Energy-BasedSeismicDesignMethodforEBFsBasedonHysteretic ...downloads.hindawi.com/journals/ace/2019/3180596.pdf · 2019-11-19 · performance-based design methodology for constructing

Research ArticleEnergy-BasedSeismicDesignMethodforEBFsBasedonHystereticEnergy Spectra and Accumulated Ductility Ratio Spectra

Cuiling Ma 12

1College of Civil and Transportation Engineering Hohai University Nanjing 210098 China2Department of Civil Engineering Hefei University Hefei 230601 China

Correspondence should be addressed to Cuiling Ma ling3701163com

Received 14 June 2019 Revised 22 October 2019 Accepted 30 October 2019 Published 19 November 2019

Academic Editor Rosario Montuori

Copyright copy 2019 Cuiling Ma(is is an open access article distributed under the Creative Commons Attribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

In the case of far field earthquakes structural failure often results from accumulated damage caused by cyclic effects and gradualaccumulation of energy (is paper proposes an energy-based seismic design method for steel eccentrically braced frames (EBFs)with two shear links at every story according to the energy balance concept (e proposed method is theoretically supported byhysteretic energy spectra and accumulated ductility ratio spectra according to the Chinese soil classification Furthermore themethod can be used to clarify the relationship between cumulative hysteretic energy and one-way pushover energy For de-veloping the method it is assumed that all the hysteretic energy is dissipated by the shear links column bases and beam ends ofthe frames at both sides (erefore the parts outside the links including beam segments braces and columns are speciallydesigned to perform elastically during an earthquake Furthermore a V-scheme steel EBF with ten stories and three spans isdesigned (e seismic performances of the designed structure such as story drift and energy dissipation are evaluated bynonlinear static analysis and time-history analysis Finally the reliability and accuracy of the proposed seismic design methodare validated

1 Introduction

As for conventional seismic analysis of structure it is usuallyconducted on the basis of the strength and displacementwithout considering the progressive damage to the structurecaused by the duration of ground motion Compared withstrength- or displacement-based seismic designs an energy-based seismic design is preferable as it can include moreground motion characteristics

(e concept of energy-based design was originally in-troduced by Housner [1] and has attracted extensive at-tention from researchers and engineers worldwide Ozsaracet al [2] analyzed the energy-based responses of simplestructural systems by using a large set of simulated groundmotion records and showed that energy is a relatively stableparameter when compared with other response parametersChao and Goel [3] suggested that a controlled structure ismainly dependent on three major factors namely thedistribution of design lateral force the predictable global

yield mechanism and the target drift In addition Leela-taviwat et al [4] proposed a simplified energy-based plasticdesign method for moment steel frames In addition boththe pseudovelocity design spectrum and the earthquakeinput energy equations of elastic systems were employed toobtain the design base shear Afterwards this design methodwas further developed to be employed in the design of otherstructural systems For example Lee [5] presented a newdesign procedure based on inelastic analysis for moment-resisting frames in severe seismic zones Chao and Goeldeveloped a seismic design method for steel concentricbraced frames [6] and a performance-based plastic designfor seismic-resistant special truss moment frames [7] Kimet al [8] proposed an energy-based seismic design procedurefor framed structures with buckling-restrained braces(BRBs) (e input seismic energy was estimated from adesign spectrum and the elastic and hysteretic energy wascomputed using the energy balance concept (e cross-sectional area of braces required to meet a given target

HindawiAdvances in Civil EngineeringVolume 2019 Article ID 3180596 11 pageshttpsdoiorg10115520193180596

displacement was obtained by equating the energy demandto hysteretic energy dissipated by the BRBs Sahoo and Chao[9] presented a performance-based plastic design (PBPD)methodology for the design of buckling-restrained bracedframes (BRBFs) (e design base shear was obtained on thebasis of energy-work balance by using the preselected targetdrift and yield mechanism Akbas et al [10] proposed aperformance-based design methodology for constructingregular moment-resisting steel frames with the collapseprevention standard Mastrandrea and Piluso [11] presenteda design methodology aiming at the development of acollapse mechanism of a global type for K-scheme eccen-trically braced frames accounting for second-order effectsFinally the inelastic performances of EBFs by static anddynamic nonlinear analyses confirmed the achievement ofthe design goal Montuori et al [12] designed a number ofmoment-resisting frames-eccentrically braced frame (MRF-EBF) dual systems with both theory of plastic mechanismcontrol (TPMC) and Eurocode 8 and evaluated TPMCaccuracy by means of pushover analyses Afterwards theyinvestigated the influence of the bracing scheme [13] andlink configuration [14] on the seismic performances ofMRF-EBFs dual systems (e four different bracing schemes in-cluded K-scheme D-scheme V-scheme and Y-scheme (eseismic performances have been analyzed by means of in-cremental dynamic analyses at last DellrsquoAglio et al designedseveral steel moment-resisting frames (MR frames) bymeans of both the performance-based plastic design (PBPD)approach and TPMC [15] and proposed a new refinedPBPD considering second-order effects for steel moment-resisting frames [16] Finally the seismic performances ofsuch MR frames have been investigated by both pushoverand dynamic nonlinear analyses

Choi and Kim [17] and Sun et al [18] suggested cal-culating the accumulated plastic deformation of structuresby employing the accumulated ductility ratio spectra (eyalso revealed the relationship between the accumulatedhysteretic energy and the hysteretic energy of monotonoussideway structures Furthermore Choi and Kim [19]designed three frame structures with buckling-restrainedbraces (BRBs) by employing the energy balance concept afterthe construction of a hysteretic energy spectrum and anaccumulated ductility spectrum Using the normalizedhysteretic energy spectrum and the accumulated ductilityspectrum Sun et al [18] developed an energy-based seismicdesign method for steel plate shear walls (SPSWs) Kharmaleand Ghosh [20] proposed a performance-based plastic de-sign (PBPD) method for SPSW systems with rigid beam-to-column connections this method sets a specific ductilitydemand and a preferred yield mechanism as its performancetargets Xiong et al [21] presented a PBPD methodologybased on the energy-work balance concept for steel con-centrically braced frames Mezgebo and Lui [22] proposed aprocedure for designing steel moment frames by utilizingseismic hysteretic energy spectra

However most of the abovementioned researches werelimited to moment-resisting frames steel concentricallybraced frames steel frames of special truss moment andSPSWs and they were inapplicable to steel EBFs with two

shear links at every story Moreover all the mentionedenergy spectra were developed on the basis of non-Chinesesite classification and are inapplicable in China

EBFs are deemed as excellent structures to resistearthquakes as they colligate the ductility of moment frameswith the stiffness of braced frames In this paper hystereticenergy spectra and accumulated ductility ratio spectraestablished according to the Chinese site classification areused to propose an energy-based seismic design method forV-scheme EBFs Moreover a ten-story three-span V-EBF isdesigned and its seismic behavior is evaluated

2 Hysteretic Energy Spectra and AccumulatedDuctility Ratio Spectra

21 Hysteretic Energy Spectra Bruneau and Wang [23]stated that it is more rational to calculate seismic inputenergy by using the relative energy equation (e motionequation for an inelastic single-degree-of-freedom (SDOF)system subjected to the unidirectional horizontal groundmotions at given times is as follows

m eurox + c _x + fs minus m euroxg (1)

wherem denotes the mass c denotes the viscous dampingcoefficient fs denotes the restoring force x denotesthe relative displacement relative to ground _x and eurox

denote the velocity and acceleration of the mass rela-tive to ground respectively and euroxg denotes groundacceleration

(rough integration of an earthquakersquos whole durationthe energy equation can be obtained as follows

