Study of Higher Mode

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Advances in Science and TechnologyResearch JournalVolume 10, No. 29, March 2016, pages 13–27DOI: 10.12913/22998624/61926

Research Article

Received: 2015.12.15Accepted: 2016.02.01Published: 2016.03.01

STUDY OF HIGHER MODE EFFECTS AND LATERAL LOAD PATTERNS INPUSHOVER ANALYSIS OF STEEL FRAMES WITH STEEL SHEAR WALL

Mohammad Ghanoonibagha 1, Mohammad Reza Ashra Gol 2, Mohammad Reza Ranjbar 3

1 Department of Civil Engineering, East Tehran Branch, Islamic Azad University, Tehran, Iran, e-mail:[email protected]

2 School of Civil Engineering, Iran University of Science and Technology, Narmak, Tehran, Iran3 Technical Faculty of Mapping, Zabol University, Zabol, Iran

ABSTRACTWhen an earthquake occurs, the structure will enter into a nonlinear stage; therefore,new approaches based on nonlinear analysis are needed to ourish with the purpose ofmore realistic investigations on seismic behavior and destruction mechanism of struc-tures. According to the modern philosophy, “Performance-based Earthquake Engi-neering” is formed in which simple nonlinear static analyses are mostly used in orderto determine the structure’s behavior in nonlinear stage. This method assumes that thestructure response is only controlled by the main mode and the shape of this mode willremain the same, while it enters the nonlinear stage. Both of these assumptions areapproximations, especially in high buildings, which have a long period. It seems thatconstant load pattern used in these methods cannot consider all of the effects properly.In this paper, an attempt was made to study the accuracy of these methods in com-

parison to nonlinear dynamic analysis, by considering various load patterns existingin FEMA, also load patterns proportional to higher modes in nonlinear static method,and employing an approximative method of MPA modal analysis, study the accuracyof these methods in comparison to nonlinear dynamic analysis. For this purpose, threesteel frames of 4, 8, and 12-stories with steel shear wall have been studied.

Keywords : load patterns, steel shear wall, static nonlinear, dynamic nonlinear.

INTRODUCTION

With advancements in earthquake recognition,appearing growth in seismic improvement con-

cepts and performance-based design, consideringan accurate and realistic form of the structure be-havior tends to gain more importance than before.It is essential to discuss various factors which de-

pict the precise structure behavior, because it leadsto a better prediction and prevention of damage.In fact, nowadays, only horrible and destructivedisasters like earthquake in metropolises can fea-ture the valuable aspects of the above mentionedissue. Moreover, demolition of buildings whichare vulnerable to earthquakes and construction

of alternative buildings requires enormous wasteof time and cost that in some cases providing thenecessary stuff is not even possible.

Among the methods which help the improve-ment and retro tting of the buildings againstearthquake is the steel shear wall method. In this

present study the effects of higher modes in ret-

ro tting of structures by means of shear wall wasinvestigated.

In commencement of steel shear walls con-struction in the United States of America and Ja-

pan, vertical and horizontal stiffeners was usedwhich restricted the buckling of sheet and im-

proved the shear resistance of steel sheet. How-ever, welding, which is necessary for junction ofstiffeners to wall, was costly and time-consum-ing; as a result, plenty of studies and examina-tions were conducted on shear walls without stiff-

ener in US and Japan. The main idea for the usageof steel plate shear walls without stiffeners is to pro t from diagonal strain eld that is present af -


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ter the buckling of steel sheet. This phenomenonis post-buckling in steel sheet, which is commonin beam-plates. In this case the panel resists untilthe yielding of the steel sheet which will causethem to endure considerable forces.

The rst studies on beam-plates were in1980’s at Alberta University, Canada by Coolak,Driver, Timler and et al. [1, 2, 3]. Following them,many other scientists, e.g. Bruneau and Bhag-wagar [4], Berman and Bruneau [5], Elghali et al.[6, 7], Astaneh Asl [8, 9], and Sabouri Ghomi [10,11] have examined numerous tests on the subject.

