energy dissipation and local, story, and global ductility...

Research ArticleEnergy Dissipation and Local Story and Global DuctilityReduction Factors in Steel Frames under VibrationsProduced by Earthquakes

Alfredo Reyes-Salazar 1 Eden Bojorquez 1 Juan Bojorquez1

Federico Valenzuela-Beltran 2 and Mario D Llanes-Tizoc 1

1Facultad de Ingenierıa Universidad Autonoma de Sinaloa Culiacan CP 80040 Sinaloa Mexico2Instituto de Ingenierıa Universidad Nacional Autonoma de Mexico CP 04510 Ciudad de Mexico Mexico

Correspondence should be addressed to Alfredo Reyes-Salazar reyesuasedumx

Received 5 June 2018 Accepted 17 September 2018 Published 14 October 2018

Academic Editor Giorgio Dalpiaz

Copyright copy 2018 Alfredo Reyes-Salazar et al +is is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work isproperly cited

Ductility plays a central role in seismic analysis and design of steel buildings A numerical investigation regarding theevaluation of energy dissipation ductility and ductility reduction factors for local story and global structural levels isconducted Some steel buildings and strong motions which were part of the SAC Steel Project are used Bending localductility capacity (microLϕ) of beams can reach values of up to 20 as shown in experimental investigations +e values are largerfor medium than for low-rise buildings reflecting the effect of the structural complexity on microLϕ Most of the dissipated energyoccurs on beams however resultant stresses at columns are also significantly reduced by beam yielding A value of 13 isproposed for the ratio of global to local ductility thus if local ductility capacity is stated as the basis for the design globalductility capacity can be calculated by using this ratio It is implicitly assumed in seismic codes that the magnitude of theglobal ductility reduction factor is about 4 according to the results found in this paper it is not justified a value of 3 isobserved to be more reasonable According to the well-known ratio of the ductility reduction factor to ductility this ratioshould be unity for the models under consideration the results of this study indicate that for global response parametersa value of 34 is more appropriate and that for local response parameters values larger than 2 can be reached the implicationof this is that using simplified methods like the static equivalent lateral force may result in nonconservative designs froma global structural point of view but in conservative designs from a local point of view A value of 8 is proposed for the ratio ofthe global ductility reduction factor to the global normalized energy

1 Introduction

Even though building structures undergo significantnonlinear deformations when subjected to strong earth-quakes simple elastic procedures are still used to determinethe seismic demands (International Building Code (IBC)[1] National Building Code of Canada (NBCC) [2] MexicoFederal District Code (MFDC) [3] and Eurocode 8 (EC)[4]) Simplified methods like the Static Equivalent LateralForce (SELF) are broadly used for regular buildings withrelatively short periods (low- and medium-rise) Howeverwhile using this procedure in steel buildings it is not

possible to properly capture the effects of nonlinearityintroduced by large deformations by the connections andby nonlinear geometry In addition dissipation of energydue to yielding of the material is considered in a very crudeway According to the method static analysis of thebuildings subjected to equivalent lateral forces which arerelated to the properties of the structure and the seismicityof the region provides the design forces In the procedurethe ductility parameter (micro) plays an important role in thedetermination of the design seismic forces since it is as-sociated with the energy dissipation structural capacityproduced by nonlinear behavior allowing for a reduction

HindawiShock and VibrationVolume 2018 Article ID 9713685 19 pageshttpsdoiorg10115520189713685

of the elastic strength demands the larger the ductility thesmaller the design seismic forces In fact the magnitude ofthe reduction of the elastic design seismic forces directlydepend on a parameter that in general can be called ldquothereduction factorrdquo which in turn greatly depends on anassociated parameter called the ductility reduction factor(Rmicro) [5 6] It is particularly important for steel structuressince the beneficial effect of ductility and energy dissipationis supposed to come from different sources However thereis not unanimity on the profession on how to define it it isargued that this parameter is constantly used in the pro-fession in an indirect way to estimate the building seismicdesign forces but there is no engineering definition of it inour specifications [7 8] Defining the magnitude of theseparameters represents one of the most controversial issuesin the SELF procedure

+e reduction factor receives the name of the responsemodification factor (R) force modification factor (Rd)seismic reduction factor (Qprime) and seismic reduction factor(qprime) in the IBC NBCC MFDC and EC codes respectively Itis implicitly or explicitly assumed in these codes that duc-tility represents the capacity of the structure to dissipateenergy and that the reduction of the elastic demands im-portantly depends on the ductility capacity

+us the ductility parameter and the ductility reductionfactors play a central role in the seismic design of steelbuildings for that reason it has been an important researchtopic during the last recent decades However there aremany aspects that need additional attention some of themare addressed in this research As it is further elaboratedbelow the central objective of this paper is to evaluate theductility parameter the ductility reduction factor (Rmicro) forsteel buildings with moment-resisting frames (MRF) fordifferent structural levels (local story and global) relatingthem with the dissipated energy +e evaluation of the micro andRmicro parameters according to sophisticated nonlinear analysisprocedures to capture the effects of the mentioned sources ofnonlinearity is needed It is accepted that nonlinear timehistory analysis is the most accurate and reliable analysisprocedure providing a realistic modeling of the structure aswell as of the cyclic load deformation characteristics of itsstructural elements Extensive seismic nonlinear time-history analyses are performed in this investigation toreach the objectives of the study +e results are comparedwith those specified in the codes

2 Literature Review and Objectives

Investigations regarding nonlinear analysis of buildingsunder the action of earthquakes following different objec-tives have been conducted by many researchers during thelast decades In this regard since this dissipation of energyallows for a reduction of the elastic seismic forces thequantification of the ductility demand the ductility re-duction factor and the force (or seismic) reduction factor isof particular interest +ere have been many studies con-sidering concrete or steel buildings modeled as SDOF orsimple systems Introduced first in ATC [9] at the end of the70s the modification factor was used to reduce the elastic

response (base shear) obtained from a 5 damped accel-eration response spectra Among the first investigations wecan also find those of Newmark and Hall [10] and theyproposed a procedure to relate Rμ and μ based on the basicelastic design spectra Hadjian [11] calculated the spectralaccelerations considering the nonlinear deformation ofstructures Miranda and Bertero [12] proposed simplifiedexpressions to estimate the inelastic design spectra asa function of the maximum tolerable ductility Whitakeret al [13] proposed calculating R as the product of factorsaccounting for viscous damping ductility and overstrengthArroyo-Espinoza and Teran-Gilmore [14] from the dynamicresponse of SDOF systems proposed expressions to calculateRmicro Levy et al [15] derived approximate harmonic equivalentstiffness and damping for bilinear systems in the context ofearthquake resistant Karmakar and Gupta [16] by usingelastoplastic oscillators performed a parametric study toestimate the dependence of strength reduction factors onstrong motion duration earthquake magnitude geologicalsite conditions and epicentral distance Rupakhety andSigbjornsson [17] presented ground-motion predictionequations which describe constant-ductility inelastic spec-tral ordinates and structural behavior factors to be appliedwithin the framework of Eurocode 8 Sanchez-Ricart [18]reviewed the backgrounds that support the values of thereduction factor in the United States Europe and JapanHalabian and Kabiri [19] evaluated the effect of the foun-dation flexibility on the ductility reduction factors of rein-forced concrete stack-like structures AlHamaydeh et al [20]investigated the force reduction factors for reinforce con-crete frame buildings designed according to the IBC codeNaimi et al [21] studied the reduced beam section approachvia the introduction of multilongitudinal voids in the beamweb for various beam depths where the ANSYS finite el-ement program was used in the numerical simulation Animprovement in the connection ductility was observed sincethe input energy was dissipated uniformly along the beamlength Azimi et al [22] proposed a new beam to columnconnection and numerically and experimentally showed thatthe new connection could improve the ultimate structurallateral resistance ductility and energy dissipation capacityFanaie and Shamlou [23] calculated the overstrengthductility and response modification factors for framesbraced with a different type of buckling restrained bracesZhai et al [24] investigated the strength reduction factor ofSDOF systems with constant ductility performance sub-jected to the mainshock-aftershock sequence-type groundmotions Wang et al [25] studied the nonlinear behavior ofprestressed steel reinforced concrete beams by using finiteelement analysis Based on the model they analyzed theeffect of prestressed force to the stiffness the ultimatebearing capacity and ductility of the beams Cho et al [26]investigated the shear design equations for prestressedhollow-core slabs and examined the magnitude of thestrength reduction factors based on the structural reliabilitytheory +e results showed that the shear strengths of themembers with the heights of more than 315mm are ex-cessively safe whereas some members with low depths didnot satisfy the target reliability index

2 Shock and Vibration

+ere are also several studies regarding the evaluation Rμand μ factors for multidegree of freedom (MDOF) systemsNassar and Krawinkler [27] studied the relationship betweenforce reduction factors and ductility for SDOF and sim-plified (three-story single-bay)MDOF systems Moghaddamand Mohammadi [28] introduced a modification to theresponse modification factor and proposed an approach toevaluate the seismic strength and ductility demands ofMDOF structures Elnashai and Mwafy [29] investigated therelationship between the lateral capacity the design forcereduction factor the ductility factor and the overstrengthfactor for reinforced-concrete buildings Reyes-Salazar [8]studied the ductility capacity of plane steel moment-resistingframes Medina and Krawinkler [30] presented an evalua-tion on drift demands for regular moment-resisting framestructures subjected to ordinary ground motions consid-ering the uncertainty due to differences in the frequencycontent of the ground motions De Stefano et al [31] studiedthe effects of the overstrength on the seismic behavior ofmultistory asymmetric buildings Cai et al [32] estimatedductility reduction factors for MDOF systems by modifyingductility reduction factors of SDOF systems througha modification factor Chopra [33] studied the ductilityreduction factors for MDOF systems modeled as shearbuildings and their corresponding equivalent SDOF sys-tems Mollaioli and Bruno [34] developed constant ductilityspectra for SDOF and MDOF systems Vielma et al [35]studied the seismic damage and safety assessment ofbuildings with low ductility used in Spain by using pushoverand dynamics analysis Ceylan et al [36] estimated thestrength reduction factor for prefabricated industrialstructures having a single story one and two bays Honglueel al [37] estimated the accuracy of strength reductionfactors proposed by other investigators by using a suite ofnear-fault earthquake records with directivity-inducedpulses Ganjavi and Hao [38] studied the seismic responseof linear and nonlinear MDOF systems subjected to a groupof earthquakes recorded on alluvium and soft soils Serroret al [39] evaluated the values of both damping and ductilityreduction factors for steel moment-resisting frames withsupplemental linear viscous dampers Bojorquez et al [40]assessed the effect of cumulative damage on the strengthrequirements of degrading structures through the evaluationof the target ductility and corresponding strength reductionfactors of simple degrading structures +e results provideinsight into all relevant parameters that should be consid-ered during seismic design of earthquake-resistant struc-tures and some recommendations to evaluate the effect ofcumulative damage on seismic design are suggestedChaulagain et al [41] by using pushover analysis studied theeffects of overstrength on the ductility factor of reinforcedconcrete buildings Reyes-Salazar et al [42] studied theductility reduction factor for buildings with moment-resisting steel frames (MRSF) which were modeled ascomplex MDOF systems considering an intermediate levelof inelastic structural deformation Vuran and Aydınoglu[43] developed simple capacity and ductility demand esti-mation tools for coupled core wall systems to be implementedduring the preliminary design stage of such structural system

Gomez-Martınez et al [44] analytically studied the local andglobal ductility of wide-beam reinforced concrete moment-resisting frames Liu et al [45] for the SDOF system andconsidering spatially varying ground motions developeda new response spectrum method by incorporating theductility factor and strain rate into the conventional responsespectrummethod Hashemi et al [46] presented the results ofstudies on two important seismic parameters namely duc-tility and response modification factor for moment-resistingframes with concrete-filled steel tube columns

+e abovementioned studies represent a significantcontribution regarding the evaluation of ductility or ductilityreduction factors however in most of them SDOF systemsor a limited level of inelastic deformation were considered+erefore they did not explicitly consider the energy dis-sipation associated with nonlinear behavior of the structuralelements existing in actual systems It has been shown[847ndash49] that ductility demands and the ductility reductionfactors depend on the amount of dissipated energy which inturn depends on the pattern of plastic hinges formed in theframes as well as on the loading unloading and reloadingprocess at plastic hinges In addition a limited level of in-elastic deformation is not associated with the ductility ca-pacity Moreover local story and global ductility as well aslocal story and global ductility reduction factors as well asrelationships among them taking into account the dissipatedenergy have not been studied

+e objectives of this research are as follows

(1) Calculate local ductility demands (in terms of cur-vatures) and capacities for individual structural el-ements (beams and columns) as well as story andglobal ductility demands and capacities +e ratio oflocal to global ductility is also estimated

(2) Calculate the ductility reduction factors as well as theratio of the ductility reduction factor to ductility forthe three structural levels under consideration andcompare them with those specified in the codes

(3) Estimate the energy demands for local story andglobal levels as well as the ratio of the ductility re-duction factor to dissipated energy

3 Methods Procedure and Structural Models

31 Steel Building Models As part of the SAC Steel Project[50] several steel building models were designed which aresupposed to satisfy the code requirements at the timethe project started for the following cities Los Angeles (IBC)Seattle (IBC) and Boston (BOCA) [51] +e perimetermoment-resisting frames (PMRF) of the 3- and 10-levelbuildings used in the project located in the Los Angeles areaare considered in this study to address the issues discussedearlier Isometric views of the buildings are shown in Figures 1and 2 where the PMRF can be easily identified (exteriorframes) they are referred hereafter as Models 1 and 2 re-spectively +e beams and columns of the models weredesigned following the strong column-weak beam (SC-WB)concept sizes of beams and columns for the PMRF as re-ported are given in Table 1 +e first three translational

Shock and Vibration 3

periods of the plane frames (lateral vibrations) are 103 s 030 sand 015 s for the 3-level model the corresponding values forthe 10-level model are 241 s 089 s and 05 s e damping isconsidered to be 3 of the critical Each column is representedby one element and each girder by two elements having a nodeat the midspan e RUAUMOKO software [52] is used toperform the required step-by-step nonlinear seismic analysis

It is worth to mention that some results of the SAC SteelProject are given in a research report [50] where many aspectsof the seismic performance of the mentioned steel framemodels subjected to earthquake groundmotions are presentede strong motions were scaled according to several returnperiods story drifts of about 1 2 3 and 4 and a littlelarger (between 5 and 6) were developed in the models

z yx

313prime

630prime

430primeN

Figure 1 Isometric view of the 3-level building

12prime

18prime

813prime

530prime

530prime

z yx

N



+e frames are modeled as complex 2D MDOF systemshaving three degrees of freedom per node +e Newmarkconstant average acceleration method lumped mass matrixRayleigh damping and large displacement effects are con-sidered within the Ruaumoko Computer Program envi-ronment while performing the required nonlinear seismicanalysis the time increment in the analysis was 001 s +epanel zone was considered to be rigid Typical input data asground accelerations boundary conditions node co-ordinates and elastic and inelastic section properties aregiven or read within the computer program No strengthdegradation member bilinear behavior with 5 of the initialstiffness in the second zone and concentrated plasticity wereassumed +e interaction axial load-bending moment isgiven by the yield interaction surface proposed by Chen andAtsuta [53]

32 Earthquake Loading When a structure is subjected tothe action of two different strong motions even when theyare normalized with respect to the same peak ground ac-celeration or with respect to any other parameter it is ex-pected to respond differently reflecting the influence of thefrequency content of the motions and of the structural vi-bration modes +us to get meaningful results the modelsunder consideration are excited by twenty strong motions intime domain whose characteristics are given in Table 2 +epredominant periods of the strong motions range from 011to 062 sec +e earthquake time histories were obtainedfrom the Data Sets of the National Strong Motion Program(NSMP) of the United States Geological Surveys (USGS)For a given direction half of the seismic loading and thetributary gravity loading are assigned to the correspondingPMRF In order to have different levels of structural de-formation as well as moderate and significant nonlinearbehavior the strong motions are scaled in terms of Saevaluated at the fundamental lateral vibration period(Sa(T1)) ranging from 04 g to 12 g for the 3-level model and

from 02 g to 06 g for the 10-level model with increments of02 g +erefore the maximum values of the seismic in-tensities are Sa 12 g and 06 g for the 3- and 10-levelmodels respectively +us considering two models twentystrong motions two horizontal seismic components and sixseismic intensities in addition to the elastic analyses morethan one thousand of nonlinear analyses of MDOF systemswere performed

+e abovementioned maximum levels of seismic in-tensities produce a deformation state which is very close tothat of a collapse mechanism where interstory drifts ofabout 5 were developed for some strong motions there-fore they are associated with the structural and ductilitycapacity +is is concordant with the results of some ex-perimental studies where it has been shown that moment-resisting steel frames may undergo interstory displacementsof up to 5 (and even larger) and still be able to vibrate ina stable manner [54ndash58] +us the ductility values obtainedfor this level of deformation according to the differentdefinitions are assumed to be the ductility capacity

It is important to note that UBC-1994 in Sections 16291and 16292 states ldquoDynamic analysis procedures when usedshall conform to the criteria established in this section +eanalysis shall be based on an appropriate ground motionrepresentation +e ground motions representation shallas a minimum be one having a 10 probability of beingexceeded in 50 rdquo +e expression ldquoas a minimumrdquoimplies that larger intensities (and larger drifts) of the strongmotions can be used In addition according to the particularobjectives stated in our paper we need a deformation stateclose to that of a collapse mechanism which is developed fordrifts of about 5 for some strong motions

In addition to the seismic loading the following gravityloads [50] were used in the analysis (a) the floor dead loadfor weight calculations was 96 psf (b) the floor dead load formass calculations was 86 psf (c) the roof dead load was83 psf (d) the reduced live load per floor and for roof was20 psf +e seismic mass for the entire structure was asfollows (a) for the roof of the 3-level building it was7090 kips-sec2ft (b) for floor 2 of the 3-level building it was6553 kips-sec2ft (c) for the roof of the 10-level building itwas 7310 kips-sec2ft (d) for floor 2 of the 10-level buildingit was 6904 kips-sec2ft (e) for floors 3 to 9 of the 10-levelbuilding it was 6786 kips-sec2ft