1113946t

0m eurox _xdt + 1113946

t

0c eurox _xdt + 1113946

t

0fs _xdt minus 1113946

t

0m euroxg _xdt (2)

where t is the timeEquation (2) can be expressed as

EKr + ED + EE + EH EIr (3)

where EKr is the kinetic energy ED is the energy dissipated bythe viscous damping EE is the elastic strain energy within theSDOF system EH is the hysteretic energy dissipated byinelastic behavior and EIr is the total input energy in-troduced by the earthquake

Under a far field earthquake structural failures usuallyresult from accumulative damage because of gradual ac-cumulation of the energy and cyclic effects As a result theaccumulated hysteretic energy can be treated as a rationalindex for far field seismic damage EH can be expressed interms of the equivalent velocity VEH [24]

VEH

2EH

m

1113970

(4)

where m denotes the mass(e equivalent velocity spectrum meeting the Chinese

site classification was developed by Ma et al [25] Figure 1shows the fitted spectral smooth curves

(e corresponding mathematical expressions are asfollows

2 Advances in Civil Engineering

VEH T

T11113888 1113889η1η2REHμVEHmax 0leTleT1

VEH η1η2REHμVEHmax T1 leTleT2

VEH T2

T1113874 1113875

c

η1η2REHμVEHmax T2 leTle 6

(5)

where T1 denotes the separation period between the hori-zontal segment and the rising segment T2 denotes theseparation period between the declining segment and thehorizontal segment (as shown in Figure 1) η1 denotes thecorresponding acceleration amplitude correction factor andis computed using equation (6) η2 denotes the structuraldamping ratio correction factor and is computed usingequation (7) REHmicro denotes the correction factor of struc-tural ductility and is computed using equation (8) c denotesthe declining segment attenuation index and is computedusing equation (9) andVEHmax denotes the peak value of theequivalent velocity spectrum of accumulated hystereticenergy at a structural damping ratio ζ of 005 an accelerationamplitude of 02 g a ductility factor μ of 2 and a postyieldstiffness ratio p of 00 (as listed in Table 1)

η1 euroxg

eurox02g (6)

where eurox02g denotes the acceleration amplitude corre-sponding to VEHmax

η2 1 +005 minus ζ01 + 15ζ

(7)

where ζ denotes the structural damping ratio

REHμ 1 +μ minus 2

25 + 2μ (8)

where μ denotes the structural ductility ratio

c c1 +005 minus ζ04 + 6ζ

(9)

where the values of c1 given in Table 1 are associated withthe site group and soil type

22 Accumulated Ductility Ratio Spectra Under a far fieldearthquake the accumulative ductility of a structure

resulting from the lateral irregular cyclic displacement canbe represented by the accumulative ductility ratio (NEHμ)Teran-Gilmore et al [26] pointed out that the accumulativeductility ratiomdashthe ratio of cumulative plastic displacementand the yield displacement of the structuremdashcan be calcu-lated using the following equation

NEHμ EHμ

Fy middot δy (10)

where EHμ denotes the structural accumulative hystereticenergy under seismic effects Fy denotes the structural yieldstrength and δy denotes the yield displacement of thestructure

On the basis of inelastic time-history analysis NEHμ foran SDOF system at a given natural time period and aconstant ductility ratio can be obtained Considering thesoil types in China NEHμ average values for 15 groups ofground motions with different T ζ μ and p values areselected (en equations (11)ndash(14) for the accumulatedductility ratio spectrum are proposed (e analysis alsoreveals that the effect of period is not apparent and can beneglected

NEHμ α middot β middot f(T ζ μ p)

α middot β middot f(ζ) middot f(p) middot f(μ)(11)

f(ζ) 052ζ + 075 (12)

f(p) minus 62p2

+ 40p + 0856 (13)

f(μ) 163μ2 + 075μ minus 238 (14)

where α denotes the effect factor for the site type the valuesof which are 11 11 10 12 and 13 for soil types I0 I1 IIIII and IV respectively and β denotes the effect factor forthe site group the values of which are 10 11 and 10 for sitegroups 1 2 and 3 respectively

Table 1 Equivalent velocity spectrum parameters when the ac-celeration amplitude is 02 g

Soil type Site group VEHmax (ms) T1 (S) T2 (S) c1

I0Group 1 014 009 038 028Group 2 030 031 071 046Group 3 052 073 228 031


IIGroup 1 024 020 045 03Group 2 045 040 110 04Group 3 065 095 22 02

IIIGroup 1 030 020 10 035Group 2 040 040 20 075Group 3 075 120 470 082

IVGroup 1 048 040 125 090Group 2 055 060 120 100Group 3 120 085 485 120

VEH = η1η2REHμVEHmax

VEH = (T2T1)γη1η2REHμVEHmax

VEH = (TT1)η1η2REHμVEHmax

VEH

0 6T1 T2 T

Figure 1 (ree-segment model of equivalent velocity spectra ofaccumulated hysteretic energy

Advances in Civil Engineering 3

3 Energy-BasedDesignApproach forSteelEBFs

31 Design Procedures Using the proposed accumulatedductility ratio spectrum and accumulated hystereticenergy spectrum an energy-based design approach forsteel EBFs with a V-scheme (V-EBFs) is proposed asfollows

(1) Preselect the desirable plastic mechanism Figure 2shows a V-EBF subjected to design lateral forces inits maximum drift state At the middle of the span allthe inelastic deformations are intended to be con-fined within the shear links in the form of shearyielding Since the plastic hinges developed at thecolumn bases are almost unavoidable in a rareearthquake the desired global plastic mechanism foran EBF is formed by the yielding of the shear linksand the plastic hinges at the column bases and beamends of both side frames

(2) Obtain preliminary design for each member and thefirst few vibration mode shapes and structural pe-riods through modal analysis

(3) Calculate the structural accumulative hystereticenergy demands by using the accumulated hystereticenergy spectra and the modal-energy-decompositionapproach

(e accumulated hysteretic energy demand of theV-EBF can be seen in Figure 2 that shows a V-EBFsubjected to design lateral forces in its maximumdrift state At the middle of the span all the in-elastic deformations are intended to be confinedwithin the shear links in the form of shear yieldingSince the plastic hinges developed at the columnbases are almost unavoidable in a rare earthquakethe desired global plastic mechanism for an EBF isformed by the yielding of the shear links and theplastic hinges at the column bases and beam endsof the both side frames obtained using equations(15)ndash(19) (e right-hand side of equation (15) canbe interpreted as denoting the modal-energy-de-composition approach applicable for inelasticmultidegree-of-freedom (MDOF) systems Sub-sequently satisfactory energy estimates are ob-tained [27]

Eh(MDOF) 1113936

Nj1Eh(MDOF)jΓ2j1113936

Nj1Xmassj

(15)

Eh(ESDOF)j 12Mlowastj V

2EHj (16)

Mlowastj ϕT

j Mϕj (17)

Γj 1113936

ni1miφij

1113936ni1miφ2

ij

(18)

Xmassj 1113936

ni1miϕij1113872 1113873

2

1113936ni1mi( 1113857 1113936

ni1miϕ

2ij1113872 1113873

(19)

where Eh(MDOF) denotes the total accumulated hyster-etic energy demand of an MDOF and Eh(ESDOF)j is theaccumulated hysteretic energy demand of an equivalentSDOF system corresponding to the jth modeMlowastj is theeffective mass acquired through the jth mode Γj is themodal participation factor of the jthmodeXmass j is themass participation factor of the jth mode VEHj is theequivalent velocity of the SDOF system correspondingto the jthmode ϕj is the jthmode with n elementsN isthe total number of mode shapes let N 3 for theV-EBF and n is the total number of stories