MODELING OF STEEL SHEAR WALLS

Steel shear wall systems without stiffenerinclude steel plate panel, two boundary columnsand horizontal beams at the bottom. It is requiredthat each steel shear wall resists horizontal shearof stories and overturning anchor due to lateralloads. The shear wall, along with two columns,acts as a vertical cantilever beam-plate. Columnsact as sheet beam ange, wall panels as websheets and bottom beams as transverse stiffen-ers of web sheets. Investigations on panel behav-iors in the case of no stiffener showed that therewould be much more ductility and energy dissipa-

tion comparing to the case where stiffener exists;as a result there have been recent trends towardsthe matter in United States and Canada.

Theoretical studies on design and analysis ofsteel shear walls concluded in two ultimate be-havioral models of the context. The rst modelis based on substitution of diagonal strips withdoubler plate (strip model) which has been intro-duced by Thorburn (1983) in order to design steelshear walls. It is also accepted as an appendix toCanadian Steel Standard (CAN/CSA S16-01) and

is shown in Figure 1 [12]. Moreover, this methodis mentioned in seismic provisions for StructuralSteel Buildings (AISC 2005) in chapter 17 [13].The second model is based on the plastic yield-ing of the plate with surrounding frame (plasticyielding model) presented by Sabouri & Roberts(1991) [10]. In this study the rst model is em -

ployed to design steel shear walls. The design procedure is that rstly for pre -

liminary cross sections design of beam, columnand web, similar shear wall is approximated bya vertical truss with tension braces. In fact, eachsteel plate is represented by an equivalent brace.After the structural analysis and calculation of

cross-sectional area of braces, based on the elas-tic stress energy formula (equation 1) for the as-sumed angle of the tension eld, the steel platethickness can be achieved. Then, by using stiff-ness of beam, column, and plate thickness, theangle of the tension eld ( α) is taken place in thesheet.

2sinLsinA2

t s b (1)

where: Ω S – system’s over-strength factor,which is 1.2 for shear walls;

θ – the angle between brace and column. L – distance between column centerlines. α – the angle of inclination of the tension

eld in the steel plate (angle of replaceddiagonal strips with vertical direction)according to gure 1 which is obtainablefrom equation (2).

As in the current study, the steel panels do nothave hardening (stiffener), though they possesshigh width-to-thickness ratio, and when lateralforces are prescribed, they behave as deep beamsheets. The tension eld is formed in tensile diam -eter direction and considerable forces are imposedin this way, while in direction of compression di-ameter with critical plate-buckling little tensionstake form. When force side changes, direction oftension eld and forces transfer is inversed. Theinclination angle of the tension eld depends tothe geometrical properties of building and crosssections of walls boundary members (beam andcolumn). The Canadian Standard proposes thefollowing equation for this angle calculation:

)LI360/hA/1(ht1

A2/Lt1tan

c3

s bsw

cw4

(2)

Fig. 1. Thorburn strip model (using truss elements) [1]


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where: L and hs are length and height of throat,A b, A c, I c are cross sections of beam, col-umn and the moment of inertia of a col-umn respectively, while t w is the thicknessof the web.

After that, by using equation (3) sheet is trans-formed into some equivalent strips. Regardingthe experimental results and recommendationsof other researchers (Astaneh [8, 9]) at least 10members in the throat were used while creatingdiagonal strips. The cross section area of thesemembers is in rectangular form and is equal tothe distance between two strips; the thickness ofthe members is the same as the calculated thick-ness of the design.

wss tn

sinhcosLA

(3)

where: L, h are width and height of wall throat.

In order to insure the quality of the side col-umns stiffness that will not endure any sufferingfrom buckling while they are exposed to diamet-rical tension, the moment of inertia should be asfollows:

L

h.t00307.0I

4s

c

(4)

In this method, the Canadian Standard setsthis commitment that besides the initial design,columns should be controlled with B coef cientfor forces from gravity loads combined with in-creased loads due to earthquake (equation (5)).The B Coef cient is in fact the ratio of the ex -

pected resistance of wall to the design shear inthe nal case. Therefore, the increased resistanceof the wall sheet can be observed in the nal caseand the columns are designed for that.

u

e

V

VB

(5)

2sinLtFR 5.0V cf wyye

(6)where: R y – is the ratio of average steel yielding

tension to design yield tension,Fy – is steel plate’s design yield tension,Lcf – is the net distance between columns.α – is the inclination angle of the diamet-rical tension eld in steel plate,

tw – is the thickness of the web plate.