33DuctilityDefinitions +e discussions made in Sections 1and 2 clearly indicate that the parameter ductility is a con-cept of central importance in seismic analysis and design ofsteel buildings In this regard the different types of ductilityexisting in a steel building must be considered [10] Withina SDOF system context ductility is defined as the ratio of themaximum inelastic displacement (Dmax) to the yield dis-placement (Dy) Dmax is calculated as the maximum dis-placement that the system undergoes during the applicationof the seismic loading and Dy as the displacement of thesystem when yielding occurs on it for the first time ForMDOF systems however it is not clearly stated how todefine these two parameters (Dmax and Dy) in addition and

Table 1 Beam and columns sections for Models 1 and 2

Model StoryColumns

GirderExterior Interior

112 W14X257 W14X311 W33X11823 W14X257 W14X312 W30X116

3ROOF W14X257 W14X313 W24X68

2

minus11 W14X370 W14X500 W36X16012 W14X370 W14X500 W36X160

23 W14X370 W14X500W14X455 W36X160

34 W14X370 W14X455 W36X135

45 W14X370W14X283 W14X455W14X370 W36X135

56 W14X283 W14X370 W36X135

67 W14X283W14X257 W14X370W14X283 W36X135

78 W14X257 W14X283 W30X99

89 W14X257W14X233 W14X283W14X257 W27X84

9ROOF W14X233 W14X257 W24X68


as commented above it is necessary to properly consider thedifferent levels of ductility (local story and global) It isgenerally accepted that local ductility is larger than storyductility which in turn is larger than global ductility It mustbe noted that ductility demand is different from ductilitycapacity For example for the case of a particular story storyductility demand can be defined as the ratio of the maximumrelative lateral displacement (drift) of the story during theapplication of the seismic loading to the corresponding driftwhen first yielding occurs at any member of the story whileductility capacity is the ratio of the maximum permissibleinelastic drift to the drift when first yielding occurs Ductilitycapacity is usually obtained from experimental results forindividual members (local ductility) For that reason someresearchers [59] suggest using local ductility as the basis fordesign because there are numerous laboratory studies onductility for members +erefore it is important to relate thelocal to the story or to the overall structural ductility (globalductility)

+eoretically ductility capacity should be reachedwhen a collapse mechanism develops in the structure Toobtain this it needs to be guaranteed that plastic mo-ments are reached at positions of maximum momentsbefore failure due to instability namely local buckling orlateral torsional buckling in a member or in a connectionoccurs For the case of steel buildings local ductility (microLϕ)for a flexural member will be associated with the rota-tional deformation of the member It is defined fora given joint as the ratio of the maximum inelasticcurvature that the joint undergoes during the total timeof excitation (ϕmax) to the curvature of the joint whenit yields for the first time (ϕy) Mathematically it isexpressed as

μLϕ ϕmax

ϕy

(1)

+us as soon as any of the joints of a given memberyields for the first time the corresponding curvature isidentified as ϕy for that particular member In a similarmanner the curvature is calculated at each time incrementof the analysis and the largest one is identified as ϕmax for thenode andmember under consideration+is type of ductilitydemand will be calculated for beams as well as for thosecolumns where plasticization is producedmainly by bendingmoments as it will be further discussed below this is the casefor most columns particularly for the 10-level building

Story ductility is defined in terms of lateral drifts +eductility of a story (microS) is defined as the ratio of the max-imum inelastic drift of the story during the total time ofexcitation (Δmax) to the drift of the story when any of itsmembers yields for the first time (Δy) Mathematically wehave

μS Δmax

Δy (2)

Regarding the Δy parameter in Equation (2) it is as-sumed that for a given story the beams and columnsconnecting beneath it are part of the story For examplefor the 3-story model (top story) going from the top to thebottom the first three beams and four columns are con-sidered to be part of the third story in the same mannerthe second set of three beams and four columns areconsidered to be part of Story 2 and so on +en in the microSdefinition the expression ldquothe drift of the story when anyof its members yields for the first timerdquo refers to firstyielding of any beam or column that is part of the storyunder consideration

Since global ductility should represent the overallstructural inelastic deformation some researchers suggestdefining it in terms of relative lateral displacements[5 10 58] Here it is defined as the mean value of the storyductilities mathematically we have

Table 2 Earthquake records N-S component

No Place Date Station Tn (sec) ED (km) M PGA (cmsec2)1 Landers California 28061992 Fun Valley Reservoir 361 011 31 73 2132 Mammoth Lakes California 27051980 Convict Creek 016 12 63 3163 Victoria 09061980 Cerro Prieto 016 37 61 6134 Parkfield California 28092004 Parkfield Joaquin Canyon 017 15 60 6095 Puget Sound Washington 29041965 Olympia Hwy Test Lab 017 89 65 2166 Long Beach California 10031933 Utilities Bldg Long Beach 020 29 63 2197 Sierra El Mayor Mexico 04042010 El centro California 021 77 72 5448 PetroliaCape Mendocino California 25041992 Centerville Beach Naval Facility 021 22 72 4719 Morgan Hill 24041984 Gilroy Array Sta 4 022 38 62 39510 Western Washington 13041949 Olympia Hwy Test Lab 022 39 71 29511 San Fernando 09021971 Castaic-Old Ridge Route 023 24 66 32812 Mammoth Lakes California 25051980 Long Valley Dam 024 13 65 41813 El Centro 18051940 El Centro-ImpVall Irr Dist 027 12 70 35014 Loma Prieta California 18101989 Palo Alto 029 47 69 37815 Santa Barbara California 13081978 UCSB Goleta FF 036 14 51 36116 Coalinga California 02051983 Parkfield Fault Zone 14 039 38 62 26917 Imperial Valley California 15101979 Chihuahua 040 19 65 26218 Northridge California 17011994 Canoga Park Santa Susana 060 16 67 60219 Offshore Northern California 10012010 Ferndale California 061 43 65 43120 Joshua Tree California 23041992 Indio Jackson Road 062 26 61 400


microG 1n

1113944

n

i1microS( 1113857i (3)

where n is the number of stories

34 Ductility Reduction Factor As for the ductility pa-rameter the ductility reduction factors are estimated fordifferent structural levels +is parameter in general can beexpressed as

Rmicro Re

Ri

(4)

where Re represents the peak value of a given local story orglobal response parameter obtained from elastic analyses(without considering dissipation of energy) and Ri repre-sents the same but nonlinear analyses (consideringdissipation of energy) are considered instead Forthe case of bending moments which is a local responseparameter Equation (4) takes the following particularform

RmicroLϕ Me

Mi (5)

where RmicroLϕ is the bending local ductility reduction factorand Me and Mi are the elastic and inelastic peak bendingmoments respectively at a given joint of a given memberEquation (5) will be used to calculate the reduction inbending moments for both beam and columns Re-ductions in axial loads on columns are not calculatedsince as stated above the number of cases where dissi-pation of energy due to plasticization by the axial loadoccurs is very small in comparison with that of bendingmoments

+e story ductility reduction factor (RmicroS) is calculated as

RmicroS Vse

Vsi (6)

where Vse and Vsi are the elastic and inelastic peak values ofthe interstory shears respectively +e global ductility re-duction factors (RmicroG) are calculated as the mean values ofRmicroS and it is

RμG 1n

1113944

n

i1RμS1113872 1113873

i (7)

35 Dissipated Energy +e dissipated energy is also calcu-lated for local story and global levels +e normalizeddissipated energy at a given joint (ELϕ) of a given beam iscalculated as

ELϕ EDϕ

ECϕ (8)

where EDϕ is the energy demand and ECϕ is the energycapacity of a member under the action of only bendingmoment ECϕ in Equation (8) is estimated by the followingequation [60 61]

ECϕ MP θpa (9)

where MP and θpa in Equation (9) in turn represent theplastic moment and the cumulative plastic rotation capacityof a member under bending respectively Even thoughexperiments to estimate the θpa parameter are not commonthere is some experimental evidence to provide a reasonablevalue A value of 023 for θpa will be used in this paper[60ndash65]

For all the beams of a story the average normalizeddissipated energy per joint ((ELϕ)SB) can be calculated as

ELϕ1113872 1113873SB 12q

1113944

2q

j1ELϕ1113872 1113873

j (10)

where q is the number of beams in the story+e normalized dissipated energy by bending at a col-

umn (ElowastLϕ) is calculated as

ElowastLϕ

EDϕ

ElowastCϕ (11)

where ElowastCϕ is the reduced energy capacity of a column due tothe presence of axial loads Taking into account that (a) theSC-WB concept was followed in the design of the structuralmodels implying that most of the hysteretic dissipated en-ergy will occur in beams by the action of bending moments(b) experimental studies regarding the cumulative plasticrotation capacity of a member under the combined action ofbending moment and axial load are rare and (c) the level ofaverage axial load demands observed in this study impliesa reduction of the bending moment capacity in columns ofabout 30ndash50 it is conservatively assumed in this researchthat the cumulative plastic rotation capacity of a memberunder the action of bending and axial load is one third of thatof θpa +en

ElowastCϕ

13

MPθpa1113872 1113873 (12)

For all the columns of a story it is obtained as

ElowastLϕ1113872 1113873SC

12r

1113944

2r

k1ElowastLϕ1113872 1113873

k (13)

where (ElowastLϕ)SC is the normalized energy per joint and r is thenumber of columns +e average normalized dissipatedenergy per joint in a given story (ES) is calculated as

ES 1

(2q + 2r)1113944

2q

j1ELϕ1113872 1113873

j+ 1113944

2r

k1ElowastLϕ1113872 1113873

k⎛⎝ ⎞⎠ (14)

Finally the normalized dissipated energy for the wholeframe (EG) is calculated as

EG 1n

1113944

n

i1Es( 1113857i (15)

All the parameters in Equation (15) were defined earlier


4 Results and Discussion

41 Objective 1 Results in Terms of Ductility

411 Local Ductility +e bending local ductility parameter(Equation (1)) is calculated for each individual beam andcolumns of the two models for the seismic intensities of eachstrong motion mentioned in Section 32 First the modelsare subjected to the simultaneous action of the horizontalseismic component oriented in the NS direction the verticalseismic component and the gravity loads +en the modelsare subjected to a similar set of loads but the other hori-zontal (EW) seismic component is applied instead It isassumed in this research that structural members have noproblems of lateral torsional and local or shear buckling inthe panel zone As stated above in Section 33 bending localductilities are expressed in terms of curvatures in this paperLocal ductilities expressed in terms of rotations are expectedto be smaller

For a given story the microLϕ values are averaged first overall the beams (Equations (10)) and then over all thecolumns (Equations (12)) It must be noted that eventhough the SC-WB concept was followed in the modeldesign plastic hinges were developed in some columnsparticularly for the 10-level model and the largest intensityof the strong motions Plots for the resulting averages aredeveloped for each strong motion but they are not pre-sented about 30 plots were developed Only the funda-mental statistics in terms of the mean values (MV)calculated over all the strong motions are given +eresults are presented in Table 3 for the 3-level model and inFigures 3(a)ndash3(d) for the 10-level model +e term ldquoSTrdquo inthe table and in figures stands for the story level Resultsindicate that for the beams of the 3-level building themaximum bending ductility demands occur in general forthe second story For the case of columns unlike whatobserved for beams the mean values of microLϕ tend to de-crease with the story number but the mean values aremuch smaller than those of beams in fact for the twolowest intensities (Sa 04 g and 06 g) they are essentiallyequal to unity for the two upper stories implying noyielding For both beams and columns the mean valuestend to increase with the seismic intensity and are largerfor the NS than that for the EW direction +e largestobserved values for beams are 1186 and 932 for the NSand EW direction respectively

+e results for the 10-level building resemble those of the3-level building in the sense that the mean values of microLϕ aremuch larger for beams than for columns However unlikethe 3-level building the mean values tend to decrease withthe story number for beams and as for the 3-story buildingthe microLϕ mean values tend to decrease with the story numberfor columns No yielding occurs in columns in most of thecases for the two lowest intensities of the strong motions(Sa 02 g and 04 g) +e only additional observation thatcan be made is that for the larger strong motion intensitiesthe maximum mean values of the bending local ductilitydemands for beams are larger for the 10-level building thanthat for the 3-level building (143 against 1186)

It is worth to mention that moderate yielding occurredfor seismic intensities of 04 g and 02 g for the 3- and 10-level structural models respectively the correspondingseismic intensities for significant deformation as stated inSection 32 are 12 g and 06 g for the 3- and 10-level modelsrespectively Even though it is not shown in the paper thedrifts for these significant levels of deformation were about5 for many of the strong motions +us the mean values ofmicroLϕ shown in Table 3 or in Figures 3(a)ndash3(d) are associatedwith the structural capacity and are assumed to be thebending local ductility capacity Even though as statedearlier results for individual strong motions are not in-cluded in the paper it was observed that the maximumvalues of microLϕ were close to 20 for some particular earthquakeand stories +ere is some evidence in the literature[1066ndash68] that the bending local ductility capacity can reachvalues larger than 20 however it was for monotonic loadingand individual members It was also observed that fora given value of Sa the magnitude of microLϕ significantly variesfrom one seismic motion to another in spite of the structuraldeformation in terms of Sa for each seismic motion was thesame reflecting the effect of the frequency content on thevalues of the microLϕ parameter +e coefficients of variation(COV) are not shown either but it can be said that theuncertainty in the estimation of microLϕ is moderated in most ofthe cases (COVsim020ndash045)

412 Story Ductility Similar to the microLϕ parameter the microSvalues as defined by Equation (2) are calculated forboth structural models and horizontal directions and plotsfor individual strong motions are developed but are notpresented +e mean values for all seismic intensitiesand structural directions are presented in Table 4 andFigures 4(a) and 4(b) for the 3- and 10-level buildingsrespectively It can be observed that similar to microLϕ for beamsthe mean values of microS do not present any tendency with thestory number for the case of the 3-level building for the 10-level building however unlike the case of microLϕ the values donot tend to decrease with height By comparing the results ofTable 3 and Figures 3(a)ndash3(d) with those of Table 4 andFigures 4(a) and 4(b) it is observed that for beams microS ismuch smaller than microLϕ the mean values for the maximumseismic intensity range from 384 to 428 and from 249 to519 for the 3- and 10-level models respectively Both microLϕand microS mean values for beams tend to increase with theseismic intensity

413 Global Ductility +e global ductility values (microG) arenow discussed +e results are given in Table 5 for the twobuildings the two horizontal directions and all seismicintensities It can be observed that the mean values of microGtend to increase (as expected) with the strong motion in-tensity and that they are quite similar for the two buildingsfor the demands associated with themaximum deformations(ductility capacity) microG takes values of 395 and 389 for theNS and EW directions respectively for the 3-level buildingthe corresponding values are 411 and 360 for the 10-level


Table 3 Mean values of microLϕ RmicroLϕ and QL 3-level building

Parameter Type of member STNS direction EW directionSag values Sag values

04 06 08 10 12 04 06 08 10 12

microLϕ

Beams1 261 427 599 823 1022 219 356 456 633 7812 248 460 717 957 1186 226 415 587 769 9323 201 431 671 894 1120 199 373 559 767 930

Columns1 106 132 195 265 370 101 125 172 222 2872 100 100 109 125 141 100 101 103 121 1293 100 100 106 112 123 100 100 102 113 126

RmicroLϕ

Beams1 168 229 289 345 406 154 212 268 322 3912 166 225 279 328 386 155 211 265 316 3813 158 211 260 306 360 150 201 250 297 354

Columns1 152 187 225 260 298 135 166 200 235 2792 150 185 219 251 286 137 171 201 232 2713 155 195 228 259 295 143 181 217 251 292

QL

Beams1 064 054 048 042 040 070 060 059 051 0502 067 049 039 034 033 069 051 045 041 0413 079 049 039 034 032 075 054 045 039 038

Columns1 143 142 115 098 081 134 133 116 106 0972 150 185 201 201 203 137 169 195 192 2103 155 195 215 231 240 143 181 213 222 232

Sag=02Sag=04Sag=06

0

2

4

6

8

10

12

14

16

Mea

n of

μLϕ

3 4 5 6 7 8 9 102Story number

(a)

Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

0

2

4

6

8

10

12

Mea

n of

μLϕ

(b)

Sag=02Sag=04Sag=06

0

1

2

3

4

5

6

Mea

n of

μLϕ

3 4 5 6 7 8 9 102Story number

(c)

Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

0

1

2

3

4

Mea

n of

μLϕ

(d)

Figure 3 Continued


building By comparing the results of Table 5 with those ofmicroLϕ for beams (Table 3 and Figures 3(a) and 3(b)) it is notedthat as for the case microS the values are signicantly smallerfor microG

414 Ratio of Local to Global Ductility As stated above theestimation of ductility capacity is commonly based on ex-perimental studies of individual members For this reason itis suggested [59] considering local ductility as the basis for

Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

0

1

2

3

4

5

6M

ean

of R

μLϕ

(e)

Sag=02Sag=04Sag=06

0

1

2

3

4

5

6

Mea

n of

RLμ

ϕ

3 4 5 6 7 8 9 102Story number

(f )

Sag=02Sag=04Sag=06

0

1

2

3

4

Mea

n of

RLϕ

3 4 5 6 7 8 9 102Story number

(g)

Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

0

1

2

3

4

Mea

n of

RLϕ

(h)

Figure 3 10-level building Mean values of microLϕ (a) beams NS (b) beams EW (c) columns NS (d) columns EW Mean values of RmicroLϕ(e) beams NS (f ) beams EW (g) columns NS (h) columns EW

Table 4 Statistics for microS RmicroS and QS 3-level building

Parameter STNS direction EW directionSag values Sag values

04 06 08 10 12 04 06 08 10 12

microS1 161 199 281 344 395 148 190 280 289 4282 170 220 286 331 399 165 215 258 309 3543 153 193 269 299 390 152 210 272 319 384

