa(T1), and the dispersion givenby the standard deviation of the natural log, (lnSa(T1)), both ofwhich are obtained from IDA data. In brief, FCs in this research arebasedon the two-parameter lognormal distribution function to getan S-shape curve. This approach was used by several researchers inthe literature (e.g.[14,26]) and proved to give precise results.

Qualitative structural performance levels: IO, LS, and CP

mentioned above are reported in [7]. For RC frame structures,FEMA 356 recommendations further give a quantitative formatfor these PLs through assigning to them deterministic interstorydrift limits of 1%, 2%, and 4% of the story height for IO, LS, and CPperformance levels, respectively. Although these suggested limitsare approximate, they are deemed fairly reasonable for buildingsdesigned for seismic loading [27]. For the sake of the currentstudy of low- to mid-rise ductile RC moment resisting frameslocated in moderate seismic zones, it is practically adequate tofurther assume that checking conformity with IO performancelevel corresponding to IDRmax = 0.01 could be associated with the10% in 10 yrs hazard of [3,4]. Similarly, the 10% in 50 yrs (i.e., thedesign level earthquake as set by most seismic codes worldwide)and the 2% in 50 yrs events could hence represent the hazardassociated with LS and CP performance levels corresponding to

IDRmax = 0.02 and 0.04, respectively.Fig. 5 shows samples of developed FCs for 8-story SFB and

PFB frames designed according to both CCD and MCD approachesfor various PLs introduced above. For similar data related to the4-story case study frames not given herein for space limita-tions one could refer to [19]. Note that the smaller (i.e., milder)slopes of FCs depict more uncertainty in the system. FromFig. 5,it could be thus easily observed that there is much more uncer-tainty associated with CP limit state, as expected, followed by LSperformance level, and then finally by IO reporting the least un-certainty. Moreover, it is obvious fromFig. 5that MCD frames aremore vulnerable to damage than their corresponding CCD framesat a given IM reflected by a particular Sa(T1), especially at severePLs such as CP; and similarly, PFB frames are more prone to dam-

age than their equivalent SFB frames for either CCD or MCD ap-proaches. One should however note that FCs of the type shown in

Fig. 5only reflect (and consider) record-to-record variability anddo not account for modeling uncertainties and other aspects ofthe ground motions such as consideration of the spectral shape( parameter) introduced in the literature by Baker and Cor-nell[28]. FCs accounting for these additional sources of uncertain-ties have been developed in the literature by different researcherseither forRC ductile andordinarymoment frames[21,22] orfor ac-tively and passively controlledstructures composed of Steelductilemoment resisting frames [29]. These studies concluded the impor-tance of the inclusion of such uncertainty sources for an accurateperformance prediction of structures located in high seismic zones.However, in a very recent study[30] on the seismic fragilities ofRC frames in regions ofmoderateseismicity, it has been concludedthat fragilities that are developed under the assumption that allstructural parameters are deterministic and equal to their median(or mean) values are sufficient for purposes of earthquake dam-age and loss estimation in regions of moderate seismicity. Not ac-counting for modeling uncertainties in the fragility analysis in thecurrent research may be therefore justified since all case studyframes are located in moderate seismic zones. Moreover, consid-ering capacity and modeling uncertainties in the FCs only changesthe slope of the curve while its center (i.e., the median correspond-ing to P[PL|Sa(T1)] = 0.5) remains unaltered [29] which keeps ourconclusions basedon medianvalues, andpresented in thenext sec-tion, generally unaffected. This is basically the classic first-orderassumption identified in [31] which may be considered a validapproximation although not entirely true; a recent study by Lielet al.[32]shows that there are some situations where the epis-temic uncertainty may shift the median.

