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Introduction

Nonlinear static analysis is a simplified analysisprocedure that can be useful for estimatingseismic demands and providing valuableinformation about the locations of structuralweaknesses and failure mechanisms in theinelastic range.[ [Krawinkler , H., andseneviratna G.D.P.K., 1998]. Also pushoveranalysis has the advantage that it is capable ofconsidering a response spectrum of codes asdemand diagram to estimate the earthquakeinduced response of structures [Chopra and Goel,1999]. This method is recommended as astandard tool for assessment proposes and designverification [FEMA 273].

However this procedure contains severalprincipal limitations [Kim S. and DAmore, E.,1999]. One of the momentous deficiencies of thisprocedure is that it is based on the assumptionthat the response quantity of interest is drivenprimarily by response in a single mode and

inelastic action is uniformly distributed over theheight of the building [Krawinkler , H., andseneviratna G.D.P.K., 1998]. This assumption isvalid only for low-rise buildings. Then severalauthors have been developing pushover-basedmethods, which do represent a major stepforward in comparison with standard equivalentelastic procedures and take into account theinfluence of higher modes. The method in whichhigher modes are taken into account varies fromprocedure to procedure.

Adaptive pushover procedures considerprogressive stiffness degradation andconsequently changes in the modal properties ateach step on the lateral story forces. Thisprovides improved response predictions [Bracciet al.1997; Gupta, B., and Kunnath, S. K. _2000].However, it was demonstrated that force-basedadaptive pushover is not more preferable overcurrent non-adaptive pushover analyses[Antoniou , S. and Pinho , R., 2004a]. Adisplacement-based adaptive pushover procedure

142 International Journal of Civil Engineerng. Vol. 6, No. 2, June 2008

Assessment of conventional nonlinear static procedures with FEMA loaddistributions and modal pushover analysis for high-rise buildings

Mehdi Poursha1, Faramarz Khoshnoudian2, AbdoReza S. Moghadam3

1PhD Candidate, Department of Civil and Environmental Engineering, Amirkabir University of Technology(Tehran polytechnic), Tehran, Iran

2Assistant Professor, Department of Civil and Enviromental Engineering, Amirkabir University of Technology(Tehran polytechnic), Tehran, Iran

3Assistant Professor, International earthquake and seismology research centre, Tehran, Iran

Abstract: The nonlinear static pushover analysis technique is mostly used in the performance-based design ofstructures and it is favored over nonlinear response history analysis. However, the pushover analysis withFEMA load distributions losses its accuracy in estimating seismic responses of long period structures whenhigher mode effects are important. Some procedures have been offered to consider this effect. FEMA andModal pushover analysis (MPA) are addressed in the current study and compared with inelastic responsehistory analysis. These procedures are applied to medium high-rise (10 and 15 storey) and high-rise (20 and30 storey) frames; efficiency and limitations of them are elaborated. MPA procedure present significantadvantage over FEMA load distributions in predicting storey drifts, but the both are thoroughly unsuccessfulto predict hinge plastic rotations with acceptable accuracy. It is demonstrated that the seismic demandsdetermined with MPA procedure will be unsatisfactory in nonlinear systems subjected to individual groundmotions which inelastic SDF systems related to significant modes of the buildings respond beyond the elasticlimit. Therefore, its inevitable to avoid evaluating seismic demands of the buildings based on individualground motion with MPA procedure.

Keywords: Modal pushover analysis, FEMA load distributions, nonlinear response history analysis, high-risebuildings

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was proposed that lateral displacements insteadof forces are monotonically applied to thestructure. It was concluded that this procedureresults in better estimates of seismic demands inrelation to force-based analyses [Antoniou , S.and Pinho , R., 2004b]

Multi-mode pushover (MMP) was identified, butthe higher mode effects wasnt quantified[Sasaki, K.K., Freeman, S.A. and Paret, T.F.,1988]. Pushover results combinations (PRC) wasproposed that estimates the maximum seismicresponses by combining the results of pushoveranalyses and utilizing a mode shape as its loadpattern in each analysis [Moghadam, A.s. , 2002].

