Analysis of the Seismic Demand of High-Performance...

Research ArticleAnalysis of the Seismic Demand of High-PerformanceBuckling-Restrained Braces under a Strong Earthquake andIts Aftershocks

Luqi Xie1 Jing Wu 1 Qing Huang2 and Chao Tong1

1Key Laboratory on Concrete and Prestressed Concrete Structures of Ministry of Education Southeast UniversityNanjing 210096 China2Architects amp Engineers Co Ltd of Southeast University Nanjing 210096 China

Correspondence should be addressed to Jing Wu seuwjseueducn

Received 15 November 2018 Accepted 9 January 2019 Published 6 February 2019

Academic Editor Raffaele Landolfo

Copyright copy 2019 Luqi Xie et al-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

-e analysis of the ductility and cumulative plastic deformation (CPD) demand of a high-performance buckling-restrained brace(HPBRB) under a strong earthquake and its aftershocks is conducted in this paper A combination of three continuous excitationswith the same groundmotion is used to simulate the affection of a strong earthquake and its aftershocks A six-story HPBRB frame(HPBRBF) is taken as an example to conduct the incremental dynamic analysis (IDA) -e seismic responses of the HPBRBFunder one two and three constant continuous groundmotions are compared-e IDA result indicates that the ductility and CPDdemand of the BRBs under the three constant continuous ground motions are significantly larger than that excited by only oneProbabilistic seismic demand analysis (PSDA) is performed using seven near-fault ground motions and seven far-fault groundmotions to consider the indeterminacy of ground motion -e probabilistic seismic demand curves (PSDCs) for the ductility andCPD demand for the HPBRB under the strong earthquake and its aftershocks are obtained in combining the probabilistic seismichazard analysis -e results indicate that the AISC threshold value of the CPD with 200 is excessively low for a HPBRBF whichsuffers the continuous strong aftershocks with near-fault excitations and a stricter threshold value should be suggested to ensurethe ductility and plastic deformation capacity demand of the HPBRB

1 Introduction

A buckling-restrained brace (BRB Figure 1) is a type ofmetal-yield energy dissipation device which can be fab-ricated in a frame structure as a brace to provide lateralstiffness during the lifetime of the structure If the framesuffers a strong earthquake the BRB will yield before themain structural members and dissipate the seismic energyprotecting the main structural members from severedamage [1] -e BRB could be used as a brace and damperin newly built structures as well as a seismic retrofittingmeasure to existing structures [2] -e BRBs on structuresin high seismic zones tend to experience high-strain cyclicdeformation under strong earthquakes and aftershocksand high-strain low-cycle fatigue failure may occur on the

BRBs after several large-strain cycles -e seismic capacityof a structure largely depends on the low-cycle fatigueproperty of the BRBs [3 4] which is closely related to theductility (μ) and the cumulative plastic deformation(CPD) of the BRB expressed as follows

μ maxεtmax εcmax

111386811138681113868111386811138681113868111386811138681113872 1113873

εy

CPD 1113944Δεpi

11138681113868111386811138681113868

11138681113868111386811138681113868

εy

(1)

where εtmax is the maximum tensile strain of the BRB εcmax isthe maximum compressive strain Δεpi is the strain ampli-tude of the ith cycle and εy is the yield strain of the BRB

HindawiAdvances in Civil EngineeringVolume 2019 Article ID 1482736 14 pageshttpsdoiorg10115520191482736

Researchers have performed extensive studies on theBRB frame (BRBF) to measure the demand of the energydissipation capacity of the BRB and studies on the low-cyclefatigue property of BRBs in a single ground motion havebeen relatively fully developed FEMA-450 [5] comments theCPD demand of a BRB no less than 140 through experi-mental studies and nonlinear time-history analyses Sabelli[6] proposed that the demand should reach 185 based on thetime-history analyses on a three-story and a six-story BRBFIwata et al [7] suggested that the CPD should reach 292while Usami et al [8] proposed the CPD capacity no lessthan 400 ANSIAISC [9] stipulates that the CPD of the BRBshould be at least 200 to ensure the requirement of the low-cycle fatigue property

BRBs that fulfill the above CPD requirement are sup-posed to help the frames resist one strong ground motionwhile it should be replaced in time after a strong earthquaketo restore the capacity of the structures However the existedresearch about earthquake records indicate that strongearthquakes often arise with several strong aftershocks [10]and the interval between the shocks is too short to replacethe BRBs Furthermore aftershocks may cause furtherdamage accumulation which leads to the failure of the BRBand results in the collapse of the frame structure especiallyfor near-fault ground motions To resist the strong after-shocks the demand of the ductility and the CPD should beraised Usami et al [11] proposed the high-performance BRB(HPBRB) in which the special performance requirementscan be summarized as follows (1) stable hysteretic char-acteristics and high energy dissipation capacity (2) highdeformation capacity (3) high low-cycle fatigue strength (4)easy and low-cost fabrication and construction (5) highdurability and (6) no need for replacement under contin-uous strong earthquakes It is concluded that a high low-cycle fatigue capacity is needed to ensure the energy dis-sipation capacity of the BRB by selecting high-ductility steelResearchers proposed a series of novel HPBRBs which wasbased on the construction of the specimens and the materialspecimens Jia et al [12] proposed an assembled buckling-restrained brace wrapped with carbon or basalt fiber whichcould improve the restraining members and sufficientductility and energy dissipation capacity Jia et al [13]proposed a type of fish-bone BRB (FB-BRB) which could

avoid strain concentration along the length of the coremember and improve the energy dissipation capacity duringa strong earthquake or subsequent repeated aftershocksWang et al [14] proposed a novel BRB with partial bucklingrestraint in which only the edge parts of the core memberare strained and other parts are designed for visual in-spection on damage monitoring Chen et al [15] experi-mentally studied on the effect of the unbonding materials onthe mechanic behavior of all-steel BRBs and suggested thatthe unbonding materials should be applied for high-performance BRBs with a relatively long yielding segmentand thin core plate Guo et al [16ndash19] proposed a series ofhigh-performance BRBs such as shuttle-shaped BRBs [16]cross-arm pretensioned cable stayed BRBs [17 18] andcorrugated-web-connected BRBs [19] Xie et al [20] pro-posed a type of weld-free all-steel BRBs in which the coremember is fabricated absolutely in high-strength boltswithout any weld and a high CPD could be seen in the low-cycle fatigue tests Besides Hoveidae et al [21] numericallystudied the seismic behavior of short-core all-steel BRB(SCBRB) in which the relationship between the ductilitydemand and the core length was analyzed Vafaei andEskandari [22] studied on the seismic response of BRBssubjected to the fling step and forward directivity near-faultground motions and confirmed that the near-fault groundmotions imposed higher demands on the structuresHowever a unified demand for the ductility and CPD of aBRB under the action of a strong earthquake and its af-tershocks has not been unified yet

In this paper the distribution characteristics of ductilityand CPD of BRBs are determined by the incremental dy-namic analysis (IDA) [23] using three continuous equal-intensity earthquake ground motions to consider the effectof an earthquake and its aftershocks As it is essential toanalyze the randomness of the response by the probabilitymethod the seismic demand of the ductility and CPD of theBRB are concluded through the probability seismic demandanalysis (PSDA) [24] -e seismic demand index of μ andCPD of the HPBRB is also suggested in this paper whichcould be used as a threshold value criterion formanufacturing HPBRB

2 Application of PSDA in HPBRB Design

According to the theory proposed by the PEER the seismicresponse of a structure is described as the engineering de-mand parameter (EDP) and the peak ground acceleration(PGA) of the ground motion is chosen as the intensitymeasure (IM) in this paper while the considered period oftime is determined as 50 years according to the designreference period of the common engineering structures inChina When the probabilistic seismic hazard curve (PSHC)of the PGA under the condition of a given site is combinedwith the probability distribution of the EDP under the givenPGA the probability of the EDP of the structure exceeding acertain value in 50 years can be obtained

-e probabilistic seismic demand λEDP (δ) which is theprobability of the EDP exceeding a certain value δ in 50years can be divided into two parts one part is the

Figure 1 A BRB frame (a library in the USA)

2 Advances in Civil Engineering

conditional probability of exceeding the demand value δunder the condition PGA A -e other is the probabilityof PGA of the ground motion around the value A -eformula of probabilistic seismic demand can beexpressed as

λEDP(δ) 1113946A

P[EDPgt δ |PGA A] middot dλPGA(A)1113868111386811138681113868

1113868111386811138681113868 (2)

where P[EDPgt δ |PGA A] is the probability of exceeding aspecified EDP level δ given as a level of PGAA -e dif-ferential of the ground motion hazard curve dλPGA (A) λPGA(A)minusλPGA (A+dA) is the probability that the value of PGAbelongs to (AA+dA) in 50 years where dA is a small incrementin PGA

Incremental dynamic analysis (IDA) is conducted in thispaper to obtain the accurately seismic responses of the HPBRBframe (HPBRBF) under different levels of ground motion in-tensity which is an essential step in PSDA-e essence of IDA inthis paper is scaling the PGA of one groundmotion into severaldifferent levels to form a series of ground motions -en thenonlinear dynamic time-history analyses on the HPBRBF areconducted based on each ground motion and the IDA curveswhich can reveal the relationships between the EDP of theHPBRBF and the PGA of the ground motions are obtainedFurthermore a series of seismic recording should be selected toconduct the IDA and the statistical analysis of the seismicdemand curves of IDA considering the randomness of theearthquake is essential

-e analysis steps of PSDA are as follows

(1) Establish the computational model of the HPBRBF(2) Select the seismic records and determine the PGA(3) Select the appropriate parameters of the EDP and

conduct IDA(4) Conduct statistical analysis of the seismic demand

curves of IDA along with the probability distributionof seismic demand parameters and calculate theprobability of the EDP exceeding a certain valuedemand under a specified PGA

(5) Obtain the probability seismic hazard curves(PSHCs) of the PGA under certain conditions

(6) Establish the probability seismic demand curves(PSDCs) according to the conditional probability ofthe seismic demand under the specified PGA and itsPSHC