In this approach, axial forces in the columndue to earthquake should be obtained from over-turning anchor BM u where M u is the anchor at

column’s end due to seismic loads V u. BM u an-chor must be considered at least for two rst sto -ries. After that, the anchor in other stories is cal-

culated from multiplication of overturning anchorof that storey to coef cient B. Moreover, bendinganchors of columns which are due to tension eldof the web plate must increase according to B co-ef cient then the design continues.

For studying and calculation of structures vibration modes, they can be modeled in CSI groupsoftware environments including Etabs2000,Sap2000, and Perform 3D. In the present re-search, the results obtained from nonlinear staticanalysis of three building frames under differentlateral loading patterns are compared with the re-sults of nonlinear dynamic analysis.

REVIEW OF STU5DIED MODELS

In purpose of simplicity, the studied models ofthe present study were considered as three build-ing frames of 4, 8, and 12 symmetrical stories,

ve throats with 4 meter width along with aver -age bending steel frame. The height of all storiesis equal to 3.3 meters high. The structure roofs areconsidered to be built from joist and to be rigid.The aim of the base improvements and structuresusages is educational matters. The gravity load-ing is computed according to Iranian loadingstandard [14]. In addition, base shear was takeninto account corresponding to standard 2800 [15],then harm amount study for buildings has beenmade according to criteria mentioned in Fema356[16] and techniques presented in reference book[17]. It was revealed that the under study build-ings are not capable to respond to the prescribedloading and hence require improvements. As aresult, for structural reform the steel shear wallis employed. For the purpose of designing steelshear wall, lateral loading due to earthquake must

be calculated rst. Appendix R from American

standard has proposed R = 11 for bending framedual system behavior coef cient with steel shearwalls without stiffeners. In this case, by having R,earthquake can be calculated according to corre-sponding static method in Iranian 2800 standard.

Building plans which have been studied in this paper is presented in Figures 2a (4 storey buildingframe), 3a (8 storey building frame), 4a(12 storey

building frame) besides the results of conductedanalysis according to the following explanations.

The masonry assumptions are as follows:

Steel St37, yield tension F y=2400 kg/cm2

, elasticstiffness E = 2.1×10 6 kg/cm 2. The structural load-ing and nonlinear joints de nition (for all beams


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and columns) and computation of change in targetlocation are all according to criteria written in theFema 356 and ATC 40 [18]. It worth mention-ing that, the force-web strip members’ locationchange curve is modeled by two line elasto-plas-tic model. The effects of hardening stress are alsoconsidered with a slope of 3% in recessive part.Modeling parameters and acceptance criteria ofshear wall elements as an axial member in thetraction is like an ordinary traction member (ac-cording to FEMA 356 and seismic AISC criteria)and has small compression resistance.

THE PROCEDURE AND TECHNIQUES OFMODELS ANALYSIS

Nonlinear dynamic analyzing method andmodal analysis

In order to perform nonlinear dynamic anal-ysis on the frames, also modal increased loadanalysis of a system with one degree of freedomseven pairs of registered acceleration mappingconsist of: El centro, Kobe, Naghan, ChiChi, SanFernando, Northridge, Bam are used; all of thesemappings are held on type II (according to Irani-an standard 2800) as time history of earth drastic

movement. Regarding Iranian Standard 2800, allof these acceleration mappings should be tanta-mount. In this study, the average spectrum fromseven pair of acceleration mapping is coordinatedwith design spectrum of Standard 2800 for soiltype II. After that, nonlinear dynamic analysis of

principal structure is held by means of selectedacceleration mappings.

Following that, by operating modal analy-sis the numerical amount of ω n and ϕn is calcu-lated for each mode. Then, Pushover analysisfor each mode is done with load distribution

pattern of *n nS m= φ , and the base shear-roof displacement curve ( V b –V m) is idealized by a bi-linear procedures. After all, the fundamentalcurve is transferred by ( F sn/ Ln) – D n format foreach mode [19, 20].

