EnhancedSeismicStructuralReliabilityonReinforcedConcrete ... · 2021. 2. 9. · mechanism, the...

Research ArticleEnhanced Seismic Structural Reliability on Reinforced ConcreteBuildings by Using Buckling Restrained Braces

Victor Baca1 Juan Bojorquez 1 Eden Bojorquez 1 Herian Leyva1

Alfredo Reyes-Salazar1 Sonia E Ruiz 2 Antonio Formisano3 Leonardo Palemon4

Robespierre Chavez1 and Manuel Barraza 5

1Facultad de Ingenierıa Universidad Autonoma de Sinaloa Culiacan 80040 Mexico2Instituto de Ingenierıa Universidad Nacional Autonoma de Mexico Mexico 04510 Mexico3Department of Structures for Engineering and Architecture University of Naples Naples 80125 Italy4Departamento de Ingenierıa Civil Universidad Autonoma del Carmen Cd del Carmen 24180 Mexico5Facultad de Ingenierıa Arquitectura y Disentildeo Universidad Autonoma de Baja California Ensenada 22860 Mexico

Correspondence should be addressed to Juan Bojorquez jbm_squall_cloudhotmailcom

Received 5 August 2020 Revised 24 December 2020 Accepted 28 January 2021 Published 9 February 2021

Academic Editor Francisco Beltran-Carbajal

Copyright copy 2021 Victor Baca et al is is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

e control of vibrations and damage in traditional reinforced concrete (RC) buildings under earthquakes is a difficult task Itrequires the use of innovative devices to enhance the seismic behavior of concrete buildings In this paper we design RC buildingswith buckling restrained braces (BRBs) to achieve this objective For this aim three traditional RC framed structures with 3 6 and9 story levels are designed by using the well-known technique nondominated sorting genetic algorithm (NSGA-II) in order toreduce the cost and maximize the seismic performance en equivalent RC buildings are designed but including bucklingrestrained braces Both structural systems are subjected to several narrow-band ground motions recorded at soft soil sites ofMexico City scaled at different levels of intensities in terms of the spectral acceleration at first mode of vibration of the structureSa(T1)en incremental dynamic analysis seismic fragility and structural reliability in terms of themaximum interstory drift arecomputed for all the buildings For the three selected structures and the equivalent models with BRBs it is concluded that theannual rate of exceedance is considerably reduced when BRBs are incorporated For this reason the structural reliability of the RCbuildings with BRBs has a better behavior in comparison with the traditional reinforced concrete buildings e use of BRBs is agood option to improve strength and seismic behavior and hence the structural reliability of RC buildings subjected to strongearthquake ground motions

1 Introduction

In the past few years an extensive amount of buildings hassuffered damage due to medium and large earthquakesStructural systems have evolved in order to reduce seismicdamage Nowadays one of the most used structural systems isthat based on reinforced concrete frames Reinforced concretebuildings have been frequently used nevertheless the maindisadvantage of them is the difficulty to be repaired after theoccurrence of an earthquake Furthermore RC structures lo-cated on seismic zones usually are subjected to large peakinterstory drift displacements produced by the lateral loads

Since the seismic design regulations recommend the control ofmaximum interstory drift as the main engineering demandparameter in order to achieve a good structural performance asKrawinkler and Gupta suggest [1] it is necessary to reduce thepeak drift demands in RC buildings e displacement ontraditional concrete buildings can be reduced by means ofconcentrically braces e objective of the braces in structuralframes is to increase the stiffness and to reduce the lateraldisplacements due to earthquakes [2 3] In spite of the ad-vantages of typical braced frames several studies have high-lighted that frequent damage has been observed on this type ofstructural system in past earthquakes such as the 1985 Mexico

HindawiShock and VibrationVolume 2021 Article ID 8816552 12 pageshttpsdoiorg10115520218816552

earthquake 1989 Loma Prieta earthquake 1994 Northridgeearthquake and 1995 Hyogo-ken Nanbu earthquake amongothers [4ndash9] as it was indicated by Sabelli et al [10] Inparticular the unsymmetrical properties in tension andcompression and the large strength deterioration in com-pression reduce considerably the performance of the braces Inorder to have the same mechanical properties in tension andcompression of the braces a new type of brace named bucklingrestrained brace which consists of a ductility steel core that isforced to have similar yield in tension and compression byrestrained the buckling has been suggested [11ndash17] Severalexperimental tests have demonstrated that the cyclic behaviorof the BRBs is stable and almost bilinear in particular Palazzoet al [18] concluded that it is feasible to design buckling re-strained braces that are efficient robust virtually maintenance-free durable reasonably cheap easy to produce and made ofbasic and easily replaceable materials For this reason althoughthe seismic response of reinforced concrete frames withbuckling restrained braces has been studied usually 2D systemsare considered for the dynamic analyses moreover the ad-vantages of BRBs on RC buildings in terms of structuralfragility and reliability are not commonly assessed Motivatedby the need to observe the advantages of BRBs in the seismicperformance in terms of structural fragility and reliability of 3Dreinforced concrete framed buildings in the present study theseismic performance of 3DRC buildings and equivalent 3DRCstructures with BRBs is assessed For the purpose of this workthree structural RC buildings with 3 6 and 9 stories aredesigned according to the Mexico City Seismic Design Pro-visions (MCSDP) [19] In addition three equivalent concretebuildings with BRBs are designed It is important to say that forthe seismic design of all the buildings the NSGA-II approach[20 21] is used in order to reduce the cost and increase thestructural capacity in accordance with the MCSDP e 3Dframed buildings in both type of structural systems are sub-jected to 30 groundmotion records obtained from soft soil sitesof Mexico City scaled at different spectral accelerations at firstmode of vibration of the structureus a total of 3600 seismicanalyses have been performed e numerical results of theanalyses suggest that the seismic performance of reinforcedconcrete buildings with buckling restrained braces is superiorto that of the structural behavior of traditional buildings in-dicating the advantages of this structural system For thisreason BRBs can increase considerably the structural reliabilitywhen they are incorporated in reinforced concrete framesMoreover the damage in the buildings with BRBs is con-centrated in the braces which can be replaced after the oc-currence of an earthquake It is important to say that althoughsoil structure interaction was not taken into account noticethat similar conclusions are expected because this effect in-creases the period of vibration of a building [22 23]