RmicroS

1 146 190 237 276 310 133 173 211 251 2892 144 186 230 268 305 136 184 225 268 3063 145 184 217 247 276 136 175 208 236 267

QS

1 091 095 084 080 078 090 091 075 087 0682 085 085 080 081 076 082 086 087 087 0863 095 095 081 083 071 089 083 076 074 070


design In this regard it is important to nd a relationship(Q microGmicroLϕ) between global and local ductility e microGvalues given in Table 5 and the microLϕ values averaged over allthe beams of the frames are used to calculate theQ ratioeresults are summarized in the second row of Table 5 It isobserved that the ratio values tend to decrease with theintensity of the earthquake Based on the results obtained for

the maximum deformation under consideration (036 044037 and 035) a value of 13 is proposed for the Q ratio

42 Objective 2 Results for Ductility Reduction Factor

421 Local Ductility Reduction Factor e local story andglobal ductility reduction factors as given by Equations

Sag=02Sag=04Sag=06

0

1

2

3

4

5

6M

ean

of micro

S

3 4 5 6 7 8 9 102Story number

(a)

Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

0

1

2

3

4

5

Mea

n of

microS

(b)

Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

0

1

2

3

4

Mea

n of

Rmicros

(c)

Sag=02Sag=04Sag=06

0

1

2

3

4

5

Mea

n of

Rmicros

3 4 5 6 7 8 9 102Story number

(d)

Figure 4 10-level building Mean values of microS (a) NS direction (b) EW direction Mean values of RmicroS (c) NS direction (d) EW direction

Table 5 Mean of microG Q RmicroG and QG parameters 3- and 10-level buildings

Parameter

3-level 10-levelNS direction EW direction NS direction EW directionSag values Sag values Sag values Sag values

04 06 08 10 12 04 06 08 10 12 02 04 06 02 04 06microG 161 204 279 325 395 155 205 270 305 389 186 292 411 166 267 360Q 068 046 042 036 036 072 054 051 042 044 067 043 037 072 046 035RmicroG 135 177 215 252 287 145 187 228 264 297 147 228 297 149 234 309QG 084 087 077 078 073 094 091 084 087 076 079 078 072 090 088 086


(5)ndash(7) respectively are now calculated Bending localductility reduction factors (RmicroLϕ) is discussed first As for themicroLϕ parameter for a given story the RmicroLϕ values are aver-aged first over all the beams and then over all the columnsPlots for the resulting averages as for the other parametersare developed for individual strong motions but they arenot presented Only the mean values are given and dis-cussed +e results are presented in Table 3 for the 3-levelmodel while those of the 10-level building are given inFigures 3(e)ndash3(h)

It can be seen that for beams of the 3-level building themean values of RmicroLϕ tend to decrease with the story numberbut tend to increase with the seismic intensity implying thatthe magnitude of the reduction of the bending moments ofbeams produced by yielding decreases with the storynumber but it increases with the strong motion intensity+is variation with the story number is not observed forcolumn moments in fact the maximum reductions occurfor the upper level It is also shown that the mean values ofRmicroLϕ are larger for beams than that for columns and thevalues larger than 4 are observed for beams However forsome cases of columns RmicroLϕ can be significant even if plastichinges are not developed For example for columns of Story3 (ST 3) NS direction and Sa 06 g RmicroLϕ equals 195 thisis an interesting point since although yielding did not occuron these columns (ie microLϕ 100) bending moments areconsiderably reduced implying that yielding on beams re-duce not only their bending moments but also those ofcolumns From the results of the 10-level building it can beobserved that the maximum values of RmicroLϕ occur for the twostories below the roof (the values larger than 5 are observedfor Sa 06 g) and that these values are larger than those ofthe 3-level building

422 Story Ductility Reduction Factor +e story ductilityreduction factor (RmicroS) calculated according to Equation (6)is now discussed Even though as for the case of storyductility demands RmicroS is calculated for several levels ofstructural deformation the value of this parameter associ-ated with a deformation state close to that of a collapsemechanism is that considered in the seismic guidelines [69]+e results are given in Table 4 and in Figures 4(c) and 4(d)for the 3- and 10-level models respectively For the 3-levelbuilding no trend is observed between the mean values andthe story number For the case of the maximum de-formation the mean values are 310 and 306 for the NS andEW directions respectively As for the case of local and storyductility the values are larger for RmicroLϕ than for RmicroS andhowever the differences are larger for the case of ductilitydemands For the 10-level building unlike the 3-storybuilding themean values of RmicroS even though not in a perfectway tend to increase with the story number+e values seemto be larger for the 10-level building than that for the 3-levelbuilding values larger than 4 are observed in some cases

423 Global Ductility Reduction Factor +emean values ofglobal ductility reduction factors (RmicroG) are presented in

Table 5 for all cases +e results indicate that for maximumdeformation RmicroG are quite similar for both structuralmodels and the values range from 287 to 309 It is im-plicitly assumed in the seismic codes mentioned in Section 1that the magnitude of the global ductility reduction factor isabout 4 According to the results found in this paper thisvalue is not justified a value of 3 seems to be morereasonable

424 Ratio of Ductility Reduction Factor to Ductility+e ratios of the ductility reduction factor to ductility forlocal (QL) story (QS) and global (QG) structural levels arepresented in this section +ey are expressed as

QL RmicroLϕ

microLϕ

QS RmicroS

microS

QG RmicroG

microG

(16)

+e values of QL are given in last rows of Table 3 and inFigure 5 for the 3- and 10-level buildings respectively +eresults indicate that this ratio significantly varies with thetype of the structural element (beam or column) storynumber strong motion intensity and building height Forbeams of the twomodels theQL values tend to decrease withthe strong motion intensity but they tend to increase withthe story number for the 3-level building For the case ormaximum deformation QL is quite similar for the twomodels the values range from 032 to 06 Most of theobservations made for beams apply to the case of columnsand however an important difference is that the QL valuesare significantly larger for columns the values of up to 24and 30 are observed for the 3- and 10-level buildings re-spectively +is result has an important implication whilethe well-known ratio between ductility reduction factor toductility [10 33] indicates that for the structural modelsunder consideration (fundamental lateral vibration periodsof 103 and 241) the maximum reduction in the elasticforces should be equal to ductility capacity and the results inthis paper show that the reduction for local response pa-rameters like bending moment in columns can be muchlarger than that +e implication of this is that the design ofcolumns will be too conservative if the reduction is per-formed according to the mentioned well-known ratio

+e results forQS are presented in the last rows of Table 4and in Figure 6 for the 3- and 10-level buildings re-spectively while those of QG are given in the last row ofTable 5 +e QS values resemble those of QL in the sense thatthey decrease with the strong motion intensity and that theyare quite similar for the two buildings However they can besignificantly larger for the case of beams for the maximumdeformation they range from 068 to 086 and from 060 to110 for the 3- and the 10-level buildings respectivelyRegarding the QG parameter the results in Table 5 indicatethat as for the local and story ratios QG decreases with the


Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

00

02

04

06

08

10Q

L rat

io

(a)

Sag=02Sag=04Sag=06

00

02

04

06

08

10

12

QL r

atio

3 4 5 6 7 8 9 102Story number

(b)

Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

0

1

2

3

4

QL r

atio

(c)

Sag=02Sag=04Sag=06

0

1

2

3

4

QL r

atio

3 4 5 6 7 8 9 102Story number

(d)

Figure 5 QL ratio 10-level building (a) beams NS (b) beams EW (c) columns NS (d) columns EW

Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

00

04

08

12

QS r

atio

(a)

Sag=02Sag=04Sag=06

00

04

08

12

QS r

atio

3 4 5 6 7 8 9 102Story number

(b)

Figure 6 10-level building QS ratio (a) NS direction (b) EW direction


intensity of the earthquakes for the level of deformationassociated with ductility capacity (Sa 12 g and 06 g) ittakes values of 073 076 072 and 086 +us from anoverall point of view the ratio of the global ductility re-duction factor to global ductility is about 34 and it is thevalue proposed in this study +is value is smaller than thevalue of 100 specified by the well-known ratio [10 33]abovementioned +e implication of this is that if the valueof 100 is used to calculate the global ductility reductionfactor from a global point of view nonconservative designsmay result

43 Objective 3 Dissipated Energy

431 Local Story and Global Normalized Dissipated Energyper Joint As for the ductility demand and ductility re-duction factor parameters the dissipated energy is calcu-lated for three levels +e mean values of (ELϕ)SB (ElowastLϕ)SCES and EG are calculated according to Equations (10)(13)ndash(15) respectively Plots for individual strong mo-tions were developed for each beam column story andthe whole structure however only the results in terms ofthe mean values averaged over all the strong motionsare given below For the case of the 3-level building themean values of (ELϕ)SB and (ElowastLϕ)SC are given in Table 6while those of ES and EG are given in Tables 7 and 8 re-spectively +e corresponding results for the 10-levelbuilding are given in Figures 7 and 8 and in Table 8 InTable 8 the symbols ldquoB +Crdquo or ldquoBrdquo indicate that EG wascalculated considering beam and columns or only beamsrespectively

Results for the 3-level building indicate that (ELϕ)SB(ElowastLϕ)SC and ES tend to decrease with height and that(ELϕ)SB is much larger than (ElowastLϕ)SC as expected For the10-level building (ELϕ)SB and(ElowastLϕ)SC tend to increase anddecrease with the story number respectively however ESdoes not show a clear tendency From a global point of view(Table 8) it is shown that the values of the global nor-malized dissipated energy (EG) even for the maximumdeformation are relatively small when beams and columnsare considered the maximum observed values are 0129and 0218 for the 3- and 10-level buildings respectively+ese relatively small values of EG are due to the fact thatthe normalized energy demands in columns are quite smallso the average values obtained from Equations (14) and (15)for the whole frame are expected to be small too +e EGparameter is also calculated by assuming that the plasti-cization of the steel frames perfectly follows the strongcolumn-weak beam concept in other words the dissipa-tion of energy in columns is not considered It is observedfrom Table 8 in this case that the maximum values of EGare now 0324 and 0475 for the 3- and 10-level modelsrespectively

432 Ratio of Ductility Reduction Factor to NormalizedDissipated Energy It is clear that the reduction of the re-sponse from the elastic to the inelastic case due to yielding ofthe material which is quantified by the ductility reduction

factor is produced by the dissipated energy In this regardit may be of interest to study the ratio of the ductilityreduction factor to dissipated energy In this section of thepaper the ratio of the story ductility reduction factor tostory normalized dissipated energy (PS) and the ratio ofglobal ductility reduction factor to global normalizeddissipated energy (PG) are given and discussed +ey arecalculated as

PS RmicroS

ES

PG RmicroG

EG

(17)

+e results for PS are given in Table 9 and in Figure 9 forthe 3- and 10-level models respectively +e results for PGare given in Table 8 for both models In the calculation of ESonly the dissipated energy at beams is considered A value ofPS RmicroS or PG RmicroG would mean that ES 10 or EG 10which in turn would correspond to the idealized hypo-thetical case where all structural elements simultaneouslyreach for every strong motion the energy capacity In otherwords the energy demand equals the energy capacity in allcases Obviously it is not the case and as shown belowvalues much larger than RmicroS or RmicroG are obtained for PS or PGrespectively

It is observed from Table 9 and Figure 9 that the PS valuessignificantly vary with the model height the story numberand the strong motion intensity Since energy dissipationproduces the response reduction one could expect a similarvariation of RmicroS and ES which would approximately implya constant value for PS however these two parameters varyin a different proportion +e results clearly indicate that PStends to significantly increase with the story number for the3-level building this trend is not observed for the 10-levelbuilding For both buildings the PS values significantlydecrease with the strong motion intensity in most of thecases One reason for this is that as stated before the seismicresponse significantly varies from one ground motion toanother even though the level of deformation in terms of Sais approximately the same for any of the strong motions+is variation is observed even for two strong motions witha similar predominant period +ese differences are due inpart to the inherent variability existing in ground motionscharacterized by their frequency contents it causes that theresponse be very sensitive to the particular characteristics ofa given story or of a given building model and to the groundmotion under consideration +is sensitivity is quite dif-ferent from one response parameter to another and seems tobemuch larger for dissipation of energy than for the ductilityreduction factor

Results in Table 8 indicate that some of the observationsmade before for PS apply the PG Ratio Based on the resultsassociated with the maximum structural deformationa value of 8 is proposed for this ratio +us if the globalnormalized dissipated energy is estimated for a steelbuilding with the structural system under considerationthe global ductility reduction factor can be estimated aseight times EG


5 Conclusions

+e ductility parameter plays a central role in seismicanalysis and design of steel buildings However it is stillused in an indirect way A numerical investigation re-garding the evaluation of local (microLϕ) story (microS) and global(microG) ductility local (RmicroLϕ) story (RmicroS) and global (RmicroG)ductility reduction factors as well as local (ELϕ) story (ES)and global (EG) normalized dissipated energy for steelbuildings with moment-resisting frames which weredesigned following the strong column-weak beam conceptis presented in this paper +e ratios of microG to microLϕ (Q) RmicroLϕto microLϕ (QL) RmicroS to microS (QS) RmicroG to microG (QG) RmicroS to ES (PS)and RmicroG to EG (PG) are also calculated 3- and 10-levelbuildings and some strong motions used in the SAC SteelProject are used in the study +e mentioned parametersare calculated for several intensities of the strong motionsResults of the study indicate that any of the above-mentioned parameters significantly may vary with thestrong motion the seismic intensity the structural elementthe story number and the structural model +e mainfindings are as follows

(1) Bending local ductility capacity (microLϕ) of beams canreach values of up to 20 for some individual strongmotions as observed in some experimental in-vestigations On an average basis microLϕ ranges from

7 to 14 +e values are larger for the 10-levelbuilding than for the 3-level building reflecting theeffect of the structural complexity on the microLϕ pa-rameter Many of the observations made for microLϕapply to microS but the values are much smaller thanthose of microLϕ they range from 3 to 5 +e corre-sponding values of microG range from 36 to 395 Avalue of 13 is proposed for the Q ratio +us iflocal ductility capacity is stated as the basis for thedesign global ductility capacity can be calculatedby using this ratio

(2) +emean values of RmicroLϕ for beams range between 35and 5 which are larger than those of columns Eventhough yielding did not occur in columns for manycases a considerable reduction is observed inbending moments implying that yielding on beamsreduce not only their bending moments but alsothose of columns +e maximum mean values of RmicroSis about 40 +e RmicroG mean values range from 287 to309 It is implicitly assumed in the seismic codes thatthe magnitude of the global ductility reduction factoris about 4 According to the results found in thispaper this value is not justified a value of 3 seems tobe more reasonable and is proposed in this study

(3) +emaximum values ofQL range from 032 to 06 forbeams for columns however they are significantly

Table 6 Mean values of (ELϕ)SB and (ElowastLϕ)SC 3-level building

Type of member STNS direction EW directionSag values Sag values

04 06 08 10 12 04 06 08 10 12

Beams (ELϕ)SB1 0053 0147 0256 0379 0512 0045 0114 0188 0274 03762 0022 0072 0140 0216 0298 0018 0055 0109 0170 02423 0008 0033 0069 0113 0161 0007 0025 0057 0096 0141

Columns (ElowastLϕ)SC

1 0003 0010 0025 0046 0076 0003 0007 0017 0031 00502 0001 0003 0004 0007 0013 0001 0003 0004 0006 00103 0001 0001 0002 0004 0007 0001 0001 0002 0004 0007

Table 7 Mean values of ES 3-level building

STNS direction EW directionSag values Sag values

04 06 08 10 12 04 06 08 10 121 0020 0056 0102 0157 0221 0017 0043 0074 0112 01582 0008 0026 0050 0077 0108 0007 0020 0039 0061 00873 0003 0012 0024 0040 0058 0003 0009 0020 0035 0052

Table 8 Mean values of EG for the 3- and 10-level buildings

Parameter Member


04 06 08 10 12 04 06 08 10 12 02 04 06 02 04 06

EGB+C 0011 0031 0059 0091 0129 0009 0024 0044 0069 0099 0026 0111 0218 0017 0083 0171B 0028 0084 0155 0236 0324 0023 0065 0118 018 0253 0076 0314 0383 0047 0241 0475

PG 482 211 139 107 89 630 288 193 147 117 193 73 78 317 97 65


Sag=02Sag=04Sag=06

000

010

020

030

040

050

060

070M

ean

of (E

Lϕ) S

B bea

ms

3 4 5 6 7 8 9 102Story number

(a)

Sag=02Sag=04Sag=06

000

010

020

030

040

050

060

070

080

Mea

n of

(ELϕ

) SB b

eam

s

3 4 5 6 7 8 9 102Story number

(b)

Sag=02Sag=04Sag=06

000002004006008010012014016018020

Mea

n of

(Elowast

Lϕ) S

C co

lum

ns

3 4 5 6 7 8 9 102Story number

(c)

Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

000002004006008010012014016018

Mea

n of

(Elowast

Lϕ) S

C co

lum

ns

(d)

Figure 7 Mean values of local normalized energy demands 10-level building (a) beams NS (b) beams EW (c) columns NS(d) columns EW

Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

000

005

010

015

020

025

030

035

040

Mea

n of

ES s

tory

(a)

Sag=02Sag=04Sag=06

000

005

010

015

020

025

030

Mea

n of

ES s

tory

3 4 5 6 7 8 9 102Story number

(b)

Figure 8 Mean values of story normalized energy demands 10-level building (a) NS direction (b) EW direction


larger values larger than 2 are observed in manycases e maximum values of QS range from 060 to110 while those ofQG from 073 to 086ese valuesare smaller than the specied well-known ratio of100e implication of this is that if the value of 100is used to calculate the global ductility reductionfactor from a global point of view nonconservativedesigns may result while from a local point of viewas is the case of columns very conservative designsmay result A value of QG of 34 is proposed in thisstudy