System nonlinear dynamic analysis SDOFof nth mode is operated for each of the accelera-tion mappings in order to calculate the maximumdeformation ( D n) with force – displacement rela-tion (( F sn/ Ln) – D n). For each mode the averageof responses are calculated and it is followed bythe calculation of the maximum roof displace-ment or target displacement for each mode. Until

reaching the target displacement the main struc-ture (MDOF) will be assumed as push. Responsequantity in target displacement in each mode iscalculated and overall response for adequatemodes are combined by statistical methods suchas SRSS.

In this paper, the responses resulted fromMPA method (Modal Pushover Analysis) andconventional Pushover method with FEMA loaddistribution pattern is compared with responsesfrom nonlinear dynamic technique. Responsequantities include maximum storey displacement,relative storey displacement, and base shear. Inorder to conduct system nonlinear dynamic anal-ysis MDOF, SAP2000 v. 14 is employed; also fornonlinear static analysis Etabs2000 v. 9.7 soft-ware is used which are approved by Berkley uni-versity researchers.

Pushover analysis according to FEMA 273

In this study, in order to avoid errors fromdifferent approximative methods of target dis-

placement determination into calculations, roofdisplacement resulted from MPA method is usedfor FEMA load distribution patterns. Thereby, forstructure pushover analysis, with relative load

pattern modes, uniform and SRSS is operated.Three main FEMA load patterns which were

studied in this research and the pushover analysisis held upon them can be summarized as follows:

Uniform distribution: in this pattern, the pre-scribed forces into each storey is relative to themass and is obtained from the following equation:

i

N

i

j j

m

mS

1

*

(7)

Equivalent lateral force (ELF): which is usu-ally used when more than 75 percent of overallmass contributes in the base mode on the understudy direction.

k ii

N

i

k j j

j

hm

hmS

1

*

(8)

where: i is the number of storey and i = 1, 2, …, N.

In the above equation k = 1 for the base periodT 1 ≤ 0.5, k = 2 for T 1 ≥ 2.5 seconds and varies lin -early between these two amounts.

SRSS pattern (distribution) – lateral load inthis method is dependent on Inertia forces de-duced from elastic spectrum analysis. In this anal-


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ysis the modes contributions must be to the extentthat 90 percent of the mode mass contribution to

be taken into account. This analysis takes place by appropriate earthquake spectrum.

i

N

1i

j j

f

f f ~

(9)

According to FEMA guidelines, other properload patterns which have previously been exam-ined and controlled, can replace the above ternate

patterns.

EXAMINED OUTCOME PARAMETERSFROM ANALYSIS RESULTS

Following the conducted analysis, by pre-scribing the existing FEMA patterns and loadmode patterns applied in MPA method on se-lected modes, a comparison of these methods’ ac-curacy and ability in facing structural responseswith results from the precise method of nonlineardynamic analysis is done.

As it was mentioned before, the response pa-rameters which have been derived from analysis andhave been compared to each other are as follows:

• the maximum oor displacement in percent -

age from building’s height, FloorDisplacement 100

HeightFrame

(10)

• relative oor displacement in percent (DriftRatio),

FloorDrift 100StoryHeight

(11)

• base shear from the above mentioned param-eters, the second parameter has the most im-

portance in estimation of building destruction.

Next in this section, signi cant points in con -

ducted analysis and a summary of principal meth-ods are presented together with the manipulatedmethod in this study.

Idealization of bilinear pushover curve

Various methods can be applied for makingnonlinear systems as bilinear ones. In this paper,it is intended to equalize the structure capacitycurve, thus, MATLAB programming environ-ment is used in order to make the structure ca-

pacity curve bilinear, according to FEMA 356.Therefore, the equivalent pushover curve of asystem with one degree of freedom is idealized

in a way that the area beneath the bilinear curveis equal to the area under the pushover curve.Because the maximum amount of roof drift isnot given at the beginning, choosing the ultimate

point of pushover curve and the surface under itcan raise some doubts. Hence, in order to deter-mine the area under the pushover curve and its

bilinear idealization an iterating method is employed. On the rst step, a point is assumed asthe selected displacement target on the pushovercurve, and then the area under the curve is calcu-lated right from the assumed point. According tothis calculated area, the pushover curve is ideal-ized in a bilinear form. By means of the achieved

bilinear curve, the nonlinear dynamic analysis is performed and the peak displacement of the ideal bilinear system can be obtained. This peak displacement is compared with the initial assumed point. If these two points coincide, the target isreached, else the peak displacement due fromnonlinear dynamic analysis is substituted withthe initial presumed point and the process is onceagain repeated until the initial assumed point andthe corresponding point of peak displacement fora system with one degree of freedom would con-verge equally with each other.