9. Evaluation of R and Rd values endorsed by ECP 201

[equivalent toqandqd values of EC 8]

In this section, two previously highlighted hazards are consid-ered and are provided in Fig. 6 for illustration purposes. A brief im-portant description of these two hazard levels is presented belowwhileTable 5reports the actual numbers depicting these hazardlevels in terms of Sa(T1). Sa(T1) will be referred to from now onby Sa for brevity. The first hazard level is Sa(10% in 50 yrs) that isspecified by[3] and other similar worldwide building codes seis-mic provisions as the design-basis earthquake in which the per-formance objectives for a given building are limited to structuraldamage (i.e., Life Safety). The value of Sa(10% in 50 yrs) is directlyextracted from ERS in [3] for each case study frame. The codeR-value is eventually based upon this hazard level; therefore, theproduct ofo d(or, more precisely

o d) shapingRat this

level should be consistent with the code, where dis the dynamiccomponent ofR as demonstrated inFig. 6.On the other hand, thesecond hazard level of interest is Sa(2% in 50 yrs) as specified inUS seismic provisions (e.g.[5]) referring to the maximum capableearthquake in which the performance objectives for a building arenear collapse (or in brief, the associated implied behavior is thatthestructure will maintain Collapse Prevention for this 2% in 50 yrshazard). Valuesof Sa(2% in 50 yrs) arederived forcase study framesbased on the work in [33,34] relating the two above mentionedhazard values for Egypt as follows; Sa(10% in 50) 0.55 Sa(2% in50). This value of 0.55 is the equivalent of the 2/3 factor adoptedin [5] for the US and further endorsed by California practice[1].

Relying on information provided by IDA results and generated

FCs, median Sa(LS) values corresponding to IDRmaxreaching or ex-

ceeding IDRtarget = 0.02, as well as median Sa(CP) values corre-sponding to IDRmax reaching or exceeding IDRtarget = 0.04, may

be easily determined. For completeness, Sa(IO) values that could

be related to IDRtarget = 0.01 (and hence associated with a 10%in 10 yrs hazard) could be also retrieved, although relating this IO


9/13


(a) 8S-CCD-PFB frame. (b) 8S-CCD-SFB frame.

(c) 8S-MCD-PFB frame. (d) 8S-MCD-SFB frame.

Fig. 5. Fragility curves for investigated 8-story CCD- and MCD-PFB and SFB frames.

Table 5

Summary ofSa(PL)/Sa(hazard) ratios for case study frames for various performance levels.

Building type IO performance level LS performance level CP performance level

Sa (10% in 10) (g) Sa(IO)

Sa(10% in 10) Sa (10% in 50) (g)

Sa(LS)Sa(10% in 50)

Sa (2% in 50) (g) Sa(CP)

Sa(2% in 50)


4S-CCD-PFB 0.118 2.97 0.211 2.84 0.383 3.13

4S-CCD-SFB 0.141 2.84 0.252 2.98 0.457 2.84

8S-CCD-PFB 0.077 1.95 0.137 2.92 0.249 3.41

8S-CCD-SFB 0.082 3.05 0.147 3.06 0.267 3.45


4S-MCD-PFB 0.097 2.49 0.173 2.77 0.314 3.12

4S-MCD-SFB 0.141 2.70 0.252 2.98 0.457 2.84

8S-MCD-PFB 0.059 1.19 0.105 1.14 0.191 1.15

8S-MCD-SFB 0.069 2.31 0.123 2.44 0.223 2.29

performance level to a specific earthquake hazard and to a par-ticular IDRtarget is not as apparent as LS and CP levels. To exam-ine the implications of these data on the safety/reliability of trialdesigns developed in this research, three limit state ratios are re-

ported inTable 5comparing Sa(IO,) Sa(LS), and Sa(CP) to the haz-ard accelerations Sa(10% in 10), Sa(10% in 50), and Sa(2% in 50),

respectively. Note that the Sa(PL)/Sa(hazard) ratios simply furnishmargins against satisfying various code expected performance lev-els associated with different hazards of interest. These ratios fairlyexceed 1.0 for all frames which indicates that all case study framesperform well in excess of code expectations at the various PLs in-vestigated herein. One should realize that a lower value for this ra-tio (or for this margin) for any particular frame at one PL relative to

the other (e.g., LS versus CP) indicates that this PL governs the de-sign of the frame. A general note worth pointing is that referring to

Table 5, allcase study frames(irrespective of theheight, frame typeor design procedure) feature almost consistent value of that mar-

gin at the three PLs of interest, except for one or two frames. Such

exception even only occurs for the IO performance level whereas

consistency in that margin still holds for the other two (LS and CP)levels. Such observation points to a certain homogeneity and uni-

formity preserved by the code seismic design procedure as well as

by the MCD procedure proposed in this paper.