(4) e ELϕ values for beams for maximum de-formation range from 015 to 07 which are muchlarger than those of columns and larger than thoseof ESemaximum values of EG range from 025 to047e values of the PS ratio signicantly decreasewith the strong motion intensity and signicantlyincrease with the story number in most of the casesBased on the results associated with the maximumdeformation a value of 8 is proposed for the PGratio

Data Availability

Data used to support the ndings of this study are in-cluded within the article and data supporting this studyare from previously reported studies which have beencited

Disclosure

Any opinions ndings conclusions or recommendationsexpressed in this publication are those of the authors and donot necessarily reyenect the views of the sponsors

Conflicts of Interest

e authors declare that there are no conyenicts of interestregarding the publication of this paper

Acknowledgments

e research presented in this paper was nancially sup-ported by La Universidad Autonoma de Sinaloa (UAS)under grant PROFAPI-2015235

References

[1] International Code Council International Building CodeInternational Code Council Falls Church VA USA 2009

[2] NBCC Canadian Commission on Building and Fire Codese National Building Code of Canada National ResearchCouncil Ottawa Canada 2010

[3] MFDC Government of the Federal District ComplementaryTechnical Norms for Seismic Design Osectcial Gazette of theFederal District Mexico 2004

[4] EC Committee European de Normalization EuropeanStandard Eurocode 8 Design of Structures for EarthquakeResistance CEN Brussels Belgium 2004

Table 9 PS ratio 3-level building


04 06 08 10 12 04 06 08 10 121 275 129 93 73 61 296 152 112 92 772 655 258 164 124 102 756 335 206 158 1263 1813 558 314 219 171 1943 700 365 246 189

Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

0

10

20

30

40

50

60

P S ra

tio

(a)

Sag=02Sag=04Sag=06

0

10

20

30

40

50

60

70

80

90

P S ra

tio3 4 5 6 7 8 9 102

Story number

(b)

Figure 9 PS ratio 10-level building (a) NS direction (b) EW direction


[5] C M Uang ldquoEstablishing R (or Rw) and Cd factors forbuilding seismic provisionsrdquo Journal of Structural EngineeringASCE vol 117 no 1 pp 19ndash28 1991

[6] C M Uang ldquoStructural overstrength and limit state philos-ophy in seismic design provisionsrdquo Report No CE-91-03Department of Civil Engineering Northeastern University1991

[7] SAC ldquoSteel moment frame connectionsrdquo Advisory No 3D-146 Structural Engineers Associated of California AppliedTechnology Council and California University for Research inEarthquake Engineering Sacramento CA USA 1995

[8] A Reyes-Salazar ldquoDuctility and ductility reduction factorsrdquoStructural Engineering and Mechanics An InternationalJournal vol 13 no 4 pp 369ndash385 2002

[9] Applied Technology Council ldquoTentative provisions for thedevelopment of seismic regulation buildingsrdquo Rep No ATC-3-06 Applied Technology Council Redwood City CA USA1978

[10] N M Newmark and W J Hall Earthquake Spectra andDesign Monograph Series Earthquake Engineering ResearchInstitute Berkeley CA USA 1982

[11] A H Hadjian ldquoAn evaluation of the ductility reduction factorQ in the 1976 regulations for the federal district of MexicordquoEarthquake Engineering and Structural Dynamics vol 18pp 217ndash231 1989

[12] E Miranda and V Bertero ldquoEvaluation of strength reductionfactors for earthquake-resistant designrdquo Earthquake Spectravol 10 no 2 pp 357ndash379 1994

[13] A Whittaker G Hart and C Rojahn ldquoSeismic responsemodification factorsrdquo Journal of Structural Engineeringvol 125 no 4 pp 438ndash444 1999

[14] D Arroyo-Espinoza and A Teran-Gilmore ldquoStrength re-duction factors for ductile structures with passive energydissipating devicesrdquo Journal of Earthquake Engineering vol 7no 2 pp 297ndash325 2003

[15] R Levy A Rutenberg and K H Qadi ldquoEquivalent lineari-zation applied to earthquake excitations and the R-micro-T0 re-lationshipsrdquo Engineering Structures vol 28 no 2pp 216ndash228 2006

[16] D Karmakar and V K Gupta ldquoA parametric study ofstrength reduction factors for elasto-plastic oscillatorsrdquoSadhana vol 31 no 4 pp 343ndash357 2006

[17] R Rupakhety and R Sigbjornsson ldquoGround-motion pre-diction equations (GMPEs) for inelastic response andstructural behavior factorsrdquo Bulletin of Earthquake Engi-neering vol 7 no 3 pp 637ndash659 2009

[18] L Sanchez-Ricart ldquoAssessment and management of risk forengineered systems and geohazardsrdquo Georisk vol 4 no 4pp 208ndash229 2010

[19] A M Halabian and S Kabiri ldquoEffect of foundation flexibilityon ductility reduction factors or RC stack-like structuresrdquoEarthquake Engineering and Engineering Vibration vol 10no 2 pp 277ndash329 2011

[20] M AlHamaydeh S Abdullah A Hamid and A MustaphaldquoSeismic design factors for RC special moment resistingframes in Dubai UAErdquo Earthquake Engineering amp Engi-neering Vibration vol 10 no 4 pp 495ndash506 2011

[21] S Naimi M Celikag and A A Hedayat ldquoDuctility en-hancement of post-Northridge connections by multi-longitudinal voids in the beam webrdquo Scientific World Journalvol 2013 Article ID 515936 14 pages 2013

[22] M Azimi A B Adnan A R B M Sam et al ldquoSeismicperformance of RC beam-column connections with contin-uous rectangular spiral transverse reinforcements for low

ductility classesrdquo Scientific World Journal vol 2014 ArticleID 802605 12 pages 2014

[23] N Fanaie and S O Shamlou ldquoResponse modification factorof mixed structuresrdquo Steel and Composite Structures vol 19no 6 pp 1449ndash1466 2015

[24] C H Zhai W P Wen S Li and L L Xie ldquo+e ductility-based strength reduction factor for the mainshockndashaftershocksequence-type ground motionsrdquo Bulletin of Earthquake En-gineering vol 13 no 10 pp 2893ndash2914 2015

[25] C Wang Y Shen R Yang and Z Wen ldquoDuctility and ul-timate capacity of prestressed steel reinforced concretebeamsrdquo Mathematical Problems in Engineering vol 2017Article ID 1467940 6 pages 2017

[26] H C Cho M K Park H Ju et al ldquoShear strength re-duction factor of prestressed hollow-core slab units basedon the reliability approachrdquo Advances in Materials Scienceand Engineering vol 2017 Article ID 8280317 11 pages2017

[27] A Nassar and H Krawinkler ldquoSeismic demands of SDOF andMDOF systemsrdquo Report No 95 John A Blume EarthquakeEngineering Center Stanford University Stanford CA USA1991

[28] H Moghaddam and R K Mohammadi ldquoDuctility reductionfactor of MDOF shear-building structuresrdquo Journal ofEarthquake Engineering vol 5 no 1 pp 425ndash440 2001

[29] A S Elnashai and A M Mwafy ldquoOverstrength and forcereduction factors of multistorey reinforced-concrete build-ingsrdquo Structural Design of Tall and Special Buildings vol 11no 5 pp 329ndash351 2002

[30] R Medina and H Krawinkler ldquoStrength demand issuesrelevant for the seismic design of moment-resisting framesrdquoEarthquake Spectra vol 21 no 2 pp 415ndash439 2005

[31] M De Stefano E M Marino and P P Rossi ldquoEffect ofoverstrength on the seismic behaviour of multi-storey regu-larly asymmetric buildingsrdquo Bulletin of Earthquake Engi-neering vol 4 no 1 pp 23ndash42 2006

[32] J Cai J Zhou and X Fang ldquoSeismic ductility reductionfactors for multi-degree-of-freedom systemsrdquo Advances inStructural Engineering vol 9 no 5 pp 591ndash601 2006

[33] A K Chopra Dynamics of Structures Prentice-Hall UpperSaddle River NJ USA 2007

[34] FMollaioli and S Bruno ldquoInfluence of side effects on inelasticdisplacement ratios for SDOF and MDOF systemsrdquo Com-puters amp Mathematics with applications vol 55 no 2pp 184ndash207 2008

[35] J C Vielma A H Barbat and S Oller ldquoSeismic safety of lowductility structures used in Spainrdquo Bulletin of EarthquakeEngineering vol 8 no 1 pp 135ndash155 2010

[36] M Ceylan M H Arslan R Ceylan M Y Kaltakci andY Ozbay ldquoA new application area of ANN and ANFISdetermination of earthquake load reduction factor of pre-fabricated industrial buildingsrdquo Civil Engineering and Envi-ronmental Systems vol 27 no 1 pp 53ndash69 2010

[37] Q Honglue Z Jianjing and J X Zhao ldquoStrength reductionfactors for seismic analyses of buildings exposed to near-faultground motionsrdquo Earthquake Engineering and EngineeringVibration vol 10 no 2 pp 195ndash209 2011

[38] B Ganjavi and H Hao ldquoEffect of structural characteristicsdistribution of strength demand and ductility reduction factorof MDOF systems considering soil-structure interactionrdquoEarthquake Engineering and Engineering Vibration vol 11no 2 pp 205ndash220 2012

[39] M H Serror R A Diab and S A Mourad ldquoSeismic forcereduction factor for steel moment resisting frames with


supplemental viscous dampersrdquo Earthquakes and StructuresAn International Journal vol 7 no 6 pp 1171ndash1186 2014

[40] E Bojorquez S E Ruiz A Reyes-Salazar and J BojorquezldquoDuctility and strength reduction factors for degradingstructures considering cumulative damagerdquo Scientific WorldJournal vol 2014 Article ID 575816 7 pages 2014

[41] H Chaulagain H Rodrigues E Spacone et al ldquoResponsereduction factor of irregular RC buildings in Kathmanduvalleyrdquo Earthquake Engineering amp Engineering Vibrationvol 13 no 3 pp 455ndash470 2014

[42] A Reyes-Salazar E Bojorquez J I Velazquez-DimasA Lopez-Barraza and J L Rivera-Salas ldquoDuctility andductility reduction factors for steel buildings consideringdifferent structural representationsrdquo Bulletin of EarthquakeEngineering vol 13 no 6 pp 1749ndash1771 2015

[43] E Vuran and M N Aydınoglu ldquoCapacity and ductility de-mand estimation procedures for preliminary design of cou-pled core wall systems of tall buildingrdquo Bulletin of EarthquakeEngineering vol 14 no 3 pp 721ndash745 2016

[44] F Gomez-Martınez A Alonso-Duran F De Luca andG M Verderame ldquoDuctility of wide-beam RC frames aslateral resisting systemrdquo Bulletin of Earthquake Engineeringvol 14 no 6 pp 1545ndash1569 2016

[45] G Liu J Lian C Liang and M Zhao ldquoStructural responseanalysis in time and frequency domain considering bothductility and strain rate effects under uniform and multiple-support earthquake excitationsrdquo Earthquakes and Structuresvol 10 no 5 pp 989ndash1012 2016

[46] S S Hashemi K Sadeghi M Vaghefi and K ShayanldquoEvaluation of ductility and response modification factor inmoment-resisting steel frames with CFT columnsrdquo Earth-quakes and Structures vol 12 no 6 pp 643ndash652 2017

[47] A Reyes-Salazar and A Haldar ldquoDissipation of energy in steelframes with PR Connectionsrdquo Structural Engineering andMechanics vol 9 no 3 pp 241ndash256 2000

[48] A Reyes-Salazar and A Haldar ldquoEnergy dissipation at PRframes under seismic loadingrdquo Journal of Structural Engi-neering ASCE vol 127 no 5 pp 588ndash593 2001

[49] A Reyes-Salazar and A Haldar ldquoSeismic response and energydissipation in partially restrained and fully restrained steelframes an analytical studyrdquo Steel amp Composite Structuresvol 1 no 4 pp 459ndash480 2001

[50] FEMA Federal EmergencyManagement Agency ldquoState of theart report on systems performance of steel moment framessubjected to earthquake ground shaking SAC steel projectrdquoReport 355C FEMA Federal Emergency ManagementAgency Oakland CA USA 2000

[51] BOCA National Building Code Building Officials amp CodeAdministration International Inc Country Club Hills ILUSA 12th edition 1993

[52] A J Carr ldquoRUAUMOKOrdquo Inelastic Dynamic Analysis Pro-gram Department of Civil Engineering University of Can-terbury Christchurch New Zealand 2011

[53] W F Chen and T Atsuta ldquoInteraction equations for biaxiallyloaded sectionsrdquo Fritz Laboratory Report (72-9) Paper 284Lehigh University Bethlehem Pennsylvania USA 1971

[54] C W Roeder S P Scheiner and J E Carpenter ldquoSeismicbehavior of moment-resisting steel frames analytical studyrdquoJournal of Structural Engineering ASCE vol 119 no 6pp 1866ndash1884 1993

[55] C W Roeder S P Scheiner and J E Carpenter ldquoSeismicbehavior of moment-resisting steel frames experimentalstudyrdquo Journal of Structural Engineering ASCE vol 119no 6 pp 1885ndash1902 1993

[56] R T Leon and K J Shin ldquoPerformance of semi-rigid framesrdquoin Proceedings of Structure Congress pp 1020ndash1035 BostonMassachusetts USA 1995

[57] M N Naderand and A Astaneh ldquoDynamic behavior offlexible semirigid and rigid framesrdquo Journal of ConstructionalSteel Research vol 18 no 3 pp 179ndash192 1991

[58] A Osman A Ghobarah and R M Korol ldquoImplications ofdesign philosophies of seismic response of steel momentsframerdquo Earthquake Engineering and Structural Dynamicsvol 24 no 1 pp 127ndash143 1995

[59] J D Osteraas and H Krawinkler ldquoStrength and ductilityconsiderations in seismic designrdquo Report No 90 BlumeEarthquake Engineering Center Stanford University 1990

[60] B Akbas Energy-based earthquake resistant design of steelmoment resisting frames PhD thesis Department of Civiland Architectural Engineering Illinois Institute of Technol-ogy Chicago IL USA 1997

[61] B Akbas J Shen and H Hao ldquoEnergy approach inperformance-based design of steel moment resisting framesfor basic safety objectiverdquo Structural Design of Tall Buildingsvol 10 no 3 pp 193ndash217 2001

[62] B Calderoni and Z Rinaldi ldquoInelastic dynamic and staticanalysis for steel MRF seismic designrdquo in Behaviour of SteelStructures in Seismic Areas STESSA 2000 Balkema Rotter-dam Netherlands 2000

[63] B Calderoni and Z Rinaldi ldquoSeismic performance evaluationfor steel MRF nonlinear dynamic and static analysesrdquo Steeland Composite Structures An International Journal vol 2no 2 pp 113ndash128 2002

[64] M Brescia R Landolfo O Mammana et al ldquoPreliminaryresults of an experimental program on the cyclic response androtation capacity of steel membersrdquo in Behaviour of SteelStructures in Seismic Areas STESSA 2009 CRC Press Phil-adelphia PA USA 2009

[65] E Bojorquez A Reyes-Salazar A Teran-Gilmore andS E Ruiz ldquoEnergy-based damage index for steel structuresrdquoSteel and Composite Structures An International Journalvol 4 no 10 pp 331ndash348 2010

[66] T V Galambos Structural Members and Frames PrenticeHall Englewood Cliffs NJ USA 2016

[67] A Liew L Gardner and P Block ldquoMoment-curvature-thrustrelationships for beam-columnsrdquo Structures vol 11pp 146ndash154 2017

[68] J Zhou F He b and T Liu ldquoCurvature ductility of columnsand structural displacement ductility in RC frame structuressubjected to ground motionsrdquo Soil Dynamics and EarthquakeEngineering vol 63 pp 174ndash183 2014

[69] C M Uang and M Bruneau ldquoState-of-the-art review onseismic design of steel structuresrdquo Journal of Structural En-gineering ASCE vol 144 no 4 article 03118002 2018


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of the elastic strength demands the larger the ductility thesmaller the design seismic forces In fact the magnitude ofthe reduction of the elastic design seismic forces directlydepend on a parameter that in general can be called ldquothereduction factorrdquo which in turn greatly depends on anassociated parameter called the ductility reduction factor(Rmicro) [5 6] It is particularly important for steel structuressince the beneficial effect of ductility and energy dissipationis supposed to come from different sources However thereis not unanimity on the profession on how to define it it isargued that this parameter is constantly used in the pro-fession in an indirect way to estimate the building seismicdesign forces but there is no engineering definition of it inour specifications [7 8] Defining the magnitude of theseparameters represents one of the most controversial issuesin the SELF procedure

+e reduction factor receives the name of the responsemodification factor (R) force modification factor (Rd)seismic reduction factor (Qprime) and seismic reduction factor(qprime) in the IBC NBCC MFDC and EC codes respectively Itis implicitly or explicitly assumed in these codes that duc-tility represents the capacity of the structure to dissipateenergy and that the reduction of the elastic demands im-portantly depends on the ductility capacity

+us the ductility parameter and the ductility reductionfactors play a central role in the seismic design of steelbuildings for that reason it has been an important researchtopic during the last recent decades However there aremany aspects that need additional attention some of themare addressed in this research As it is further elaboratedbelow the central objective of this paper is to evaluate theductility parameter the ductility reduction factor (Rmicro) forsteel buildings with moment-resisting frames (MRF) fordifferent structural levels (local story and global) relatingthem with the dissipated energy +e evaluation of the micro andRmicro parameters according to sophisticated nonlinear analysisprocedures to capture the effects of the mentioned sources ofnonlinearity is needed It is accepted that nonlinear timehistory analysis is the most accurate and reliable analysisprocedure providing a realistic modeling of the structure aswell as of the cyclic load deformation characteristics of itsstructural elements Extensive seismic nonlinear time-history analyses are performed in this investigation toreach the objectives of the study +e results are comparedwith those specified in the codes