Determination of the peak displacementfor nonlinear systems with one degree offreedom

In conventional Pushover methods, for deter-mining the peak displacement of equivalent sys-tem with one degree of freedom and estimationof target displacement in different orders, variousmethods can be used. These methods can be cat-egorized in three groups:

• FEMA 356 method (displacement coef cientmethods), in this method the response of a

nonlinear system with one degree of freedomis estimated from the elastic response of sys-tem with one degree of freedom and by meansof adjustment factors.

• Capacity spectrum method (ATC-40), in thismethod the simpli ed elastic response spec -trum (demand spectrum) is used in accelera-tion-displacement (ADRS) format. In fact, in-stead of using inelastic demand spectrum theelastic spectrum equivalent with high damp-ing is applied. Besides, the nonlinear systemwith one degree of freedom is equalized witha linear system with low stiffness and highdamping ratio.


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• N2 method, in this method in order to estimatethe maximum displacement of the equivalentsystem with one degree of freedom, inelasticspectrum with different formation ratio (µ) isdirectly used.

Averaging of target displacement

The accuracy of the MPA method is totallydependent to severity of earth movements. Theresults of this method can be trusted only if theMPA procedure is performed for some earth-quakes and from the achieved results are aver-aged. This process requires massive and timeconsuming calculations.

In this study and during the performed proce-dures, seven pairs of accelerating mappings are

used for nonlinear dynamic analysis but the re-cords are compared according to 2800 standardcriteria whose responses must be averaged basedon FEMA 356. The common method in averag-ing is arithmetical method in which the sum ofresponses is divided by their number and the con-tribution of each response in the average amountis supposed equal. This method is valid for es-timating linear methods but because of compli-cated essence of responses in nonlinear dynamicanalysis, this method does not seem to be proper.Therefore, there is another method which is ex-

ponential averaging. Converting the sophisticated parameters to logarithmic coordinates will causethe changes to accede to linear state which is usu-al in seismic engineering.

In this paper, the arithmetical averagingmethod is employed; however, for maximum dis-

placement of equivalent system with one degreeof freedom under nonlinear dynamic analysis re-garding the nonlinear nature of the responses, ex-

ponential averaging is used.For utilization of exponential averaging

method, average D i is obtained from the follow-ing equation:

n

ii 1

Ln(D )ˆ

D(n) expn

(12)

RESULTS PRESENTATION ANDEVALUATION OF PERFORMED ANALYSIS

FOR UNDER STUDY BUILDING FRAMES

Analyzing 4-storey frame with steel shear wall

For the analyzed 4-sorey structure illustratedin Figure 2a, a different analysis of nonlinearstatic and dynamic, which was explained in the

previous sections, were performed. The resultsfrom nonlinear dynamic analysis of 4-storeyframe are achieved according to selected accel-eration mapping and pursuant to the process thathave been described previously. The amountsof relative displacement and maximum storeydisplacement in nonlinear dynamic analysis of a4-storey building are depicted in Figures 2b and2c respectively.

Moreover, a modal analysis is the rst imple -mented for the structure; subsequently, in accor-dance with each of the rst three modes, the push -over analysis with load pattern proportion to eachmode is performed. In Figures 2d and 2g, respons-es of structure modal analysis, vibration mode ofstructure, bilinear idealized capacity curve (baseshear according to roof displacement), base build-ing shear, and effective base shear is shown. Inaddition, considering the implemented analysis,

respectively in Figures 2h and 2i the results of rela-tive displacements and maximum storey displace-ment for different vibration modes are demon-strated and compared with the results of nonlineardynamic analysis.