As the main performance indexes of a BRB are ductility andCPD they are chosen as the EDPs when conducting PSDA foran HPBRB Based on considering the randomness of the in-tensity and frequency of earthquakes and their aftershocks theIDA is conducted to obtain the PSDC of the HPBRBs on theframe Combined with the PSHC of specific site conditions thePSDC of the HPBRB can be obtained through the probabilitymethod including the PSDC of ductility and CPD

3 Model of HPBRBF and Ground Motions

-e HPBRB frame (HPBRBF) model is chosen as a six-storyoffice building composed of a steel frame and Chevron

HPBRBs [25] -e height of the story is 39m and the spanof the frame is 80m -e base of the column is fully re-strained on the ground -e elevation of the frame is shownin Figure 2 According to the Code of Seismic Design ofBuildings in China (GB50011-2010) [26] the building isdesigned in a zone whose seismic precautionary intensity is8deg the character of the site belongs to Type III and the designcharacteristic period of ground motion belongs to the firstgroup -e seismic precautionary intensity is stipulated byldquoStandard for classification of seismic protection of buildingconstruction (GB50223-2008)rdquo in China -e seismic pre-cautionary intensity stands for the seismic intensity whoseexceedance probability is 10 in 50 years while 8deg stands forthe fortification acceleration is 20ms2 -e nominal valuesof the dead load and the live load are 60 kNm2 and 30 kNm2 respectively -e uniformly distributed loads are sim-plified into a series of concentrated loads on the nodes ofbeam elements of the structure

-e steel frame is composed of welded H-section beamsand box-section columns -e beams are fixed with thecolumns In addition the BRBs are jointed with the frame Itis assumed that the yield stress of steel (fy) for both beamsand columns is 345MPa while that for the BRB is 235MPaYoungrsquos modulus (Es) and Poissonrsquos ratio of the steel are206000Nmm2 and 03 respectively -e density of steel is7850 kgm3 -e section parameters of the members on theHPBRBF are shown in Table 1

Nonlinear dynamic time history analysis is performed bySeismoStruct (SeismoSoft [27]) -e beams and columns ofthe frame are modelled as the load-based inelastic fiber spaceframe beam-column element (infrmFB) -e load-displacement relation of the beams and the columns canbe obtained by integrating the nonlinear uniaxial stress-strain relations of the entire fibers on the sections of theinfrmFBs under the plane-section assumption -e HPBRBsare modelled as the nonlinear truss elements which can onlybear axial force -e axial elastic stiffness of the elements isdetermined by the material model and the section param-eters Since the HPBRBs installed in the frame with con-nection parts and transition parts at two ends would occupysome geometric dimension in actual engineering the lengthof an HPBRB yielding segment is assumed as only about halfof the geometric element length used in the model [28] Asthe strain of the BRB should be calculated as the ratio be-tween the deformation and the length of the yielding seg-ment the simplified numerical model of BRB in this studyassumed that the full length of the member is arranged as theyielding segment and the result of the analysis model shouldbemultiplied by 2 in the postprocessing process to obtain theductility and the CPD of the HPBRB in the actual structureA bilinear stress-strain relation with Et Es100 (where Et isthe tangent modulus after yield) and a kinematic hardeningrule are adopted for the steel beams and columns whileEt E60 for the HPBRB members in the time-historyanalysis according to Usami et al [28] Owing to thecomplexity of the beam element modelling a simplifiedmodel for BRBs is then considered which models the BRBwith a truss element using a bilinear stress-strain relation-ship with a kinematic hardening rule According to Usami

Advances in Civil Engineering 3

et al [28] the truss model with a strain hardening stiffness ofEs60 exhibits close energy dissipation capacity to the beamelement modelling result and thus it is believed to beappropriate for modelling the BRBs -erefore the trussmodel with the bilinear constitutive model is applied toBRBs in the analysis of the present study -e period ofvibration of the selected model is 0980 s

It is worth mentioning that the value ofABRB in Table 1 isreferred to the yielding core-e stiffness and the strength ofthe BRB is mainly affected by that of the yielding segment inthe postyielding stage according to the theory of stiffness inseries of the core member which could be expressed as

KBRB 1

1Ki( 1113857 + 2Kcon( 1113857 + 2Ktr( 1113857( 1113857 (3)

where Ki EAiLi is the stiffness of the yielding segmentwhile Kcon EAconLcon and Ktr EAtrLtr are the stiffness ofconnection and transition segments of the BRBAiAcon andAtr refers to the sectional area of the yielding segmenttransition segment and connection segment respectivelywhile Li Lcon and Ltr are the length of the three segments AsE is Youngrsquos modulus of Q235 steel it should be replaced asEt which is the tangent modulus in the postyielding stageBecause only the yielding segment yields during theearthquake the postyielding stiffness of the BRB mainlydepends on that of the yielding segment Besides thestrength of BRB is determined by the minimum sectionalarea of the whole brace and thus the simplified model couldreplicate the stiffness and strength properly

It can be concluded from the existed ground motionrecords that the near-fault ground motions with velocitypulse may cause a relatively large peak ground velocity

(PGV) and PGA-e near-fault ground motions will make awide acceleration sensitive region which may significantlyaffect the structural response and this effect would signif-icantly increase the roof-displacement interstory drift andthe demand of the base shear force of the HPBRBF Kalkanand Kunnath [29] proposed that the near-fault should bedefined as fault distance less than 20 km as well as PGVPGAgt 02 In this study seven near-fault ground motionswhose fault distances are within 15 km with PGVPGAgt 02are selected from the PEER ground motion database con-sidering the duration the magnitude the epicenter distanceand the site condition of the ground motion along with themagnitude of all the selected records greater than 60 Be-sides seven far-fault ground motions are selected from thePEER ground motion database according to the principalthat the deviation of the mean accelerogram spectrum fromthe target spectrum is minimum [30] as is shownin Figure 3 -e target spectrum is selected according toldquoCode for seismic design of buildings (GB50011-2010)rdquo inChina in which the seismic precautionary intensity is 8deg asis shown in Figure 3 -e mean spectrum of the selectedground motions is also shown in the figure in which thedeviations between the mean spectrum and target spectrumis minimum between the period 08 s to 10 s As the periodof vibration of the selected model is 0980 s the groundmotion records could be used

-e parameters of the ground motion records are shownin Tables 2 and 3 in which the PGV and the PGA are listed-e site types in the table are classified according to theUSGS classification criteria of the United States which isclose to the Type III site specified in the Code for SeismicDesign of Buildings in China (GB50011-2010) It should be

Table 1 Member section of the beam column and BRBs of the six-story HPBRBF

Story SC (mm) IC (mm) SB (mm) MB (mm) ABRB (mm2) Ctimes t Ctimes t H middot htimes btimes tw times tf H middot htimes btimes tw times tf1-2 390times15 510times 27 450times 200times10times16 500times 250times12times 20 37313-4 370times13 440times16 450times 200times10times16 500times 250times12times 20 31425-6 330times11 400times14 450times 200times10times16 500times 250times12times 20 2281Note SC is the dimensions of the side columns IC is the dimensions of the inner columns SB is the dimensions of the side beamsMB is the dimensions of themiddle beams ABRB is the sectional area of HPBRBs -e symbol ldquordquo represents the square steel pipe which could be regarded as the box-section columns

8000 times 3 = 24000

3900

0times

6=

2340

00

Figure 2 Elevation of the frame


noted that the vertical component of the records areneglected according to GB50011-2010 as the total height ofthe model is only 234m while the span length is 8m

It can be concluded from the comparison between thenear-fault and far-fault ground motion velocity time-historycurves that the structural response to the near-fault earth-quake is far greater than that of the far-fault earthquake -enear-fault earthquake ground motions generate a velocitypulse with a large amplitude a long cycle and a shortduration whose peak amplitude region in the accelerationresponse spectrum is wide and generally appears in the longperiod section -erefore the IDAs of the BRBF understrong earthquakes and their aftershocks are conductedunder near-fault ground motions and far-fault groundmotions respectively -e influence of the two types ofground motions is considered synthetically and the ductilityand CPD demand of the HPBRB are concluded

4 Response of HPBRBF under a StrongEarthquake and Its Aftershocks

IDA is performed on the aforementioned six-story steelHPBRBF to obtain the performance demand of the BRBsAccording to the destructive earthquakes in recent decadesstrong earthquakes which may experience multiple times ofstrong aftershocks after the main shock frequently in whichthe groundmotion intensity may be lower or higher than themain shock -ough the aftershocks are never the same ofthe main shock the historic records of the strong aftershocksare random Without loss of generality a series of contin-uous same record could be used to simulate the strongaftershocks or repeated earthquakes [31] Besides the se-lection of the ground motions for simulating the aftershockscould also be consulted by Hu et al and Das et al[32 33] Inthis paper three continuous excitations with the same

0 1 2 3 4 5 60

10

20

Actual spectrumMean spectrumTarget spectrum

T (s)

S a (m

s2 )

Figure 3 Acceleration spectrum of the selected ground motions

Table 2 Parameters of near-field seismic recording

No Ground motion Magnitude Station Site type Fault distance (km) PGA (g) PGV (cms) PGVPGA (s)1 Imperial Valley 65 955 EC C D 42 036 766 02132 Imperial Valley 65 5154ECC092 C D 76 0235 688 02933 N Palm Springs 60 5071MV C D 101 0205 409 02044 Northridge 67 0655JFP C D 62 0424 1062 02505 Kocaeli 74 Yarimca C D 26 0268 657 02456 Kobe 69 Takatori C D 03 0611 1271 02087 Chi-Chi 76 CHY-101 C D 1114 044 115 0261