Moreover, relying on such more-or-less uniformity in these

reported margin values, one could further draw some global

conclusions based on average values of these margins calculated

for thethree considered performance levels(IO, LS andCP) for eachcase study frame. One could then notice that the lowest average

margin is scored for the 8S-MCD-PFB (1.16); whereas it was onaverage 2.76 for the same frame in the CCD procedure (i.e., roughly


10/13


Fig. 6. Schematic of theR-factor components and hazard levels considered.

2.4timeslarger). This reflects the effect of the significant reductionin the concrete dimensions due to the MCD procedure, and hencethe magnified tortuousPeffects. Enforcing ECP 201 restrictive

limitations on design interstory drifts (by imposing the 0.2aglower bound to the code DRS while checking drifts in the designprocedure whereas ignoring the upper bound on dssimilar to thatset in [4]and explained in Section3)will apparently resolve thisissue but this is not the correct approach. It has been previouslydemonstrated (refer to SD,DRS in Eq. (2)andFig. 1(b)) that suchlower bound on acceleration in absence of the upper bound ondsresults in unrealistic spectral displacement values for medium-to long-period structures. Furthermore, these displacements seemeven unboundedwith the increase of the period of vibration whichis physically impossible. Therefore, it is still beneficial to follow theproposed MCD procedure (i.e., pursuing same trend as illustratedby SD,ERS in Eq. (3) and Fig. 1(b)) but performing alternativelythe design considering a priori lower R values. Such step is

recommended in order to guarantee a reasonably larger margin ofsafety against reaching or exceeding LS and CP performance levelsfor these mid-rise perimeter framed buildings.

On the other hand, other case study frames (pertaining to4-story SFB and PFB buildings and 8-story SFB buildings) areobserved to have margins against satisfying IO, LS and CPperformance levels more than doublethose scoredby the8S-MCD-PFB frame(Table 5). These case study frames further reveal thatfollowing the MCD procedure with code-specified R value of 7 isstill a good option that keeps a more economic design than theCCDprocedure yetwith an adequate margin of safetyagainst exceedingthese differentperformancelevels. Moreover,it maybe noted from

Table 5 that Sa(PL)/Sa(hazard) ratios associated with LS and CPperformance levels remain practically unaltered for the studied4-story frames (either SFB or PFB) irrespective of the adopted

design method (CCD or MCD); this is an evidence that low-rise structures are less prone to damage that may result fromdetrimentalPeffects.

In a complementary step for evaluation of codes designprocedure implications, estimates ofR and Rd are then obtained(i.e., extracted) from the detailed nonlinear inelastic static(pushover) and time history (IDA) analyses supplemented by FCs.For instance, an estimate forRmay be obtained as

R =Base shear corresponding to a given PL (CP or LS)

Design base shear, Vdesign(4)

and adopting a SDOF approximation, this relation might besimplified as

R =Sa(CP or LS)

Vdesign/W=

Sa(CP or LS)

Sa,design(5)

where Wis the seismic weight of the building. Sa(CP or LS) medianvalues are easily determined for each frame from the IDA resultsand fragility curves referred to above. Furthermore, Rd can bedetermined as

Rd = IDRinelasticcorresponding to LS

IDRelasticcorresponding to LSR. (6)

IDRinelasticin Eq. (6) due to a given record can be generally easilyextracted from the IDA results; it is simply equal to 0.02 in thecontext of this study since this value corresponds to the limit seta priori for the LS performance level. On the other hand, IDRelasticmay be calculated by performing an elastic time history analysis ofthestructure under thesame recordscaled to Sa(T1) correspondingto LS performance level (i.e., corresponding to IDRinelastic = 0.02).