(4) Determine the distribution pattern of structurallateral forces the design lateral forces are determinedby utilizing the shear distribution factor βi obtainedthrough nonlinear time-history analysis for steelEBFs [3] βi is expressed as

βi Vi

Vn

1113936

ni Wihi

Wnhn

1113888 1113889

075Tminus 02

(20)

Fn VWnhn

1113936nj1Wjhj

⎛⎝ ⎞⎠

075Tminus 02

(21)

Fi βi minus βi+1( 1113857Fn when i n βi+1 0

(22)

Vi βi

β1V (23)

where βi denotes the shear distribution factor at level iV is the design base shear Fi and Fn denote the lateral

LL LθPθP

θPθP

F1

Fi

hi

Fn

Figure 2 Desired plastic mechanism


forces applied at level i and top level n respectively Vi

and Vn denote the story shear forces at level i and thetop (nth) level respectively Wi Wj and Wn denotethe structural weight at levels i j and the top (nth) levelrespectively hihj and hn denote the story height at thelevels i j and roof from ground respectively and T

denotes the fundamental structural period(5) Calculate the design lateral force the accumulated

hysteretic demand Eh(MDOF) of the V-scheme EBF isexpressed as the external work done by the designlateral force

Eh(MDOF) η(1 minus p) 1113944n

i1FiθyhiNEhμ (24)

where η is the parameter of the pinching effect (085 forthe V-EBF) θy is the global yield drift angle (in ra-dians) NEhμ is the accumulated ductility ratio of theV-EBF p is the postyield stiffness Fi is the lateral forceat the story level i hi is the height of the story level ifrom the ground and n is the total number of storiesBy substituting equations (20)ndash(22) in equation (24)the value of Fn is obtained

Fn Eh(MDOF)

η(1 minus p)NEhμθy1113936ni1 βi minus βi+1( 1113857hi

(25)

(e story shear Fi (i 1 n) and Vi are obtainedusing equations (22) and (23) respectively Note thatthe story shear force and design lateral force requiredare associated with the distribution of lateral forcesand the structural intended target ductility ratio

(6) Perform proportioning of the link beam andmembers outside the linksFor the V-EBF inelastic actions are intended tooccur only in the shear links column bases andbeam ends of both side frames Under a rareearthquake the distribution of shear link strengthalong the building height is consistent with thedistribution of the story shear force Hence the sheardistribution factor (βi) can be used to distribute theyielding of links along the V-EBF heightAccording to Figure 2 and the principle of virtualwork equation (26) can be obtained by equating theexternal work to the internal work under a givenlink plastic rotation angle cp of the V-EBF(Figure 3)

1113944

n

i1Fihiθp 1113944

n

i14fyWpsbiθp + 2fyWpmcθp

+ 2fyWpscθp + 1113944n

i12βiVtscpe

(26)

Nonlinear time-history analysis reveals that only asmall amount of energy less than 2 is dissipated bythe plastic hinges developed at the beam ends of bothside frames It is almost impossible that the beam endsyield at the same time (erefore for simplicity andobtaining more conservative results the hystereticenergy of the beam ends in equation (26) can beneglected and the equation can be expressed as

1113944n

i1Fihiθp 2fyWpmcθp + 2fyWpscθp

+ 1113944n

i12βiVtscpe

(27)

Vts 1113936

ni1Fihi minus 2fy Wpmc + Wpsc1113872 1113873

L1113936ni1βi

(28)

where L is the span length e is the shear link length Vtsis the required shear strength of links at the top storywhich is the only unknown term in equation (27) θp isthe V-EBF global inelastic drift which is the differencebetween the preselected target drift (θu) and the yielddrift (θy) fy is the nominal yield strength of steel cp isthe link plastic rotation angle and Wpmc and Wpsc arethe required plastic section modulus of middle columnbases and side column bases respectively (n βi Fi andhi have been explained previously) Note that no ex-ternal work done by gravity loading needs to be in-cluded (e required link shear strength at any story ican be determined as Vis βiVts(e elements outside the shear links including beamsegments braces and columns are performed based onthe capacity design approach It is assumed that the bracescan bear whole story shear force and still maintain elas-ticity (e axial force of braces can then be expressed as

θP

ΔP

γP

L

γP

h

e e

γP = (L2e) θP

Figure 3 Link rotation angle of V-EBF


Ni Vi

2 cos θi

(29)

where Vi θi and Ni respectively are the story shearforce the slope of the brace and the axial force of bracesat the ith storyOnce the plastic link shear forces are determined the framecan be cut into several free bodies of columns and beamsegments as illustrated in Figures 4ndash7(e required strengthof these members can be calculated using these free bodies(e required balancing lateral forces applied on some freebodies are assumed to maintain the same distribution asrepresented by equation (22) and can be easily calculatedusing the moment equilibrium of these free bodiesIn Figures 4ndash7Mpsbi is the nominal plastic moment of aside beam at story iVsbi is the shear force of the side beamend at story i Prici (Preci) is the vertical force resulting fromtributary gravity loading at story i Fricn (Frecn) is therequired balancing lateral force that can be regarded as thelateral force sheared by the column at the top (nth) story

Nrec (Nric) is the axial force at the column base Vrec (Vric)is the shear force at the column base Mprec (Mpric) is thenominal plastic moment at the column base Gsbi andGmbi are the concentrated loading of the side beam andthe middle beam at story i respectively wsbi and wmbi arethe uniform distribution loading of the side beam and themiddle beam at story i respectively Vpsi is the nominalplastic shear strength of the link at story i Msi is the linkend moment and βi is the shear distribution factor atstory i obtained using equation (20)

(e maximum expected force of link shear (Vu) canbe considerably higher than the strength of nominalplastic shear (Vps) resulting primarily from materialoverstrength strain hardening and the developmentof shear resistance in the link flanges For confiningall the inelastic activity to the shear links whilekeeping the other elements essentially elastic when

Frecn

Precn

(βi ndash βi+1) Frecn

hi

Vrec

Nrec

Mprec

PreciVsbi

Mpsbi

Vsbn

Mpsbn

Figure 4 Free body diagram of the right exterior column

Wsbi

Gsbi Gsbi

MpsbiMpsbi

L3 L3 L3

Figure 5 Free body diagram of the side span beam

Vsbi

Vsbn

Mpsbn

Mpsbi

FricnMsn

VpsnPricn

PriciVpsi

Msi

(βi ndash βi+1) Fricn

Vric

Nric

Mpric

hi

Figure 6 Free body diagram of the right interior column

Msi Msi

WmbiGmbi Gmbi

L3(L3) ndash e (L3) ndash e

Figure 7 Free body diagram of middle span beam


rare earthquakes occur scale factors should beemployed to increase the required strength of theparts outside the links For beams columns andbraces the scale factors are all 11 For the scaledstrength required the columns beams and bracesare designed in accordance with Chinese codes

(7) Iterate design until convergence when the differencebetween Ti+1 and Ti is smaller than 2 the iterationprocess can be stopped where Ti+1 and Ti are thefundamental structural period of (i+1)th and ith iter-ations respectively

An example is presented in the following sections todescribe the details of the design process

32 Description of Design Structure (e elevation and planlayout of a 10-story building are shown in Figure 8 (ebuilding is located at site group 2 with soil type II and thedesign earthquake acceleration amplitude is 052 g 2 of anearthquake with a return period of 50 years Each member ismade of Q235 steel and the link length is 08m InFigure 8(a) the dashed lines denote secondary beams whichare hinged to the primary beams