Following the performed nonlinear analysison 4-storey structure frame, pushover analysisstudy according to FEMA guideline is carried out.In Figure 2j, the results from structure pushoveranalysis and the shape of structure lateral load

pattern is shown based on the three methods men-

tioned in this section. For these analysis and lat-eral load patterns, the idealized bilinear diagramof capacity curve (base shear according to roofdisplacement) can be achieved which have beenconsidered in the conclusion section. In the fol-lowing, in Figures 2k and 2l the nal results of

Table 1. Amounts of building base shear in 4-storey frame by means of MPA estimations (in 3 modes), FEMA,and estimation errors

Base shear [ton] Error [%]

Fema MPA(3 mode)

RHA(Avg)

FemaMPAUniform ELF SRSS Uniform ELF SRSS

135 111 108 120 105 28 6 3 13


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Fig. 2a. Frame under study of 4-storey buildingframe

Fig. 2b. Relative displacement in nonlineardynamic analysis

Fig. 2c. Maximum storey displacement in non-linear dynamic analysis

Fig. 2d. Structure mode shape in three rst modes

Fig. 2e. Pushover curve for rst structure vibra -tion mode shape Fig. 2f. Pushover curve for second mode


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Fig. 2g. Pushover curve for third mode

Fig. 2h. determination of relative storey displacement from MPA estimations

Fig. 2i. Determination of maximum storey displacement from MPA estimations

Fig. 2j. FEMA load distribution patterns scheme

Fig. 2k. relative storey displacement from MPAand FEMA estimations

Fig. 2l. maximum storey displacement fromMPA and FEMA estimations

Fig. 2. Analysis results for 4-storey structure


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relative storey displacement and maximum displacements by different methods are shown.

Table 1 summarizes the result comparison of base shear structure of 4-storey frame under vari-ous analysis.

Results from 8-storey frame analysis withsteel shear wall

For the 8-storey frame pictured in Figure 3a,various nonlinear static and dynamic analyseslikewise sections 4 and 5 have been performed.The results achieved from nonlinear dynamicanalysis on 8-storey frame according to selectedacceleration mappings and the mentioned pro-cedure, the relative displacement and maximumstorey displacement diagrams in nonlinear dy-

namic analysis are depicted in Figures 3b and 3c.In other stages of the analyses, for the rst

structure the modal analysis is conducted; then based on each three rst modes, the pushoveranalysis with load pattern proportionate to eachmode is implemented.

Based on the results from structure mode shapein three rst modes in Figure 3d, the pushover loadcurve (capacity or base shear curve in contrary toroof displacement) are drawn in Figures 3e and3g. In these gures the bilinear idealized capac -ity curves of the structure (base shear accordingto roof displacement and effective base shear) can

be observed. In Figures 3h and 3i, the results fromrelative displacement and the maximum story dis-

placement of MPA estimation in comparison withnonlinear dynamic method are presented. More-over, for the performed nonlinear analysis of the8-storey structural frame (as middle order frames),the pushover analysis is done according to FEMAguideline and load patterns. Figure 3j shows thestructure lateral load pattern according to the threemethods denoted before. For the accomplished

pushover analysis with the recommended lateralload patterns, the bilinear idealized capacity curve(base shear according to roof displacement) isachieved. In Figures 3k and 3l the nal relativestory displacement and the maximum displace-ments can be observed based on different meth-

ods. In Table 2, the result of comparison betweenthe structure base shear under different analysismethod for 8-storey frame is shown.

Results from 12-storey frame analysis withsteel shear wall

For the 12-storey frame structure shown inFigure 4a, different static and dynamic nonlin-ear analyses have been performed. The resultsfrom nonlinear dynamic analysis for this frameaccording to selected acceleration mappings andthe previously stated procedure are drawn in aform of relative displacement and maximum sto-rey displacement diagrams which are depicted inFigures 4b and 4c.