Table 3 Parameters of far-field seismic recording

No Ground motion Magnitude Station Site type Fault distance (km) PGA (g) PGV (cms) PGVPGA (s)1 Cape Mendocino 71 89324RDO C D 185 0549 421 00772 Superstition Hills 67 5062SSWR C D 271 0167 183 01103 Coalinga 64 36227PC C D 255 0227 236 01044 Northridge 67 90013BH C D 196 0516 628 02085 Landers 73 22074YFS C D 249 0152 297 01956 Kobe 69 SHI090 C D 155 0212 279 01327 San Fernando 66 LA-HSL C D 212 0174 149 0086


amplitude are used as the groundmotion for a single analysisto consider the effect of an earthquake and its aftershocksDuring the procedure of IDA the ground motions are scaledto different intensities to draw IDA curves Take the near-fault ground motion of Northridge (No 4 in Table 2) forexample the intensity of the PGA of groundmotion is scaledfrom 1ms2 to 10ms2 with an interval of 1ms2-e groundmotion with a PGA scaled to 6ms2 as an example is seen inFigure 4

-e mean interstory drift and residual drift of theHPBRBF model along the building height under the rareearthquake whose seismic precautionary intensity is 8deg(ie PGA is 4 ms2) is plotted in Figure 5 in which themean value of the responses under the near-fault groundmotions and far-fault ground motions are exhibitedrespectively Meanwhile the mean ductility demand ofHPBRBs along the building height in this condition isalso plotted in Figure 6 in which Figure 6(a) is the re-sponse under near-fault ground motions whileFigure 6(b) is that under the far-fault ones It can be seenthat the maximum lateral drift demand is basicallyconcentrated on the 2nd or 3rd story of the structurewhile the residual drift distribution could be seen near tozero A similar distribution could also be seen in Figure 6-us the BRBs in the 3rd story could be selected as therepresentative example for further analysis on the duc-tility demand of BRBs Besides it can also be seen that arelatively large drift and BRB ductility could be obtainedin the top story which is consistent with Costanzo et al[34] -us in order to improve the lateral distribution ofdrift demand (ie the ductility demand in BRBs) it canbe very efficient to stiffen the top story which couldfurther improve the seismic performance on the chevronBRB frames

-e variation tendency of the ductility and the CPD ofthe HPBRB in the left side of the 3rd story with the increasingof seismic intensities in the end of different phases arepresented in Figure 7

It can be seen in Figure 7 that the ductility of the BRBalmost remained the same among the three phases of ex-citation when the structure experiences a slight groundmotion (PGAlt 3ms2) and the increase of the CPD aftereach phase is also relatively small However when the PGAincreases to a value larger than 4ms2 the ductility and theCPD of the BRB in the second phase become significantlylarger than that in the first phase for the same PGA Fur-thermore the response would further increase when thethird phase acts on the frame with a slight increase inamplitude -is phenomenon is more obvious with in-creasing PGA According to the aforementioned phenom-enon it can be inferred that the demand of the BRB ductilityunder three equal-amplitude excitations is higher than thatunder only one Moreover the demand of the CPD of theBRB almost linearly increases with increasing number of thephases implying that the accumulation of the plastic de-formation caused by each phase is almost the same It canalso be concluded that higher performance requirements ofthe HPBRB should be proposed to achieve the target that no

replacement of the HPBRB is needed during a strongearthquake and its aftershocks

Figure 8 shows the normalized hysteretic curves ofthe BRBs in the third story of the HPBRBF -e two BRBsin the same story behave like an antisymmetric formnamely the left-side BRB is mainly in compression whilethe right-side BRB is mainly in tension -e gravity loadof the beam-column joints may cause axial deformationof the column resulting in a compressive stress on theBRBs before the earthquake excitation and the com-pressive stress could be named as ldquoinitial stressrdquo Whenthe structure is subjected to ground motion the BRBmainly in compression will yield first while the BRBmainly in tension will yield later due to the existence ofthe ldquoinitial stressrdquo As the ldquoinitial stressrdquo caused by thegravity load of the floor exists in the BRB the maximumpressure and the deformation of the BRB on the com-pression side are slightly larger than the maximumtensile force and deformation of the BRB on the tensionside

5 IDA for the Ductility

As the near-fault ground motions contain a velocity pulsethat is particularly distinct compared to that for the far-fault ground motions the ground motions for IDA in thispaper are divided into two groups -e near-fault groundmotion PGAs in Table 2 are scaled to a total of 10 seismicintensities (from 1ms2 to 10ms2) with an interval of1ms2 while the far-fault ground motion PGAs in Table 3are scaled to a total of 12 seismic intensities (from 1ms2to 12ms2) with an interval of 1ms2 A set of calculationsunder 154 earthquake ground motions is used to generatethe IDA According to the method above a series of datapoints of the engineering demand parameters μ at eachPGA level under different ground motions can be ob-tained -e discrete data points obtained at different PGAlevels in the same ground motion can be interpolated toplot the IDA curves of the BRB ductility as shown inFigure 9

It can be seen in Figure 9 that the response on the BRBductility demand of the structure under the near-faultground motions is 3sim5 times larger than that under thefar-fault ground motions which indicate that the re-sponse of the long-period structure under the near-faultearthquake is relatively larger and this phenomenonshould be considered in the structural design If theHPBRB ductility demand is determined by the responseunder the far-fault ground motions the design of theHPBRB members may be partially unsafe under a near-fault ground motion Hence the influence of near-faultground motion should be considered appropriately in thelong-period structure and its component design

A statistical analysis is conducted on the structural re-sponse under the two groups of ground motions and thethree quantiles of 84 50 and 16 can be further ob-tained in which the response of the structure under the


seismic motion is usually assumed to follow the lognormaldistribution

Φln D84 minus λD

ζD

1113888 1113889 84

Φln D50 minus λD

ζD

1113888 1113889 50

Φln D16 minus λD

ζD

1113888 1113889 16

(4)

where Φ(middot) is the cumulative distribution function of thestandard normal distribution λD is the logarithmic averagevalue ofD and ζD is the logarithmic standard deviation ofDwhich is used to describe the dispersion of D D84 D50and D16 expressed as follows

D50 exp λD( 1113857

D84 exp λD + ζD( 1113857

D16 exp λD minus ζD( 1113857

(5)

-e distribution curves of D84 D50 and D16 for theductility (μ) are shown in Figure 10

It can be found in Figure 10 that when the seismic in-tensity is relatively slight (PGAlt 2ms2 for near-faultground motions and PGAlt 4ms2 for far-fault groundmotions) the discreteness of the BRB ductility is relativelysmall as is the variations of the μ However the discretenessof the BRB ductility will arise with the increase of PGA andthis trend tends to be more obvious after PGA more than6ms2

6 IDA for the CPD

-e analysis method for the CPD of a BRB is similar to that forthe BRB ductility -e discrete data points of the CPD resultsobtained at different PGA levels in the same groundmotion canbe interpolated and the IDA curve of the BRBCPD is plotted asshown in Figure 11

It can be seen in Figure 11(a) that the discreteness ofthe response data is higher when taking the CPD as theEDP under the near-fault ground motions than that whenusing the ductility -is phenomenon is more significantfor the far-fault ground motion which is shown inFigure 11(b) However the variation tendency of the CPDcurve is consistent with that of the ductility curve and thecurves of D84 D50 and D16 for CPD are shown inFigure 12

As seen in Figure 12 when the structure is excited witha relatively slight ground motion (PGA lt 2ms2 for thenear-fault ground motions and PGA lt 4ms2 for the far-fault ones) the discreteness of the CPD is small and closeto zero indicating that only part of the BRBs will yieldwith a small plastic strain while other BRBs still remainelastic However when the PGA increased to more than2ms2 the discreteness of the BRB CPD increases and theamplitude can be seen more obvious with increasing PGAFurthermore this tendency is much more obvious in thestatistical distribution curve of the far-fault seismic re-sponse -is is because the BRB CPD is related to not onlythe BRB maximum strain but also to the cyclic number ofthe BRBs Due to the differences among the variousground motions when the frame was considered underthe aftershocks the residual deformation of the frame ineach earthquake excitation will affect the statistical resultsof the CPD

ndash6

ndash4

ndash2

0

2

4

6

8

0 20 40 60 80

Acce

lera

tion

(ms

2 )

Time (s)

Figure 4 Seismic ground motion of Northridge

00 05 10 15 200

1

2

3

4

5

6

Far-faultNear-fault

Far-fault residualNear-fault residual

Leve

l

Interstory drift ratio ()

Figure 5 Interstory and residual drift ratio along the buildingheight


7 PSHC of the PGA

As the probability of the PGA exceeding a given value A isdefined in a 50-year period according to the Seismic Ground

Motion Parameter Zonation Map of China (GB18306-2001)[35] in China it is assumed that the probability distributionof the PGA conforms to the extreme-II distribution and theprobability of the PGA exceeding the value A in 50 years is

0 3 6 9 12 150

1

2

3

4

5

6

Leve

l

Ductility

1st phase2nd phase3rd phase

(a)

Leve

l


0 3 6 9 12 150

1

2

3

4

5

6

Ductility

(b)

Figure 6 Ductility distribution of HPBRBs along the building height (a) near-fault condition (b) far-fault condition

0

2

4

6

8

10

0 10 20 30μ

PGA

(ms

2 )


(a)

0

2

4

6

8

10

0 200 400 600 800

PGA

(ms

2 )

CPD


(b)

Figure 7 Comparison of the three seismic response of a BRB (a) PGA-ductility (b) PGA-CPD

ndash15

ndash1

ndash05

0

05

1

15

ndash12 ndash8 ndash4 0 4 8

σ max

σy

εmaxεy

(a)

σ max

σy

εmaxεy

ndash15

ndash1

ndash05

0

05

1

15

ndash8 ndash4 0 4 8 12

(b)

Figure 8 Hysteretic curves of BRBs on the third floor (a) BRB on the left (b) BRB on the right


λPGA(A) 1minusFII(A) 1minus exp minusA

Ag1113888 1113889

minusk⎡⎣ ⎤⎦ (6)

where Ag is the PGA whose exceedance probability is 632in 50 years and k is a shape factor of the distribution of theground motion

According to the statistical result of Gao and Bao [36] kand Ag are 235 and 0385A10 respectively in which A10 isthe PGA whose exceedance probability in 50 years is 10namely the design basic acceleration in Chinese Code [22]and A10 is 2ms2 as suggested by the code in which theseismic fortification intensity is 8deg -e character of the sitebelongs to Type III and the design characteristic period of