(e vertical loads applied on the V-EBF are calculated onthe basis of the corresponding tributary areas (e con-centrated force and position are listed in Table 2 (e lateralresisting systems consist of two V-EBFs in each directionAssuming that the total horizontal seismic load is borne bythe two V-EBFs half of the total building mass is lumped atthe frame joints given in Table 3

From Table 2 the sectional dimensions of the beamscolumns and braces of the V-EBFs can be determinedpreliminarily by using the design software (e capacities ofdifferent components are designed as described below

33 V-EBF Design

331 Preselected Plastic Mechanism According to existingresearch the drift ratio θy between two adjacent layers of astructure is 0003 and the target ductility ratio micro is set to 35

332 Natural Vibration Characteristics of Structure Forensuring 90 of mass participation the first three modes ϕj(j 1 2 3) and periods Tj (j 1 2 3) are calculated(e valuesof Γj Xmasj and Mlowastj are calculated (Table 4) using equations(17)ndash(19) respectively Due to limited space the data inTable 2 and the following sections are of the final iteration

333 Accumulated Hysteretic Energy Demand and DuctilityRatio of V-EBF (e equivalent velocities of the first threemodes can be calculated using equations (5)ndash(9) at p

005 and ζ 005 (e values VEH1 1218ms VEH2

1355ms and VEH3 08643ms are obtained (e ac-cumulated hysteretic energy demand can be determined asEh(MODF) 29559 kNmiddotm by using equations (15)ndash(19)

(e accumulated ductility ratio of the V-EBF is calcu-lated as NEhμ 1795 by using equations (11)ndash(14) withp 005 ζ 005 μ 35 α 10 and β 11

334 Shear Link Design On the basis of the distributionpattern of lateral forces as shown by equations (20)ndash(23)and the virtual work principle as expressed by equations(24)ndash(28) the required link shear strength at any story i canbe determined as Vis βiVts

Generally axial force effects do not need to be consid-ered during shear link design and the required areas of thelink web at any story can be calculated

Atw geVts

058fy

Aiw βiAtw

(30)

(e link flanges are the same as the middle beam (elink section should also satisfy the width-thickness limita-tions and the stiffener requirements provided in Chineseseismic provisions

335 Design of Members outside Links (e capacity methodsuggested in Section 31 can be used to design members

2340

0

1 2 3 4 5 6

780039000

7800 7800 7800 7800

C

A

B

D

V-EBF

V-EBF

V-EB

F

V-EB

F

7800

7800

7800

(a)

3300

times 1

0 =

3300

0

DA7800 times 3 = 23400

(b)

Figure 8 Structure (a) plane and (b) elevation views (unit mm)


outside the links (e final member sections obtained afterthe iterative design process are given in Table 5

4 Performance Evaluation of Designed V-EBF

To study the performance of the designed V-EBF under rareearthquakes with 2 probability of being the heaviest in 50years both static pushover analysis and time-history dy-namic analysis are performed (e evaluation is mainlyaimed at illustrating the effectiveness of the proposed designmethod For this purpose both dead loads and half of live

loads are placed on the frame during nonlinear staticpushover and time-history dynamic analyses and theseismic masses are lumped at frame joints (e staticpushover analysis is conducted using SAP2000 whileABAQUS is adopted for the dynamic analysis

41 Nonlinear Static Analysis Results By employing thelateral load distribution pattern specified in equations(20)ndash(22) the frame is pushed monotonically until a roofdrift ratio of 2 is obtained

Table 2 Vertical load values and positions of the frame

PositionTop floor Other floors

Exterior columns Interior columns Secondary beams Exterior columns Interior columns Secondary beams

Vertical load(kN)

Deadload

Liveload

Deadload

Liveload

Deadload

Liveload

Deadload

Liveload

Deadload

Liveload

Deadload

Liveload

919 507 1099 1014 1099 1014 1150 2028 998 4056 998 4056

Table 4 Modal factors

Mode Tj(s) Γj Xmaxj Mlowastj (kg)

1 1437 142 0718 14200002 04501 minus 0614 0166 15100003 02552 0294 0046 1850000

Table 5 Member sections of 10-story V-EBF

Number of storiesColumn sections Beam sections

Brace sectionInterior column Exterior column Middle beam Side beam

1-2 650lowast 35 400lowast18 H550lowast 300lowast 20lowast 30 H300lowast 300lowast18lowast 22 H300lowast 300lowast16lowast 203ndash5 600lowast 30 400lowast18 H550lowast 300lowast18lowast 24 H300lowast 300lowast18lowast 22 H300lowast 300lowast16lowast 206ndash8 450lowast 25 400lowast18 H500lowast 300lowast16lowast 20 H300lowast 300lowast18lowast 22 H250lowast 250lowast16lowast 209-10 400lowast 20 400lowast18 H500lowast 300lowast14lowast18 H300lowast 300lowast18lowast 22 H250lowast 250lowast12lowast14

Table 3 Masses at the nodes of the frame


Exterior columns Interior columns Exterior columns Interior columnsMass (kg) 707440 1061158 683833 1025750

(0 323 33041)

(2 54813)

0

1000

2000

3000

4000

5000

6000

7000

0 05 1 15 2 25

Base

shea

r (kN

)

Roof dri ratio ()

Figure 9 Pushover curve of the 10-story V-EBF


(e pushover curve is shown in Figure 9 It shows clearlythat the lateral bearing capacity is 33041 kN correspondingto the onset of stiffness deterioration which is 181 largerthan that of the design base shear (is may be attributed tothe fact that the improved overall lateral resistance ability ofthe frame is due to the material strain hardening and thedevelopment of shear resistance in the link flanges (e ratioof the structural yield driftmdashthe assumed yield drift ratiogiven in Section 33mdashis approximately 03 (erefore a03 yield drift for a 10-story V-EBF is generally reasonable

Furthermore the order of appearance and the location ofplastic hinges in the frame are also obtained from thepushover analysis Plastic hinges first occur at the linksfollowed by the side beam ends and column bases Figure 10shows the quantity and location of plastic hinges when theframe is pushed to roof drift ratios of 105 and 2 which isalmost identical to the prediction made by the preselectedyield mechanism

Clearly the proposed design method can reliably predictthe yield drift design base shear and the location of plastichinges

42 Nonlinear Dynamic Analysis Results A finite elementmodel is developed for the V-EBF by employing ABAQUSMoreover the beam elements (B32) are utilized to simulatethe braces columns and beams To capture local instabilitythe links are meshed with a four-node reduced integrationshell element (S4R) Furthermore both hinged beam-braceconnections and rigid beam-column connections are alsoemployed It is found that the out-of-plane degrees of

L LL

hi

E

D

C

CP

LS

IO

B

(a)

L L L

hi

E

D

C

CP

LS

IO

B

(b)

Figure 10 Inelastic activity of the 10-story V-EBF at a roof drift ratio of (a) 105 and (b) 2 ( yielding in link and plastic hinge)

1

2

3

4

5

6

7

8

9

10

0 05 1 15 2 25

Stor

y le

vel

Maximum interstory dri angle ()

P322P733P735P742P947P951

P961P1766RSN2602EP216Limit

Figure 11 Maximum interstory drift angles of 10-story V-EBF


freedom of the beam and shell element in the plane frame arerestrained

A total of 10 ground motion records are selected as inputearthquakes and the acceleration amplitudes are scaled to510 cms2 which corresponds to a rare earthquake (eselected records are strictly required to satisfy the criteria foreach record it is expected that (1) the ratio of the calculatedcumulative hysteretic energy of the structure is not less than60 and (2) themean ratio of all records is not less than 80

(e average value of total dissipated hysteretic energy ofthe V-EBF for the 10 records is 27053 kNm which isslightly lower than the design requirement(is result showsthat the proposed design method is rather conservative inseismic design