2 Buckling Restrained Braces

e innovative buckling restrained braces are devices used asseismic energy absorption elements with the aim of reducingthe damage in a structure under strong earthquake eventsey consists of a steel section enclosed in a tubular or cy-lindrical case filled with concrete or mortar Figure 1 shows

the topology and components of this brace [11 24] whichmakes it possible to take advantage of the full capacity of steelcore and to obtain a symmetrical and highly stable cyclicbehavior in comparison with conventional braces In addi-tion BRBs can be easily replaced in case of damage

Different experimental studies on this type of deviceshave been carried out Teran-Gilmore and Virto-Cambray[25] performed cyclic test at multiple BRBs using circulartube or angle steel cores concluding that both developedstable hysteretic behavior and similar resistance to bothcompression and tension Khampanit et al [2] proposed anenergy-based design methodology by comparing experi-mental studies between a reinforced concrete bare frame anda reinforced concrete braced frame Guerrero et al [26]carried out a comparative study between two 5-story steelframes with and without BRB at 110 scale factor undernarrow-band seismic records obtained in Mexico City eresults demonstrated a considerable decrease in terms ofdisplacements maximum interstory drift and floor accel-erations for braced frames as well as an increase of stiffnessand damping of the system Similarly studies have beencarried out on newmethods to adequately model this type ofbraces Rahnavard et al [27] compared hysteresis curves ofexperimental studies with a simple numerical model in orderto avoid large computational time for the analyses In ad-dition they have used this type of brace for retrofit orstrengthening of concrete buildings [28] In this study aconsiderable difference is observed in lateral resistancecyclic behavior and energy dissipation capacity e lateralstiffness that a BRB brings to a floor can be obtained re-gardless of the core area as shown in the following equation[29]

KL

(AL)

E cos2 θc + η(1 minus c)

E cos2 θ

LRF

(1)

where L is the total length of the brace E is the elasticmodulus θ is the angle of inclination Lc is the length ofelement without connections c is the relation between Lcand L η is the relation between average axial strains ofoutside and inside the core and LRF is a factor that considersthe region of higher axial stiffness at the ends of the braceTeran-Gilmore and Ruiz-Garcıa [30] determined that underthe consideration of Lc it is equal to half value of L and thatthe average area outside the core is three times the area ofcore LRF is equal to 0667 erefore the actual stiffness thatBRB brings to the system depends on the difference betweenthe core and connection areas rough this type ofmechanism the reinforced concrete braced and unbracedbuildings were designed using the NSGA-II approach asexplained below Finally the seismic reliability when bothstructural systems are subjected to narrow-band motionsrecorded in Mexico City is compared

3 Methodology

31 Seismic Design of the RC Models Using NSGA-IICurrently there are a large number of studies on the ap-plication of optimization techniques for structural design

2 Shock and Vibration

especially using genetic algorithms [31] e aim of thisapproach is to generate a random population of solutionsclassifying them according to their goodness as a solution tothe problem using a fitness function e closest solutionsthat satisfy the problem are used to obtain new solutionsthrough a crossover procedure maintaining the best char-acteristics of each solution is procedure is repeated up tothe desired cycles or generation number and finally it is ableto find optimal results A typical genetic algorithm is basedon the following parameters

(1) Fitness function it consists of creating one or morefunctions that adequately evaluate the ability of eachsolution to solve the problem In addition penaltiesare included in order to eliminate those solutionsthat do not comply simple requirements in this casesome penalties can be adequate beam-columnsconnections excessive or inadequate height of sec-tion and excessive displacement among others It isimportant to classify individuals using these values

(2) Crossover it is based on getting new solutions fromthe best ones To this aim each one is represented bya binary codification and the combination of twodifferent codes at any point generates new ones isexchange is similar to that obtained in sexualreproduction

(3) Mutation it consists of generating diversity by thechange of a single bit from binary code using adesired probability that determines which solutionsmutate

For seismic design purposes it is necessary to use amultiobjective optimization technique such as NSGA-II[21] is method has been useful for the seismic design of2D and 3D framed steel buildings compared with anotheroptimization technique [32] for multiobjective design ofgreen buildings [33] Furthermore it has recently been usedfor the optimal design of structures equipped with semi-active fluid viscous dampers [34]