Incremental response spectrum analysis (IRSA)has been developed. The IRSA method addressesthe issue of higher modes using piecewise elastic(spectral) modal analysis with constant structuraland dynamic properties between the occurrencesof the two successive plastic hinges, usingconsistent theoretical approach [Aydinoglu,M.N., 2003].

In other studies modal pushover analysis (MPA)was proposed that pushover analyses are carriedout separately for each significant mode, and thecontributions from individual modes tocalculated are combined using an appropriatecombination rule (SRSS or CQC) to calculateresponse quantities (displacements, drifts, etc.).Of course, the rule of superposition of modalresponses is not reasonable in the inelastic rangeof the response because modes are not uncoupledanymore. It was shown that MPA procedure iscapable of estimating displacements and storeydrifts with acceptable accuracy but it fails toprovide satisfactory results for plastic rotations ofthe hinges [Chopra , A.K. and Goel, R.K., 2002].In another research, it was demonstrated thatMPA procedure is more reliable than FEMA loaddistributions in computing seismic demands ofSAC (9 and 20 storey) buildings [ Goel , R.K.,and Chopra, A.K., 2004].

Also, a modified version of MPA (MMPA) hasbeen proposed in which the inelastic responseobtained from first-mode pushover analysis has

been combined with the elastic contribution ofhigher modes [Chopra, A. K., Goel, R. K., andChintanapakdee, C. 2004].

The above-mentioned discussion clarifies theimportance of higher mode effects in pushoveranalyses of long period structures in the recentstudies. In view of this matter, MPA has achieveda preference over current procedures due tosimplicity and attractiveness. So its necessary tobe verified for a wide range of buildings andensembles of ground motions. The principleobjective of this paper is to appraise modalpushover analysis (MPA) and elaborateattentively its effectiveness and limitations.Additionally the degree of accuracy of FEMAforce distributions in pushover analysis will beinvestigated in this paper. For that reason, MPAand FEMA force distributions will be applied tofour steel special moment-resisting high-riseframes possessing various heights. It is noted thatthe seismic demands produced by nonlinearresponse history analyses are treated asbenchmark results and will be compared withthose obtained by approximate pushoverprocedures.

Details of MPA procedure

MPA procedure is an improved pushoverprocedure proposed to estimate seismic demandsof buildings taking into account of higher modeeffects and retaining the simplicity of invariantload distributions. Modal pushover analysis(MPA) utilizes the concept of modalcombinations through several pushover analysesusing invariant load patterns based on elasticmode shapes where the total response isdetermined with combination of each mode at theend.

Details of MPA procedure are illustrated as aseries of following steps [Chopra , A.K. and GoelR.K., 2002]:

1. Compute the natural frequencies, wn , andmode shapes, n. These properties are determinedwith eigen analysis of the linearly-elastic

143Mehdi Poursha, Faramarz Khoshnoudian, AbdoReza Sarvghad Moghadam

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structure for the first three modes. It is necessaryto be normalized mode-shape n so that the roofcomponent of n equals to unity ( n=1).

2. Develop the base-shear roof displacement(Vbn urn ) pushover curve for the nth-modeemploying the load distribution Sn*=M n

3. Idealize the pushover curve as a bilinear curve(Figure 1).

4. Transform the idealized pushover curve intothe Fsn/Ln Dn relation (Figure 1) by utilizingformulas as follow:

(1)

where

(2)

(3)

(4)

5. Compute the peak deformation, Dn , of the nth-mode inelastic SDF system (Figure 2) with force-deformation relation of Figure 1 by solvingEquation :

(5)

It can be calculated from the inelastic response(or design) spectrum.

6. Calculate the peak roof displacement urnorelated to the nth-mode inelastic SDF systemfrom:

(6)

7. Compute other favorite responses, rno ,at urno

8. Iterate Steps 3 to 7 for as many modes asrequired for sufficient accuracy.

9. Calculate the total response by combining thecontribution of peak modal responses usingpertinent combination rule such as SRSS andCQC.