Figures 11 and 12 show the maximum interstory driftangle profiles and their average values respectively underdifferent records It can be observed in Figure 12 that theinterstory drift angles are closer to 1 preselected targetdrift and the frame indicates uniform interstory drift

5 Conclusions

In this paper a method for the performance-based seismicdesign of V-EBFs is proposed and validated through

nonlinear static and dynamic analyses (e following con-clusions can be drawn

(1) (e accumulated ductility ratio spectrum is closelyrelated to the soil type site group and structuraldamping ratio as well as the ductility and postyieldstiffness ratio However the effect of the structuralperiod on the accumulated ductility ratio spectra canbe neglected Finally the mathematical expressionsfor an accumulated ductility ratio spectrum that is inaccordance with the classification of Chinese soilsites can be obtained

(2) A procedure for the energy-based seismic design ofV-EBFs is proposed by employing both hystereticenergy spectra and accumulated ductility spectrawhich are applicable in China

(3) According to the results obtained from pushoveranalysis the yield drift design base shear and lo-cation of plastic hinges coincide with the predictionsmade by employing the proposed design method

(4) (e performance validation of V-EBFs shows thatthe preselected yield mechanism and target ductilityare reasonable based on the results of the nonlinearstatic and dynamic analyses (e proposed designmethod for V-EBFs is rather conservative

Data Availability

(e data used to support the findings of this study areavailable from the corresponding author on reasonablerequest

Conflicts of Interest

(e author declares no conflicts of interest

Acknowledgments

(is research was funded by the National Natural ScienceFoundation of China (Grant no 51278320) and NaturalScience Foundation of Hefei University (Grant nos18ZR14ZDA and 15KY01ZD) which are gratefullyacknowledged

References

[1] G W Housner ldquoLimit design of structures to resist earth-quakesrdquo in Proceedings of the 1st World Conference Earth-quake Engineering Berkeley CA USA 1956

[2] V Ozsarac S Karimzadeh M A Erberik and A AskanldquoEnergy-based response of simple structural systems by usingsimulated ground motionsrdquo Procedia Engineering vol 199pp 236ndash241 2017

[3] S H Chao and S C Goel ldquoPerformance-based seismic designof EBF using target drift and yield mechanism as performancecriteriardquo Report no UMCEE 05-05 Department of Civil andEnvironmental Engineering University of Michigan AnnArbor MI USA 2005

[4] S Leelataviwat S C Goel and B Stojadinovic ldquoTowardperformance-based seismic design of structuresrdquo EarthquakeSpectra vol 15 no 3 pp 435ndash461 1999

0

1

2

3

4

5

6

7

8

9

10

0 05 1 15 2

Stor

y le

vel

Interstory dri angle ()

Interstory driangleLimit

Figure 12 (e average values of the interstory drift angle underdifferent earthquakes


[5] S S Lee Performance-based design of steel moment framesusing target drift and yield mechanism PhD thesis De-partment of Civil and Environmental Engineering Universityof Michigan Ann Arbor MI USA 2002

[6] S H Chao and S C Goel ldquoA seismic design method for steelconcentric braced frames for enhanced performancerdquo inProceedings of the 4th international conference on earthquakeengineering Taipei Taiwan October 2006

[7] S H Chao and S C Goel ldquoPerformance-based plastic designof seismic resistant special truss moment framesrdquo Report noUMCEE 06-03 Department of Civil and EnvironmentalEngineering University of Michigan Ann Arbor MI USA2006

[8] J Kim H Choi and L Chung ldquoEnergy-based seismic designof structures with buckling-restrained bracesrdquo Steel andComposite Structures vol 4 no 6 pp 437ndash452 2004

[9] D R Sahoo and S-H Chao ldquoPerformance-based plasticdesign method for buckling-restrained braced framesrdquo En-gineering Structures vol 32 no 9 pp 2950ndash2958 2010

[10] B Akbas J Shen and H Hao ldquoEnergy appproach inpeformance-based seismic design of steel moment resistingframes for basic safety objectiverdquoBe Structural Design of TallBuildings vol 10 no 3 pp 193ndash217 2001

[11] L Mastrandrea and V Piluso ldquoPlastic design of eccentricallybraced frames II failure mode controlrdquo Journal of Con-structional Steel Research vol 65 no 5 pp 1015ndash1028 2009

[12] R Montuori E Nastri and V Piluso ldquo(eory of plasticmechanism control for MRF-EBF dual systems closed formsolutionrdquo Engineering Structures vol 118 pp 287ndash306 2016

[13] R Montuori E Nastri and V Piluso ldquoInfluence of thebracing scheme on seismic performances of MRF-EBF dualsystemsrdquo Journal of Constructional Steel Research vol 132pp 179ndash190 2017

[14] R Montuori E Nastri and V Piluso ldquoPreliminary analysison the influence of the link configuration on seismic per-formances of MRF-EBF dual systems designed by TPMCrdquoIngegneria Sismica vol 33 no 3 pp 52ndash64 2016

[15] G DellrsquoAglio R Montuori E Nastri et al ldquoA critical reviewof plastic design approaches for failure mode control of steelmoment resisting framesrdquo Ingegneria Sismica vol 34 no 4pp 82ndash102 2017

[16] G DellrsquoAglio R Montuori E Nastri and V Piluso ldquoCon-sideration of second-order efects on plastic design of steelmoment resisting framesrdquo Bulletin of Earthquake Engineeringvol 17 no 6 pp 3041ndash3070 2019

[17] H Choi and J Kim ldquoEnergy-based seismic design of buck-ling-restrained braced frames using hysteretic energy spec-trumrdquo Engineering Structures vol 28 no 2 pp 304ndash3112006

[18] G H Sun Q Gu R Q He et al ldquoPerformance based seismicdesign of steel plate shear walls using hysteretic energyspectrumrdquo Journal of Building Structures vol 32 no 11pp 126ndash133 2011 in Chinese

[19] H Choi and J Kim ldquoEvaluation of seismic energy demandand its application on design of buckling-restrained bracedframesrdquo Structural Engineering and Mechanics vol 31 no 1pp 93ndash112 2009

[20] S B Kharmale and S Ghosh ldquoPerformance-based plasticdesign of steel plate shear wallsrdquo Journal of ConstructionalSteel Research vol 90 pp 85ndash97 2013

[21] E-G Xiong H He F-F Cui and L Bai ldquoEnergy-basedresponse of simple structural systems by using simulatedground motionsrdquo Periodica Polytechnica Civil Engineeringvol 60 no 1 pp 127ndash134 2016

[22] M G Mezgebo and E M Lui ldquoA new methodology forenergy-based seismic design of steel moment framesrdquoEarthquake Engineering and Engineering Vibration vol 16no 1 pp 131ndash152 2017

[23] M Bruneau and N Wang ldquoSome aspects of energy methodsfor the inelastic seismic response of ductile SDOF structuresrdquoEngineering Structures vol 18 no 1 pp 1ndash12 1996

[24] C C Chou and C M Uang ldquoAn evaluation of seismic energydemand an attenuation approachrdquo PEER Report 200004Pacific Earthquake Engineering Research Center College ofEngineering University of California Berkeley CA USA2000

[25] C L Ma Q Gu and G H Sun ldquoMathematical expression ofdesign hysteretic energy spectra based on Chinese soil typerdquoMathematical Problems in Engineering vol 2019 Article ID3483516 10 pages 2019

[26] A Teran-Gilmore E Avila and G Rangel ldquoOn the use ofplastic energy to establish strength requirements in ductilestructuresrdquo Engineering Structures vol 25 no 7 pp 965ndash9802003