In this study three RC buildings with 3 6 and 9 storiesnamed RC3 RC6 and RC9 and equivalent structural models

with BRBs (named RC3-BRB RC6-BRB and RC9-BRB)were designed evaluating two fitness functions the cost andthe maximum interstory drift While the main character-istics of the structural models are shown in Table 1 Figure 2illustrates a 3D view of the braced building with 6 storylevels Notice that all the buildings were designed underseismic loads corresponding to soft soil sites of Mexico CityIt was proposed to use a different section of beam andcolumn for each 3 floors and one BRB section for all theframed buildings

e full procedure used for the seismic design of thethree framed RC buildings is illustrated in Figure 3 (seeLeyva et al [35] for more details about this approach) esame procedure was used for the seismic design of the RCbuildings with BRBs

As it was indicated before Figure 3 shows a flowchart ofthe design procedure In first place a number of generationand population are proposed notice that the first generationis randomly created en we proceed to carry out the mainparameters of the genetic algorithm especially the fitnessfunctions (2) and (3) crossover and mutation in order toobtain the individuals of the new generation is procedureis repeated and better results are expected as the number ofgenerations increases It is important to mention that thefitness functions were calibrated based on numerous tests ofthe algorithm

F1 IMIDC5slabC

3dCconC

110s (2)

F2 C13

C5slabC

3dCconC

110s (3)

where F1 and F2 are the fitness functions of maximuminterstory drift (MID) and cost respectively F1 has theobjective to find the lightest sections comparing MID with atarget drift (TD) as shown in the following equation

IMID TDMID

(4)

With F2 it is intended to obtain the most economicalsections taking into account the materials and labor cost ofthe building

Unrestrainednon yielding

segment

Restrainednon yieldingsegment

Restrained yielding segment

Unbonding material

L

Lc

Steel jacket

ConcreteSteel core

Figure 1 Buckling restrained brace parts and cross section components

Shock and Vibration 3

Table 1 Main geometric characteristics of the designed structural models

Model Number of floors Bay dir X Bay dir Y Interstory height (m) Bay length (m) Total height (m)RC3 RC3-BRB 3 3 3 35 7 105RC6 RC6-BRB 6 3 3 35 7 21RC9 RC9-BRB 9 3 3 3 5 27

Figure 2 3D view of the reinforced concrete building with BRBs (model RC-BRB6)

No

Building properties

Number of generations and

population

Generation 1 Calculation of design parameters

Structural analysis and fitness functions

Select the best individuals Crossing

Mutation

New generation needed

Yes

No

ResultsIs POS definedYes

Plot results

Figure 3 Flowchart used for the seismic design of the three-dimensional RC buildings [35]


C Cr + Cc + Cl (5)

where Cr Cc Cl and C are reinforcement concrete laborand total costs respectively

e other parameters are used as design constraints if theindividual does not satisfy the requirements of displacement(Cd) strength (Cs) constructive feasibility of connections(Ccon) and slab thickness (Cslab)

is procedure was computed several times for eachmodel studied to define the well-known Pareto frontier [21]Table 2 shows the final sections and the main properties ofthe structural models obtained

32 Earthquake Ground Motions For the dynamic analysesof the structural models thirty narrow-band earthquakeground motions recorded at soft soil sites of Mexico City areused e soft soil ground motion records were selectedbecause they demand high energy on structures in com-parison to firm soil accelerograms [36 37] e groundmotions were recorded in sites where the soil period is abouttwo seconds and severe level of damage in structures wasobserved during the 1985 Mexico City Earthquake In Ta-ble 3 some important characteristics of the records are il-lustrated Notice that PGA and PGV denote the peak groundacceleration and velocity and tD indicates the Trifunac andBrady duration [38]

33 Structural Reliability Assessment e incremental dy-namic analysis [39] is used to assess the seismic performanceof the RC buildings under narrow-band motions scaled atdifferent intensity levels in terms of spectral acceleration atfirst mode of vibration of the structure Next the well-known seismic performance-based assessment proceduresuggested by the Pacific Earthquake Engineering Center [40]in the United States was employed in this study whichindicates that the mean annual rate of exceeding (MARE) acertain engineering demand parameter (EDP) such as peakinterstory drift in this way exceeding a certain level edp canbe computed as follows

λ(EDP gt edp) 1113946IM

P[EDP gt edp |IM im]

middot dλIM(im)1113868111386811138681113868

1113868111386811138681113868

(6)

where IM denotes the ground motion intensity measure (inthis study the spectral acceleration at the first-mode periodof vibration was used as IM) and P[EDPgt edp | IM im]represents the fragility curve which is the conditionalprobability that a EDP exceeds a certain level of edp giventhat the IM is evaluated at the ground motion intensitymeasure level im Furthermore dλIM(im) refers to thedifferential of the seismic hazard curve of the site of interestIn this context the conditional probability that EDP exceedsa certain level of edp can be obtained using incremental

dynamic analyses and estimating probabilistic of the EDP ofinterest e second term in equation (6) is represented bythe seismic hazard curve which can be computed fromconventional probabilistic seismic hazard analysis evaluatedat the ground motion intensity level im It is important tonote that the ground motion intensity measure plays animportant role for assessment of the seismic performancewhich is the joint between seismology and earthquake en-gineering As stated Sa(T1)was selected as IM andmaximuminterstory drift (MID) as EDP in such a way that equation (6)can be expressed as follows

λ(MIDgtmid) 1113946Sa(T)1

P MIDgtmid|Sa(T)1 sa1113858 1113859

middot dλSa T1( ) sa( 111385711138681113868111386811138681113868

11138681113868111386811138681113868

(7)

where dλSa(T1)(sa) λSa(T1)(sa) minus λSa(T1)(sa + dsa) is thehazard curve differential expressed in terms of Sa(T1) eseismic reliability of the selected RC and RC-BRB structureswas evaluated using equation (7) in terms of the maximuminterstory drift demands In the evaluation of the first termin the integrand for the case of maximum interstory driftdemands a lognormal cumulative probability distributionwas used [41] For this reason the termP[MIDgtmid|Sa(T1) sa] is analytically evaluated asfollows