FEMA load distributions

Three lateral load distributions stipulated inFEMA-273 are as follows [Building SeismicSafety Council, 2000]:

1. Uniform distribution: s*i= mi , in which mi isthe mass and s*I is the lateral force at i-th floor.(where the floor number i=1,2N)

2. Equivalent lateral force (ELF) distribution: Avertical distribution proportional to the values of

where the exponent k = 1for fundament period T1O 0.5sec, k = 2 forT1P2.5sec; and Linear interpolation shall beused in between. hi , hx are heights from the baseto floor level i and x, respectively.

3. SRSS distribution: A vertical distributionproportional to the story shear distributioncalculated by combining modal responses from aresponse spectrum analysis of the building,including sufficient modes to capture at least90% of the total building mass, and using theappropriate ground motion spectrum. Thisdistribution shall be used when the period of the


Fig.1 Properties of the nth-"mode" inelastic SDF system from the pushover Curve [Chopra , A.K. and Goel , R.K., 2002]

rnn

rnyny

n

bny

n

sny uDM

V

L

F,

*

nTn

Tn

n m

mi

miL Tnn

nnn LM*

tuL

FDwD g

n

snnnnn &&&&& 2

nrnnrno Du

s*i= )/()(1

ki

N

ii

kxx hmhm

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fundamental mode exceeds 1.0 second.

Structural models

The structures considered are the 10, 15, 20 and30-story two dimensional buildings, designedaccording to AISC-ASD89. Seismic effectsdetermined in accordance with the requirementsof Iranian code of practice for seismic resistantdesign of buildings. An amplification factor of07R was applied to the drifts obtained fromelastic analysis to obtain the maximum inelasticdisplacements. The results satisfied allowabledrift criteria of code after some iteration[Standard No. 2800-05]. All buildings areassumed to be founded on firm soil type II ofIranian seismic code (class C of NEHRP) andlocated in the region of highest seismicity. Thebuildings lateral load-resisting system is steelspecial moment-resisting frame (SMRF). Itsnoted that Configuration of these buildings isshown in figure 3. All buildings are 15 m inwidth. The bays are 5 m on center with threebays. Story heights of all buildings are 3.2 m. Theseismic mass of all levels of the each structure areassumed to be equal and the values of them are

given in table 1. More details of these buildingsare listed in table 1. The sections of beam andcolumn elements are considered plate girder andbox, respectively.

This model is based on centerline dimensions ofthe bare frame in which beams and columnsextend from centerline to centerline. Thestrength, dimension, and shear distortion of panelzones are neglected but P- (second order)effects are included.

The first three periods for linearly elasticvibration resulted from eigen analysis of thestructures are presented in table 1.

The nonlinear force-displacement or moment-rotation behavior occurs in discrete hinges fornonlinear static and nonlinear response historyanalyses. Hinges are introduced into frameelements and assigned at end location along theframe elements. Also hinge properties areintroduced based on FEMA-273 criteria. CoupledP- M3 hinge based on the interaction of axialforce and bending moments and M3 hinge basedon only bending moment are considered at thehinge location of column and beam elements,


Fig.2 Conceptual explanation of uncoupled modal RHAof inelastic MDF systems [Chopra , A.K. and Goel , R.K.,

2002]

No. No. of stories H

(m) b

(m)

Seismic mass of floors

(kg-sec2/m)

Periods

T1 (Sec) T2 (Sec) T3 (Sec)

B1 10 32 15 5440 1.697 0.605 0.347 B2 15 48 15 5546 2.338 0.854 0.493 B3 20 64 15 5600 3.092 1.135 0.670 B4 30 96 15 5650 3.866 1.381 0.798

Table 1 Characteristics of analytical cases

Fig.3 Configuration of selected two dimensional buildings

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respectively.

Ground-Motion Scaling

Seven ground motions were selected from thePacific Earthquake Engineering Research(PEER) Center strong ground motion database(http://peer.berkeley.edu). Ground motions wereintended to be far at least 12 km from a faultrupturing. Also the Soil at the site corresponds toNEHRP Site Class C. To ensure that thestructures respond well into the inelastic rangewhen subjected to ground motions, the recordswere scaled up to 0.7g. More Characteristics ofthe used records are given in table 2. The elasticpseudo acceleration and deformation and themedian spectra for 5% damping ratio arepresented in Figure 4. The median spectrum is

shown by a thicker line.