[27] C-C Chou and C-M Uang ldquoA procedure for evaluatingseismic energy demand of framed structuresrdquo EarthquakeEngineering amp Structural Dynamics vol 32 no 2 pp 229ndash244 2003


International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

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VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

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Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

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Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018


Chemical EngineeringInternational Journal of Antennas and

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Navigation and Observation


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wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

displacement was obtained by equating the energy demandto hysteretic energy dissipated by the BRBs Sahoo and Chao[9] presented a performance-based plastic design (PBPD)methodology for the design of buckling-restrained bracedframes (BRBFs) (e design base shear was obtained on thebasis of energy-work balance by using the preselected targetdrift and yield mechanism Akbas et al [10] proposed aperformance-based design methodology for constructingregular moment-resisting steel frames with the collapseprevention standard Mastrandrea and Piluso [11] presenteda design methodology aiming at the development of acollapse mechanism of a global type for K-scheme eccen-trically braced frames accounting for second-order effectsFinally the inelastic performances of EBFs by static anddynamic nonlinear analyses confirmed the achievement ofthe design goal Montuori et al [12] designed a number ofmoment-resisting frames-eccentrically braced frame (MRF-EBF) dual systems with both theory of plastic mechanismcontrol (TPMC) and Eurocode 8 and evaluated TPMCaccuracy by means of pushover analyses Afterwards theyinvestigated the influence of the bracing scheme [13] andlink configuration [14] on the seismic performances ofMRF-EBFs dual systems (e four different bracing schemes in-cluded K-scheme D-scheme V-scheme and Y-scheme (eseismic performances have been analyzed by means of in-cremental dynamic analyses at last DellrsquoAglio et al designedseveral steel moment-resisting frames (MR frames) bymeans of both the performance-based plastic design (PBPD)approach and TPMC [15] and proposed a new refinedPBPD considering second-order effects for steel moment-resisting frames [16] Finally the seismic performances ofsuch MR frames have been investigated by both pushoverand dynamic nonlinear analyses

Choi and Kim [17] and Sun et al [18] suggested cal-culating the accumulated plastic deformation of structuresby employing the accumulated ductility ratio spectra (eyalso revealed the relationship between the accumulatedhysteretic energy and the hysteretic energy of monotonoussideway structures Furthermore Choi and Kim [19]designed three frame structures with buckling-restrainedbraces (BRBs) by employing the energy balance concept afterthe construction of a hysteretic energy spectrum and anaccumulated ductility spectrum Using the normalizedhysteretic energy spectrum and the accumulated ductilityspectrum Sun et al [18] developed an energy-based seismicdesign method for steel plate shear walls (SPSWs) Kharmaleand Ghosh [20] proposed a performance-based plastic de-sign (PBPD) method for SPSW systems with rigid beam-to-column connections this method sets a specific ductilitydemand and a preferred yield mechanism as its performancetargets Xiong et al [21] presented a PBPD methodologybased on the energy-work balance concept for steel con-centrically braced frames Mezgebo and Lui [22] proposed aprocedure for designing steel moment frames by utilizingseismic hysteretic energy spectra

However most of the abovementioned researches werelimited to moment-resisting frames steel concentricallybraced frames steel frames of special truss moment andSPSWs and they were inapplicable to steel EBFs with two

shear links at every story Moreover all the mentionedenergy spectra were developed on the basis of non-Chinesesite classification and are inapplicable in China

EBFs are deemed as excellent structures to resistearthquakes as they colligate the ductility of moment frameswith the stiffness of braced frames In this paper hystereticenergy spectra and accumulated ductility ratio spectraestablished according to the Chinese site classification areused to propose an energy-based seismic design method forV-scheme EBFs Moreover a ten-story three-span V-EBF isdesigned and its seismic behavior is evaluated

2 Hysteretic Energy Spectra and AccumulatedDuctility Ratio Spectra

21 Hysteretic Energy Spectra Bruneau and Wang [23]stated that it is more rational to calculate seismic inputenergy by using the relative energy equation (e motionequation for an inelastic single-degree-of-freedom (SDOF)system subjected to the unidirectional horizontal groundmotions at given times is as follows

m eurox + c _x + fs minus m euroxg (1)

wherem denotes the mass c denotes the viscous dampingcoefficient fs denotes the restoring force x denotesthe relative displacement relative to ground _x and eurox

denote the velocity and acceleration of the mass rela-tive to ground respectively and euroxg denotes groundacceleration

(rough integration of an earthquakersquos whole durationthe energy equation can be obtained as follows

1113946t

0m eurox _xdt + 1113946

t

0c eurox _xdt + 1113946

t

0fs _xdt minus 1113946

t

0m euroxg _xdt (2)

where t is the timeEquation (2) can be expressed as

EKr + ED + EE + EH EIr (3)

where EKr is the kinetic energy ED is the energy dissipated bythe viscous damping EE is the elastic strain energy within theSDOF system EH is the hysteretic energy dissipated byinelastic behavior and EIr is the total input energy in-troduced by the earthquake

Under a far field earthquake structural failures usuallyresult from accumulative damage because of gradual ac-cumulation of the energy and cyclic effects As a result theaccumulated hysteretic energy can be treated as a rationalindex for far field seismic damage EH can be expressed interms of the equivalent velocity VEH [24]

VEH

2EH

m

1113970

(4)

where m denotes the mass(e equivalent velocity spectrum meeting the Chinese

site classification was developed by Ma et al [25] Figure 1shows the fitted spectral smooth curves

(e corresponding mathematical expressions are asfollows


VEH T



VEH T2

T1113874 1113875

c


(5)


η1 euroxg

eurox02g (6)


η2 1 +005 minus ζ01 + 15ζ

(7)


REHμ 1 +μ minus 2

25 + 2μ (8)


c c1 +005 minus ζ04 + 6ζ

(9)




NEHμ EHμ

Fy middot δy (10)





f(ζ) 052ζ + 075 (12)

f(p) minus 62p2

+ 40p + 0856 (13)

f(μ) 163μ2 + 075μ minus 238 (14)












VEH

0 6T1 T2 T









Eh(MDOF) 1113936


Nj1Xmassj

(15)


2EHj (16)

Mlowastj ϕT

j Mϕj (17)

Γj 1113936

ni1miφij

1113936ni1miφ2

ij

(18)

Xmassj 1113936

ni1miϕij1113872 1113873

2

1113936ni1mi( 1113857 1113936

ni1miϕ

2ij1113872 1113873

(19)



βi Vi

Vn

1113936

ni Wihi

Wnhn

1113888 1113889

075Tminus 02

(20)

Fn VWnhn

1113936nj1Wjhj

⎛⎝ ⎞⎠

075Tminus 02

(21)


(22)

Vi βi

β1V (23)


LL LθPθP

θPθP

F1

Fi

hi

Fn








i1FiθyhiNEhμ (24)


Fn Eh(MDOF)


(25)



1113944

n

i1Fihiθp 1113944

n



i12βiVtscpe

(26)


1113944n


+ 1113944n

i12βiVtscpe

(27)

Vts 1113936


L1113936ni1βi

(28)


θP

ΔP

γP

L

γP

h

e e

γP = (L2e) θP



Ni Vi

2 cos θi

(29)




Frecn

Precn


hi

Vrec

Nrec

Mprec

PreciVsbi

Mpsbi

Vsbn

Mpsbn


Wsbi

Gsbi Gsbi

MpsbiMpsbi

L3 L3 L3


Vsbi

Vsbn

Mpsbn

Mpsbi

FricnMsn

VpsnPricn

PriciVpsi

Msi


Vric

Nric

Mpric

hi


Msi Msi

WmbiGmbi Gmbi










33 V-EBF Design









Atw geVts

058fy

Aiw βiAtw

(30)