P MIDgtmid|Sa T1( 1113857 sa( 1113857

1 minusΦlnmid minus 1113954μln MID|Sa T1( )sa

1113954σlnMID|Sa T1( )sa

⎛⎝ ⎞⎠

(8)

where 1113954μln MI D|Sa(T1)saand 1113954σ ln MID|Sa(T1)sa

are the geometricmean and standard deviation of the natural logarithm of theMID respectively and Φ(middot) is the standard normal cu-mulative distribution function It is important to say thatBojorquez et al [42] suggested the use of Sa(T1) as intensitymeasure for records having similar values of Np [43]

4 Comparison of the Seismic Performance ofthe RC and RC-BRB StructuresNumerical Results

41 Incremental Dynamic Analysis With the aim to assessand compare the structural fragility and reliability of bothselected building models types the first step is the devel-opment of incremental dynamic analysis (IDA) curves Forthis aim the peak interstory drift is computing at differentvalues of the intensity measure Sa(T1) for all the narrow-band records under consideration Note that the Ruaumokosoftware has been used for the 3600 dynamic analysesFigure 4 compares the incremental dynamic analysis curvesfor the structural models RC and RC-BRB It is observed that


the maximum interstory drift in general tends to increase forall the building models as Sa(T1) also increases In particularthe maximum interstory drift for a specific value of Sa(T1) issmaller in the case of the BRB buildings For example for thestructural frame with 6 story levels and a value of Sa(T1)equal to 900 cms2 the peak drift for the traditional RC6model could be larger than 02 while in the case of RC6-BRB it is smaller than 01 In other words the uncertainty inthe structural response prediction also tends to increase forlarger values of Sa(T1) and this is especially true for theunbraced RC buildings Figure 5 compares the standarddeviation of the seismic response for the buildings with 3stories at different performance levels in terms of the medianmaximum interstory drift As it was expected the values ofthe standard deviation are larger for the RC3 model in

comparison with the RC3-BRB building Finally Figure 6shows the seismic performance in terms of damage con-figuration of the BRBs for the model RC-BRB6 under recordnumber one It is observed that the structural damage isconcentrated in the BRBs of the lower stories as it is il-lustrated in the hysteretic curves of the braced for two in-tensity levels in terms of Sa(T1) It is important to say that forthe selected scaling levels of the ground motion records theBRBs have not reached their maximum capacity

42 Structural Fragility e structural fragility curves forthe RC and RC-BRB buildings are computed in this sectionvia equation (8) in terms of maximum interstory drift eMexico City Building Code and Bojorquez et al [42]

Table 2 Main properties of the six RC building models (dimensions in cm)

Model property RC3 RC3-BRB RC6 RC6-BRB RC9 RC9-BRBColumn1 55times 55 40times 40 65times 65 55times 55 55times 55 60times 60Column2 65times 65 50times 50 55times 55 45times 45Column3 45times 45 35times 35Beam1 35times 65 30times 65 45times100 35times 75 40times 75 30times 55Beam2 35times 75 35times 65 40times 70 30times 60Beam3 30times 60 25times 50BRB (area) 40 52 36Period (s) 069 042 087 072 092 087

Table 3 Selected ground motion records

Record Date Magnitude Station PGA (cms2) PGV (cms) tD (s)1 19091985 81 SCT 1780 595 3482 21091985 76 Tlahuac deportivo 487 146 3993 25041989 69 Alameda 450 156 3784 25041989 69 Garibaldi 680 215 6555 25041989 69 SCT 449 128 6586 25041989 69 Sector popular 451 153 7947 25041989 69 Tlatelolco TL08 529 173 5668 25041989 69 Tlatelolco TL55 495 173 5009 14091995 73 Alameda 393 122 53710 14091995 73 Garibaldi 391 106 86811 14091995 73 Liconsa 301 962 60012 14091995 73 Plutarco Elıas Calles 335 937 77813 14091995 73 Sector popular 343 125 101214 14091995 73 Tlatelolco TL08 275 78 85915 14091995 73 Tlatelolco TL55 272 74 68316 09101995 75 Cibeles 144 46 85517 09101995 75 CU Juarez 158 51 97618 09101995 75 Centro urbano Presidente Juarez 157 48 82619 09101995 75 Cordoba 249 86 105120 09101995 75 Liverpool 176 63 104521 09101995 75 Plutarco Elıas Calles 192 79 137522 09101995 75 Sector popular 137 53 98423 09101995 75 Valle Gomez 179 718 62324 11011997 69 CU Juarez 162 59 61125 11011997 69 Centro urbano Presidente Juarez 163 55 85726 11011997 69 Garcıa Campillo 187 69 57027 11011997 69 Plutarco Elıas Calles 222 86 76728 11011997 69 Est 10 Roma A 210 776 74129 11011997 69 Est 11 Roma B 204 71 81630 11011997 69 Tlatelolco TL08 160 72 575


indicated that the control of a maximum interstory drift of002 guarantees a good seismic performance Here thefragility curves are computed and compared for both se-lected structural systems using the suggested 002 maxi-mum interstory drift value Figure 7 compares the seismicfragility for the 3 6 and 9 story levels of RC and RC-BRBbuildings e results suggest that the probability of ex-ceeding the maximum interstory drift is larger for thetraditional reinforced concrete frames for all the consid-ered scaling levels in terms of spectral acceleration For

example the probability to exceed a peak drift of 002 whenSa(T1) is equal to 1000 cms2 is 08 for the RC3 buildingwhile in the case of the equivalent RC3-BRB structure isabout 045 indicating that the performance of RC3-BRB issuperior in comparison with RC3 e same conclusion isvalid for the tallest buildings in fact as the level of stories ofthe buildings increases the BRBs tend to decrease theprobability of exceedance in such a way that the effec-tiveness of buckling restrained braces is larger for tallerbuildings