Analyses and assumptions

In order to deliberate MPA procedure and FEMAload distributions and to put forward some pointsabout them, several types of analysis areperformed: nonlinear response history analysis(NL-RHA), pushover analysis using the threeforce distributions in FEMA-273 and Modalpushover analysis (MPA) considering threemodes. MPA is performed for each groundmotion to obtain its seismic demands and themedian values are determined over ensembles ofseven ground motions. The computer programSAP2000, nonlinear version was employed toperform nonlinear static and dynamic analyses[Computers and Structures, 2004].


No. Earthquake Name Date Magnitude Station Name Station Number

Component (deg)

PGA (g)

1 Duzce, Turkey 1999/11/12 Ms ( 7.3 ) Lamont 1061 E 0.134

2 Northridge 1994/01/17 Ms ( 6.7 ) LA -

Baldwin Hills

24157 90 0.239

3 Trinidad, California 1980/11/08 Ms (7.2 ) Rio Dell

Overpass, FF

1498 270 0.147

4 Victoria, Mexico 1980/06/09 Ms ( 6.4 ) Cerro Prieto 6604 45 0.621

5 Hollister 1986/01/26 Ml ( 5.5 ) SAGO South - Surface

47189 3295 0.09

6 Imperial Valley 1979/10/15 Ms ( 6.9 ) Parachute Test Site 5051 315 .204

7 Morgan Hill 1984/04/24 Ms ( 6.1 ) Corralitos 57007 310 0.109

8 Landers 1992/06/28 Ms ( 7.4 ) Boron Fire 33083 0 0.119

(a)

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 2 4 6

Natural vibration period,Tn(sec)

pseudo-acceleration,A/g

(b)

0

5

10

15

20

25

0 2 4 6Natural vibration period,Tn(sec)

Deformation, D(cm)

Fig.4 (a) Pseudo acceleration spectra and (b) deformation spectra of far field records set of ground motions, dampingratio=5%.

Table 2 List of used ground motions

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Gravity loads and P- effects were included in allanalyses. Pushover analyses are performed byfirst applying gravity loads, followed bymonotonically increasing lateral forces with aspecified height-wise distribution. The P-effects due to gravity loads are considered for thefirst mode in MPA procedure. [Chopra , A.K. andGoel , R.K., 2001]. The responses resulted frompushover analyses are compared with the medianof maximum seismic demands computed byrigorous NL-RHA analyses for an ensemble ofground motions described earlier. Nonlinearresponse history analysis is performed usingnumerical implicit wilson- time integrationmethod in which parameter determines thestability and accuracy characteristics of themethod and the value of 1.4 is allocated for thisparameter. A damping ratio of 5% is consideredfor the first and third modes of vibration to definethe Rayleigh damping matrix.

To establish the target displacement, either acapacity spectrum approach [ATC-40] or adisplacement coefficient approach [FEMA273/356] is utilized. Also, target displacementwould be assumed equal to the maximumdynamic roof displacement [Tso WK, MoghadamAS., 1998; Mwafy A.M. and Elnashai A.S., 2001;Moghadam, A.s., 2002]. In this research, thetarget displacement at roof in pushover analysesis assumed as the median values of maximum topfloor displacements of the structures, resultedfrom seven NL-RHA analyses. The values oftarget displacements are 26.92, 33.05, 38.27,61.26 cm for B1, B2, B3 and B4 buildings,respectively.

The earthquake-induced demands are computedfor the modeling buildings introduced earlier. Fora yielding structure, the occurrence of structuraldamage is more closely related to story drift[Chopra , A.K. and Goel , R.K., 2001]. Therefore,in performance-based seismic evaluation, inter-story drift is an important attribute for damagecontrol. Also, in order to evaluate performance ofstructural component, it is necessary to computehinge plastic rotations and compare them withacceptability criteria based on FEMA-273/356.