2340

0

1 2 3 4 5 6

780039000

7800 7800 7800 7800

C

A

B

D

V-EBF

V-EBF

V-EB

F

V-EB

F

7800

7800

7800

(a)

3300

times 1

0 =

3300

0

DA7800 times 3 = 23400

(b)











Vertical load(kN)

Deadload

Liveload

Deadload

Liveload

Deadload

Liveload

Deadload

Liveload

Deadload

Liveload

Deadload

Liveload

919 507 1099 1014 1099 1014 1150 2028 998 4056 998 4056



1 1437 142 0718 14200002 04501 minus 0614 0166 15100003 02552 0294 0046 1850000








(0 323 33041)

(2 54813)

0

1000

2000

3000

4000

5000

6000

7000

0 05 1 15 2 25

Base

shea

r (kN

)

Roof dri ratio ()







L LL

hi

E

D

C

CP

LS

IO

B

(a)

L L L

hi

E

D

C

CP

LS

IO

B

(b)


1

2

3

4

5

6

7

8

9

10

0 05 1 15 2 25

Stor

y le

vel


P322P733P735P742P947P951








5 Conclusions







Data Availability




Acknowledgments


References





0

1

2

3

4

5

6

7

8

9

10

0 05 1 15 2

Stor

y le

vel































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


VEH T



VEH T2

T1113874 1113875

c


(5)


η1 euroxg

eurox02g (6)


η2 1 +005 minus ζ01 + 15ζ

(7)


REHμ 1 +μ minus 2

25 + 2μ (8)


c c1 +005 minus ζ04 + 6ζ

(9)




NEHμ EHμ

Fy middot δy (10)





f(ζ) 052ζ + 075 (12)

f(p) minus 62p2

+ 40p + 0856 (13)

f(μ) 163μ2 + 075μ minus 238 (14)












VEH

0 6T1 T2 T









Eh(MDOF) 1113936


Nj1Xmassj

(15)


2EHj (16)

Mlowastj ϕT

j Mϕj (17)

Γj 1113936

ni1miφij

1113936ni1miφ2

ij

(18)

Xmassj 1113936

ni1miϕij1113872 1113873

2

1113936ni1mi( 1113857 1113936

ni1miϕ

2ij1113872 1113873

(19)



βi Vi

Vn

1113936

ni Wihi

Wnhn

1113888 1113889

075Tminus 02

(20)

Fn VWnhn

1113936nj1Wjhj

⎛⎝ ⎞⎠

075Tminus 02

(21)


(22)

Vi βi

β1V (23)


LL LθPθP

θPθP

F1

Fi

hi

Fn








i1FiθyhiNEhμ (24)


Fn Eh(MDOF)


(25)



1113944

n

i1Fihiθp 1113944

n



i12βiVtscpe

(26)


1113944n


+ 1113944n

i12βiVtscpe

(27)

Vts 1113936


L1113936ni1βi

(28)


θP

ΔP

γP

L

γP

h

e e

γP = (L2e) θP



Ni Vi

2 cos θi

(29)




Frecn

Precn


hi

Vrec

Nrec

Mprec

PreciVsbi

Mpsbi

Vsbn

Mpsbn


Wsbi

Gsbi Gsbi

MpsbiMpsbi

L3 L3 L3


Vsbi

Vsbn

Mpsbn

Mpsbi

FricnMsn

VpsnPricn

PriciVpsi

Msi


Vric

Nric

Mpric

hi


Msi Msi

WmbiGmbi Gmbi










33 V-EBF Design









Atw geVts

058fy

Aiw βiAtw

(30)



2340

0

1 2 3 4 5 6

780039000

7800 7800 7800 7800

C

A

B

D

V-EBF

V-EBF

V-EB

F

V-EB

F

7800

7800

7800

(a)

3300

times 1

0 =

3300

0

DA7800 times 3 = 23400

(b)











Vertical load(kN)

Deadload

Liveload

Deadload

Liveload

Deadload

Liveload

Deadload

Liveload

Deadload

Liveload

Deadload

Liveload

919 507 1099 1014 1099 1014 1150 2028 998 4056 998 4056



1 1437 142 0718 14200002 04501 minus 0614 0166 15100003 02552 0294 0046 1850000








(0 323 33041)

(2 54813)

0

1000

2000

3000

4000

5000

6000

7000

0 05 1 15 2 25

Base

shea

r (kN

)

Roof dri ratio ()







L LL

hi

E

D

C

CP

LS

IO

B

(a)

L L L

hi

E

D

C

CP

LS

IO

B

(b)


1

2

3

4

5

6

7

8

9

10

0 05 1 15 2 25

Stor

y le

vel


P322P733P735P742P947P951








5 Conclusions







Data Availability




Acknowledgments


References





0

1

2

3

4

5

6

7

8

9

10

0 05 1 15 2

Stor

y le

vel































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia








Eh(MDOF) 1113936


Nj1Xmassj

(15)


2EHj (16)

Mlowastj ϕT

j Mϕj (17)

Γj 1113936

ni1miφij

1113936ni1miφ2

ij

(18)

Xmassj 1113936

ni1miϕij1113872 1113873

2

1113936ni1mi( 1113857 1113936

ni1miϕ

2ij1113872 1113873

(19)



βi Vi

Vn

1113936

ni Wihi

Wnhn

1113888 1113889

075Tminus 02

(20)

Fn VWnhn

1113936nj1Wjhj

⎛⎝ ⎞⎠

075Tminus 02

(21)


(22)

Vi βi

β1V (23)


LL LθPθP

θPθP

F1

Fi

hi

Fn








i1FiθyhiNEhμ (24)


Fn Eh(MDOF)


(25)



1113944

n

i1Fihiθp 1113944

n



i12βiVtscpe

(26)


1113944n


+ 1113944n

i12βiVtscpe

(27)

Vts 1113936


L1113936ni1βi

(28)


θP

ΔP

γP

L

γP

h

e e

γP = (L2e) θP



Ni Vi

2 cos θi

(29)




Frecn

Precn


hi

Vrec

Nrec

Mprec

PreciVsbi

Mpsbi

Vsbn

Mpsbn


Wsbi

Gsbi Gsbi

MpsbiMpsbi

L3 L3 L3


Vsbi

Vsbn

Mpsbn

Mpsbi

FricnMsn

VpsnPricn

PriciVpsi

Msi


Vric

Nric

Mpric

hi


Msi Msi

WmbiGmbi Gmbi










33 V-EBF Design









Atw geVts

058fy

Aiw βiAtw

(30)



2340

0

1 2 3 4 5 6

780039000

7800 7800 7800 7800

C

A

B

D

V-EBF

V-EBF

V-EB

F

V-EB

F

7800

7800

7800

(a)

3300

times 1

0 =

3300

0

DA7800 times 3 = 23400

(b)











Vertical load(kN)

Deadload

Liveload

Deadload

Liveload

Deadload

Liveload

Deadload

Liveload

Deadload

Liveload

Deadload

Liveload

919 507 1099 1014 1099 1014 1150 2028 998 4056 998 4056



1 1437 142 0718 14200002 04501 minus 0614 0166 15100003 02552 0294 0046 1850000








(0 323 33041)

(2 54813)

0

1000

2000

3000

4000

5000

6000

7000

0 05 1 15 2 25

Base

shea

r (kN

)

Roof dri ratio ()







L LL

hi

E

D

C

CP

LS

IO

B

(a)