05

04

03

02

0

01

0 500 1000 1500 2000Sa (T1) (cms2)

Max

imum

inte

rsto

ry d

ri

(a)

0 500 1000 1500 2000Sa (T1) (cms2)

05

04

03

02

0

01Max

imum

inte

rsto

ry d

ri

(b)

0 500 1000 1500 2000Sa (T1) (cms2)

05

04

03

02

0

01Max

imum

inte

rsto

ry d

ri

(c)

0 500 1000 1500 2000Sa (T1) (cms2)

05

04

03

02

0

01Max

imum

inte

rsto

ry d

ri

(d)

0 500 1000 1500 2000Sa (T1) (cms2)

05

04

03

02

0

01Max

imum

inte

rsto

ry d

ri

(e)

0 500 1000 1500 2000Sa (T1) (cms2)

05

04

03

02

0

01Max

imum

inte

rsto

ry d

ri

(f )

Figure 4 Incremental dynamic analysis curves for the buildings (a) RC3 (b) RC3-BRB (c) RC6 (d) RC6-BRB (e) RC9 and (f) RC9-BRB


43 Structural Reliability e structural reliability isassessed by means of the fragility curves combined with theseismic hazard curves to calculate the mean annual rate ofexceedance a maximum interstory drift threshold For thepresent study the spectral acceleration hazard curves cor-responding to the first-mode period of vibration of eachbuilding and for the Secretarıa de Comunicaciones yTransportes (SCT) site in Mexico City were developed fol-lowing the procedure suggested by Alamilla [44] eseismic hazard curves in terms of peak interstory drift for theRC and the RC-BRB buildings are compared in Figure 8efigure suggests that the mean annual rate of exceeding aspecific value of maximum interstory drift is larger for thetraditional reinforced concrete buildings For this reasonthe BRBs on reinforced concrete buildings increase con-siderably the structural reliability which is valid for all the

selected buildings is is especially valid as the number ofstories tend to increase as it was indicated in the case of theseismic fragility e mean annual rate of exceedance athreshold equals 002 in terms of MID for the RC and RC-BRB is given in Table 4 Note that it corresponds to targetstructural reliability levels of buildings designed according totheMexican Building Codeus theMARE values in termsof peak drift for the BRB buildings are considerably reducedin comparison to those of the RC structures provided by theMexico City Building Code In other words it is observedthat the values of themean annual rates of exceedance for theRC-BRB systems are smaller than those of the traditional RCbuildings Note that there are other structural systems toimprove the seismic reliability of buildings such as post-tensioned connections [45] e results indicate that the useof BRBs in buildings is a good solution in order to reduce

002 004 006 0080 01Median maximum interstory dri

0

02

04

06

08

1

Stan

dard

dev

iatio

n

RC3-BRBRC3

Figure 5 Comparison of the standard deviation at different performance levels in terms of the median maximum interstory drift value forthe buildings RC3 and RC3-BRB

Sa = 400cms2 Sa = 700cms2


ForceDisp

lace

men

t

ForceDisp

lace

men

t

Force

Disp

lace

men

t

Force

Disp

lace

men

t

Figure 6 Damage configuration of the RC6-BRB and hysteretic curves of the braces for two intensity levels


500 1000 1500 20000Sa (T1) (cms2)

0

02

04

06

08

1P

[MID

gt 0

02

| Sa]

RC3RC3-BRB

(a)

500 1000 1500 20000Sa (T1) (cms2)

0

02

04

06

08

1

P [M

ID gt

00

2 | Sa]

RC6RC6-BRB

(b)

500 1000 1500 20000Sa (T1) (cms2)

0

02

04

06

08

1

P [M

ID gt

00

2 | Sa]

RC9RC9-BRB

(c)

Figure 7 Fragility curves for maximum interstory drift and all the studied buildings

0010005 00150 0025002 003Maximum interstory dri

10ndash7

10ndash6

10ndash5

10ndash4

10ndash3

10ndash2

Mea

n an

nual

rate

of e

xcee

danc

e

RC3RC3-BRB

(a)

0005 001 0015 002 0025 0030Maximum interstory dri

10ndash7

10ndash6

10ndash5

10ndash4

10ndash3

10ndash2

Mea

n an

nual

rate

of e

xcee

danc

e

RC6RC6-BRB

(b)