0

2

4

6

8

10

0 10 20 30 40

PGA

(ms

2 )

μ

(a)

PGA

(ms

2 )

0

2

4

6

8

10

12

0 10 20 30 40μ

(b)

Figure 9 IDA curves of the BRB ductility (a) response to near-fault ground motion (b) response to far-fault ground motion

0

2

4

6

8

10

0 10 20 30 40

PGA

(ms

2 )

μ

165084

(a)

PGA

(ms

2 )

165084

0

2

4

6

8

10

12

0 10 20 30 40μ

(b)

Figure 10 Distribution statistics of BRB ductility (a) response to near-fault ground motion (b) response to far-fault ground motion

0

2

4

6

8

10

0 200 400 600 800CPD

PGA

(ms

2 )

(a)

0

2

4

6

8

10

12

0 200 400 600 800

PGA

(ms

2 )

CPD

(b)

Figure 11 IDA curves of the CPD of a BRB (a) response to near-fault ground motion (b) response to far-fault ground motion


groundmotion belongs to the first group Eq (6) can then beexpressed as

λPGA(A) 1minusFII(A) 1minus exp minus0516Aminus235

1113872 1113873 (7)

-e probability of the PGA exceeding the value A in 50years can be obtained by Eq (7) and the PSHC of the PGA ofthe model in this paper is expressed in Figure 13

-e probability density function curve of the PGA ex-ceeding a determined value A in 50 years can be obtained bytaking the derivative of Eq (7) which is expressed as Eq (8)and shown in Figure 14

dλPGA(A)

dA 0626A

minus57middot exp minus0516A

minus2351113872 1113873 (8)

8 Seismic Demand Analysis of HPBRB

81 Probabilistic Seismic Demand Curves According to theaforementioned analysis when the EDP is assumed to obeythe lognormal distribution the logarithmic standard de-viation of the EDP is a variable for the different amplitudesof ground motions To fully consider the discreteness of theground motions the numerical method is used to solve Eq(2) whose basic idea is to divide the whole integral interval[Amin Amax] into several subintervals [Ai Ai+1] i 1 2 n in which A1 Amin and An+1 Amax and n 600 in thisexample Eq (2) can be further expressed as

λEDP δj1113872 1113873 1113944n

i1P EDPgt δj PGA Ai

11138681113868111386811138681113960 1113961 middotdλPGA(A)

dA

1113868111386811138681113868111386811138681113868Ai

middot ΔAi

(9)

where ΔAi Ai+1minusAi-e specific steps are as follows

(1) Select an EDP value δj and choose the integral rangeof the PGA as [0 6]ms2 and divide the PGA rangeinto identical 600 parts

(2) Conduct an interpolation of the quantile curvesaccording to the statistical results of the IDA curves

and obtain the corresponding EDP logarithmicmeanvalue λi and the logarithmic standard deviation ζi ineach interval Ai (i 1 2 600)

(3) Calculate the conditional probability of EDPgt δjunder the given PGAAi with the assumption thatthe EDP obeys the lognormal distribution

P EDPgt δj PGA Ai

11138681113868111386811138681113960 1113961 1minusP EDPle δj PGA Ai

11138681113868111386811138681113960 1113961

1minusΦln δj minus λi

ζ i

1113888 1113889

(10)

0

2

4

6

8

10

0 200 400 600 800

PGA

(ms

2 )

CPD

165084

(a)

PGA

(ms

2 )

165084

0

2

4

6

8

10

12

0 200 400 600 800CPD

(b)

Figure 12 Distribution statistics of the BRB CPD (a) response to near-fault ground motion (b) response to far-fault ground motion

001

01

1

01 1 10

λ PG

A (A

)

PGA (ms2)

Figure 13 PSHC of the PGA

0

05

1

15

2

25

0 2 4 6

dλPG

A (A

)dA

PGA (ms2)

Figure 14 Probability distribution of PGA


where Φ(middot) is the standard normal distribution function

(4) Obtain the probability of EDPgt δj in 50 yearsconsidering the probability that the PGA is aroundthe value Ai which is the product of the shaded areasshown in Figures 15(a) and 15(b)

(5) Repeat steps (3) and (4) for different Ai and sum-marize the results to obtain the probability thatEDPgt δj in 50 years λEDP (δj)

(6) Repeat steps (1) to (5) for another EDP δj and fit theseries of discrete data points and draw the PSDC

9 PSDC of HPBRB Ductility

-e exceedance probability of the BRB ductility demand in50 years under the two types of ground motion analyses isshown in Figure 16

Combined with the PSHC the HPBRB ductility demandfor a determined exceedance probability which is demandedfor an HPBRBF under a strong earthquake and its after-shocks within the 50-year design reference period can bedetermined As is analyzed in Section 3 the theoretical valueobtained from this section should be multiplied by 2 toobtain the true HPBRB ductility demand of the actualstructure

It can be seen in Figure 16 that the HPBRB ductilitydemand of μ is 134 for the near-fault ground motions underthe condition that the exceedance probability of the BRBductility demand in 50 years is 5 while 257 for 2 and 33for 1 However the ductility demand for the far-faultground motion group is 58 91 and 114 respectivelyfor the condition in which the exceedance probability is 52 and 1 It can be seen that the HPBRB ductility demandfor the near-fault groundmotion is much larger than that forthe far-fault ground motion and the former is nearly threetimes than that of the latter

10 PSDC of HPBRB CPD

It can be determined from Figure 17 that the HPBRB CPDdemand is 190 for the near-fault ground motions as theexceedance probability in 50 years is 5 while CPD demandof 310 and 640 are needed under the condition that theexceedance probability is 2 and 1 respectively Howeverthe CPD demand for the far-fault ground motion group is60 100 and 180 respectively as the exceedance probabilityin 50 years is 5 2 and 1 It can also be seen that theHPBRB CPD demand for the near-fault ground motion ismuch larger than that for the far-fault ground motion andthe former is nearly three times than that of the latter

-e limit value for CPD demand of 200 suggested byANSIAISC [11] seems to be reasonable for the condition ofthe far-fault ground motions but it may be excessively lowfor the near-fault strong ground motions -e HPBRB CPDdemand with 98 assurance rate is much larger than thelimit value of the AISC and the demand with 99 assurancerate is more than twice than that of the AISC limit whichindicates that the CPD demand for the HPBRB is expected tobe higher in order to ensure a high low-cycle fatigue capacity

for the HPBRB under the excitation of a strong earthquakeand its aftershocks Since a significant randomness on theCPD of HPBRBs is existed the minimum threshold of theCPD demand should be determined Furthermore it isnecessary to put forward a stricter minimum threshold valuein order to satisfy the demand for HPBRBs

In conclusion the ductility and CPD demand of theHPBRB in the frame under different exceedance probabil-ities are listed in Table 4 It is suggested that the designdemand for ductility and CPD of HPBRBs should follow thecondition that the exceedance probability is 1

11 Conclusions

-e analyses of the ductility and CPD demand of an HPBRBunder a strong earthquake and its aftershocks are conductedin this paper A six-story BRBF is taken as an example anear-fault ground motion Northridge is selected to conductthe IDA on the BRBF -e seismic responses of the BRBFunder one two and three constant continuous groundmotions are compared -e IDA result indicates that theductility and CPD demand of the BRBs under the threeconstant continuous ground motions are significantly largerthan that excited by only one ground motion -is trendbecomes more significant with increasing PGA of theground motion -e CPD demand for three earthquakes isnearly 3 times than that for only one earthquake when thePGA is larger than 2ms2-e analysis result indicates that itis essential to conduct research on the EDP demand ofHPBRBs under strong earthquakes and continuous strongaftershocks

Seven near-fault ground motions and seven far-faultground motions are selected to consider the in-determinacy of ground motion and the PGA ranges from1ms2 to 10ms2 (1ms2 to 12ms2 for the far-fault mo-tions) A total of 154 ground motions are used to excite theBRBFs and the IDA curves are obtained by statisticsProbability seismic hazard analysis (PSHA) is performed toobtain the PSHC for the PGA -en the PSDCs for theductility and CPD demand for the HPBRB under threeconstant continuous strong earthquakes are obtainedthrough PSDA -ese curves indicate that the ductilitydemand and CPD demand for the HPBRB under the near-fault ground motions are much larger than those under thefar-fault ground motions and the CPD demand under thenear-fault ground motions is approximately three timeslarger than that under the far-fault ones -e analysis resultsindicate that the ductility demand for the HPBRB under thenear-fault earthquake condition is 257 when the exceedanceprobability in 50 years is 2 while it is 33 when theexceedance probability in 50 years is strictly controlled to1 the CPD demand is 310 and 640 respectively for theexceedance probability 2 and 1 in 50 years If the designdoes not require the consideration of the effect of near-faultearthquakes the demand of the ductility and CPD of a BRBcan be properly relaxed at 114 and 180 respectively for theexceedance probability in 50 years is 1 It is seen in theAISC that the minimum threshold of the CPD of BRBs is200 which may be reasonable for the structures under the


Table 4 Ductility and CPD demand of an HPBRB

EDP

Exceedance probability ()μ CPD

Near-fault Far-fault Near-fault Far-fault5 134 58 190 602 257 91 310 1001 330 114 640 180

0001

001

01

1

0 400 800 1200 1600

Exce

edan

ce p

roba

bilit

y

CPD

(a)

0001

001

01

1

0 50 100 150 200 250 300 350

Exce

edan

ce p

roba

bilit

y

CPD

(b)

Figure 17 PSDCs of the BRB CPD (a) near-fault ground motion group (b) far-fault ground motion group

0001

001

01

1

0 10 20 30 40 50 60

Exce

edan

ce p

roba

bilit

y

μmax

(a)

0001

001

01

1

0 4 8 12 16 20 24

Exce

edan

ce p

roba

bilit

y

μmax

(b)