Results and Discussion

Results of all analyses are briefly presented here.Floor displacements, Story drift ratios (storydrifts / height of story), hinge plastic rotations ofinternal beam at all floor levels are calculated byaforementioned procedures. The results ofpushover analyses are obtained at the targetdisplacements. Also the errors of pushoveranalyses relative to exact solutions (benchmarkresults) obtained by NL-RHA are extracted.

MPA procedure is executed according to detailsexpressed earlier. Properties of modal inelasticSDF systems are summarized in Table 3. Thistable provides evidence that yieldingdeformation, Dny of inelastic SDF systembecomes less for higher frequency modes, butinstead there is a consequential increase inyielding force deformation, Fsny / Ln. This meansthat the slope of first branch of force-displacement diagram of inelastic SDF systemincreases for higher modes. It is rational due to


build

ings

Properties Ln (kg) n*nM (kg)

Fsny / Ln (cm/sec2)

Dny(cm)

Fsno Ln (cm/sec2)

Dno(cm)

Tn(sec)

n(%)

B1 Mode 1 302446.6 1.357 410473.4 220.946 16.196 252.776 36.841 1.697 5 Mode 2 -116712 -.544 63519.96 1492.444 13.702 1767.61 41.341 0.605 3.86 Mode 3 76243.2 0.296 22556.84 4275.864 13.025 5063.95 42.250 0.347 5

B2 Mode 1 443560.9 1.387 615252.8 148.776 20.709 172.696 46.859 2.338 5 Mode 2 -156249 -.595 92922.94 954.33 17.342 1137.27 42.037 0.854 3.85 Mode 3 100061.9 .335 33548.81 2494.873 15.168 3104.77 44.738 0.493 5

B3 Mode 1 577620.6 1.412 815768.6 113.524 27.687 125.042 54.875 3.092 5 Mode 2 -204590 -.646 132090.2 741.917 23.651 845.711 54.210 1.135 3.93 Mode 3 123552.8 0.390 48221.01 1806.267 20.246 2152.23 64.055 0.670 5

B4 Mode 1 827751.7 1.459 1207721 123.604 47.128 133.201 82.246 3.866 5 Mode 2 -329979 -0.707 233249.5 572.348 26.899 684.357 67.198 1.381 3.87 Mode 3 170719.1 0.413 70568.92 1639.815 26.149 1951.71 78.623 0.798 5

Table 3 Modal properties of inelastic SDF systems in modal pushover analyses

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the fact that higher modes have higher frequencyand the structure exhibits more stiffness in highermodes. Its notable that the initial slope of force-deformation diagram related to nth mode is equalto the square of frequency of nth mode. Force-deformation (Fsn / Ln Dn) diagram of aninelastic SDF system subjected to Northridgescaled up to 0.7g is shown in figure 5. Thissystem is related to the first mode of MPAprocedure in 15 storey building. Target displacements of roof, umo are individually

calculated from peak deformation of inelasticSDF systems subjected to scaled ground motionsand results are presented in Table 4. Figures 6to 9 show height-wise distribution of floordisplacements, storey drift ratios computed withMPA procedure and nonlinear response historyanalyses for buildings B1 to B4, respectively.Also, the errors of the results estimated withMPA are presented in relation to benchmarksolution (NL-RHA) in these figures. The figuresprovide results individually for each of the


-180

-120

-60

0

60

120

180

-30 -20 -10 0 10 20 30

Deformation (cm)

Force (kg.cm/s^2)

Fig.5 Force-deformation (Fsn/ Ln - Dn) diagram of an inelastic SDF system subjected to Northridge scaled up to 0.7g forthe first mode of MPA in 15 storey building

BU

ILD

ING

Ground Motion

Mode 1 Mode 2 Mode 3

Dn(cm) rnou Dn(cm) rnou )(cmDn rnou

B1

Northridge 22.44 1.385 30.455 8.27 0.604 4.501 3.93 0.302 1.163 Duzce 20.76 1.281 28.175 5.67 0.414 3.086 9.94 0.763 2.941