RetrievedRd/R (calculated as the ratio of the median, I DR, valuesof IDRinelasticand IDRelasticfor the set of 20 records as per Eq.(6))is given in Table 6 for each of the case study frames. Notethat Rd/R values, if calculated for CP hazard level, would holdless significance since checking drifts in all worldwide seismicprovisions is seldom related to such a high hazard. In the currentstudy, Rd/R ratio retrieved from the two-dimensional dynamic

analysis is therefore only evaluated at the LS performance level.Referring to Table 6, overall average Rd/R ratio for all MCD

and CCD ductile moment resisting frames studied herein could becalculated and is found to range between 1.1 and 1.2. This ratiocould be directly compared to ECP 201 recommended value of0.7 [3], or to the value of 1.0 (supporting the concept of the EqualDisplacement Rule) proposed in EC8 [4]. Note that the 1.1 valuein the range reported above refers to the Rd/Rratio averaged onlyfor the four case study frames dimensioned according to the CCDprocedure; while the 1.2 represents the value of the Rd/R ratioaveraged for the same four frames but when designed accordingto the proposed MCD technique. Both average values for this ratiosupport applying the Equal Displacement Rule, such as in [4],for more compatible, representative and realistic estimates of the

inelastic displacement demand based on the elastic demand. AnRd/Rvalue of 1 shall therefore be promoted instead of keeping thecurrent ECP201 endorsed value of 0.7 [3]. Such recommendation isbasically also to ensure some conservatism in the design estimatesof the inelastic displacement demands when applying seismicdesign procedures in[3].

It is also worth reporting that regular low- to mid-risestructures studied herein (featuring uniform distribution of massand stiffness) have been found to show a first mode dominatedbehavior with limited localization of drift demands. As a result,Rd/R ratio scores practically close values whether estimated (usingEq.(6)) based on maximum IDR or roof drift values. This resultis particularly also due to the fact that Rd values are basicallyretrieved in the current research at LS performance level at which

only little plastification occurs and hence limited localization takesplace. Rd/R ratio retrieved per Eq. (6) for the types of framesinvestigated herein accounts for both global(i.e., roof drift) versuslocal (i.e., IDR) effects (though with a marginal resulting difference)together withelasticversusinelasticeffects.

For completeness, same steps have been implemented to esti-mate as well Rd/R ratios corresponding to the IO performance levelassociated with IDRinelastic = 0.01, and a value of about 1.1 stillholds,on average, forall (CCD andMCD) case study frames. This re-sult further confirms that it is certainly more suitable to apply theEDR in order to deliver representative and conservative estimatesof inelastic displacement of these ductile moment frames relyingon elastic displacement values obtained from a linear analysis.

Alternatively, as mentioned before, the R value may be rather

simply disaggregated into the product of its static, previouslydefined, part o (or, more precisely o ) and its other dynamic


11/13


Table 6

Summary of retrievedRandRdvalues for the case study frames for the LS performance level.

Building type Sa,ULT(g) d(LS) R(LS) = d(LS)o R(LS) = d(LS)

o Rd/R


4S-CCD-PFB 0.165 3.63 9.2 12.0 1.0

4S-CCD-SFB 0.190 3.94 12.9 14.9 1.3

8S-CCD-PFB 0.122 3.27 6.2 8.0 0.8

8S-CCD-SFB 0.133 3.39 7.8 8.9 1.3


4S-MCD-PFB 0.126 3.83 7.4 9.6 1.14S-MCD-SFB 0.190 3.94 12.9 14.9 1.3

8S-MCD-PFB 0.075 1.59 1.9 2.4 1.4

8S-MCD-SFB 0.133 2.25 5.2 6.0 1.0

component,d as shown schematically inFig. 6.d is calculatedas follows

d =Sa(CP or LS)

Sa,ULT(7)

where Sa,ULT is given (Table 6)as Vu/Wfollowing the same SDOFapproximation previously mentioned (refer toFig. 6)and can beextracted from the pushover analysis results.

Now that all parameters have been properly defined, estimatesof R are computed for each of the case study frames at each ofthe two previously defined hazard levels of interest, LS and CP,and values are presented in Tables 6 and 7, respectively. In anattempt to reconcile the code-specified R value adopted a prioriin the design with expected (and modeled) behavior using dataextracted from the static and dynamic inelastic analyses describedabove, R values reported in Tables 6 and 7 referring to LS andCP performance levels, respectively, are compared to a value of 7and 12.7, respectively. Implied are the facts that (1) the code[3]specified R value of 7 is calibrated for the LS performance levelcorresponding to the design-basis earthquake; while as (2) thevalue of 12.7 associated with CP level is based on the fact that the2% in 50 yrs level is simply (1/0.55=) 1.82 times that of the 10% in