Figure 16 PSDC of the HPBRB ductility (a) near-fault ground motion group (b) far-fault ground motion group

PGA

dλPG

A (A

)dA

Ai Ai+ 1

(a)

lnδjlnEDP

P

PGA = Ai

(b)

Figure 15 (a) Probability distribution of PGA and (b) probability distribution of EDP under PGAAi


far-fault ground motion however this value is excessivelylow for the condition of continuous strong aftershocks ofnear-fault excitations Furthermore as there is a largerandomness on the CPD capacity of HPBRBs this papersuggests that the minimum threshold of the CPD demandshould be determined by a low exceedance probability

Data Availability

-e data used to support the findings of this study are in-cluded within the article

Conflicts of Interest

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

Acknowledgments

-e authors would like to acknowledge financial supportfrom the China National Key Research and DevelopmentProgram (2016YFC0701403) the National Natural ScienceFoundation of China (51278105) and the Priority AcademicProgram Development of Jiangsu Higher Education In-stitutions (PAPD)

References

[1] G Della Corte M DrsquoAniello R Landolfo andF M Mazzolani ldquoReview of steel buckling-restrained bracesrdquoSteel Construction vol 4 no 2 pp 85ndash93 2011

[2] L Di Sarno and G Manfredi ldquoExperimental tests on full-scaleRC unretrofitted frame and retrofitted with buckling-restrained bracesrdquo Earthquake Engineering amp StructuralDynamics vol 41 no 2 pp 315ndash333 2011

[3] T Usami T Sato and A Kasai ldquoDeveloping high-performance buck-ling-restrained bracesrdquo Journal of struc-tural engineering (JSCE) vol 55A pp 719ndash729 2009 inJapanese

[4] C-L Wang T Usami and J Funayama ldquoImproving low-cycle fatigue performance of high-performance buckling-restrained braces by toe-finished methodrdquo Journal ofEarthquake Engineering vol 16 no 8 pp 1248ndash1268 2012

[5] FEMA-450 NEHRP Recommended Provisions for SeismicRegulations for New Buildings and Other Structures FederalEmergency Management Agency Washington DC USA2003

[6] R Sabelli Research on Improving the Design and Analysis ofEarthquake-Resistant Steel-Braced Frames EERI OaklandCA USA 2001

[7] M Iwata T Kato and A Wada ldquoPerformance evaluation ofbuckling-restrained braces in damage-controlled structuresrdquoin Behavior of Steel Structures in Seismic Areas pp 37ndash43STESSA San Francisco CA USA 2003

[8] T Usami A Kasai and M Kato ldquoBehavior of buckling-restrained bracemembersrdquo in Proceedings of 4th InternationalConference on STESSA 2003-Behavior of Steel Structures inSeismic Areas pp 211ndash216 Naples Italy June 2003

[9] ANSIAISC 360-10 Seismic Provisions of Structural SteelBuildings American Institute of Steel Construction ChicagoIL USA 2010

[10] L Di Sarno ldquoEffects of multiple earthquakes on inelasticstructural responserdquo Engineering Structures vol 56pp 673ndash681 2013

[11] T Usami ldquoDeveloping high-performance damage controlseismic dampersrdquo in Proceedings of the 10th Symposium onDuctile Design Method for Bridges (Special Lecture) pp 11ndash22Tokyo Japan 2007

[12] M Jia X Yu D Lu and B Lu ldquoExperimental research ofassembled buckling-restrained braces wrapped with carbon orbasalt fiberrdquo Journal of Constructional Steel Research vol 131pp 144ndash161 2017

[13] L-J Jia H Ge R Maruyama and K Shinohara ldquoDevelop-ment of a novel high-performance all-steel fish-bone shapedbuckling-restrained bracerdquo Engineering Structures vol 138pp 105ndash119 2017

[14] C-L Wang Q Chen B Zeng and S Meng ldquoA novel bracewith partial buckling restraint an experimental and numericalinvestigationrdquo Engineering Structures vol 150 pp 190ndash2022017

[15] Q Chen C-L Wang S Meng and B Zeng ldquoEffect of theunbonding materials on the mechanic behavior of all-steelbuckling-restrained bracesrdquo Engineering Structures vol 111pp 478ndash493 2016

[16] Y-L Guo J-S Zhu P Zhou and B-L Zhu ldquoA new shuttle-shaped buckling-restrained brace -eoretical study onbuckling behavior and load resistancerdquo Engineering Struc-tures vol 147 pp 223ndash241 2017

[17] Y-L Guo P-P Fu P Zhou and J-Z Tong ldquoElastic bucklingand load resistance of a single cross-arm pre-tensioned cablestayed buckling-restrained bracerdquo Engineering Structuresvol 126 pp 516ndash530 2016

[18] Y-L Guo P Zhou M Andrew Bradford Y-L Pi J-Z Tongand P-P Fu ldquo-eoretical and numerical studies of elasticbuckling and load resistance of double cross-arm pre-tensioned cable stayed buckling-restrained bracesrdquo Engi-neering Structures vol 153 pp 674ndash699 2017

[19] B-L Zhu Y-L Guo P Zhou M A Bradford and Y-L PildquoNumerical and experimental studies of corrugated-web-connected buckling-restrained bracesrdquo Engineering Struc-tures vol 134 pp 107ndash124 2017

[20] L Xie J Wu and Q Huang ldquoExperimental study on low-cycle fatigue performance of weld-free buckling-restrainedbracesrdquo Journal of Earthquake Engineering vol 22 no 8pp 1392ndash1414 2018

[21] N Hoveidae R Tremblay B Rafezy and A DavaranldquoNumerical investigation of seismic behavior of short-coreall-steel buckling restrained bracesrdquo Journal of ConstructionalSteel Research vol 114 pp 89ndash99 2015

[22] D Vafaei and R Eskandari ldquoSeismic response of megabuckling-restrained braces subjected to fling-step andforward-directivity near-fault ground motionsrdquo StructuralDesign of Tall and Special Buildings vol 24 no 9 pp 672ndash686 2014

[23] D Vamvatsikos and C A Cornell ldquoIncremental dynamicanalysisrdquo Earthquake Engineering amp Structural Dynamicsvol 31 no 3 pp 491ndash514 2002

[24] P Tothong and N Luco ldquoProbabilistic seismic demandanalysis using advanced ground motion intensity measuresrdquoEarthquake Engineering amp Structural Dynamics vol 36no 13 pp 1837ndash1860 2007

[25] Y Ding and Y Zhang ldquoDesign and seismic response of tallchevron panel buckling-restrained braced steel framesrdquoStructural Design of Tall and Special Buildings vol 22 no 14pp 1083ndash1104 2011


[26] GB 50011-2010 Code for Seismic Design of Buildings Ministryof Housing and Urban-Rural Development of the PeoplersquosRepublic of China Beijing China 2010 in Chinese

[27] S SeismoSoft ldquoA computer program for static and dynamicnonlinear analysis of framed structuresrdquo 2016 httpwwwseismosoftcom

[28] T Usami Z Lu and H Ge ldquoA seismic upgrading method forsteel arch bridges using buckling-restrained bracesrdquo Earth-quake Engineering amp Structural Dynamics vol 34 no 45pp 471ndash496 2005

[29] E Kalkan and S K Kunnath ldquoEffects of fling step and forwarddirectivity on seismic response of buildingsrdquo EarthquakeSpectra vol 22 no 2 pp 367ndash390 2006

[30] N Jayaram T Lin and J W Baker ldquoA computationallyefficient ground-motion selection algorithm for matching atarget response spectrum mean and variancerdquo EarthquakeSpectra vol 27 no 3 pp 797ndash815 2011

[31] X Chen H Ge and T Usami ldquoSeismic demand of buckling-restrained braces installed in steel arch bridges under repeatedearthquakesrdquo Journal of Earthquake and Tsunami vol 5no 2 pp 119ndash150 2011

[32] S Hu P Gardoni and L Xu ldquoStochastic procedure for thesimulation of synthetic main shock-aftershock ground mo-tion sequencesrdquo Earthquake Engineering amp Structural Dy-namics vol 47 no 11 pp 2275ndash2296 2018

[33] S Das and V K Gupta ldquoWavelet-based simulation ofspectrum-compatible aftershock accelerogramsrdquo EarthquakeEngineering amp Structural Dynamics vol 37 no 11pp 1333ndash1348 2008

[34] S Costanzo M DrsquoAniello and R Landolfo ldquoSeismic designcriteria for chevron CBFs proposals for the next EC8 (part-2)rdquo Journal of Constructional Steel Research vol 138pp 17ndash37 2017

[35] GB18306-2001 Seismic Ground Motion Parameter ZonationMap of China Bureau of Quality and Technical Supervision ofthe Peoplersquos Republic of China Beijing China 2001 inChinese

[36] X W Gao and A B Bao ldquoProbabilistic model and its sta-tistical parameters for seismic loadrdquo Earthquake Engineeringand Engineering Vibration vol 5 no 1 pp 13ndash22 1985 inChinese


International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018


Active and Passive Electronic Components

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of



Journal ofEngineeringVolume 2018

SensorsJournal of



RotatingMachinery


Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation


Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

Researchers have performed extensive studies on theBRB frame (BRBF) to measure the demand of the energydissipation capacity of the BRB and studies on the low-cyclefatigue property of BRBs in a single ground motion havebeen relatively fully developed FEMA-450 [5] comments theCPD demand of a BRB no less than 140 through experi-mental studies and nonlinear time-history analyses Sabelli[6] proposed that the demand should reach 185 based on thetime-history analyses on a three-story and a six-story BRBFIwata et al [7] suggested that the CPD should reach 292while Usami et al [8] proposed the CPD capacity no lessthan 400 ANSIAISC [9] stipulates that the CPD of the BRBshould be at least 200 to ensure the requirement of the low-cycle fatigue property