2 Literature Review and Objectives

Investigations regarding nonlinear analysis of buildingsunder the action of earthquakes following different objec-tives have been conducted by many researchers during thelast decades In this regard since this dissipation of energyallows for a reduction of the elastic seismic forces thequantification of the ductility demand the ductility re-duction factor and the force (or seismic) reduction factor isof particular interest +ere have been many studies con-sidering concrete or steel buildings modeled as SDOF orsimple systems Introduced first in ATC [9] at the end of the70s the modification factor was used to reduce the elastic

response (base shear) obtained from a 5 damped accel-eration response spectra Among the first investigations wecan also find those of Newmark and Hall [10] and theyproposed a procedure to relate Rμ and μ based on the basicelastic design spectra Hadjian [11] calculated the spectralaccelerations considering the nonlinear deformation ofstructures Miranda and Bertero [12] proposed simplifiedexpressions to estimate the inelastic design spectra asa function of the maximum tolerable ductility Whitakeret al [13] proposed calculating R as the product of factorsaccounting for viscous damping ductility and overstrengthArroyo-Espinoza and Teran-Gilmore [14] from the dynamicresponse of SDOF systems proposed expressions to calculateRmicro Levy et al [15] derived approximate harmonic equivalentstiffness and damping for bilinear systems in the context ofearthquake resistant Karmakar and Gupta [16] by usingelastoplastic oscillators performed a parametric study toestimate the dependence of strength reduction factors onstrong motion duration earthquake magnitude geologicalsite conditions and epicentral distance Rupakhety andSigbjornsson [17] presented ground-motion predictionequations which describe constant-ductility inelastic spec-tral ordinates and structural behavior factors to be appliedwithin the framework of Eurocode 8 Sanchez-Ricart [18]reviewed the backgrounds that support the values of thereduction factor in the United States Europe and JapanHalabian and Kabiri [19] evaluated the effect of the foun-dation flexibility on the ductility reduction factors of rein-forced concrete stack-like structures AlHamaydeh et al [20]investigated the force reduction factors for reinforce con-crete frame buildings designed according to the IBC codeNaimi et al [21] studied the reduced beam section approachvia the introduction of multilongitudinal voids in the beamweb for various beam depths where the ANSYS finite el-ement program was used in the numerical simulation Animprovement in the connection ductility was observed sincethe input energy was dissipated uniformly along the beamlength Azimi et al [22] proposed a new beam to columnconnection and numerically and experimentally showed thatthe new connection could improve the ultimate structurallateral resistance ductility and energy dissipation capacityFanaie and Shamlou [23] calculated the overstrengthductility and response modification factors for framesbraced with a different type of buckling restrained bracesZhai et al [24] investigated the strength reduction factor ofSDOF systems with constant ductility performance sub-jected to the mainshock-aftershock sequence-type groundmotions Wang et al [25] studied the nonlinear behavior ofprestressed steel reinforced concrete beams by using finiteelement analysis Based on the model they analyzed theeffect of prestressed force to the stiffness the ultimatebearing capacity and ductility of the beams Cho et al [26]investigated the shear design equations for prestressedhollow-core slabs and examined the magnitude of thestrength reduction factors based on the structural reliabilitytheory +e results showed that the shear strengths of themembers with the heights of more than 315mm are ex-cessively safe whereas some members with low depths didnot satisfy the target reliability index














z yx

313prime

630prime

430primeN


12prime

18prime

813prime

530prime

530prime

z yx

N











Model StoryColumns


112 W14X257 W14X311 W33X11823 W14X257 W14X312 W30X116

3ROOF W14X257 W14X313 W24X68

2


23 W14X370 W14X500W14X455 W36X160

34 W14X370 W14X455 W36X135

45 W14X370W14X283 W14X455W14X370 W36X135

56 W14X283 W14X370 W36X135

67 W14X283W14X257 W14X370W14X283 W36X135

78 W14X257 W14X283 W30X99

89 W14X257W14X233 W14X283W14X257 W27X84

9ROOF W14X233 W14X257 W24X68




μLϕ ϕmax

ϕy

(1)



μS Δmax

Δy (2)






microG 1n

1113944

n

i1microS( 1113857i (3)



Rmicro Re

Ri

(4)


RmicroLϕ Me

Mi (5)



RmicroS Vse

Vsi (6)


RμG 1n

1113944

n

i1RμS1113872 1113873

i (7)


ELϕ EDϕ

ECϕ (8)


ECϕ MP θpa (9)



ELϕ1113872 1113873SB 12q

1113944

2q

j1ELϕ1113872 1113873

j (10)



ElowastLϕ

EDϕ

ElowastCϕ (11)


ElowastCϕ

13

MPθpa1113872 1113873 (12)



12r

1113944

2r

k1ElowastLϕ1113872 1113873

k (13)


ES 1

(2q + 2r)1113944

2q

j1ELϕ1113872 1113873

j+ 1113944

2r

k1ElowastLϕ1113872 1113873

k⎛⎝ ⎞⎠ (14)


EG 1n

1113944

n

i1Es( 1113857i (15)














04 06 08 10 12 04 06 08 10 12

microLϕ

Beams1 261 427 599 823 1022 219 356 456 633 7812 248 460 717 957 1186 226 415 587 769 9323 201 431 671 894 1120 199 373 559 767 930

Columns1 106 132 195 265 370 101 125 172 222 2872 100 100 109 125 141 100 101 103 121 1293 100 100 106 112 123 100 100 102 113 126

RmicroLϕ

Beams1 168 229 289 345 406 154 212 268 322 3912 166 225 279 328 386 155 211 265 316 3813 158 211 260 306 360 150 201 250 297 354

Columns1 152 187 225 260 298 135 166 200 235 2792 150 185 219 251 286 137 171 201 232 2713 155 195 228 259 295 143 181 217 251 292

QL

Beams1 064 054 048 042 040 070 060 059 051 0502 067 049 039 034 033 069 051 045 041 0413 079 049 039 034 032 075 054 045 039 038

Columns1 143 142 115 098 081 134 133 116 106 0972 150 185 201 201 203 137 169 195 192 2103 155 195 215 231 240 143 181 213 222 232

Sag=02Sag=04Sag=06

0

2

4

6

8

10

12

14

16

Mea

n of

μLϕ

3 4 5 6 7 8 9 102Story number

(a)

Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

0

2

4

6

8

10

12

Mea

n of

μLϕ

(b)

Sag=02Sag=04Sag=06

0

1

2

3

4

5

6

Mea

n of

μLϕ

3 4 5 6 7 8 9 102Story number

(c)

Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

0

1

2

3

4

Mea

n of

μLϕ

(d)

Figure 3 Continued




Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

0

1

2

3

4

5

6M

ean

of R

μLϕ

(e)

Sag=02Sag=04Sag=06

0

1

2

3

4

5

6

Mea

n of

RLμ

ϕ

3 4 5 6 7 8 9 102Story number

(f )

Sag=02Sag=04Sag=06

0

1

2

3

4

Mea

n of

RLϕ

3 4 5 6 7 8 9 102Story number

(g)

Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

0

1

2

3

4

Mea

n of

RLϕ

(h)




04 06 08 10 12 04 06 08 10 12

microS1 161 199 281 344 395 148 190 280 289 4282 170 220 286 331 399 165 215 258 309 3543 153 193 269 299 390 152 210 272 319 384

RmicroS

1 146 190 237 276 310 133 173 211 251 2892 144 186 230 268 305 136 184 225 268 3063 145 184 217 247 276 136 175 208 236 267

QS

1 091 095 084 080 078 090 091 075 087 0682 085 085 080 081 076 082 086 087 087 0863 095 095 081 083 071 089 083 076 074 070






Sag=02Sag=04Sag=06

0

1

2

3

4

5

6M

ean

of micro

S

3 4 5 6 7 8 9 102Story number

(a)

Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

0

1

2

3

4

5

Mea

n of

microS

(b)

Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

0

1

2

3

4

Mea

n of

Rmicros

(c)

Sag=02Sag=04Sag=06

0

1

2

3

4

5

Mea

n of

Rmicros

3 4 5 6 7 8 9 102Story number

(d)



Parameter










QL RmicroLϕ

microLϕ

QS RmicroS

microS

QG RmicroG

microG

(16)




Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

00

02

04

06

08

10Q

L rat

io

(a)

Sag=02Sag=04Sag=06

00

02

04

06

08

10

12

QL r

atio

3 4 5 6 7 8 9 102Story number

(b)

Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

0

1

2

3

4

QL r

atio

(c)

Sag=02Sag=04Sag=06

0

1

2

3

4

QL r

atio

3 4 5 6 7 8 9 102Story number

(d)


Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

00

04

08

12

QS r

atio

(a)

Sag=02Sag=04Sag=06

00

04

08

12

QS r

atio

3 4 5 6 7 8 9 102Story number

(b)









PS RmicroS

ES

PG RmicroG

EG

(17)





5 Conclusions








04 06 08 10 12 04 06 08 10 12

Beams (ELϕ)SB1 0053 0147 0256 0379 0512 0045 0114 0188 0274 03762 0022 0072 0140 0216 0298 0018 0055 0109 0170 02423 0008 0033 0069 0113 0161 0007 0025 0057 0096 0141


1 0003 0010 0025 0046 0076 0003 0007 0017 0031 00502 0001 0003 0004 0007 0013 0001 0003 0004 0006 00103 0001 0001 0002 0004 0007 0001 0001 0002 0004 0007



04 06 08 10 12 04 06 08 10 121 0020 0056 0102 0157 0221 0017 0043 0074 0112 01582 0008 0026 0050 0077 0108 0007 0020 0039 0061 00873 0003 0012 0024 0040 0058 0003 0009 0020 0035 0052


Parameter Member


04 06 08 10 12 04 06 08 10 12 02 04 06 02 04 06

EGB+C 0011 0031 0059 0091 0129 0009 0024 0044 0069 0099 0026 0111 0218 0017 0083 0171B 0028 0084 0155 0236 0324 0023 0065 0118 018 0253 0076 0314 0383 0047 0241 0475

PG 482 211 139 107 89 630 288 193 147 117 193 73 78 317 97 65


Sag=02Sag=04Sag=06

000

010

020

030

040

050

060

070M

ean

of (E

Lϕ) S

B bea

ms

3 4 5 6 7 8 9 102Story number

(a)

Sag=02Sag=04Sag=06

000

010

020

030

040

050

060

070

080

Mea

n of

(ELϕ

) SB b

eam

s

3 4 5 6 7 8 9 102Story number

(b)

Sag=02Sag=04Sag=06

000002004006008010012014016018020

Mea

n of

(Elowast

Lϕ) S

C co

lum

ns

3 4 5 6 7 8 9 102Story number

(c)

Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

000002004006008010012014016018

Mea

n of

(Elowast

Lϕ) S

C co

lum

ns

(d)


Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

000

005

010

015

020

025

030

035

040

Mea

n of

ES s

tory

(a)

Sag=02Sag=04Sag=06

000

005

010

015

020

025

030

Mea

n of

ES s

tory

3 4 5 6 7 8 9 102Story number

(b)





Data Availability


Disclosure




Acknowledgments


References







04 06 08 10 12 04 06 08 10 121 275 129 93 73 61 296 152 112 92 772 655 258 164 124 102 756 335 206 158 1263 1813 558 314 219 171 1943 700 365 246 189

Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

0

10

20

30

40

50

60

P S ra

tio

(a)

Sag=02Sag=04Sag=06

0

10

20

30

40

50

60

70

80

90

P S ra

tio3 4 5 6 7 8 9 102

Story number

(b)










































































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia














z yx

313prime

630prime

430primeN


12prime

18prime

813prime

530prime

530prime

z yx

N











Model StoryColumns


112 W14X257 W14X311 W33X11823 W14X257 W14X312 W30X116

3ROOF W14X257 W14X313 W24X68

2


23 W14X370 W14X500W14X455 W36X160

34 W14X370 W14X455 W36X135

45 W14X370W14X283 W14X455W14X370 W36X135

56 W14X283 W14X370 W36X135

67 W14X283W14X257 W14X370W14X283 W36X135

78 W14X257 W14X283 W30X99

89 W14X257W14X233 W14X283W14X257 W27X84

9ROOF W14X233 W14X257 W24X68




μLϕ ϕmax

ϕy

(1)



μS Δmax

Δy (2)






microG 1n

1113944

n

i1microS( 1113857i (3)



Rmicro Re

Ri

(4)


RmicroLϕ Me

Mi (5)



RmicroS Vse

Vsi (6)


RμG 1n

1113944

n

i1RμS1113872 1113873

i (7)


ELϕ EDϕ

ECϕ (8)


ECϕ MP θpa (9)



ELϕ1113872 1113873SB 12q

1113944

2q

j1ELϕ1113872 1113873

j (10)



ElowastLϕ

EDϕ

ElowastCϕ (11)


ElowastCϕ

13

MPθpa1113872 1113873 (12)



12r

1113944

2r

k1ElowastLϕ1113872 1113873

k (13)


ES 1

(2q + 2r)1113944

2q

j1ELϕ1113872 1113873

j+ 1113944

2r

k1ElowastLϕ1113872 1113873

k⎛⎝ ⎞⎠ (14)


EG 1n

1113944

n

i1Es( 1113857i (15)














04 06 08 10 12 04 06 08 10 12

microLϕ

Beams1 261 427 599 823 1022 219 356 456 633 7812 248 460 717 957 1186 226 415 587 769 9323 201 431 671 894 1120 199 373 559 767 930

Columns1 106 132 195 265 370 101 125 172 222 2872 100 100 109 125 141 100 101 103 121 1293 100 100 106 112 123 100 100 102 113 126

RmicroLϕ

Beams1 168 229 289 345 406 154 212 268 322 3912 166 225 279 328 386 155 211 265 316 3813 158 211 260 306 360 150 201 250 297 354

Columns1 152 187 225 260 298 135 166 200 235 2792 150 185 219 251 286 137 171 201 232 2713 155 195 228 259 295 143 181 217 251 292

QL

Beams1 064 054 048 042 040 070 060 059 051 0502 067 049 039 034 033 069 051 045 041 0413 079 049 039 034 032 075 054 045 039 038

Columns1 143 142 115 098 081 134 133 116 106 0972 150 185 201 201 203 137 169 195 192 2103 155 195 215 231 240 143 181 213 222 232

Sag=02Sag=04Sag=06

0

2

4

6

8

10

12

14

16

Mea

n of

μLϕ

3 4 5 6 7 8 9 102Story number

(a)

Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

0

2

4

6

8

10

12

Mea

n of

μLϕ

(b)

Sag=02Sag=04Sag=06

0

1

2

3

4

5

6

Mea

n of

μLϕ

3 4 5 6 7 8 9 102Story number

(c)

Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

0

1

2

3

4

Mea

n of

μLϕ

(d)

Figure 3 Continued




Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

0

1

2

3

4

5

6M

ean

of R

μLϕ

(e)

Sag=02Sag=04Sag=06

0

1

2

3

4

5

6

Mea

n of

RLμ

ϕ

3 4 5 6 7 8 9 102Story number

(f )

Sag=02Sag=04Sag=06

0

1

2

3

4

Mea

n of

RLϕ

3 4 5 6 7 8 9 102Story number

(g)

Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

0

1

2

3

4

Mea

n of

RLϕ

(h)




04 06 08 10 12 04 06 08 10 12

microS1 161 199 281 344 395 148 190 280 289 4282 170 220 286 331 399 165 215 258 309 3543 153 193 269 299 390 152 210 272 319 384

RmicroS

1 146 190 237 276 310 133 173 211 251 2892 144 186 230 268 305 136 184 225 268 3063 145 184 217 247 276 136 175 208 236 267

QS

1 091 095 084 080 078 090 091 075 087 0682 085 085 080 081 076 082 086 087 087 0863 095 095 081 083 071 089 083 076 074 070






Sag=02Sag=04Sag=06

0

1

2

3

4

5

6M

ean

of micro

S

3 4 5 6 7 8 9 102Story number

(a)

Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

0

1

2

3

4

5

Mea

n of

microS

(b)

Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

0

1

2

3

4

Mea

n of

Rmicros

(c)

Sag=02Sag=04Sag=06

0

1

2

3

4

5

Mea

n of

Rmicros

3 4 5 6 7 8 9 102Story number

(d)



Parameter










QL RmicroLϕ

microLϕ

QS RmicroS

microS

QG RmicroG

microG

(16)




Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

00

02

04

06

08

10Q

L rat

io

(a)

Sag=02Sag=04Sag=06

00

02

04

06

08

10

12

QL r

atio

3 4 5 6 7 8 9 102Story number

(b)

Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

0

1

2

3

4

QL r

atio

(c)

Sag=02Sag=04Sag=06

0

1

2

3

4

QL r

atio

3 4 5 6 7 8 9 102Story number

(d)


Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

00

04

08

12

QS r

atio

(a)

Sag=02Sag=04Sag=06

00

04

08

12

QS r

atio

3 4 5 6 7 8 9 102Story number

(b)









PS RmicroS

ES

PG RmicroG

EG

(17)





5 Conclusions








04 06 08 10 12 04 06 08 10 12

Beams (ELϕ)SB1 0053 0147 0256 0379 0512 0045 0114 0188 0274 03762 0022 0072 0140 0216 0298 0018 0055 0109 0170 02423 0008 0033 0069 0113 0161 0007 0025 0057 0096 0141


1 0003 0010 0025 0046 0076 0003 0007 0017 0031 00502 0001 0003 0004 0007 0013 0001 0003 0004 0006 00103 0001 0001 0002 0004 0007 0001 0001 0002 0004 0007



04 06 08 10 12 04 06 08 10 121 0020 0056 0102 0157 0221 0017 0043 0074 0112 01582 0008 0026 0050 0077 0108 0007 0020 0039 0061 00873 0003 0012 0024 0040 0058 0003 0009 0020 0035 0052


Parameter Member


04 06 08 10 12 04 06 08 10 12 02 04 06 02 04 06

EGB+C 0011 0031 0059 0091 0129 0009 0024 0044 0069 0099 0026 0111 0218 0017 0083 0171B 0028 0084 0155 0236 0324 0023 0065 0118 018 0253 0076 0314 0383 0047 0241 0475