50 yrs level [34].Referring toTable 4,note that R values based on o (instead

of simply R values based on o) and reported in Tables 6and 7are more realistic values that rationally represent the actualbehavior and that are more adequate to be compared to code-specified R values. It may be accordingly observed that R (LS)values computed for 4-story (i.e., low-rise) case study frames ofeither the SFB or the PFB type designed according to either theCCDor theMCD procedureshow a great deal of conservatismwhencompared to the code value of 7 (Table 6). Level of conservatism inthese versions of the case study frames is even more pronouncedwhen looking into the CP performance level (Table 7) with allreported R valuessignificantly higherthan 12.7. It is though worthreporting that the dynamic part, d, ofR

is more contributing

to the final value of R than its static counterpart, o . On theother hand, it may be noted that the performance of the 8-story(mid-rise) CCD case study frames either ofthe SFB orthe PFB type just marginally exceeds that implied by the code-specified R of7 calibrated for LS performance level.Retrieved performance of the8S-CCD-PFBand 8S-CCD-SFB frames shows R(LS) valuesof 8.0and8.9, respectively. The margin to code R value is though improvedfor these two frames at the CP level as shown inTable 7whereretrieved R(CP) values of 17.0 and 18.2, respectively, are recordedcompared to a corresponding target value of R of 12.7 at thisPL. The only exception to the so far quite adequate performanceguaranteed by code pre-specified R values takes place for mid-rise 8-story frames designed according to the MCD techniqueproposed in this research. To be more specific, retrieved R values

of 2.4 and 6.0 (Table 6)associated with LS level for 8S-MCD-PFBand 8S-MCD-SFB, respectively, emphasize the non-conservative

current code value ofR = 7.0. Same poor results persist for thesame frames at the CP level as shown in Table 7.

It is therefore highly recommended that whenever this MCDprocedure is promoted, the relevant code provisions should assignlower values ofR for mid-rise moment resisting frame buildingsespecially of the perimeter framed type. It may however be moreprudent to propose this reduction explicitly in the overstrengthcomponent ofR rather than inherently in the aggregated R value

that includes combined contributions from overstrength, ductility,besides other factors of relevance. In addition, an investigation forgenerating adequate (and efficient) P factors to be considered inthe design phase in line with the MCD technique presented hereinis undergoing by the authors.

The recommendation for lower R values may be also prefer-ably equally applicable to mid-rise CCD moment frame buildings(either of the SFB or PFB type) especially if it is required that codeRvalues maintain a certain level of conservatism in the design. Toillustrate the need for such recommendation, one should note thatif the values ofR(LS) = 8.0 and 8.9 retrieved for 8S-CCD-PFB and8S-CCD-SFB, respectively, and reported inTable 6,were not cal-culated based on median values of Sa(LS), but were instead esti-mated from IDAs and FCs based on an Sa(LS)value corresponding

to a lower conditional probability of exceeding the IDRtargetasso-ciated with LS level (i.e., corresponding to P[IDRmax IDRtarget =0.02|Sa(T1)] < 0.5 referring to the relevant FC), we would haveended up with smallerd(LS), and hence lower R

(LS). This wouldhave probably lead toR (LS)values less than 7.0 thus revealing anon-conservative code R value for the design of these CCD mid-risemoment frames. In general, the FCs make the approach presentedherein more versatile and capable of encompassing wide range ofestimates for retrievedRvalues corresponding to different proba-bilities. Considering lower conditional probabilities as highlightedabove and studying their consequent effects is under scrutiny bythe authors.

Nonetheless, it is importantto highlight that (1) the adoption ofonly rectangular sections along all beams in the current computer

models of the investigated frames when performing inelasticpushover and dynamic analyses rather than L- or T-sections wheredeemed appropriate based on the continuously changing directionof the bending moment demands, along with (2) the use ofminimum specified (i.e., nominal) materials strength propertiesinstead of expected values, may have contributed to a relativelylow value of actual built-in overstrength, o (or

o ), and hence

to an underestimation of actual retrieved R values. The first pointwas adopted in analysis to avoid overly complicated models alongwith further ad hoc assumptions related to the effective flangewidth to be considered with L- or T-beams, that at best wouldhave added extra uncertainty to the subject instead of improvingmodeling and actual structure realization. In addition, regardingthe second point related to material properties, it was decided

by the authors to rather rely on minimum specified values toaccount for occasionally poor production of construction materials


12/13


Table 7

Summary of retrievedRvalues for the case study frames for the CP performance level.