BRBs that fulfill the above CPD requirement are sup-posed to help the frames resist one strong ground motionwhile it should be replaced in time after a strong earthquaketo restore the capacity of the structures However the existedresearch about earthquake records indicate that strongearthquakes often arise with several strong aftershocks [10]and the interval between the shocks is too short to replacethe BRBs Furthermore aftershocks may cause furtherdamage accumulation which leads to the failure of the BRBand results in the collapse of the frame structure especiallyfor near-fault ground motions To resist the strong after-shocks the demand of the ductility and the CPD should beraised Usami et al [11] proposed the high-performance BRB(HPBRB) in which the special performance requirementscan be summarized as follows (1) stable hysteretic char-acteristics and high energy dissipation capacity (2) highdeformation capacity (3) high low-cycle fatigue strength (4)easy and low-cost fabrication and construction (5) highdurability and (6) no need for replacement under contin-uous strong earthquakes It is concluded that a high low-cycle fatigue capacity is needed to ensure the energy dis-sipation capacity of the BRB by selecting high-ductility steelResearchers proposed a series of novel HPBRBs which wasbased on the construction of the specimens and the materialspecimens Jia et al [12] proposed an assembled buckling-restrained brace wrapped with carbon or basalt fiber whichcould improve the restraining members and sufficientductility and energy dissipation capacity Jia et al [13]proposed a type of fish-bone BRB (FB-BRB) which could

avoid strain concentration along the length of the coremember and improve the energy dissipation capacity duringa strong earthquake or subsequent repeated aftershocksWang et al [14] proposed a novel BRB with partial bucklingrestraint in which only the edge parts of the core memberare strained and other parts are designed for visual in-spection on damage monitoring Chen et al [15] experi-mentally studied on the effect of the unbonding materials onthe mechanic behavior of all-steel BRBs and suggested thatthe unbonding materials should be applied for high-performance BRBs with a relatively long yielding segmentand thin core plate Guo et al [16ndash19] proposed a series ofhigh-performance BRBs such as shuttle-shaped BRBs [16]cross-arm pretensioned cable stayed BRBs [17 18] andcorrugated-web-connected BRBs [19] Xie et al [20] pro-posed a type of weld-free all-steel BRBs in which the coremember is fabricated absolutely in high-strength boltswithout any weld and a high CPD could be seen in the low-cycle fatigue tests Besides Hoveidae et al [21] numericallystudied the seismic behavior of short-core all-steel BRB(SCBRB) in which the relationship between the ductilitydemand and the core length was analyzed Vafaei andEskandari [22] studied on the seismic response of BRBssubjected to the fling step and forward directivity near-faultground motions and confirmed that the near-fault groundmotions imposed higher demands on the structuresHowever a unified demand for the ductility and CPD of aBRB under the action of a strong earthquake and its af-tershocks has not been unified yet

In this paper the distribution characteristics of ductilityand CPD of BRBs are determined by the incremental dy-namic analysis (IDA) [23] using three continuous equal-intensity earthquake ground motions to consider the effectof an earthquake and its aftershocks As it is essential toanalyze the randomness of the response by the probabilitymethod the seismic demand of the ductility and CPD of theBRB are concluded through the probability seismic demandanalysis (PSDA) [24] -e seismic demand index of μ andCPD of the HPBRB is also suggested in this paper whichcould be used as a threshold value criterion formanufacturing HPBRB

2 Application of PSDA in HPBRB Design

According to the theory proposed by the PEER the seismicresponse of a structure is described as the engineering de-mand parameter (EDP) and the peak ground acceleration(PGA) of the ground motion is chosen as the intensitymeasure (IM) in this paper while the considered period oftime is determined as 50 years according to the designreference period of the common engineering structures inChina When the probabilistic seismic hazard curve (PSHC)of the PGA under the condition of a given site is combinedwith the probability distribution of the EDP under the givenPGA the probability of the EDP of the structure exceeding acertain value in 50 years can be obtained

-e probabilistic seismic demand λEDP (δ) which is theprobability of the EDP exceeding a certain value δ in 50years can be divided into two parts one part is the

Figure 1 A BRB frame (a library in the USA)



λEDP(δ) 1113946A


1113868111386811138681113868 (2)


















KBRB 1

1Ki( 1113857 + 2Kcon( 1113857 + 2Ktr( 1113857( 1113857 (3)







8000 times 3 = 24000

3900

0times

6=

2340

00







0 1 2 3 4 5 60

10

20


T (s)

S a (m

s2 )



















Φln D84 minus λD

ζD

1113888 1113889 84

Φln D50 minus λD

ζD

1113888 1113889 50

Φln D16 minus λD

ζD

1113888 1113889 16

(4)


D50 exp λD( 1113857

D84 exp λD + ζD( 1113857


(5)



6 IDA for the CPD




ndash6

ndash4

ndash2

0

2

4

6

8

0 20 40 60 80

Acce

lera

tion

(ms

2 )

Time (s)


00 05 10 15 200

1

2

3

4

5

6

Far-faultNear-fault


Leve

l




7 PSHC of the PGA



0 3 6 9 12 150

1

2

3

4

5

6

Leve

l

Ductility


(a)

Leve

l


0 3 6 9 12 150

1

2

3

4

5

6

Ductility

(b)


0

2

4

6

8

10

0 10 20 30μ

PGA

(ms

2 )


(a)

0

2

4

6

8

10

0 200 400 600 800

PGA

(ms

2 )

CPD


(b)


ndash15

ndash1

ndash05

0

05

1

15


σ max

σy

εmaxεy

(a)

σ max

σy

εmaxεy

ndash15

ndash1

ndash05

0

05

1

15


(b)




Ag1113888 1113889




0

2

4

6

8

10

0 10 20 30 40

PGA

(ms

2 )

μ

(a)

PGA

(ms

2 )

0

2

4

6

8

10

12

0 10 20 30 40μ

(b)


0

2

4

6

8

10

0 10 20 30 40

PGA

(ms

2 )

μ

165084

(a)

PGA

(ms

2 )

165084

0

2

4

6

8

10

12

0 10 20 30 40μ

(b)


0

2

4

6

8

10

0 200 400 600 800CPD

PGA

(ms

2 )

(a)

0

2

4

6

8

10

12

0 200 400 600 800

PGA

(ms

2 )

CPD

(b)





1113872 1113873 (7)



dλPGA(A)

dA 0626A


minus2351113872 1113873 (8)



λEDP δj1113872 1113873 1113944n


11138681113868111386811138681113960 1113961 middotdλPGA(A)

dA

1113868111386811138681113868111386811138681113868Ai

middot ΔAi

(9)






P EDPgt δj PGA Ai


11138681113868111386811138681113960 1113961


ζ i

1113888 1113889

(10)

0

2

4

6

8

10

0 200 400 600 800

PGA

(ms

2 )

CPD

165084

(a)

PGA

(ms

2 )

165084

0

2

4

6

8

10

12

0 200 400 600 800CPD

(b)


001

01

1

01 1 10

λ PG

A (A

)

PGA (ms2)


0

05

1

15

2

25

0 2 4 6

dλPG

A (A

)dA

PGA (ms2)
















11 Conclusions





EDP



0001

001

01

1

0 400 800 1200 1600

Exce

edan

ce p

roba

bilit

y

CPD

(a)

0001

001

01

1

0 50 100 150 200 250 300 350

Exce

edan

ce p

roba

bilit

y

CPD

(b)


0001

001

01

1

0 10 20 30 40 50 60

Exce

edan

ce p

roba

bilit

y

μmax

(a)

0001

001

01

1

0 4 8 12 16 20 24

Exce

edan

ce p

roba

bilit

y

μmax

(b)


PGA

dλPG

A (A

)dA

Ai Ai+ 1

(a)

lnδjlnEDP

P

PGA = Ai

(b)




Data Availability




Acknowledgments


References









































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



λEDP(δ) 1113946A


1113868111386811138681113868 (2)


















KBRB 1

1Ki( 1113857 + 2Kcon( 1113857 + 2Ktr( 1113857( 1113857 (3)







8000 times 3 = 24000

3900

0times

6=

2340

00







0 1 2 3 4 5 60

10

20


T (s)

S a (m

s2 )



















Φln D84 minus λD

ζD

1113888 1113889 84

Φln D50 minus λD

ζD

1113888 1113889 50

Φln D16 minus λD

ζD

1113888 1113889 16

(4)


D50 exp λD( 1113857

D84 exp λD + ζD( 1113857


(5)



6 IDA for the CPD




ndash6

ndash4

ndash2

0

2

4

6

8

0 20 40 60 80

Acce

lera

tion

(ms

2 )

Time (s)


00 05 10 15 200

1

2

3

4

5

6

Far-faultNear-fault


Leve

l




7 PSHC of the PGA



0 3 6 9 12 150

1

2

3

4

5

6

Leve

l

Ductility


(a)

Leve

l


0 3 6 9 12 150

1

2

3

4

5

6

Ductility

(b)


0

2

4

6

8

10

0 10 20 30μ

PGA

(ms

2 )


(a)

0

2

4

6

8

10

0 200 400 600 800

PGA

(ms

2 )

CPD


(b)


ndash15

ndash1

ndash05

0

05

1

15


σ max

σy

εmaxεy

(a)

σ max

σy

εmaxεy

ndash15

ndash1

ndash05

0

05

1

15


(b)




Ag1113888 1113889




0

2

4

6

8

10

0 10 20 30 40

PGA

(ms

2 )

μ

(a)

PGA

(ms

2 )

0

2

4

6

8

10

12

0 10 20 30 40μ

(b)


0

2

4

6

8

10

0 10 20 30 40

PGA

(ms

2 )

μ

165084

(a)

PGA

(ms

2 )

165084

0

2

4

6

8

10

12

0 10 20 30 40μ

(b)


0

2

4

6

8

10

0 200 400 600 800CPD

PGA

(ms

2 )

(a)

0

2

4

6

8

10

12

0 200 400 600 800

PGA

(ms

2 )

CPD

(b)





1113872 1113873 (7)



dλPGA(A)

dA 0626A


minus2351113872 1113873 (8)



λEDP δj1113872 1113873 1113944n


11138681113868111386811138681113960 1113961 middotdλPGA(A)

dA

1113868111386811138681113868111386811138681113868Ai

middot ΔAi

(9)