Trinidad 17.09 1.055 23.194 9.94 0.726 5.410 2.696 0.207 0.798 Victoria 15.78 0.974 21.416 8.74 0.638 4.757 2.83 0.217 0.837 Hollister 21.64 1.336 29.369 15.66 1.143 8.523 2.63 0.202 0.778

Imperial Valley 16.12 0.995 21.878 4.45 0.325 2.422 2.94 0.226 0.870 Morgan Hill 17.39 1.073 23.601 12.29 0.897 6.689 3.65 0.280 1.080

B2



Imperial Valley 33.4 1.613 46.328 5.29 0.305 3.146 6.78 0.447 2.273 Morgan Hill 12.71 0.614 17.630 19.82 1.143 11.787 11 0.725 3.688

B3



Imperial Valley 43.39 1.567 61.280 14.79 0.625 9.548 5.01 0.247 1.955 Morgan Hill 11.43 0.413 16.143 27.15 1.148 17.528 14.07 0.695 5.492

B4



Imperial Valley 53.16 1.128 77.560 14.28 0.531 10.093 4.7 0.180 1.943 Landers 43.73 0.928 63.802 31.01 1.153 21.918 33.7 1.289 13.930

Table 4 Peak deformation of inelastic SDF systems and target displacements of roof, umo

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ground motion records. Several importantobservations emanate from figures 6 to 9 inconjunction with table 4. If SDF systems relatedto significant modes (usually 3 modes) of thebuildings remain elastic(

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a) Floor Displacements Northridge

0

2

4

6

8

10

0.0 0.6 1.2

Floor

MPA

NL-RHA

Duzce

0.0 0.6 1.2

Trinidad

0.0 0.6 1.2

Victoria

0.0 0.6 1.2

Hollister

0.0 0.6 1.2

ImperialValley

0.0 0.6 1.2

Morgan Hill

0.0 0.6 1.2

Floor Displacement/ Height (%)

b) Storey Drifts Northridge

0

2

4

6

8

10

0 1 2

Floor

MPA

NL-RHA

Duzce

0 1 2

Trinidad

0 1 2

Victoria

0 1 2

Hollister

0 1 2

Imperialvalley

0 1 2

Morgan Hill

0 1 2

Storey drift Ratio(%)

c) Floor Displacements Northridge

0

2

4

6

8

10

-40 0 40

Floor

Duzce

-40 0 40

Trinidad

-40 0 40

Victoria

-40 0 40

Hollister

-40 0 40

Imperial Valley

-40 0 40

Morgan Hill

-40 0 40

Error (%)

d) Storey DriftsNorthridge

0

2

4

6

8

10

-60 0 60

Floor

Duzce

-60 0 60

Trinidad

-60 0 60

Victoria

-60 0 60

Hollister

-60 0 60

Imperial valley

-60 0 60

Morgan Hill

-60 0 60

Error (%)

Fig.6 Height-wise variation of floor displacements and storey drift ratios and Error of MPA for 10 storey Building


0

3

6

9

12

15

0.0 0.5 1.0

Floor

MPA

NL-RHA

Duzce

0.0 0.5 1.0

Trinidad

0.0 0.5 1.0

Victoria

0.0 0.5 1.0

Hollister

0.0 0.5 1.0

Imperial Valley

0.0 0.5 1.0

Morgan Hill

0.0 0.5 1.0



0

3

6

9

12

15

0.0 1.1 2.2

Floor

MPA

NL-RHA

Duzce

0.0 1.1 2.2

Trinidad

0.0 1.1 2.2

Victoria

0.0 1.1 2.2

Hollister

0.0 1.1 2.2

Imperial valley

0.0 1.1 2.2

Morgan Hill

0.0 1.1 2.2


c) Floor Displacements Duzce

-40 0 40

Trinidad

-40 0 40

Victoria

-40 0 40

Hollister

-40 0 40

Imperial Valley

-40 0 40

Morgan Hill

-40 0 40

Error (%)

d) Storey DriftsNorthridge

0

3

6

9

12

15

-40 0 40

Floor

Duzce

-40 0 40

Trinidad

-40 0 40

Victoria

-40 0 40

Hollister

-40 0 40

Imperial valley

-40 0 40

Morgan Hill

-40 0 40

Error (%)