Figure 8 Continued


peak drift demands of traditional structures located in highseismic zones

5 Conclusions

e seismic performance of three traditional reinforcedconcrete buildings and equivalent structures with BRBs isassessed through incremental dynamic analysis seismicfragility and structural reliability For this aim the maxi-mum interstory drift was selected as engineering demandparameter e buildings were subjected to several narrow-band motions recorded at soft soil of Mexico City eresults indicate that the maximum interstory drift demand issmaller in the case of the RC-BRB buildings in comparisonwith the reinforced concrete structures Moreover the un-certainty in the structural response prediction also tends todecrease when the BRBs are used in the RC buildings is isreflected in the fragility analysis where the probability ofexceeding the maximum interstory drift is larger for thetraditional reinforced concrete frames for all the consideredscaling levels in terms of Sa(T1) Finally theMARE a specificvalue of maximum interstory drift is larger for the tradi-tional reinforced concrete buildings in comparison with theBRB buildings For this reason the BRBs on RC buildingsincrease the structural reliability for all the buildings underconsideration is is particularly valid for the tallestbuildings studied In conclusion the use of BRBs is a goodsolution to obtain safer buildings or in order to reduce peakdrift demands of traditional structures under strongearthquake ground motions

Data Availability

e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

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

Acknowledgments

e financial support given by the Universidad Autonomade Sinaloa under grant PROFAPI is appreciatede authorsexpress their gratitude to the Consejo Nacional de Ciencia yTecnologıa (CONACYT) in Mexico for funding the researchreported in this paper under grant Ciencia Basica 287103and for the scholarships given to the PhD students esupport of the UNAM-DGAPA-PAPIIT under project noIN100320 is appreciated

References

[1] H Krawinkler and A Gupta ldquoDeformation and ductilitydemands in steel moment frame structuresrdquo Stability andDuctility of Steel Structures vol SDSSrsquo97 pp 1825ndash1830 1998

[2] A Khampanit S Leelataviwat J Kochanin and P WarnitchaildquoEnergy-based seismic strengthening design of non-ductilereinforced concrete frames using buckling-restrained bracesrdquoEngineering Structures vol 81 pp 110ndash122 2014

Table 4 Comparison of themean annual rate of exceedance (MARE) values for the RC and RC-BRB buildings for aMID value equal to 002

RC buildings MARE for MID 002 RC-BRB buildings MARE for MID 002RC3 000072 RC3-BRB 0000084RC6 000046 RC6-BRB 0000024RC9 000019 RC9-BRB 00000024


10ndash7

10ndash6

10ndash5

10ndash4

10ndash3

10ndash2

Mea

n an

nual

rate

of e

xcee

danc

e

RC9RC9-BRB

(c)

Figure 8 Comparison of the MID hazard curves for the RC and the RC-BRB buildings with (a) 3 stories (b) 6 stories and (c) 9 stories


[3] H Guerrero T Ji A Escobar and A Teran-Gilmore ldquoEffectsof buckling-restrained braces on reinforced concrete precastmodels subjected to shaking table excitationrdquo EngineeringStructures vol 163 pp 294ndash310 2018

[4] J Osteraas and H Krawinkler ldquoldquoe Mexico earthquake ofSeptember 19 1985mdashbehavior of steel buildingsrdquo EarthquakeSpectra vol 5 no 1 pp 51ndash88 1989

[5] H Kim Seismic evaluation and upgrading of braced framestructures for potential local failures PhD thesis p 290UMCEE 92-24 Dept of Civil Engineering and EnvironmentalEngineering Univ of Michigan Ann Arbor Michigan 1992

[6] R Tremblay A Filiatrault P Timler and M BruneauldquoPerformance of steel structures during the 1994 Northridgeearthquakerdquo Canadian Journal of Civil Engineering vol 22no 2 pp 338ndash360 1995

[7] Architectural Institute of Japan and Steel Committee of KinkiBranch Reconnaissance Report on Damage to Steel BuildingStructures Observed from the 1995 Hyogoken-Nanbu (Han-shinAwaji) Earthquake p 167 AIJ Tokyo 1995

[8] T Hisatoku ldquoReanalysis and repair of a high-rise steelbuilding damaged by the 1995 Hyogoken-Nanbu earth-quakerdquo in Proceedings 64th Annual Convention StructuralEngineers Association of California pp 21ndash40 StructuralEngineers Association of California Sacramento CA USAOctober 1995

[9] R Tremblay A Filiatrault M Bruneau et al ldquoSeismic designof steel buildings lessons from the 1995 Hyogo-ken Nanbuearthquakerdquo Canadian Journal of Civil Engineering vol 23no 3 pp 727ndash756 1996

[10] R Sabelli S Mahin and C Chang ldquoSeismic demands on steelbraced frame buildings with buckling-restrained bracesrdquoEngineering Structures vol 25 no 5 pp 655ndash666 2003

[11] C M Uang and M Nakashima ldquoSteel buckling-restrainedbraced framesrdquo Earthquake Engineering Recent advances andapplications CRC Press Boca Raton FL USA chapter 162004

[12] C M Uang and M Nakashima Earthquake EngineeringFrom Engineering Seismology to Performance Based Engi-neering CRC Press LLC Boca Raton FL USA 2004

[13] Q Xie ldquoState of the art of buckling-restrained braces in AsiardquoJournal of Constructional Steel Research vol 61 pp 727ndash7482005

[14] G Della Corte M DrsquoAniello R Landolfo and F MazzolanildquoReview of steel buckling restrained bracesrdquo Steel Construc-tion vol 4 no 2 pp 85ndash93 2011

[15] S Kiggins and C M Uang ldquoReducing residual drift ofbuckling-restrained braced frames as a dual systemrdquo Engi-neering Structures vol 28 pp 1525ndash1532 2006