Building type Sa,ULT(g) d(CP) R(CP) = d(CP)o R(CP) = d(CP)

o


4S-CCD-PFB 0.165 7.27 18.5 24.04S-CCD-SFB 0.190 6.84 22.4 25.8

8S-CCD-PFB 0.122 6.96 13.1 17.0

8S-CCD-SFB 0.133 6.93 15.9 18.2

Moment frames as per MCD procedure4S-MCD-PFB 0.126 7.81 15.1 19.6

4S-MCD-SFB 0.190 6.84 22.4 25.8

8S-MCD-PFB 0.075 2.92 3.4 4.4

8S-MCD-SFB 0.133 3.82 8.8 10.1

in the local market. The decisions made herein for these coupleof modeling issues will add some conservatism to the currentestimation ofRandR values reported in this paper which shouldbe generally accepted for design codes evaluations/studies.

10. Summary and conclusions

Different trial designs of ductile low- to mid-rise (4- and8-story) RC moment resisting frames located in moderate seismiczones (0.25 g) have been implemented using both space andperimeter frame configurations according to emerging Egyptianseismic code that is in line with Eurocode 8 seismic provisions.Codes controlling design criteria (including strength versusstiffness criteria, as well as currently imposed constant lowerbound on design acceleration and missing upper bound oncalculated actual expected displacement) have been addressedalong with their implicationson theframes seismic performance.Aseries of staticinelastic pushover analyses have been performedonthe case study frames. In addition, incremental dynamic analyseshave been carried out for each investigated frame under a bin of20 small magnitude large distance ground records in a multi-levelanalysis context. Fragility curves are hence developed for the casestudy frames corresponding to the probability of exceeding various

performance levels of interest including Immediate Occupancy,Life Safety and Collapse Prevention levels conditioned on anefficient Intensity Measure defined by Sa(T1). Code-CompliantDesigns as well as a proposed Modified Code Design relaxingdesign drift demands are examined to test their effectiveness andreliability. A major contribution of this paper is the evaluationof the structural response modification factors, R and Rd, usingadvanced inelastic static and time history analyses along with pre-specified hazard levels, and comparing them to code proposedvalues for ductile moment resisting frames.

The paper shows that either CCD or MCD procedure yieldslife-safe moment resisting frames that perform well relativeto seismic performance objectives and hazard levels impliedby current design codes. Moreover, retrieved margins against

satisfying various code expected performance levels associatedwith different hazards of interest (IO, LS, and CP) exceed 1.0 for allcase study frames. These margins further show consistency acrossall performance levels of interest for each investigated frame thuspointing to reasonable uniformity and homogeneity furnished bythetwo designprocedures adopted herein. Moreover,results of theinelastic static and dynamic analyses permit disaggregation of theRvalue into its component parts provided by static overstrength,o , and inelastic dynamic response, d. It may be noted that dvalues are generally larger than o values for nearly all casesinvestigated herein at either the LS or CP performance levels.It has been further noted that current code R value may benon-conservative for some of the buildings investigated in thispaper. In other words, the one size fits all approach in the

selection of response modification factors may result in significantunderestimations of internal forces and seismic demands of

moment frames of various types or height. For example, it hasbeen shown that lower R values would be better assigned bythe code for the design of mid-rise (8-story and most probablyhigher) momentframes eitherof thespaceor of theperimeter type,with a special emphasis to reduce this R value for the perimeterframe configuration particularly if the proposed MCD procedure isadopted. It may be somewhat conceptually more appropriate forthe case of MCD technique to propose such reduction explicitly inthe overstrength component ofR rather than intrinsically in the

aggregatedRvalue.The analyses also indicate that inelastic displacements would

be more accurately (andconservatively) estimated for ductile mo-ment resisting frames designed per either the CCD or the proposedMCD procedure using an equal displacement rule (implying thatRd = R), rather than through the inelastic displacement factorgiven as 0.7 in the current provisions (i.e., Rd = 0.7R)[3]. Suchrecommendation shall be well perceived by the design communityand users of ECP 201 seismic provisions especially since there isa precedent for adopting this equal displacement rule in EC8[4] which is a parent code for ECP 201 as well as in other ma-

jor building codes worldwide and in other previous published re-searches (e.g.[1]). It is however worth reporting that Rd/Rresultspresented in the current research are mainly applicable (and pro-moted) to first mode dominated structures with no irregularities

in either mass or stiffness and with limited expected localizationof drift demands up to Life Safety performance level.