L L L

hi

E

D

C

CP

LS

IO

B

(b)


1

2

3

4

5

6

7

8

9

10

0 05 1 15 2 25

Stor

y le

vel


P322P733P735P742P947P951








5 Conclusions







Data Availability




Acknowledgments


References





0

1

2

3

4

5

6

7

8

9

10

0 05 1 15 2

Stor

y le

vel































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia







i1FiθyhiNEhμ (24)


Fn Eh(MDOF)


(25)



1113944

n

i1Fihiθp 1113944

n



i12βiVtscpe

(26)


1113944n


+ 1113944n

i12βiVtscpe

(27)

Vts 1113936


L1113936ni1βi

(28)


θP

ΔP

γP

L

γP

h

e e

γP = (L2e) θP



Ni Vi

2 cos θi

(29)




Frecn

Precn


hi

Vrec

Nrec

Mprec

PreciVsbi

Mpsbi

Vsbn

Mpsbn


Wsbi

Gsbi Gsbi

MpsbiMpsbi

L3 L3 L3


Vsbi

Vsbn

Mpsbn

Mpsbi

FricnMsn

VpsnPricn

PriciVpsi

Msi


Vric

Nric

Mpric

hi


Msi Msi

WmbiGmbi Gmbi










33 V-EBF Design









Atw geVts

058fy

Aiw βiAtw

(30)



2340

0

1 2 3 4 5 6

780039000

7800 7800 7800 7800

C

A

B

D

V-EBF

V-EBF

V-EB

F

V-EB

F

7800

7800

7800

(a)

3300

times 1

0 =

3300

0

DA7800 times 3 = 23400

(b)











Vertical load(kN)

Deadload

Liveload

Deadload

Liveload

Deadload

Liveload

Deadload

Liveload

Deadload

Liveload

Deadload

Liveload

919 507 1099 1014 1099 1014 1150 2028 998 4056 998 4056



1 1437 142 0718 14200002 04501 minus 0614 0166 15100003 02552 0294 0046 1850000








(0 323 33041)

(2 54813)

0

1000

2000

3000

4000

5000

6000

7000

0 05 1 15 2 25

Base

shea

r (kN

)

Roof dri ratio ()







L LL

hi

E

D

C

CP

LS

IO

B

(a)

L L L

hi

E

D

C

CP

LS

IO

B

(b)


1

2

3

4

5

6

7

8

9

10

0 05 1 15 2 25

Stor

y le

vel


P322P733P735P742P947P951








5 Conclusions







Data Availability




Acknowledgments


References





0

1

2

3

4

5

6

7

8

9

10

0 05 1 15 2

Stor

y le

vel































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


Ni Vi

2 cos θi

(29)




Frecn

Precn


hi

Vrec

Nrec

Mprec

PreciVsbi

Mpsbi

Vsbn

Mpsbn


Wsbi

Gsbi Gsbi

MpsbiMpsbi

L3 L3 L3


Vsbi

Vsbn

Mpsbn

Mpsbi

FricnMsn

VpsnPricn

PriciVpsi

Msi


Vric

Nric

Mpric

hi


Msi Msi

WmbiGmbi Gmbi










33 V-EBF Design









Atw geVts

058fy

Aiw βiAtw

(30)



2340

0

1 2 3 4 5 6

780039000

7800 7800 7800 7800

C

A

B

D

V-EBF

V-EBF

V-EB

F

V-EB

F

7800

7800

7800

(a)

3300

times 1

0 =

3300

0

DA7800 times 3 = 23400

(b)











Vertical load(kN)

Deadload

Liveload

Deadload

Liveload

Deadload

Liveload

Deadload

Liveload

Deadload

Liveload

Deadload

Liveload

919 507 1099 1014 1099 1014 1150 2028 998 4056 998 4056



1 1437 142 0718 14200002 04501 minus 0614 0166 15100003 02552 0294 0046 1850000








(0 323 33041)

(2 54813)

0

1000

2000

3000

4000

5000

6000

7000

0 05 1 15 2 25

Base

shea

r (kN

)

Roof dri ratio ()







L LL

hi

E

D

C

CP

LS

IO

B

(a)

L L L

hi

E

D

C

CP

LS

IO

B

(b)


1

2

3

4

5

6

7

8

9

10

0 05 1 15 2 25

Stor

y le

vel


P322P733P735P742P947P951








5 Conclusions







Data Availability




Acknowledgments


References





0

1

2

3

4

5

6

7

8

9

10

0 05 1 15 2

Stor

y le

vel































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia








33 V-EBF Design









Atw geVts

058fy

Aiw βiAtw

(30)



2340

0

1 2 3 4 5 6

780039000

7800 7800 7800 7800

C

A

B

D

V-EBF

V-EBF

V-EB

F

V-EB

F

7800

7800

7800

(a)

3300

times 1

0 =

3300

0

DA7800 times 3 = 23400

(b)











Vertical load(kN)

Deadload

Liveload

Deadload

Liveload

Deadload

Liveload

Deadload

Liveload

Deadload

Liveload

Deadload

Liveload

919 507 1099 1014 1099 1014 1150 2028 998 4056 998 4056



1 1437 142 0718 14200002 04501 minus 0614 0166 15100003 02552 0294 0046 1850000








(0 323 33041)

(2 54813)

0

1000

2000

3000

4000

5000

6000

7000

0 05 1 15 2 25

Base

shea

r (kN

)

Roof dri ratio ()







L LL

hi

E

D

C

CP

LS

IO

B

(a)

L L L

hi

E

D

C

CP

LS

IO

B

(b)


1

2

3

4

5

6

7

8

9

10

0 05 1 15 2 25

Stor

y le

vel


P322P733P735P742P947P951








5 Conclusions







Data Availability




Acknowledgments


References





0

1

2

3

4

5

6

7

8

9

10

0 05 1 15 2

Stor

y le

vel































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia










Vertical load(kN)

Deadload

Liveload

Deadload

Liveload

Deadload

Liveload

Deadload

Liveload

Deadload

Liveload

Deadload

Liveload

919 507 1099 1014 1099 1014 1150 2028 998 4056 998 4056



1 1437 142 0718 14200002 04501 minus 0614 0166 15100003 02552 0294 0046 1850000








(0 323 33041)

(2 54813)

0

1000

2000

3000

4000

5000

6000

7000

0 05 1 15 2 25

Base

shea

r (kN

)

Roof dri ratio ()







L LL

hi

E

D

C

CP

LS

IO

B

(a)

L L L

hi

E

D

C

CP

LS

IO

B

(b)


1

2

3

4

5

6

7

8

9

10

0 05 1 15 2 25

Stor

y le

vel


P322P733P735P742P947P951








5 Conclusions







Data Availability




Acknowledgments


References





0

1

2

3

4

5

6

7

8

9

10

0 05 1 15 2

Stor

y le

vel































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia






L LL

hi

E

D

C

CP

LS

IO

B

(a)

L L L

hi

E

D

C

CP

LS

IO

B

(b)


1

2

3

4

5

6

7

8

9

10

0 05 1 15 2 25

Stor

y le

vel


P322P733P735P742P947P951








5 Conclusions







Data Availability




Acknowledgments


References





0

1

2

3

4

5

6

7

8

9

10

0 05 1 15 2

Stor

y le

vel































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







Data Availability




Acknowledgments


References





0

1

2

3

4

5

6

7

8

9

10

0 05 1 15 2

Stor

y le

vel































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




RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


Documents

Energy-BasedSeismicDesignMethodforEBFsBasedonHysteretic ...downloads.hindawi.com/journals/ace/2019/3180596.pdf · 2019-11-19 · performance-based design methodology for constructing