[16] M Bosco E Marino and P Rossi ldquoDesign of steel framesequipped with BRBs in the framework of Eurocode 8rdquo Journalof Constructional Steel Research vol 113 pp 43ndash57 2015

[17] A Lago D Trabucco and A Wood ldquoCase studies of tallbuildings with dynamic modification devicesrdquo DampingTechnologies for Tall Buildings Elsevier Amsterdam Neth-erlands chapter 8 2018

[18] G Palazzo F Lopez-Almansa X Cahis and F Crisafulli ldquoAlow-tech dissipative buckling restrained brace Designanalysis production and testingrdquo Engineering Structuresvol 31 pp 2152ndash2161 2009

[19] Mexico City Building Code 2017[20] K Deb Multi-objective Optimization Using Evolutionary

Algorithms John Wiley amp Sons Chichester-New York-Winheim-Brisbane-Singapore-Toronto 2001

[21] K Deb A Pratap S Agarwal and T Meyarivan ldquoA fast andelitist multiobjective genetic algorithm NSGA-IIrdquo IEEETransactions on Evolutionary Computation vol 6 no 2pp 182ndash197 2002

[22] J Aviles and L Perez-Rocha ldquoDamage analysis of structureson elastic foundationrdquo Journal of Structural Engineeringvol 133 no 10 pp 1453ndash1461 2007

[23] S Abdel M Ahmed and T Alazrak ldquoEvaluation of soil-foundation-structure interaction effects on seismic responsedemands of multi-story MRF buildings on raft foundationsrdquoInternational Journal of Advanced Structural Engineeringvol 7 no 1 pp 11ndash30 2014

[24] A Wada E Saeki T Takeuchi and A Watanabe Develop-ment of Unbounded Brace Nippon Steel Corporation BuildingConstruction and Urban Development Division Tokyo Ja-pan 1998

[25] A Teran-Gilmore and N Virto-Cambray ldquoPreliminary de-sign of low-rise buildings stiffened with buckling restrainedbraces by a displacement-based approachrdquo EarthquakeSpectra vol 25 no 1 pp 185ndash211 2009

[26] H Guerrero T Ji and J Escobar ldquoExperimental studies of asteel frame model with and without buckling-restrainedbracesrdquo Revista de Ingenierıa Sısmica vol 95 pp 33ndash52 2016

[27] R Rahnavard M Naghavi M Aboudi and M SuleimanldquoInvestigating modeling approaches of buckling-restrainedbraces under cyclic loadsrdquo Case Studies in ConstructionMaterials vol 8 pp 476ndash488 2018

[28] A Almeida R Ferreira J Proenca and A Gago ldquoSeismicretrofit of RC building structures with buckling restrainedbracesrdquo Engineering Structures vol 130 pp 14ndash22 2017

[29] R Tremblay P Bolduc R Nevilley and R DeVall ldquoSeismictesting and performance of buckling restrained bracing sys-temsrdquo Canadian Journal of Civil Engineering vol 33pp 183ndash198 2006

[30] A Teran-Gilmore and J Ruiz-Garcıa ldquoComparative seismicperformance of steel frames retrofitted with buckling buck-ling-restrained braces through the application of force-basedand displacement-based approachesrdquo Soil Dynamic andEarthquake Engineering vol 31 no 3 pp 478ndash490 2011

[31] J Holland Adaptation in Natural and Artificial Systems AnIntroductory Analysis with Applications to Biology Controland Artificial Intelligence University of Michigan Press AnnArbor Mich 1975

[32] M Barraza E Bojorquez E Fernandez-Gonzalez andA Reyes-Salazar ldquoMulti-objective optimization of structuralsteel buildings under earthquake loads using NSGA-II andPSOrdquo KSCE Journal of Civil Engineering vol 21 pp 488ndash5002017

[33] M-D Yang M-D Lin Y-H Lin and K-T Tsai ldquoMulti-objective optimization design of green building envelopematerial using a non-dominated sorting genetic algorithmrdquoApplied Jermal Engineering vol 111 pp 1255ndash1264 2017

[34] S Bakhshinezhad and M Mohebbi ldquoMulti-objective optimaldesign of semi-active fluid viscous dampers for nonlinearstructures using NSGA-IIrdquo Structures vol 24 pp 678ndash6892020

[35] H Leyva E Bojorquez J Bojorquez et al ldquoEarthquake designof reinforced concrete buildings using NSGA-IIrdquo Advances inCivil Engineering vol 2018 Article ID 5906279 11 pages2018

[36] E Bojorquez and S E Ruiz ldquoStrength reduction factors forthe valley of Mexico taking into account low cycle fatigueeffectsrdquo in Proceedings of 13o World Conference on


Earthquake Engineering Vancouver BC Canadapaper 516Vancouver BC Canada August 2004

[37] A Teran-Gilmore and J O Jirsa ldquoEnergy demands for seismicdesign against low cycle fatiguerdquo Earthquake Engineering andStructural Dynamics vol 36 pp 383ndash404 2007

[38] M D Trifunac and A G Brady ldquoA study of the duration ofstrong earthquake ground motionrdquo Bulletin of the Seismo-logical Society of America vol 65 no 3 pp 581ndash626 1975

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

[40] G G Deierlein Overview of a Comprehensive Framework forPerformance Earthquake Assessment Report PEER 200405pp 15ndash26 Pacific Earthquake Engineering Center BerkeleyCF USA 2004