Furthermore, it has been proven that it would be betterto impose the constant lower bound of 0.2ag on the designacceleration only when designing for strength of differentstructural elements. If this bound on the design accelerationresponse spectrum is equally enforced while checking drift,it will result in unrealistically large values of drift demandsunless an upper bound to the expected (actual) displacements isimplemented. In other words, the expected actual displacement,ds, need not be larger than the value derived from the elasticspectrum. Such upper bound on displacement set in[4]is more-or-less equivalent to the MCD procedure proposed in this researchand is also of primary importance when estimating actual driftssince it guarantees realistic displacement values for medium- tolong-period structures especially in case the 0.2agconstant lowerlimit to the design acceleration response spectrum is enforced inthe design procedure.

It is nonetheless important to realize that this study and theconclusions thereof are so far only valid for low- to mid-risemoment resisting framed buildings up to 8-story high locatedin moderate seismic zones (0.25 g). Extrapolation of the resultspresented herein to other seismic zones, to near-fault motionsand/or to higher moment framed buildings shall be the subject ofa similar effort before being either applied or denied.

References

[1] Mehanny SS, Cordova PP, Deierlein GG. Seismic design of composite momentframe buildings case studies and code implications. In: Engineering

foundation conference: composite construction IV. Banff (Alberta, Canada):ASCE; 2000. p. 11.


13/13


[2] Rivera JA, Petrini L, Lai CG. Do the Eurocode 8 force-based design provisionslead to the safe and predictable seismic response of RC frame buildings?In: The 14th worldconference on earthquakeengineering. Oct. 1217,Beijing,China; 2008.

[3] ECP 201. Egyptian code of practice forloads on buildingsand bridges. Ministryof Housing, Utilitiesand Urban Communities ofthe ARE. Housing andBuildingResearch Center, Egypt; 2003.

[4] Comit Europen de Normalisation, Eurocode 8 CEN. Design of structuresfor earthquake resistance. Part 1: general rules, seismic actions and rulesfor buildings. In: European Committee for Standardization. Doc. EN 1998-1,

Brussels, Belgium; 2005.[5] International code council. 2003 International building code, Falls Church,

Virginia (USA); 2003.[6] American institute of steel construction. AISC seismic provisions for structural

steel buildings. 2nd ed. Chicago (IL, USA); 1997.[7] FEMA-356. Prestandard and commentary for the seismic rehabilitation of

buildings.In: Federal emergencymanagement agency. Washington (DC, USA);2000.

[8] International conference of building officials (ICBO). 1997 Uniform buildingcode (UBC). vol. 2. Whittier (CA, USA); 1997. p. 574.

[9] American society of civil engineers. Minimum design loads for buildings andother structures. ASCE/SEI 7-05. ASCE standard no. 7-05. Virginia (USA). 2005.p. 424.

[10] ECP 203.Egyptian codeof practice fordesign of reinforced concretestructures.Ministry of housing, utilities and urban communities of the ARE. Housing andbuilding research center, Egypt. 2007.

[11] Mehanny SS, Deierlein GG. Modeling and assessment of seismic performanceof composite frames with reinforced concrete columns and steel beams. J.A.

Blume Earthq. Eng. Center. report no. 135. Stanford CA (USA). 2000.[12] Medina R. Seismic demands for non-deteriorating frame structures and theirdependence on ground motions. Ph.D. thesis. Depart. of Civil and Env. Engrg.CA (USA): Stanford University; 2002.

[13] Gupta A, Krawinkler H. Seismic demands for performance evaluation of steelmoment resistingframe structures(SAC Task5.4.3), JohnA. BlumeEarthq.Eng.Center. Report no. 132. CA (USA): Stanford University; 1999.