Following the analyses for this frame, rstly

the modal analysis is performed and then accord-ing to each three rst mode, the pushover analysiswith proportional loading pattern with each modeis done. In Figures 4d to 4g, the results of struc-ture modal analysis, vibration mode shape of thestructure, the idealized bilinear capacity curvediagram (base shear according to roof displace-ment), and the amounts of building base shear,structure effective base shear, target displacement,and corresponding yielding shear displacementare presented. In addition, regarding the analyses,Figures 4h and 4i respectively show the relativedisplacement and maximum storey displacementfor different vibration modes, in comparison withthe results from nonlinear dynamic analysis. Fi-nally, the nonlinear pushover analysis accordingto FEMA guideline is performed on the structural12-storey frame according to the explanations in

previous sections. In Figure 4j, the structure lat-eral load based on the three methods described inthis section can be observed. For these analysesand also lateral load patterns, the idealized bilin-ear capacity curve (base shear according to roofdisplacement) is calculated. The results of struc-ture pushover analysis are considered in conclu-sion section. Moreover, in gures 4k and 4l, the

nal results of relative storey displacement andmaximum displacements from various methodsare shown. In Table 3, comparison results be-



Fema MPA(3 mode)

RHA(Avg)

FemaMPAUniform ELF SRSS Uniform ELF SRSS

201 157 156 191 123 62 27 26 55


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Fig. 3h. Determination of relative storey displacement from MPA estimations




Fig. 3l. Maximum storey displacement fromMPA and FEMA estimations



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Fig. 4h. Determination of relative storey displacement from MPA estimations




Fig. 4l. Maximum storey displacement fromMPA and FEMA estimations



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tween structure base shear under different analy-sis for 12-storey frame is demonstrated.

CONCLUSIONS

In this paper, the 4-storey frame was consid-ered as short order frame, 8-storey as middle or-der frame, and 12-storey as a high order frame.According to the assumptions in this study (suchas 2-dimensional building, usage of accelerationmappings) and the performed analyses, the fol-lowing conclusions are achieved:

1. For short order frames: • Regarding the similar function of three distri-

bution load patterns and modal method in es-timation of maximum displacement and rela-tive storey displacement it can be deduced thathigher modes and the shape of the pattern doesnot have any effects on the nal response; thisdeduction can be due to the short order natureof the structure.

• For the base shear results, it can be inferredthat higher modes have unpleasant effects onresponse estimation. Moreover, the load dis-tribution gure in SRSS format will achieve

better results comparing to ELF and uniform.The performance of FEMA load distribution

patterns is relatively appropriate.

2. For middle order frames:

•

About FEMA load distribution pattern, theuniform load distribution in relative storeydisplacement estimation does not have proper

performance. Relatively, SRSS load distribu-tion pattern in relative estimation of storeydisplacement has better performance thanELF load distribution pattern.

• Uniform load distribution does not have prop-er performance in estimation of the maximumstory displacement in lower stories. ELF loaddistribution pattern comparing to other pat-terns acts more accurately.

• ELF load distribution can be achieved for rela-tive displacement and maximum displacement

of stories on one third of frames with the sameaccuracy or even better than MPA method. Inestimation of relative and maximum story dis-

placement, MPA method has weak performance. • Considering the base shear results, it can be

mentioned that higher modes have unpleasanteffects on estimating the response. Moreover,the load distribution scheme in SRSS formwill lead to better results comparing ELF anduniform.

3. For high order frames: • Uniform load distribution pattern in estima-

tion of maximum story displacement of lowerstories does not perform properly. ELF loaddistribution pattern, comparing to other pat-terns, acts more accurately. The performanceof FEMA load distribution patterns in estimat-ing maximum story displacement is unsuitable.

• MPA method, comparing to ELF and SRSS,

has weaker performance in estimation of max-imum story displacement.

• MPA method, comparing to ELF and SRSS,has much better performance in estimation ofmaximum base shear.

4. Finally, for all kinds of frames the followingconclusions can be made:

• Among the FEMA load distribution patterns,SRSS shows the stories base shear more ac-curately.

• Uniform load distribution in estimating storydisplacement, especially lower stories acts un-suitably. ELF pattern comparing to others actsmore accurately in response estimation.

• By increasing the frames’ height, the responsesresulted from load patterns and modal methodwill differ from each other.

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Fema MPA(3 mode)

RHA(Avg)

FemaMPA

Uniform ELF SRSS Uniform ELF SRSS

245 183 180 251 259 5 29 31 3


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Study of Higher Mode

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