P EDPgt δj PGA Ai


11138681113868111386811138681113960 1113961


ζ i

1113888 1113889

(10)

0

2

4

6

8

10

0 200 400 600 800

PGA

(ms

2 )

CPD

165084

(a)

PGA

(ms

2 )

165084

0

2

4

6

8

10

12

0 200 400 600 800CPD

(b)


001

01

1

01 1 10

λ PG

A (A

)

PGA (ms2)


0

05

1

15

2

25

0 2 4 6

dλPG

A (A

)dA

PGA (ms2)
















11 Conclusions





EDP



0001

001

01

1

0 400 800 1200 1600

Exce

edan

ce p

roba

bilit

y

CPD

(a)

0001

001

01

1

0 50 100 150 200 250 300 350

Exce

edan

ce p

roba

bilit

y

CPD

(b)


0001

001

01

1

0 10 20 30 40 50 60

Exce

edan

ce p

roba

bilit

y

μmax

(a)

0001

001

01

1

0 4 8 12 16 20 24

Exce

edan

ce p

roba

bilit

y

μmax

(b)


PGA

dλPG

A (A

)dA

Ai Ai+ 1

(a)

lnδjlnEDP

P

PGA = Ai

(b)




Data Availability




Acknowledgments


References









































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




KBRB 1

1Ki( 1113857 + 2Kcon( 1113857 + 2Ktr( 1113857( 1113857 (3)







8000 times 3 = 24000

3900

0times

6=

2340

00







0 1 2 3 4 5 60

10

20


T (s)

S a (m

s2 )



















Φln D84 minus λD

ζD

1113888 1113889 84

Φln D50 minus λD

ζD

1113888 1113889 50

Φln D16 minus λD

ζD

1113888 1113889 16

(4)


D50 exp λD( 1113857

D84 exp λD + ζD( 1113857


(5)



6 IDA for the CPD




ndash6

ndash4

ndash2

0

2

4

6

8

0 20 40 60 80

Acce

lera

tion

(ms

2 )

Time (s)


00 05 10 15 200

1

2

3

4

5

6

Far-faultNear-fault


Leve

l




7 PSHC of the PGA



0 3 6 9 12 150

1

2

3

4

5

6

Leve

l

Ductility


(a)

Leve

l


0 3 6 9 12 150

1

2

3

4

5

6

Ductility

(b)


0

2

4

6

8

10

0 10 20 30μ

PGA

(ms

2 )


(a)

0

2

4

6

8

10

0 200 400 600 800

PGA

(ms

2 )

CPD


(b)


ndash15

ndash1

ndash05

0

05

1

15


σ max

σy

εmaxεy

(a)

σ max

σy

εmaxεy

ndash15

ndash1

ndash05

0

05

1

15


(b)




Ag1113888 1113889




0

2

4

6

8

10

0 10 20 30 40

PGA

(ms

2 )

μ

(a)

PGA

(ms

2 )

0

2

4

6

8

10

12

0 10 20 30 40μ

(b)


0

2

4

6

8

10

0 10 20 30 40

PGA

(ms

2 )

μ

165084

(a)

PGA

(ms

2 )

165084

0

2

4

6

8

10

12

0 10 20 30 40μ

(b)


0

2

4

6

8

10

0 200 400 600 800CPD

PGA

(ms

2 )

(a)

0

2

4

6

8

10

12

0 200 400 600 800

PGA

(ms

2 )

CPD

(b)





1113872 1113873 (7)



dλPGA(A)

dA 0626A


minus2351113872 1113873 (8)



λEDP δj1113872 1113873 1113944n


11138681113868111386811138681113960 1113961 middotdλPGA(A)

dA

1113868111386811138681113868111386811138681113868Ai

middot ΔAi

(9)






P EDPgt δj PGA Ai


11138681113868111386811138681113960 1113961


ζ i

1113888 1113889

(10)

0

2

4

6

8

10

0 200 400 600 800

PGA

(ms

2 )

CPD

165084

(a)

PGA

(ms

2 )

165084

0

2

4

6

8

10

12

0 200 400 600 800CPD

(b)


001

01

1

01 1 10

λ PG

A (A

)

PGA (ms2)


0

05

1

15

2

25

0 2 4 6

dλPG

A (A

)dA

PGA (ms2)
















11 Conclusions





EDP



0001

001

01

1

0 400 800 1200 1600

Exce

edan

ce p

roba

bilit

y

CPD

(a)

0001

001

01

1

0 50 100 150 200 250 300 350

Exce

edan

ce p

roba

bilit

y

CPD

(b)


0001

001

01

1

0 10 20 30 40 50 60

Exce

edan

ce p

roba

bilit

y

μmax

(a)

0001

001

01

1

0 4 8 12 16 20 24

Exce

edan

ce p

roba

bilit

y

μmax

(b)


PGA

dλPG

A (A

)dA

Ai Ai+ 1

(a)

lnδjlnEDP

P

PGA = Ai

(b)




Data Availability




Acknowledgments


References









































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia






0 1 2 3 4 5 60

10

20


T (s)

S a (m

s2 )



















Φln D84 minus λD

ζD

1113888 1113889 84

Φln D50 minus λD

ζD

1113888 1113889 50

Φln D16 minus λD

ζD

1113888 1113889 16

(4)


D50 exp λD( 1113857

D84 exp λD + ζD( 1113857


(5)



6 IDA for the CPD




ndash6

ndash4

ndash2

0

2

4

6

8

0 20 40 60 80

Acce

lera

tion

(ms

2 )

Time (s)


00 05 10 15 200

1

2

3

4

5

6

Far-faultNear-fault


Leve

l




7 PSHC of the PGA



0 3 6 9 12 150

1

2

3

4

5

6

Leve

l

Ductility


(a)

Leve

l


0 3 6 9 12 150

1

2

3

4

5

6

Ductility

(b)


0

2

4

6

8

10

0 10 20 30μ

PGA

(ms

2 )


(a)

0

2

4

6

8

10

0 200 400 600 800

PGA

(ms

2 )

CPD


(b)


ndash15

ndash1

ndash05

0

05

1

15


σ max

σy

εmaxεy

(a)

σ max

σy

εmaxεy

ndash15

ndash1

ndash05

0

05

1

15


(b)




Ag1113888 1113889




0

2

4

6

8

10

0 10 20 30 40

PGA

(ms

2 )

μ

(a)

PGA

(ms

2 )

0

2

4

6

8

10

12

0 10 20 30 40μ

(b)


0

2

4

6

8

10

0 10 20 30 40

PGA

(ms

2 )

μ

165084

(a)

PGA

(ms

2 )

165084

0

2

4

6

8

10

12

0 10 20 30 40μ

(b)


0

2

4

6

8

10

0 200 400 600 800CPD

PGA

(ms

2 )

(a)

0

2

4

6

8

10

12

0 200 400 600 800

PGA

(ms

2 )

CPD

(b)





1113872 1113873 (7)



dλPGA(A)

dA 0626A


minus2351113872 1113873 (8)



λEDP δj1113872 1113873 1113944n


11138681113868111386811138681113960 1113961 middotdλPGA(A)

dA

1113868111386811138681113868111386811138681113868Ai

middot ΔAi

(9)






P EDPgt δj PGA Ai


11138681113868111386811138681113960 1113961


ζ i

1113888 1113889

(10)

0

2

4

6

8

10

0 200 400 600 800

PGA

(ms

2 )

CPD

165084

(a)

PGA

(ms

2 )

165084

0

2

4

6

8

10

12

0 200 400 600 800CPD

(b)


001

01

1

01 1 10

λ PG

A (A

)

PGA (ms2)


0

05

1

15

2

25

0 2 4 6

dλPG

A (A

)dA

PGA (ms2)
















11 Conclusions





EDP



0001

001

01

1

0 400 800 1200 1600

Exce

edan

ce p

roba

bilit

y

CPD

(a)

0001

001

01

1

0 50 100 150 200 250 300 350

Exce

edan

ce p

roba

bilit

y

CPD

(b)


0001

001

01

1

0 10 20 30 40 50 60

Exce

edan

ce p

roba

bilit

y

μmax

(a)

0001

001

01

1

0 4 8 12 16 20 24

Exce

edan

ce p

roba

bilit

y

μmax

(b)


PGA

dλPG

A (A

)dA

Ai Ai+ 1

(a)

lnδjlnEDP

P

PGA = Ai

(b)




Data Availability




Acknowledgments


References









































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia














Φln D84 minus λD

ζD

1113888 1113889 84

Φln D50 minus λD

ζD

1113888 1113889 50

Φln D16 minus λD

ζD

1113888 1113889 16

(4)


D50 exp λD( 1113857

D84 exp λD + ζD( 1113857


(5)



6 IDA for the CPD




ndash6

ndash4

ndash2

0

2

4

6

8

0 20 40 60 80

Acce

lera

tion

(ms

2 )

Time (s)


00 05 10 15 200

1

2

3

4

5

6

Far-faultNear-fault


Leve

l




7 PSHC of the PGA



0 3 6 9 12 150

1

2

3

4

5

6

Leve

l

Ductility


(a)

Leve

l


0 3 6 9 12 150

1

2

3

4

5

6

Ductility

(b)


0

2

4

6

8

10

0 10 20 30μ

PGA

(ms

2 )


(a)

0

2

4

6

8

10

0 200 400 600 800

PGA

(ms

2 )

CPD


(b)


ndash15

ndash1

ndash05

0

05

1

15


σ max

σy

εmaxεy

(a)

σ max

σy

εmaxεy

ndash15

ndash1

ndash05

0

05

1

15


(b)




Ag1113888 1113889




0

2

4

6

8

10

0 10 20 30 40

PGA

(ms

2 )

μ

(a)

PGA

(ms

2 )

0

2

4

6

8

10

12

0 10 20 30 40μ

(b)


0

2

4

6

8

10

0 10 20 30 40

PGA

(ms

2 )

μ

165084

(a)

PGA

(ms

2 )