[14] Chenouda M, Ayoub A. Probabilistic collapse analysis of degrading multidegree of freedom structures under earthquake excitation. Eng Struct 2009;31(12):290921.

[15] Mackie KR, Stojadinovi B. Fragility basis for California highway overpassbridge seismic decision making. PEER Report 2005/02. Berkeley (CA, USA):University of California; 2005.

[16] OpenSees.http://opensees.berkeley.eduWeb page.[17] Karsan ID, Jirsa JO. Behavior of concrete under compressive loading. J Struct

Div Proc ASCE 1969;95(ST12):254363.[18] Paulay T, Priestley MJN. Seismic design of reinforced concrete and masonry

buildings. NY (USA): John Wiley & Sons, Inc.; 1992.

[19] El Howary HA. A probabilistic frameworkfor assessingseismicperformance ofreinforcedconcretemomentframe buildings in moderateseismic zones. M.Sc.thesis. Structural Engrg. Dept., Egypt: Cairo University; 2009.

[20] FEMA-451. NEHRP Recommended provisions: design examples, prepared bythe building seismic safety council for the federal emergency managementagency. National Institute of Building Sciences, Washington (DC, USA); 2006.

[21] Haselton CB. Assessing seismic collapse safety of modern reinforced concretemoment frame buildings. Ph.D. thesis. Department of civil and environmentalengineering. CA (USA): Stanford University; 2006.

[22] Liel AB. Assessing the collapse risk of Californias existing reinforced concrete

frame structures: metrics for seismic safety decisions. Ph.D. thesis. Dept. ofCivil and Env. Engrg., Stanford Univ., CA (USA); 2008.

[23] TagawaH, MacRaeG, LowesL. Probabilistic evaluationof seismic performanceof 3-story 3D one- and two-way steel moment-frame structures. EarthquakeEng Struct Dyn 2008;37:68196.

[24] Shome N, Cornell CA. Probabilistic seismic demand analysis of nonlinearstructures. Rep. no. 35. Reliability of marine structures program. Dept. of Civiland Env. Engrg., CA: Stanford University; 1999.

[25] VamvatsikosD, Cornell CA. Incremental dynamic analysis.Earthquake Eng andStruct Dyn 2005;31(3):491514.

[26] Shinozuka M, Feng MQ, Kim HK, Kim SH. Nonlinear static procedure forfragility curve development. J Eng Mech, ASCE 2000;126(12):128795.

[27] Ramamoorthy SK. Seismic fragility estimates for reinforced concrete framedbuildings. Ph.D. dissertation. Texas (USA): Civil Engineering Dept., Texas A&MUniversity; 2006.

[28] Baker JW, Cornell CA. A vector-valued ground motion intensity measureconsisting of spectral acceleration and epsilon. Earthquake Engineering andStructural Dynamics 2005;34(10):1193217.

[29] Taylor E. The development of fragility relationships for controlled structures.M.Sc. thesis. Dept. of Civil Engineering. Saint Louis (MO, USA): WashingtonUniversity; 2007.

[30] Celik OC, EllingwoodBR. Seismic fragilitiesfor non-ductile reinforced concreteframes role of aleatoric and epistemic uncertainties. Struct Safety 2010;32(1):112.

[31] Cornell CA,Jalayer F, HamburgerRO, FoutchDA. Theprobabilistic basis forthe2000 SAC/FEMA steel moment frame guidelines. J Struct Engrg ASCE 2002;128(4):52633.

[32] Liel AB, Haselton CB, Deierlein GG, Baker JW. Incorporating modelinguncertainties in the assessment of seismic collapse risk of buildings. StructSafety 2009;31:197211.

[33] Ove Arup & Partners international. Seismic hazard assessment for LNG projectat Damietta port in Egypt. London (UK): Ove Arup & Partners International,Ltd., London Operating Centre; April, 2002.

[34] Mehanny SSF, Gendy AS, Seif SP. Seismic assessment of bridges over the riverNile.fib Symposiumon ConcreteStructures in SeismicRegions.May 69,2003.Athens (Greece); 2003.
http://opensees.berkeley.edu/http://opensees.berkeley.edu/

Documents

Evaluation of Egyptian Seismic Code Implications and System Configuration Effects