Northridge

0

3

6

9

12

15

-40 0 40

Floor


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0

5

10

15

20

0.0 0.5 1.0

Floor

MPA

NL-RHA

Duzce

0.0 0.5 1.0

Trinidad

0.0 0.5 1.0

Victoria

0.0 0.5 1.0

Hollister

0.0 0.5 1.0

Imperial Valley

0.0 0.5 1.0

Morgan Hill

0.0 0.5 1.0



0

5

10

15

20

0.0 1.3 2.6

Floor

MPA

NL-RHA

Duzce

0.0 1.3 2.6

Trinidad

0.0 1.3 2.6

Victoria

0.0 1.3 2.6

Hollister

0.0 1.3 2.6

Imperialvalley

0.0 1.3 2.6

Morgan Hill

0.0 1.3 2.6



0

5

10

15

20

-40 0 40

Floor

Duzce

-40 0 40

Trinidad

-40 0 40

Victoria

-40 0 40

Hollister

-40 0 40

Imperial Valley

-60 0 60

Morgan Hill

-40 0 40

Error (%)

d) Storey Drift RatiosNorthridge

0

5

10

15

20

-60 0 60

Floor

Duzce

-60 0 60

Trinidad

-60 0 60

Victoria

-60 0 60

Hollister

-60 0 60

Imperial valley

-60 0 60

Morgan Hill

-60 0 60

Error (%)



0

5

10

15

20

25

30

0.0 0.5 1.0

Floor

MPA

NL-RHA

Duzce

0.0 0.5 1.0

Trinidad

0.0 0.5 1.0

Victoria

0.0 0.5 1.0

Hollister

0.0 0.5 1.0

Imperial Valley

0.0 0.5 1.0

Landers

0.0 0.5 1.0



0

5

10

15

20

25

30

0.0 1.2 2.4

Floor MPA

NL-RHA

Duzce

0.0 1.2 2.4

Trinidad

0.0 1.2 2.4

Victoria

0.0 1.2 2.4

Hollister

0.0 1.2 2.4

Imperialvalley

0.0 1.2 2.4

Landers

0.0 1.3 2.



0

5

10

15

20

25

30

-40 0 40

Floor

Duzce

-40 0 40

Trinidad

-40 0 40

Victoria

-40 0 40

Hollister

-40 0 40

Imperial Valley

-40 0 40

Landers

-40 0 40

Error (%)

d) Storey Drift RatiosNorthridge

0

5

10

15

20

25

30

-40 0 40

Floor

Duzce

-40 0 40

Trinidad

-40 0 40

Victoria

-40 0 40

Hollister

-40 0 40

Imperial valley

-40 0 40

Landers

-40 0 40

Error (%)

Fig.9 Height-wise variation of floor displacements and storey drift ratios and error of MPA for 30 storey building

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a)Floor Displacements of 10 Storey Building

0

2

4

6

8

10

0.0 0.2 0.4 0.6 0.8 1.0Displacement/Height(%)

Floo

r

NL-RHA

uniform

SRSS

ELF

MPA

b)Floor Displacements of 15 Storey Building

0

3

6

9

12

15

0.0 0.2 0.4 0.6 0.8Displacement/Height(%)

Floo

r

NL-RHAuniformSRSSELFMPA

Fig.10 Height-wise variation of floor displacements of 10 and 15 storey buildings

a)Floor Displacements of 20 Storey Building

0

5

10

15

20

0.0 0.1 0.2 0.3 0.4 0.5 0.6Displacement/Height(%)

Floo

r


b)Floor Displacements of 30 Storey Building

0

5

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Fig.11 Height-wise variation of floor displacements of 20 and 30 storey buildings

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b) Story Drift Ratios of 15 Storey Building

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Fig.12 Heightwise variation of story drifts of 10 and 15 storey buildings


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Fig.13 Heightwise variation of story drifts of 20 and 30 storey buildings