PG 482 211 139 107 89 630 288 193 147 117 193 73 78 317 97 65


Sag=02Sag=04Sag=06

000

010

020

030

040

050

060

070M

ean

of (E

Lϕ) S

B bea

ms

3 4 5 6 7 8 9 102Story number

(a)

Sag=02Sag=04Sag=06

000

010

020

030

040

050

060

070

080

Mea

n of

(ELϕ

) SB b

eam

s

3 4 5 6 7 8 9 102Story number

(b)

Sag=02Sag=04Sag=06

000002004006008010012014016018020

Mea

n of

(Elowast

Lϕ) S

C co

lum

ns

3 4 5 6 7 8 9 102Story number

(c)

Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

000002004006008010012014016018

Mea

n of

(Elowast

Lϕ) S

C co

lum

ns

(d)


Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

000

005

010

015

020

025

030

035

040

Mea

n of

ES s

tory

(a)

Sag=02Sag=04Sag=06

000

005

010

015

020

025

030

Mea

n of

ES s

tory

3 4 5 6 7 8 9 102Story number

(b)





Data Availability


Disclosure




Acknowledgments


References







04 06 08 10 12 04 06 08 10 121 275 129 93 73 61 296 152 112 92 772 655 258 164 124 102 756 335 206 158 1263 1813 558 314 219 171 1943 700 365 246 189

Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

0

10

20

30

40

50

60

P S ra

tio

(a)

Sag=02Sag=04Sag=06

0

10

20

30

40

50

60

70

80

90

P S ra

tio3 4 5 6 7 8 9 102

Story number

(b)










































































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia










Model StoryColumns


112 W14X257 W14X311 W33X11823 W14X257 W14X312 W30X116

3ROOF W14X257 W14X313 W24X68

2


23 W14X370 W14X500W14X455 W36X160

34 W14X370 W14X455 W36X135

45 W14X370W14X283 W14X455W14X370 W36X135

56 W14X283 W14X370 W36X135

67 W14X283W14X257 W14X370W14X283 W36X135

78 W14X257 W14X283 W30X99

89 W14X257W14X233 W14X283W14X257 W27X84

9ROOF W14X233 W14X257 W24X68




μLϕ ϕmax

ϕy

(1)



μS Δmax

Δy (2)






microG 1n

1113944

n

i1microS( 1113857i (3)



Rmicro Re

Ri

(4)


RmicroLϕ Me

Mi (5)



RmicroS Vse

Vsi (6)


RμG 1n

1113944

n

i1RμS1113872 1113873

i (7)


ELϕ EDϕ

ECϕ (8)


ECϕ MP θpa (9)



ELϕ1113872 1113873SB 12q

1113944

2q

j1ELϕ1113872 1113873

j (10)



ElowastLϕ

EDϕ

ElowastCϕ (11)


ElowastCϕ

13

MPθpa1113872 1113873 (12)



12r

1113944

2r

k1ElowastLϕ1113872 1113873

k (13)


ES 1

(2q + 2r)1113944

2q

j1ELϕ1113872 1113873

j+ 1113944

2r

k1ElowastLϕ1113872 1113873

k⎛⎝ ⎞⎠ (14)


EG 1n

1113944

n

i1Es( 1113857i (15)














04 06 08 10 12 04 06 08 10 12

microLϕ

Beams1 261 427 599 823 1022 219 356 456 633 7812 248 460 717 957 1186 226 415 587 769 9323 201 431 671 894 1120 199 373 559 767 930

Columns1 106 132 195 265 370 101 125 172 222 2872 100 100 109 125 141 100 101 103 121 1293 100 100 106 112 123 100 100 102 113 126

RmicroLϕ

Beams1 168 229 289 345 406 154 212 268 322 3912 166 225 279 328 386 155 211 265 316 3813 158 211 260 306 360 150 201 250 297 354

Columns1 152 187 225 260 298 135 166 200 235 2792 150 185 219 251 286 137 171 201 232 2713 155 195 228 259 295 143 181 217 251 292

QL

Beams1 064 054 048 042 040 070 060 059 051 0502 067 049 039 034 033 069 051 045 041 0413 079 049 039 034 032 075 054 045 039 038

Columns1 143 142 115 098 081 134 133 116 106 0972 150 185 201 201 203 137 169 195 192 2103 155 195 215 231 240 143 181 213 222 232

Sag=02Sag=04Sag=06

0

2

4

6

8

10

12

14

16

Mea

n of

μLϕ

3 4 5 6 7 8 9 102Story number

(a)

Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

0

2

4

6

8

10

12

Mea

n of

μLϕ

(b)

Sag=02Sag=04Sag=06

0

1

2

3

4

5

6

Mea

n of

μLϕ

3 4 5 6 7 8 9 102Story number

(c)

Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

0

1

2

3

4

Mea

n of

μLϕ

(d)

Figure 3 Continued




Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

0

1

2

3

4

5

6M

ean

of R

μLϕ

(e)

Sag=02Sag=04Sag=06

0

1

2

3

4

5

6

Mea

n of

RLμ

ϕ

3 4 5 6 7 8 9 102Story number

(f )

Sag=02Sag=04Sag=06

0

1

2

3

4

Mea

n of

RLϕ

3 4 5 6 7 8 9 102Story number

(g)

Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

0

1

2

3

4

Mea

n of

RLϕ

(h)




04 06 08 10 12 04 06 08 10 12

microS1 161 199 281 344 395 148 190 280 289 4282 170 220 286 331 399 165 215 258 309 3543 153 193 269 299 390 152 210 272 319 384

RmicroS

1 146 190 237 276 310 133 173 211 251 2892 144 186 230 268 305 136 184 225 268 3063 145 184 217 247 276 136 175 208 236 267

QS

1 091 095 084 080 078 090 091 075 087 0682 085 085 080 081 076 082 086 087 087 0863 095 095 081 083 071 089 083 076 074 070






Sag=02Sag=04Sag=06

0

1

2

3

4

5

6M

ean

of micro

S

3 4 5 6 7 8 9 102Story number

(a)

Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

0

1

2

3

4

5

Mea

n of

microS

(b)

Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

0

1

2

3

4

Mea

n of

Rmicros

(c)

Sag=02Sag=04Sag=06

0

1

2

3

4

5

Mea

n of

Rmicros

3 4 5 6 7 8 9 102Story number

(d)



Parameter










QL RmicroLϕ

microLϕ

QS RmicroS

microS

QG RmicroG

microG

(16)




Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

00

02

04

06

08

10Q

L rat

io

(a)

Sag=02Sag=04Sag=06

00

02

04

06

08

10

12

QL r

atio

3 4 5 6 7 8 9 102Story number

(b)

Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

0

1

2

3

4

QL r

atio

(c)

Sag=02Sag=04Sag=06

0

1

2

3

4

QL r

atio

3 4 5 6 7 8 9 102Story number

(d)


Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

00

04

08

12

QS r

atio

(a)

Sag=02Sag=04Sag=06

00

04

08

12

QS r

atio

3 4 5 6 7 8 9 102Story number

(b)









PS RmicroS

ES

PG RmicroG

EG

(17)





5 Conclusions








04 06 08 10 12 04 06 08 10 12

Beams (ELϕ)SB1 0053 0147 0256 0379 0512 0045 0114 0188 0274 03762 0022 0072 0140 0216 0298 0018 0055 0109 0170 02423 0008 0033 0069 0113 0161 0007 0025 0057 0096 0141


1 0003 0010 0025 0046 0076 0003 0007 0017 0031 00502 0001 0003 0004 0007 0013 0001 0003 0004 0006 00103 0001 0001 0002 0004 0007 0001 0001 0002 0004 0007



04 06 08 10 12 04 06 08 10 121 0020 0056 0102 0157 0221 0017 0043 0074 0112 01582 0008 0026 0050 0077 0108 0007 0020 0039 0061 00873 0003 0012 0024 0040 0058 0003 0009 0020 0035 0052


Parameter Member


04 06 08 10 12 04 06 08 10 12 02 04 06 02 04 06

EGB+C 0011 0031 0059 0091 0129 0009 0024 0044 0069 0099 0026 0111 0218 0017 0083 0171B 0028 0084 0155 0236 0324 0023 0065 0118 018 0253 0076 0314 0383 0047 0241 0475

PG 482 211 139 107 89 630 288 193 147 117 193 73 78 317 97 65


Sag=02Sag=04Sag=06

000

010

020

030

040

050

060

070M

ean

of (E

Lϕ) S

B bea

ms

3 4 5 6 7 8 9 102Story number

(a)

Sag=02Sag=04Sag=06

000

010

020

030

040

050

060

070

080

Mea

n of

(ELϕ

) SB b

eam

s

3 4 5 6 7 8 9 102Story number

(b)

Sag=02Sag=04Sag=06

000002004006008010012014016018020

Mea

n of

(Elowast

Lϕ) S

C co

lum

ns

3 4 5 6 7 8 9 102Story number

(c)

Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

000002004006008010012014016018

Mea

n of

(Elowast

Lϕ) S

C co

lum

ns

(d)


Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

000

005

010

015

020

025

030

035

040

Mea

n of

ES s

tory

(a)

Sag=02Sag=04Sag=06

000

005

010

015

020

025

030

Mea

n of

ES s

tory

3 4 5 6 7 8 9 102Story number

(b)





Data Availability


Disclosure




Acknowledgments


References







04 06 08 10 12 04 06 08 10 121 275 129 93 73 61 296 152 112 92 772 655 258 164 124 102 756 335 206 158 1263 1813 558 314 219 171 1943 700 365 246 189

Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

0

10

20

30

40

50

60

P S ra

tio

(a)

Sag=02Sag=04Sag=06

0

10

20

30

40

50

60

70

80

90

P S ra

tio3 4 5 6 7 8 9 102

Story number

(b)










































































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




μLϕ ϕmax

ϕy

(1)



μS Δmax

Δy (2)






microG 1n

1113944

n

i1microS( 1113857i (3)



Rmicro Re

Ri

(4)


RmicroLϕ Me

Mi (5)



RmicroS Vse

Vsi (6)


RμG 1n

1113944

n

i1RμS1113872 1113873

i (7)


ELϕ EDϕ

ECϕ (8)


ECϕ MP θpa (9)



ELϕ1113872 1113873SB 12q

1113944

2q

j1ELϕ1113872 1113873

j (10)



ElowastLϕ

EDϕ

ElowastCϕ (11)


ElowastCϕ

13

MPθpa1113872 1113873 (12)



12r

1113944

2r

k1ElowastLϕ1113872 1113873

k (13)


ES 1

(2q + 2r)1113944

2q

j1ELϕ1113872 1113873

j+ 1113944

2r

k1ElowastLϕ1113872 1113873

k⎛⎝ ⎞⎠ (14)


EG 1n

1113944

n

i1Es( 1113857i (15)














04 06 08 10 12 04 06 08 10 12

microLϕ

Beams1 261 427 599 823 1022 219 356 456 633 7812 248 460 717 957 1186 226 415 587 769 9323 201 431 671 894 1120 199 373 559 767 930

Columns1 106 132 195 265 370 101 125 172 222 2872 100 100 109 125 141 100 101 103 121 1293 100 100 106 112 123 100 100 102 113 126

RmicroLϕ

Beams1 168 229 289 345 406 154 212 268 322 3912 166 225 279 328 386 155 211 265 316 3813 158 211 260 306 360 150 201 250 297 354

Columns1 152 187 225 260 298 135 166 200 235 2792 150 185 219 251 286 137 171 201 232 2713 155 195 228 259 295 143 181 217 251 292

QL

Beams1 064 054 048 042 040 070 060 059 051 0502 067 049 039 034 033 069 051 045 041 0413 079 049 039 034 032 075 054 045 039 038

Columns1 143 142 115 098 081 134 133 116 106 0972 150 185 201 201 203 137 169 195 192 2103 155 195 215 231 240 143 181 213 222 232

Sag=02Sag=04Sag=06

0

2

4

6

8

10

12

14

16

Mea

n of

μLϕ

3 4 5 6 7 8 9 102Story number

(a)

Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

0

2

4

6

8

10

12

Mea

n of

μLϕ

(b)

Sag=02Sag=04Sag=06

0

1

2

3

4

5

6

Mea

n of

μLϕ

3 4 5 6 7 8 9 102Story number

(c)

Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

0

1

2

3

4

Mea

n of

μLϕ

(d)

Figure 3 Continued




Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

0

1

2

3

4

5

6M

ean

of R

μLϕ

(e)

Sag=02Sag=04Sag=06

0

1

2

3

4

5

6

Mea

n of

RLμ

ϕ

3 4 5 6 7 8 9 102Story number

(f )

Sag=02Sag=04Sag=06

0

1

2

3

4

Mea

n of

RLϕ

3 4 5 6 7 8 9 102Story number

(g)

Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

0

1

2

3

4

Mea

n of

RLϕ

(h)




04 06 08 10 12 04 06 08 10 12

microS1 161 199 281 344 395 148 190 280 289 4282 170 220 286 331 399 165 215 258 309 3543 153 193 269 299 390 152 210 272 319 384

RmicroS

1 146 190 237 276 310 133 173 211 251 2892 144 186 230 268 305 136 184 225 268 3063 145 184 217 247 276 136 175 208 236 267

QS

1 091 095 084 080 078 090 091 075 087 0682 085 085 080 081 076 082 086 087 087 0863 095 095 081 083 071 089 083 076 074 070






Sag=02Sag=04Sag=06

0

1

2

3

4

5

6M

ean

of micro

S

3 4 5 6 7 8 9 102Story number

(a)

Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

0

1

2

3

4

5

Mea

n of

microS

(b)

Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

0

1

2

3

4

Mea

n of

Rmicros

(c)

Sag=02Sag=04Sag=06

0

1

2

3

4

5

Mea

n of

Rmicros

3 4 5 6 7 8 9 102Story number

(d)



Parameter










QL RmicroLϕ

microLϕ

QS RmicroS

microS

QG RmicroG

microG

(16)




Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

00

02

04

06

08

10Q

L rat

io

(a)

Sag=02Sag=04Sag=06

00

02

04

06

08

10

12

QL r

atio

3 4 5 6 7 8 9 102Story number

(b)

Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

0

1

2

3

4

QL r

atio

(c)

Sag=02Sag=04Sag=06

0

1

2

3

4

QL r

atio

3 4 5 6 7 8 9 102Story number

(d)


Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

00

04

08

12

QS r

atio

(a)

Sag=02Sag=04Sag=06

00

04

08

12

QS r

atio

3 4 5 6 7 8 9 102Story number

(b)









PS RmicroS

ES

PG RmicroG

EG

(17)





5 Conclusions








04 06 08 10 12 04 06 08 10 12

Beams (ELϕ)SB1 0053 0147 0256 0379 0512 0045 0114 0188 0274 03762 0022 0072 0140 0216 0298 0018 0055 0109 0170 02423 0008 0033 0069 0113 0161 0007 0025 0057 0096 0141


1 0003 0010 0025 0046 0076 0003 0007 0017 0031 00502 0001 0003 0004 0007 0013 0001 0003 0004 0006 00103 0001 0001 0002 0004 0007 0001 0001 0002 0004 0007



04 06 08 10 12 04 06 08 10 121 0020 0056 0102 0157 0221 0017 0043 0074 0112 01582 0008 0026 0050 0077 0108 0007 0020 0039 0061 00873 0003 0012 0024 0040 0058 0003 0009 0020 0035 0052


Parameter Member


04 06 08 10 12 04 06 08 10 12 02 04 06 02 04 06

EGB+C 0011 0031 0059 0091 0129 0009 0024 0044 0069 0099 0026 0111 0218 0017 0083 0171B 0028 0084 0155 0236 0324 0023 0065 0118 018 0253 0076 0314 0383 0047 0241 0475

PG 482 211 139 107 89 630 288 193 147 117 193 73 78 317 97 65


Sag=02Sag=04Sag=06

000

010

020

030

040

050

060

070M

ean

of (E

Lϕ) S

B bea

ms

3 4 5 6 7 8 9 102Story number

(a)

Sag=02Sag=04Sag=06

000

010

020

030

040

050

060

070

080

Mea

n of

(ELϕ

) SB b

eam

s

3 4 5 6 7 8 9 102Story number

(b)

Sag=02Sag=04Sag=06

000002004006008010012014016018020

Mea

n of

(Elowast

Lϕ) S

C co

lum

ns

3 4 5 6 7 8 9 102Story number

(c)

Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

000002004006008010012014016018

Mea

n of

(Elowast

Lϕ) S

C co

lum

ns

(d)


Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

000

005

010

015

020

025

030

035

040

Mea

n of

ES s

tory

(a)

Sag=02Sag=04Sag=06

000

005

010

015

020

025

030

Mea

n of

ES s

tory

3 4 5 6 7 8 9 102Story number

(b)





Data Availability


Disclosure




Acknowledgments


References







04 06 08 10 12 04 06 08 10 121 275 129 93 73 61 296 152 112 92 772 655 258 164 124 102 756 335 206 158 1263 1813 558 314 219 171 1943 700 365 246 189

Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

0

10

20

30

40

50

60

P S ra

tio

(a)

Sag=02Sag=04Sag=06

0

10

20

30

40

50

60

70

80

90

P S ra

tio3 4 5 6 7 8 9 102

Story number

(b)










































































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


microG 1n

1113944

n

i1microS( 1113857i (3)



Rmicro Re

Ri

(4)


RmicroLϕ Me

Mi (5)



RmicroS Vse

Vsi (6)


RμG 1n

1113944

n

i1RμS1113872 1113873

i (7)


ELϕ EDϕ

ECϕ (8)


ECϕ MP θpa (9)



ELϕ1113872 1113873SB 12q

1113944

2q

j1ELϕ1113872 1113873

j (10)



ElowastLϕ

EDϕ

ElowastCϕ (11)


ElowastCϕ

13

MPθpa1113872 1113873 (12)



12r

1113944

2r

k1ElowastLϕ1113872 1113873

k (13)