165084

0

2

4

6

8

10

12

0 10 20 30 40μ

(b)


0

2

4

6

8

10

0 200 400 600 800CPD

PGA

(ms

2 )

(a)

0

2

4

6

8

10

12

0 200 400 600 800

PGA

(ms

2 )

CPD

(b)





1113872 1113873 (7)



dλPGA(A)

dA 0626A


minus2351113872 1113873 (8)



λEDP δj1113872 1113873 1113944n


11138681113868111386811138681113960 1113961 middotdλPGA(A)

dA

1113868111386811138681113868111386811138681113868Ai

middot ΔAi

(9)






P EDPgt δj PGA Ai


11138681113868111386811138681113960 1113961


ζ i

1113888 1113889

(10)

0

2

4

6

8

10

0 200 400 600 800

PGA

(ms

2 )

CPD

165084

(a)

PGA

(ms

2 )

165084

0

2

4

6

8

10

12

0 200 400 600 800CPD

(b)


001

01

1

01 1 10

λ PG

A (A

)

PGA (ms2)


0

05

1

15

2

25

0 2 4 6

dλPG

A (A

)dA

PGA (ms2)
















11 Conclusions





EDP



0001

001

01

1

0 400 800 1200 1600

Exce

edan

ce p

roba

bilit

y

CPD

(a)

0001

001

01

1

0 50 100 150 200 250 300 350

Exce

edan

ce p

roba

bilit

y

CPD

(b)


0001

001

01

1

0 10 20 30 40 50 60

Exce

edan

ce p

roba

bilit

y

μmax

(a)

0001

001

01

1

0 4 8 12 16 20 24

Exce

edan

ce p

roba

bilit

y

μmax

(b)


PGA

dλPG

A (A

)dA

Ai Ai+ 1

(a)

lnδjlnEDP

P

PGA = Ai

(b)




Data Availability




Acknowledgments


References









































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


7 PSHC of the PGA



0 3 6 9 12 150

1

2

3

4

5

6

Leve

l

Ductility


(a)

Leve

l


0 3 6 9 12 150

1

2

3

4

5

6

Ductility

(b)


0

2

4

6

8

10

0 10 20 30μ

PGA

(ms

2 )


(a)

0

2

4

6

8

10

0 200 400 600 800

PGA

(ms

2 )

CPD


(b)


ndash15

ndash1

ndash05

0

05

1

15


σ max

σy

εmaxεy

(a)

σ max

σy

εmaxεy

ndash15

ndash1

ndash05

0

05

1

15


(b)




Ag1113888 1113889




0

2

4

6

8

10

0 10 20 30 40

PGA

(ms

2 )

μ

(a)

PGA

(ms

2 )

0

2

4

6

8

10

12

0 10 20 30 40μ

(b)


0

2

4

6

8

10

0 10 20 30 40

PGA

(ms

2 )

μ

165084

(a)

PGA

(ms

2 )

165084

0

2

4

6

8

10

12

0 10 20 30 40μ

(b)


0

2

4

6

8

10

0 200 400 600 800CPD

PGA

(ms

2 )

(a)

0

2

4

6

8

10

12

0 200 400 600 800

PGA

(ms

2 )

CPD

(b)





1113872 1113873 (7)



dλPGA(A)

dA 0626A


minus2351113872 1113873 (8)



λEDP δj1113872 1113873 1113944n


11138681113868111386811138681113960 1113961 middotdλPGA(A)

dA

1113868111386811138681113868111386811138681113868Ai

middot ΔAi

(9)






P EDPgt δj PGA Ai


11138681113868111386811138681113960 1113961


ζ i

1113888 1113889

(10)

0

2

4

6

8

10

0 200 400 600 800

PGA

(ms

2 )

CPD

165084

(a)

PGA

(ms

2 )

165084

0

2

4

6

8

10

12

0 200 400 600 800CPD

(b)


001

01

1

01 1 10

λ PG

A (A

)

PGA (ms2)


0

05

1

15

2

25

0 2 4 6

dλPG

A (A

)dA

PGA (ms2)
















11 Conclusions





EDP



0001

001

01

1

0 400 800 1200 1600

Exce

edan

ce p

roba

bilit

y

CPD

(a)

0001

001

01

1

0 50 100 150 200 250 300 350

Exce

edan

ce p

roba

bilit

y

CPD

(b)


0001

001

01

1

0 10 20 30 40 50 60

Exce

edan

ce p

roba

bilit

y

μmax

(a)

0001

001

01

1

0 4 8 12 16 20 24

Exce

edan

ce p

roba

bilit

y

μmax

(b)


PGA

dλPG

A (A

)dA

Ai Ai+ 1

(a)

lnδjlnEDP

P

PGA = Ai

(b)




Data Availability




Acknowledgments


References









































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



Ag1113888 1113889




0

2

4

6

8

10

0 10 20 30 40

PGA

(ms

2 )

μ

(a)

PGA

(ms

2 )

0

2

4

6

8

10

12

0 10 20 30 40μ

(b)


0

2

4

6

8

10

0 10 20 30 40

PGA

(ms

2 )

μ

165084

(a)

PGA

(ms

2 )

165084

0

2

4

6

8

10

12

0 10 20 30 40μ

(b)


0

2

4

6

8

10

0 200 400 600 800CPD

PGA

(ms

2 )

(a)

0

2

4

6

8

10

12

0 200 400 600 800

PGA

(ms

2 )

CPD

(b)





1113872 1113873 (7)



dλPGA(A)

dA 0626A


minus2351113872 1113873 (8)



λEDP δj1113872 1113873 1113944n


11138681113868111386811138681113960 1113961 middotdλPGA(A)

dA

1113868111386811138681113868111386811138681113868Ai

middot ΔAi

(9)






P EDPgt δj PGA Ai


11138681113868111386811138681113960 1113961


ζ i

1113888 1113889

(10)

0

2

4

6

8

10

0 200 400 600 800

PGA

(ms

2 )

CPD

165084

(a)

PGA

(ms

2 )

165084

0

2

4

6

8

10

12

0 200 400 600 800CPD

(b)


001

01

1

01 1 10

λ PG

A (A

)

PGA (ms2)


0

05

1

15

2

25

0 2 4 6

dλPG

A (A

)dA

PGA (ms2)
















11 Conclusions





EDP



0001

001

01

1

0 400 800 1200 1600

Exce

edan

ce p

roba

bilit

y

CPD

(a)

0001

001

01

1

0 50 100 150 200 250 300 350

Exce

edan

ce p

roba

bilit

y

CPD

(b)


0001

001

01

1

0 10 20 30 40 50 60

Exce

edan

ce p

roba

bilit

y

μmax

(a)

0001

001

01

1

0 4 8 12 16 20 24

Exce

edan

ce p

roba

bilit

y

μmax

(b)


PGA

dλPG

A (A

)dA

Ai Ai+ 1

(a)

lnδjlnEDP

P

PGA = Ai

(b)




Data Availability




Acknowledgments


References









































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




1113872 1113873 (7)



dλPGA(A)

dA 0626A


minus2351113872 1113873 (8)



λEDP δj1113872 1113873 1113944n


11138681113868111386811138681113960 1113961 middotdλPGA(A)

dA

1113868111386811138681113868111386811138681113868Ai

middot ΔAi

(9)






P EDPgt δj PGA Ai


11138681113868111386811138681113960 1113961


ζ i

1113888 1113889

(10)

0

2

4

6

8

10

0 200 400 600 800

PGA

(ms

2 )

CPD

165084

(a)

PGA

(ms

2 )

165084

0

2

4

6

8

10

12

0 200 400 600 800CPD

(b)


001

01

1

01 1 10

λ PG

A (A

)

PGA (ms2)


0

05

1

15

2

25

0 2 4 6

dλPG

A (A

)dA

PGA (ms2)
















11 Conclusions





EDP



0001

001

01

1

0 400 800 1200 1600

Exce

edan

ce p

roba

bilit

y

CPD

(a)

0001

001

01

1

0 50 100 150 200 250 300 350

Exce

edan

ce p

roba

bilit

y

CPD

(b)


0001

001

01

1

0 10 20 30 40 50 60

Exce

edan

ce p

roba

bilit

y

μmax

(a)

0001

001

01

1

0 4 8 12 16 20 24

Exce

edan

ce p

roba

bilit

y

μmax

(b)


PGA

dλPG

A (A

)dA

Ai Ai+ 1

(a)

lnδjlnEDP

P

PGA = Ai

(b)




Data Availability




Acknowledgments


References









































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia















11 Conclusions





EDP



0001

001

01

1

0 400 800 1200 1600

Exce

edan

ce p

roba

bilit

y

CPD

(a)

0001

001

01

1

0 50 100 150 200 250 300 350

Exce

edan

ce p

roba

bilit

y

CPD

(b)


0001

001

01

1

0 10 20 30 40 50 60

Exce

edan

ce p

roba

bilit

y

μmax

(a)

0001

001

01

1

0 4 8 12 16 20 24

Exce

edan

ce p

roba

bilit

y

μmax

(b)


PGA

dλPG

A (A

)dA

Ai Ai+ 1

(a)

lnδjlnEDP

P

PGA = Ai

(b)




Data Availability




Acknowledgments


References









































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



EDP



0001

001

01

1

0 400 800 1200 1600

Exce

edan

ce p

roba

bilit

y

CPD

(a)

0001

001

01

1

0 50 100 150 200 250 300 350

Exce

edan

ce p

roba

bilit

y

CPD

(b)


0001

001

01

1

0 10 20 30 40 50 60

Exce

edan

ce p

roba

bilit

y

μmax

(a)

0001

001

01

1

0 4 8 12 16 20 24

Exce

edan

ce p

roba

bilit

y

μmax

(b)


PGA

dλPG

A (A

)dA

Ai Ai+ 1

(a)

lnδjlnEDP

P

PGA = Ai

(b)




Data Availability




Acknowledgments


References









































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




Acknowledgments


References









































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


Analysis of the Seismic Demand of High-Performance...

Documents

Transcript of Analysis of the Seismic Demand of High-Performance...