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Fig.14 Errors in story drifts of 10 and 15 storey buildings


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Fig.15 Errors in story drifts of 20 and 30 storey buildings

a) Hinge Plastic Rotations of 10 Storey Building

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b) Hinge Plastic Rotations of 15 Storey Building

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Fig.16 Height-wise variation of hinge plastic rotations of 10 and 15 storey buildings


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Fig.17 Height-wise variation of hinge plastic rotations of 20 and 30 storey buildings

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a) Hinge Plastic Rotationsof 10 Storey Building

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Fig.18 Errors in hinge plastic rotations of 10 and 15 storey buildings


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FEMA-Uniform FEMA-ELF

FEMA-Uniform FEMA-ELF


Fig.20 Locations of plastic hinges yielded by several analyses for 15 storey building


( )


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MPA- 3 modes NL-RHA

MPA- 3 modes NL-RHA

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distributions and MPA procedure are unable toaccurately predict the hinge location in mediumhigh-rise buildings and high-rise ones; BothFEMA and modal pushover analyses areunsuccessful to identify yielding of the beams atupper floor levels and several other locations.(The results of other buildings arent presentedhere for the sake of briefness.)

As a matter of fact, these deficiencies pointtowards the necessity of another improvement inpushover analysis to overcome the shortcomings,compute hinge plastic rotations more reliablythan current pushover procedures and result inmore time savings compared to MPA.

Although MPA procedure conceptually is moreattractive, it needs additional effort associatedwith calculating the peak value of deformationhistory, Dn , idealizing the pushover curve as abilinear curve ,converting it into force-deformation relation for the first n modes andimplementing modal pushover analysesindividually for each of ground motions.Therefore, this procedure will run into a lot oftime if a variety of ground motion patterns isused.

Pushover analysis suffers from some limitationsand the cumulative rotation of the plastic hinge isnot considered in pushover analysis [Chopra ,A.K. and Goel , R.K., 2001]. Maybe it is possibleto propose in future a procedure whereby reversalof lateral forces is provided at some top floorlevels for the sake of higher mode effects duringa single pushover analysis. Reversal of lateralloads may help to cumulative measure ofresponse to some extent and consequently resultin satisfactory predictions of hinge plasticrotations. This issue needs to more investigation.

Conclusions

The MPA is an enhanced pushover proceduredeveloped to provide improved seismic demandpredictions when higher mode effects aresignificant. The seismic demands obtained byMPA procedure will be unreliable in nonlinear

systems subjected to individual ground motionswhich inelastic SDF systems related tosignificant modes of the buildings respondbeyond the elastic limit ( m >1). Therefore, itsnecessary to avoid evaluating seismic demands ofthe buildings based on individual ground motion.Hence, the assessment is accomplished based onthe median values obtained by an ensemble ofground motions. The MPA procedure results insignificant superiority in computing the storeydrift ratios in relation to FEMA load distributionsand it almost yields acceptable estimates forprofessional practice. FEMA load distributionsall grossly underestimate storey drift ratios atupper storeys of medium high-rise (e.g. 10 and 15storey) and high-rise (e.g. 20 and 30 storey)buildings.

Indeed, both MPA procedure and FEMA loaddistributions fail to predict with convincingaccuracy plastic rotations of hinges and toindicate locations of plastic hinges at top floorlevels. The underestimation by these proceduresis very large and even reaches by up to 100%occasionally.

Therefore, it is necessary to be developed anotherimproved pushover procedure considering highermode effects to overcome the shortcomings,compute hinge plastic rotations more reliablythan current procedures, resolve the issue ofcumulative measure of responses to some extentand result in more time savings compared toMPA. Research in this respect continues.

References

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Antoniou , S. and pinho , R., 2004b.Development and Verification of adisplacement based adaptive pushoverprocedure, journal of EarthquakeEngineering, 8(5), pp. 643-661.

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Goel , R.K., and Chopra, A.K., 2004Evaluation of modal and FEMA pushoveranalysis: SAC Buildings , EarthquakeSpectra, 20(1) , pp. 225-224.

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