ES 1

(2q + 2r)1113944

2q

j1ELϕ1113872 1113873

j+ 1113944

2r

k1ElowastLϕ1113872 1113873

k⎛⎝ ⎞⎠ (14)


EG 1n

1113944

n

i1Es( 1113857i (15)














04 06 08 10 12 04 06 08 10 12

microLϕ

Beams1 261 427 599 823 1022 219 356 456 633 7812 248 460 717 957 1186 226 415 587 769 9323 201 431 671 894 1120 199 373 559 767 930

Columns1 106 132 195 265 370 101 125 172 222 2872 100 100 109 125 141 100 101 103 121 1293 100 100 106 112 123 100 100 102 113 126

RmicroLϕ

Beams1 168 229 289 345 406 154 212 268 322 3912 166 225 279 328 386 155 211 265 316 3813 158 211 260 306 360 150 201 250 297 354

Columns1 152 187 225 260 298 135 166 200 235 2792 150 185 219 251 286 137 171 201 232 2713 155 195 228 259 295 143 181 217 251 292

QL

Beams1 064 054 048 042 040 070 060 059 051 0502 067 049 039 034 033 069 051 045 041 0413 079 049 039 034 032 075 054 045 039 038

Columns1 143 142 115 098 081 134 133 116 106 0972 150 185 201 201 203 137 169 195 192 2103 155 195 215 231 240 143 181 213 222 232

Sag=02Sag=04Sag=06

0

2

4

6

8

10

12

14

16

Mea

n of

μLϕ

3 4 5 6 7 8 9 102Story number

(a)

Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

0

2

4

6

8

10

12

Mea

n of

μLϕ

(b)

Sag=02Sag=04Sag=06

0

1

2

3

4

5

6

Mea

n of

μLϕ

3 4 5 6 7 8 9 102Story number

(c)

Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

0

1

2

3

4

Mea

n of

μLϕ

(d)

Figure 3 Continued




Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

0

1

2

3

4

5

6M

ean

of R

μLϕ

(e)

Sag=02Sag=04Sag=06

0

1

2

3

4

5

6

Mea

n of

RLμ

ϕ

3 4 5 6 7 8 9 102Story number

(f )

Sag=02Sag=04Sag=06

0

1

2

3

4

Mea

n of

RLϕ

3 4 5 6 7 8 9 102Story number

(g)

Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

0

1

2

3

4

Mea

n of

RLϕ

(h)




04 06 08 10 12 04 06 08 10 12

microS1 161 199 281 344 395 148 190 280 289 4282 170 220 286 331 399 165 215 258 309 3543 153 193 269 299 390 152 210 272 319 384

RmicroS

1 146 190 237 276 310 133 173 211 251 2892 144 186 230 268 305 136 184 225 268 3063 145 184 217 247 276 136 175 208 236 267

QS

1 091 095 084 080 078 090 091 075 087 0682 085 085 080 081 076 082 086 087 087 0863 095 095 081 083 071 089 083 076 074 070






Sag=02Sag=04Sag=06

0

1

2

3

4

5

6M

ean

of micro

S

3 4 5 6 7 8 9 102Story number

(a)

Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

0

1

2

3

4

5

Mea

n of

microS

(b)

Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

0

1

2

3

4

Mea

n of

Rmicros

(c)

Sag=02Sag=04Sag=06

0

1

2

3

4

5

Mea

n of

Rmicros

3 4 5 6 7 8 9 102Story number

(d)



Parameter










QL RmicroLϕ

microLϕ

QS RmicroS

microS

QG RmicroG

microG

(16)




Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

00

02

04

06

08

10Q

L rat

io

(a)

Sag=02Sag=04Sag=06

00

02

04

06

08

10

12

QL r

atio

3 4 5 6 7 8 9 102Story number

(b)

Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

0

1

2

3

4

QL r

atio

(c)

Sag=02Sag=04Sag=06

0

1

2

3

4

QL r

atio

3 4 5 6 7 8 9 102Story number

(d)


Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

00

04

08

12

QS r

atio

(a)

Sag=02Sag=04Sag=06

00

04

08

12

QS r

atio

3 4 5 6 7 8 9 102Story number

(b)









PS RmicroS

ES

PG RmicroG

EG

(17)





5 Conclusions








04 06 08 10 12 04 06 08 10 12

Beams (ELϕ)SB1 0053 0147 0256 0379 0512 0045 0114 0188 0274 03762 0022 0072 0140 0216 0298 0018 0055 0109 0170 02423 0008 0033 0069 0113 0161 0007 0025 0057 0096 0141


1 0003 0010 0025 0046 0076 0003 0007 0017 0031 00502 0001 0003 0004 0007 0013 0001 0003 0004 0006 00103 0001 0001 0002 0004 0007 0001 0001 0002 0004 0007



04 06 08 10 12 04 06 08 10 121 0020 0056 0102 0157 0221 0017 0043 0074 0112 01582 0008 0026 0050 0077 0108 0007 0020 0039 0061 00873 0003 0012 0024 0040 0058 0003 0009 0020 0035 0052


Parameter Member


04 06 08 10 12 04 06 08 10 12 02 04 06 02 04 06

EGB+C 0011 0031 0059 0091 0129 0009 0024 0044 0069 0099 0026 0111 0218 0017 0083 0171B 0028 0084 0155 0236 0324 0023 0065 0118 018 0253 0076 0314 0383 0047 0241 0475

PG 482 211 139 107 89 630 288 193 147 117 193 73 78 317 97 65


Sag=02Sag=04Sag=06

000

010

020

030

040

050

060

070M

ean

of (E

Lϕ) S

B bea

ms

3 4 5 6 7 8 9 102Story number

(a)

Sag=02Sag=04Sag=06

000

010

020

030

040

050

060

070

080

Mea

n of

(ELϕ

) SB b

eam

s

3 4 5 6 7 8 9 102Story number

(b)

Sag=02Sag=04Sag=06

000002004006008010012014016018020

Mea

n of

(Elowast

Lϕ) S

C co

lum

ns

3 4 5 6 7 8 9 102Story number

(c)

Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

000002004006008010012014016018

Mea

n of

(Elowast

Lϕ) S

C co

lum

ns

(d)


Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

000

005

010

015

020

025

030

035

040

Mea

n of

ES s

tory

(a)

Sag=02Sag=04Sag=06

000

005

010

015

020

025

030

Mea

n of

ES s

tory

3 4 5 6 7 8 9 102Story number

(b)





Data Availability


Disclosure




Acknowledgments


References







04 06 08 10 12 04 06 08 10 121 275 129 93 73 61 296 152 112 92 772 655 258 164 124 102 756 335 206 158 1263 1813 558 314 219 171 1943 700 365 246 189

Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

0

10

20

30

40

50

60

P S ra

tio

(a)

Sag=02Sag=04Sag=06

0

10

20

30

40

50

60

70

80

90

P S ra

tio3 4 5 6 7 8 9 102

Story number

(b)










































































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia













04 06 08 10 12 04 06 08 10 12

microLϕ

Beams1 261 427 599 823 1022 219 356 456 633 7812 248 460 717 957 1186 226 415 587 769 9323 201 431 671 894 1120 199 373 559 767 930

Columns1 106 132 195 265 370 101 125 172 222 2872 100 100 109 125 141 100 101 103 121 1293 100 100 106 112 123 100 100 102 113 126

RmicroLϕ

Beams1 168 229 289 345 406 154 212 268 322 3912 166 225 279 328 386 155 211 265 316 3813 158 211 260 306 360 150 201 250 297 354

Columns1 152 187 225 260 298 135 166 200 235 2792 150 185 219 251 286 137 171 201 232 2713 155 195 228 259 295 143 181 217 251 292

QL

Beams1 064 054 048 042 040 070 060 059 051 0502 067 049 039 034 033 069 051 045 041 0413 079 049 039 034 032 075 054 045 039 038

Columns1 143 142 115 098 081 134 133 116 106 0972 150 185 201 201 203 137 169 195 192 2103 155 195 215 231 240 143 181 213 222 232

Sag=02Sag=04Sag=06

0

2

4

6

8

10

12

14

16

Mea

n of

μLϕ

3 4 5 6 7 8 9 102Story number

(a)

Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

0

2

4

6

8

10

12

Mea

n of

μLϕ

(b)

Sag=02Sag=04Sag=06

0

1

2

3

4

5

6

Mea

n of

μLϕ

3 4 5 6 7 8 9 102Story number

(c)

Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

0

1

2

3

4

Mea

n of

μLϕ

(d)

Figure 3 Continued




Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

0

1

2

3

4

5

6M

ean

of R

μLϕ

(e)

Sag=02Sag=04Sag=06

0

1

2

3

4

5

6

Mea

n of

RLμ

ϕ

3 4 5 6 7 8 9 102Story number

(f )

Sag=02Sag=04Sag=06

0

1

2

3

4

Mea

n of

RLϕ

3 4 5 6 7 8 9 102Story number

(g)

Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

0

1

2

3

4

Mea

n of

RLϕ

(h)




04 06 08 10 12 04 06 08 10 12

microS1 161 199 281 344 395 148 190 280 289 4282 170 220 286 331 399 165 215 258 309 3543 153 193 269 299 390 152 210 272 319 384

RmicroS

1 146 190 237 276 310 133 173 211 251 2892 144 186 230 268 305 136 184 225 268 3063 145 184 217 247 276 136 175 208 236 267

QS

1 091 095 084 080 078 090 091 075 087 0682 085 085 080 081 076 082 086 087 087 0863 095 095 081 083 071 089 083 076 074 070






Sag=02Sag=04Sag=06

0

1

2

3

4

5

6M

ean

of micro

S

3 4 5 6 7 8 9 102Story number

(a)

Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

0

1

2

3

4

5

Mea

n of

microS

(b)

Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

0

1

2

3

4

Mea

n of

Rmicros

(c)

Sag=02Sag=04Sag=06

0

1

2

3

4

5

Mea

n of

Rmicros

3 4 5 6 7 8 9 102Story number

(d)



Parameter










QL RmicroLϕ

microLϕ

QS RmicroS

microS

QG RmicroG

microG

(16)




Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

00

02

04

06

08

10Q

L rat

io

(a)

Sag=02Sag=04Sag=06

00

02

04

06

08

10

12

QL r

atio

3 4 5 6 7 8 9 102Story number

(b)

Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

0

1

2

3

4

QL r

atio

(c)

Sag=02Sag=04Sag=06

0

1

2

3

4

QL r

atio

3 4 5 6 7 8 9 102Story number

(d)


Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

00

04

08

12

QS r

atio

(a)

Sag=02Sag=04Sag=06

00

04

08

12

QS r

atio

3 4 5 6 7 8 9 102Story number

(b)









PS RmicroS

ES

PG RmicroG

EG

(17)





5 Conclusions








04 06 08 10 12 04 06 08 10 12

Beams (ELϕ)SB1 0053 0147 0256 0379 0512 0045 0114 0188 0274 03762 0022 0072 0140 0216 0298 0018 0055 0109 0170 02423 0008 0033 0069 0113 0161 0007 0025 0057 0096 0141


1 0003 0010 0025 0046 0076 0003 0007 0017 0031 00502 0001 0003 0004 0007 0013 0001 0003 0004 0006 00103 0001 0001 0002 0004 0007 0001 0001 0002 0004 0007



04 06 08 10 12 04 06 08 10 121 0020 0056 0102 0157 0221 0017 0043 0074 0112 01582 0008 0026 0050 0077 0108 0007 0020 0039 0061 00873 0003 0012 0024 0040 0058 0003 0009 0020 0035 0052


Parameter Member


04 06 08 10 12 04 06 08 10 12 02 04 06 02 04 06

EGB+C 0011 0031 0059 0091 0129 0009 0024 0044 0069 0099 0026 0111 0218 0017 0083 0171B 0028 0084 0155 0236 0324 0023 0065 0118 018 0253 0076 0314 0383 0047 0241 0475

PG 482 211 139 107 89 630 288 193 147 117 193 73 78 317 97 65


Sag=02Sag=04Sag=06

000

010

020

030

040

050

060

070M

ean

of (E

Lϕ) S

B bea

ms

3 4 5 6 7 8 9 102Story number

(a)

Sag=02Sag=04Sag=06

000

010

020

030

040

050

060

070

080

Mea

n of

(ELϕ

) SB b

eam

s

3 4 5 6 7 8 9 102Story number

(b)

Sag=02Sag=04Sag=06

000002004006008010012014016018020

Mea

n of

(Elowast

Lϕ) S

C co

lum

ns

3 4 5 6 7 8 9 102Story number

(c)

Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

000002004006008010012014016018

Mea

n of

(Elowast

Lϕ) S

C co

lum

ns

(d)


Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

000

005

010

015

020

025

030

035

040

Mea

n of

ES s

tory

(a)

Sag=02Sag=04Sag=06

000

005

010

015

020

025

030

Mea

n of

ES s

tory

3 4 5 6 7 8 9 102Story number

(b)





Data Availability


Disclosure




Acknowledgments


References







04 06 08 10 12 04 06 08 10 121 275 129 93 73 61 296 152 112 92 772 655 258 164 124 102 756 335 206 158 1263 1813 558 314 219 171 1943 700 365 246 189

Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

0

10

20

30

40

50

60

P S ra

tio

(a)

Sag=02Sag=04Sag=06

0

10

20

30

40

50

60

70

80

90

P S ra

tio3 4 5 6 7 8 9 102

Story number

(b)










































































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

0

1

2

3

4

5

6M

ean

of R

μLϕ

(e)

Sag=02Sag=04Sag=06

0

1

2

3

4

5

6

Mea

n of

RLμ

ϕ

3 4 5 6 7 8 9 102Story number

(f )

Sag=02Sag=04Sag=06

0

1

2

3

4

Mea

n of

RLϕ

3 4 5 6 7 8 9 102Story number

(g)

Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

0

1

2

3

4

Mea

n of

RLϕ

(h)




04 06 08 10 12 04 06 08 10 12

microS1 161 199 281 344 395 148 190 280 289 4282 170 220 286 331 399 165 215 258 309 3543 153 193 269 299 390 152 210 272 319 384

RmicroS

1 146 190 237 276 310 133 173 211 251 2892 144 186 230 268 305 136 184 225 268 3063 145 184 217 247 276 136 175 208 236 267

QS

1 091 095 084 080 078 090 091 075 087 0682 085 085 080 081 076 082 086 087 087 0863 095 095 081 083 071 089 083 076 074 070






Sag=02Sag=04Sag=06

0

1

2

3

4

5

6M

ean

of micro

S

3 4 5 6 7 8 9 102Story number

(a)

Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

0

1

2

3

4

5

Mea

n of

microS

(b)

Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

0

1

2

3

4

Mea

n of

Rmicros

(c)

Sag=02Sag=04Sag=06

0

1

2

3

4

5

Mea

n of

Rmicros

3 4 5 6 7 8 9 102Story number

(d)



Parameter










QL RmicroLϕ

microLϕ

QS RmicroS

microS

QG RmicroG

microG

(16)




Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

00

02

04

06

08

10Q

L rat

io

(a)

Sag=02Sag=04Sag=06

00

02

04

06

08

10

12

QL r

atio

3 4 5 6 7 8 9 102Story number

(b)

Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

0

1

2

3

4

QL r

atio

(c)

Sag=02Sag=04Sag=06

0

1

2

3

4

QL r

atio

3 4 5 6 7 8 9 102Story number

(d)


Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

00

04

08

12

QS r

atio

(a)

Sag=02Sag=04Sag=06

00

04

08

12

QS r

atio

3 4 5 6 7 8 9 102Story number

(b)









PS RmicroS

ES

PG RmicroG

EG

(17)





5 Conclusions








04 06 08 10 12 04 06 08 10 12

Beams (ELϕ)SB1 0053 0147 0256 0379 0512 0045 0114 0188 0274 03762 0022 0072 0140 0216 0298 0018 0055 0109 0170 02423 0008 0033 0069 0113 0161 0007 0025 0057 0096 0141


1 0003 0010 0025 0046 0076 0003 0007 0017 0031 00502 0001 0003 0004 0007 0013 0001 0003 0004 0006 00103 0001 0001 0002 0004 0007 0001 0001 0002 0004 0007



04 06 08 10 12 04 06 08 10 121 0020 0056 0102 0157 0221 0017 0043 0074 0112 01582 0008 0026 0050 0077 0108 0007 0020 0039 0061 00873 0003 0012 0024 0040 0058 0003 0009 0020 0035 0052


Parameter Member


04 06 08 10 12 04 06 08 10 12 02 04 06 02 04 06

EGB+C 0011 0031 0059 0091 0129 0009 0024 0044 0069 0099 0026 0111 0218 0017 0083 0171B 0028 0084 0155 0236 0324 0023 0065 0118 018 0253 0076 0314 0383 0047 0241 0475

PG 482 211 139 107 89 630 288 193 147 117 193 73 78 317 97 65


Sag=02Sag=04Sag=06

000

010

020

030

040

050

060

070M

ean

of (E

Lϕ) S

B bea

ms

3 4 5 6 7 8 9 102Story number

(a)

Sag=02Sag=04Sag=06

000

010

020

030

040

050

060

070

080

Mea

n of

(ELϕ

) SB b

eam

s

3 4 5 6 7 8 9 102Story number

(b)

Sag=02Sag=04Sag=06

000002004006008010012014016018020

Mea

n of

(Elowast

Lϕ) S

C co

lum

ns

3 4 5 6 7 8 9 102Story number

(c)

Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

000002004006008010012014016018

Mea

n of

(Elowast

Lϕ) S

C co

lum

ns

(d)


Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

000

005

010

015

020

025

030

035

040

Mea

n of

ES s

tory

(a)

Sag=02Sag=04Sag=06

000

005

010

015

020

025

030

Mea

n of

ES s

tory

3 4 5 6 7 8 9 102Story number

(b)





Data Availability


Disclosure




Acknowledgments


References







04 06 08 10 12 04 06 08 10 121 275 129 93 73 61 296 152 112 92 772 655 258 164 124 102 756 335 206 158 1263 1813 558 314 219 171 1943 700 365 246 189

Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

0

10

20

30

40

50

60

P S ra

tio

(a)

Sag=02Sag=04Sag=06

0

10

20

30

40

50

60

70

80

90

P S ra

tio3 4 5 6 7 8 9 102

Story number

(b)










































































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia






Sag=02Sag=04Sag=06

0

1

2

3

4

5

6M

ean

of micro

S

3 4 5 6 7 8 9 102Story number

(a)

Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

0

1

2

3

4

5

Mea

n of

microS

(b)

Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

0

1

2

3

4

Mea

n of

Rmicros

(c)

Sag=02Sag=04Sag=06

0

1

2

3

4

5

Mea

n of

Rmicros

3 4 5 6 7 8 9 102Story number

(d)



Parameter










QL RmicroLϕ

microLϕ

QS RmicroS

microS

QG RmicroG

microG

(16)




Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

00

02

04

06

08

10Q

L rat

io

(a)

Sag=02Sag=04Sag=06

00

02

04

06

08

10

12

QL r

atio

3 4 5 6 7 8 9 102Story number

(b)

Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

0

1

2

3

4

QL r

atio

(c)

Sag=02Sag=04Sag=06

0

1

2

3

4

QL r

atio

3 4 5 6 7 8 9 102Story number

(d)


Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

00

04

08

12

QS r

atio

(a)

Sag=02Sag=04Sag=06

00

04

08

12

QS r

atio

3 4 5 6 7 8 9 102Story number

(b)









PS RmicroS

ES

PG RmicroG

EG

(17)





5 Conclusions








04 06 08 10 12 04 06 08 10 12

Beams (ELϕ)SB1 0053 0147 0256 0379 0512 0045 0114 0188 0274 03762 0022 0072 0140 0216 0298 0018 0055 0109 0170 02423 0008 0033 0069 0113 0161 0007 0025 0057 0096 0141


1 0003 0010 0025 0046 0076 0003 0007 0017 0031 00502 0001 0003 0004 0007 0013 0001 0003 0004 0006 00103 0001 0001 0002 0004 0007 0001 0001 0002 0004 0007



04 06 08 10 12 04 06 08 10 121 0020 0056 0102 0157 0221 0017 0043 0074 0112 01582 0008 0026 0050 0077 0108 0007 0020 0039 0061 00873 0003 0012 0024 0040 0058 0003 0009 0020 0035 0052


Parameter Member


04 06 08 10 12 04 06 08 10 12 02 04 06 02 04 06

EGB+C 0011 0031 0059 0091 0129 0009 0024 0044 0069 0099 0026 0111 0218 0017 0083 0171B 0028 0084 0155 0236 0324 0023 0065 0118 018 0253 0076 0314 0383 0047 0241 0475

PG 482 211 139 107 89 630 288 193 147 117 193 73 78 317 97 65


Sag=02Sag=04Sag=06

000

010

020

030

040

050

060

070M

ean

of (E

Lϕ) S

B bea

ms

3 4 5 6 7 8 9 102Story number

(a)

Sag=02Sag=04Sag=06

000

010

020

030

040

050

060

070

080

Mea

n of

(ELϕ

) SB b

eam

s

3 4 5 6 7 8 9 102Story number

(b)

Sag=02Sag=04Sag=06

000002004006008010012014016018020

Mea

n of

(Elowast

Lϕ) S

C co

lum

ns

3 4 5 6 7 8 9 102Story number

(c)

Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

000002004006008010012014016018

Mea

n of

(Elowast

Lϕ) S

C co

lum

ns

(d)


Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

000

005

010

015

020

025

030

035

040

Mea

n of

ES s

tory

(a)

Sag=02Sag=04Sag=06

000

005

010

015

020

025

030

Mea

n of

ES s

tory

3 4 5 6 7 8 9 102Story number

(b)





Data Availability


Disclosure




Acknowledgments


References







04 06 08 10 12 04 06 08 10 121 275 129 93 73 61 296 152 112 92 772 655 258 164 124 102 756 335 206 158 1263 1813 558 314 219 171 1943 700 365 246 189

Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

0

10

20

30

40

50

60

P S ra

tio

(a)

Sag=02Sag=04Sag=06

0

10

20

30

40

50

60

70

80

90

P S ra

tio3 4 5 6 7 8 9 102

Story number

(b)










































































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia








QL RmicroLϕ

microLϕ

QS RmicroS

microS

QG RmicroG

microG

(16)




Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

00

02

04

06

08

10Q

L rat

io

(a)

Sag=02Sag=04Sag=06

00

02

04

06

08

10

12

QL r

atio

3 4 5 6 7 8 9 102Story number

(b)

Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

0

1

2

3

4

QL r

atio

(c)

Sag=02Sag=04Sag=06

0

1

2

3

4

QL r

atio

3 4 5 6 7 8 9 102Story number

(d)


Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

00

04

08

12

QS r

atio

(a)

Sag=02Sag=04Sag=06

00

04

08

12

QS r

atio

3 4 5 6 7 8 9 102Story number

(b)









PS RmicroS

ES

PG RmicroG

EG

(17)





5 Conclusions








04 06 08 10 12 04 06 08 10 12

Beams (ELϕ)SB1 0053 0147 0256 0379 0512 0045 0114 0188 0274 03762 0022 0072 0140 0216 0298 0018 0055 0109 0170 02423 0008 0033 0069 0113 0161 0007 0025 0057 0096 0141


1 0003 0010 0025 0046 0076 0003 0007 0017 0031 00502 0001 0003 0004 0007 0013 0001 0003 0004 0006 00103 0001 0001 0002 0004 0007 0001 0001 0002 0004 0007



04 06 08 10 12 04 06 08 10 121 0020 0056 0102 0157 0221 0017 0043 0074 0112 01582 0008 0026 0050 0077 0108 0007 0020 0039 0061 00873 0003 0012 0024 0040 0058 0003 0009 0020 0035 0052


Parameter Member


04 06 08 10 12 04 06 08 10 12 02 04 06 02 04 06

EGB+C 0011 0031 0059 0091 0129 0009 0024 0044 0069 0099 0026 0111 0218 0017 0083 0171B 0028 0084 0155 0236 0324 0023 0065 0118 018 0253 0076 0314 0383 0047 0241 0475

PG 482 211 139 107 89 630 288 193 147 117 193 73 78 317 97 65


Sag=02Sag=04Sag=06

000

010

020

030

040

050

060

070M

ean

of (E

Lϕ) S

B bea

ms

3 4 5 6 7 8 9 102Story number

(a)

Sag=02Sag=04Sag=06

000

010

020

030

040

050

060

070

080

Mea

n of

(ELϕ

) SB b

eam

s

3 4 5 6 7 8 9 102Story number

(b)

Sag=02Sag=04Sag=06

000002004006008010012014016018020

Mea

n of

(Elowast

Lϕ) S

C co

lum

ns

3 4 5 6 7 8 9 102Story number

(c)

Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

000002004006008010012014016018

Mea

n of

(Elowast

Lϕ) S

C co

lum

ns

(d)


Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

000

005

010

015

020

025

030

035

040

Mea

n of

ES s

tory

(a)

Sag=02Sag=04Sag=06

000

005

010

015

020

025

030

Mea

n of

ES s

tory

3 4 5 6 7 8 9 102Story number

(b)





Data Availability


Disclosure




Acknowledgments


References







04 06 08 10 12 04 06 08 10 121 275 129 93 73 61 296 152 112 92 772 655 258 164 124 102 756 335 206 158 1263 1813 558 314 219 171 1943 700 365 246 189

Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

0

10

20

30

40

50

60

P S ra

tio

(a)

Sag=02Sag=04Sag=06

0

10

20

30

40

50

60

70

80

90

P S ra

tio3 4 5 6 7 8 9 102

Story number

(b)










































































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

00

02

04

06

08

10Q

L rat

io

(a)

Sag=02Sag=04Sag=06

00

02

04

06

08

10

12

QL r

atio

3 4 5 6 7 8 9 102Story number

(b)

Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

0

1

2

3

4

QL r

atio

(c)

Sag=02Sag=04Sag=06

0

1

2

3

4

QL r

atio

3 4 5 6 7 8 9 102Story number

(d)


Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

00

04

08

12

QS r

atio

(a)

Sag=02Sag=04Sag=06

00

04

08

12

QS r

atio

3 4 5 6 7 8 9 102Story number

(b)









PS RmicroS

ES

PG RmicroG

EG

(17)





5 Conclusions








04 06 08 10 12 04 06 08 10 12

Beams (ELϕ)SB1 0053 0147 0256 0379 0512 0045 0114 0188 0274 03762 0022 0072 0140 0216 0298 0018 0055 0109 0170 02423 0008 0033 0069 0113 0161 0007 0025 0057 0096 0141


1 0003 0010 0025 0046 0076 0003 0007 0017 0031 00502 0001 0003 0004 0007 0013 0001 0003 0004 0006 00103 0001 0001 0002 0004 0007 0001 0001 0002 0004 0007



04 06 08 10 12 04 06 08 10 121 0020 0056 0102 0157 0221 0017 0043 0074 0112 01582 0008 0026 0050 0077 0108 0007 0020 0039 0061 00873 0003 0012 0024 0040 0058 0003 0009 0020 0035 0052


Parameter Member


04 06 08 10 12 04 06 08 10 12 02 04 06 02 04 06

EGB+C 0011 0031 0059 0091 0129 0009 0024 0044 0069 0099 0026 0111 0218 0017 0083 0171B 0028 0084 0155 0236 0324 0023 0065 0118 018 0253 0076 0314 0383 0047 0241 0475

PG 482 211 139 107 89 630 288 193 147 117 193 73 78 317 97 65


Sag=02Sag=04Sag=06

000

010

020

030

040

050

060

070M

ean

of (E

Lϕ) S

B bea

ms

3 4 5 6 7 8 9 102Story number

(a)

Sag=02Sag=04Sag=06

000

010

020

030

040

050

060

070

080

Mea

n of

(ELϕ

) SB b

eam

s

3 4 5 6 7 8 9 102Story number

(b)

Sag=02Sag=04Sag=06

000002004006008010012014016018020

Mea

n of

(Elowast

Lϕ) S

C co

lum

ns

3 4 5 6 7 8 9 102Story number

(c)

Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

000002004006008010012014016018

Mea

n of

(Elowast

Lϕ) S

C co

lum

ns

(d)


Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

000

005

010

015

020

025

030

035

040

Mea

n of

ES s

tory

(a)

Sag=02Sag=04Sag=06

000

005

010

015

020

025

030

Mea

n of

ES s

tory

3 4 5 6 7 8 9 102Story number

(b)





Data Availability


Disclosure




Acknowledgments


References







04 06 08 10 12 04 06 08 10 121 275 129 93 73 61 296 152 112 92 772 655 258 164 124 102 756 335 206 158 1263 1813 558 314 219 171 1943 700 365 246 189

Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

0

10

20

30

40

50

60

P S ra

tio

(a)

Sag=02Sag=04Sag=06

0

10

20

30

40

50

60

70

80

90

P S ra

tio3 4 5 6 7 8 9 102

Story number

(b)










































































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia








PS RmicroS

ES

PG RmicroG

EG

(17)





5 Conclusions








04 06 08 10 12 04 06 08 10 12

Beams (ELϕ)SB1 0053 0147 0256 0379 0512 0045 0114 0188 0274 03762 0022 0072 0140 0216 0298 0018 0055 0109 0170 02423 0008 0033 0069 0113 0161 0007 0025 0057 0096 0141


1 0003 0010 0025 0046 0076 0003 0007 0017 0031 00502 0001 0003 0004 0007 0013 0001 0003 0004 0006 00103 0001 0001 0002 0004 0007 0001 0001 0002 0004 0007



04 06 08 10 12 04 06 08 10 121 0020 0056 0102 0157 0221 0017 0043 0074 0112 01582 0008 0026 0050 0077 0108 0007 0020 0039 0061 00873 0003 0012 0024 0040 0058 0003 0009 0020 0035 0052


Parameter Member


04 06 08 10 12 04 06 08 10 12 02 04 06 02 04 06

EGB+C 0011 0031 0059 0091 0129 0009 0024 0044 0069 0099 0026 0111 0218 0017 0083 0171B 0028 0084 0155 0236 0324 0023 0065 0118 018 0253 0076 0314 0383 0047 0241 0475

PG 482 211 139 107 89 630 288 193 147 117 193 73 78 317 97 65


Sag=02Sag=04Sag=06

000

010

020

030

040

050

060

070M

ean

of (E

Lϕ) S

B bea

ms

3 4 5 6 7 8 9 102Story number

(a)

Sag=02Sag=04Sag=06

000

010

020

030

040

050

060

070

080

Mea

n of

(ELϕ

) SB b

eam

s

3 4 5 6 7 8 9 102Story number

(b)

Sag=02Sag=04Sag=06

000002004006008010012014016018020

Mea

n of

(Elowast

Lϕ) S

C co

lum

ns

3 4 5 6 7 8 9 102Story number

(c)

Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

000002004006008010012014016018

Mea

n of

(Elowast

Lϕ) S

C co

lum

ns

(d)


Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

000

005

010

015

020

025

030

035

040

Mea

n of

ES s

tory

(a)

Sag=02Sag=04Sag=06

000

005

010

015

020

025

030

Mea

n of

ES s

tory

3 4 5 6 7 8 9 102Story number

(b)





Data Availability


Disclosure




Acknowledgments


References







04 06 08 10 12 04 06 08 10 121 275 129 93 73 61 296 152 112 92 772 655 258 164 124 102 756 335 206 158 1263 1813 558 314 219 171 1943 700 365 246 189

Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

0

10

20

30

40

50

60

P S ra

tio

(a)

Sag=02Sag=04Sag=06

0

10

20

30

40

50

60

70

80

90

P S ra

tio3 4 5 6 7 8 9 102

Story number

(b)










































































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


5 Conclusions








04 06 08 10 12 04 06 08 10 12

Beams (ELϕ)SB1 0053 0147 0256 0379 0512 0045 0114 0188 0274 03762 0022 0072 0140 0216 0298 0018 0055 0109 0170 02423 0008 0033 0069 0113 0161 0007 0025 0057 0096 0141


1 0003 0010 0025 0046 0076 0003 0007 0017 0031 00502 0001 0003 0004 0007 0013 0001 0003 0004 0006 00103 0001 0001 0002 0004 0007 0001 0001 0002 0004 0007



04 06 08 10 12 04 06 08 10 121 0020 0056 0102 0157 0221 0017 0043 0074 0112 01582 0008 0026 0050 0077 0108 0007 0020 0039 0061 00873 0003 0012 0024 0040 0058 0003 0009 0020 0035 0052


Parameter Member


04 06 08 10 12 04 06 08 10 12 02 04 06 02 04 06

EGB+C 0011 0031 0059 0091 0129 0009 0024 0044 0069 0099 0026 0111 0218 0017 0083 0171B 0028 0084 0155 0236 0324 0023 0065 0118 018 0253 0076 0314 0383 0047 0241 0475

PG 482 211 139 107 89 630 288 193 147 117 193 73 78 317 97 65


Sag=02Sag=04Sag=06

000

010

020

030

040

050

060

070M

ean

of (E

Lϕ) S

B bea

ms

3 4 5 6 7 8 9 102Story number

(a)

Sag=02Sag=04Sag=06

000

010

020

030

040

050

060

070

080

Mea

n of

(ELϕ

) SB b

eam

s

3 4 5 6 7 8 9 102Story number

(b)

Sag=02Sag=04Sag=06

000002004006008010012014016018020

Mea

n of

(Elowast

Lϕ) S

C co

lum

ns

3 4 5 6 7 8 9 102Story number

(c)

Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

000002004006008010012014016018

Mea

n of

(Elowast

Lϕ) S

C co

lum

ns

(d)


Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

000

005

010

015

020

025

030

035

040

Mea

n of

ES s

tory

(a)

Sag=02Sag=04Sag=06

000

005

010

015

020

025

030

Mea

n of

ES s

tory

3 4 5 6 7 8 9 102Story number

(b)





Data Availability


Disclosure




Acknowledgments


References







04 06 08 10 12 04 06 08 10 121 275 129 93 73 61 296 152 112 92 772 655 258 164 124 102 756 335 206 158 1263 1813 558 314 219 171 1943 700 365 246 189

Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

0

10

20

30

40

50

60

P S ra

tio

(a)

Sag=02Sag=04Sag=06

0

10

20

30

40

50

60

70

80

90

P S ra

tio3 4 5 6 7 8 9 102

Story number

(b)










































































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


Sag=02Sag=04Sag=06

000

010

020

030

040

050

060

070M

ean

of (E

Lϕ) S

B bea

ms

3 4 5 6 7 8 9 102Story number

(a)

Sag=02Sag=04Sag=06

000

010

020

030

040

050

060

070

080

Mea

n of

(ELϕ

) SB b

eam

s

3 4 5 6 7 8 9 102Story number

(b)

Sag=02Sag=04Sag=06

000002004006008010012014016018020

Mea

n of

(Elowast

Lϕ) S

C co

lum

ns

3 4 5 6 7 8 9 102Story number

(c)

Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

000002004006008010012014016018

Mea

n of

(Elowast

Lϕ) S

C co

lum

ns

(d)


Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

000

005

010

015

020

025

030

035

040

Mea

n of

ES s

tory

(a)

Sag=02Sag=04Sag=06

000

005

010

015

020

025

030

Mea

n of

ES s

tory

3 4 5 6 7 8 9 102Story number

(b)





Data Availability


Disclosure




Acknowledgments


References







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RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




Data Availability


Disclosure




Acknowledgments


References







04 06 08 10 12 04 06 08 10 121 275 129 93 73 61 296 152 112 92 772 655 258 164 124 102 756 335 206 158 1263 1813 558 314 219 171 1943 700 365 246 189

Sag=02Sag=04Sag=06

3 4 5 6 7 8 9 102Story number

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P S ra

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(a)

Sag=02Sag=04Sag=06

0

10

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80

90

P S ra

tio3 4 5 6 7 8 9 102

Story number

(b)










































































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia









































































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


energy dissipation and local, story, and global ductility...

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