[41] E Bojorquez and J Ruiz-Garcıa ldquoResidual drift demands inmoment-resisting steel frames subjected to narrow-bandearthquake ground motionsrdquo Earthquake Engineering andStructural Dynamics vol 42 pp 1583ndash1598 2013

[42] E Bojorquez A Teran-Gilmore S E Ruiz and A Reyes-Salazar ldquoEvaluation of structural reliability of steel framesinterstory drift versus plastic hysteretic energyrdquo EarthquakeSpectra vol 27 no 3 pp 661ndash682 2011

[43] E Bojorquez and I Iervolino ldquoSpectral shape proxies andnonlinear structural responserdquo Soil Dynamics and EarthquakeEngineering vol 31 no 7 pp 996ndash1008 2011

[44] J L Alamilla Reliability-based Seismic Design Criteria forFramed Structures PhD esis Universidad NacionalAutonoma de Mexico UNAM Mexico 2001

[45] E Bojorquez A Lopez-Barraza A Reyes-Salazar et alldquoImproving the structural reliability of steel frames usingposttensioned connectionrdquo Advances in Civil Engineeringvol 2019 Article ID 8912390 10 pages 2019


earthquake 1989 Loma Prieta earthquake 1994 Northridgeearthquake and 1995 Hyogo-ken Nanbu earthquake amongothers [4ndash9] as it was indicated by Sabelli et al [10] Inparticular the unsymmetrical properties in tension andcompression and the large strength deterioration in com-pression reduce considerably the performance of the braces Inorder to have the same mechanical properties in tension andcompression of the braces a new type of brace named bucklingrestrained brace which consists of a ductility steel core that isforced to have similar yield in tension and compression byrestrained the buckling has been suggested [11ndash17] Severalexperimental tests have demonstrated that the cyclic behaviorof the BRBs is stable and almost bilinear in particular Palazzoet al [18] concluded that it is feasible to design buckling re-strained braces that are efficient robust virtually maintenance-free durable reasonably cheap easy to produce and made ofbasic and easily replaceable materials For this reason althoughthe seismic response of reinforced concrete frames withbuckling restrained braces has been studied usually 2D systemsare considered for the dynamic analyses moreover the ad-vantages of BRBs on RC buildings in terms of structuralfragility and reliability are not commonly assessed Motivatedby the need to observe the advantages of BRBs in the seismicperformance in terms of structural fragility and reliability of 3Dreinforced concrete framed buildings in the present study theseismic performance of 3DRC buildings and equivalent 3DRCstructures with BRBs is assessed For the purpose of this workthree structural RC buildings with 3 6 and 9 stories aredesigned according to the Mexico City Seismic Design Pro-visions (MCSDP) [19] In addition three equivalent concretebuildings with BRBs are designed It is important to say that forthe seismic design of all the buildings the NSGA-II approach[20 21] is used in order to reduce the cost and increase thestructural capacity in accordance with the MCSDP e 3Dframed buildings in both type of structural systems are sub-jected to 30 groundmotion records obtained from soft soil sitesof Mexico City scaled at different spectral accelerations at firstmode of vibration of the structureus a total of 3600 seismicanalyses have been performed e numerical results of theanalyses suggest that the seismic performance of reinforcedconcrete buildings with buckling restrained braces is superiorto that of the structural behavior of traditional buildings in-dicating the advantages of this structural system For thisreason BRBs can increase considerably the structural reliabilitywhen they are incorporated in reinforced concrete framesMoreover the damage in the buildings with BRBs is con-centrated in the braces which can be replaced after the oc-currence of an earthquake It is important to say that althoughsoil structure interaction was not taken into account noticethat similar conclusions are expected because this effect in-creases the period of vibration of a building [22 23]

2 Buckling Restrained Braces

e innovative buckling restrained braces are devices used asseismic energy absorption elements with the aim of reducingthe damage in a structure under strong earthquake eventsey consists of a steel section enclosed in a tubular or cy-lindrical case filled with concrete or mortar Figure 1 shows

the topology and components of this brace [11 24] whichmakes it possible to take advantage of the full capacity of steelcore and to obtain a symmetrical and highly stable cyclicbehavior in comparison with conventional braces In addi-tion BRBs can be easily replaced in case of damage

Different experimental studies on this type of deviceshave been carried out Teran-Gilmore and Virto-Cambray[25] performed cyclic test at multiple BRBs using circulartube or angle steel cores concluding that both developedstable hysteretic behavior and similar resistance to bothcompression and tension Khampanit et al [2] proposed anenergy-based design methodology by comparing experi-mental studies between a reinforced concrete bare frame anda reinforced concrete braced frame Guerrero et al [26]carried out a comparative study between two 5-story steelframes with and without BRB at 110 scale factor undernarrow-band seismic records obtained in Mexico City eresults demonstrated a considerable decrease in terms ofdisplacements maximum interstory drift and floor accel-erations for braced frames as well as an increase of stiffnessand damping of the system Similarly studies have beencarried out on newmethods to adequately model this type ofbraces Rahnavard et al [27] compared hysteresis curves ofexperimental studies with a simple numerical model in orderto avoid large computational time for the analyses In ad-dition they have used this type of brace for retrofit orstrengthening of concrete buildings [28] In this study aconsiderable difference is observed in lateral resistancecyclic behavior and energy dissipation capacity e lateralstiffness that a BRB brings to a floor can be obtained re-gardless of the core area as shown in the following equation[29]

KL

(AL)

E cos2 θc + η(1 minus c)

E cos2 θ

LRF

(1)

where L is the total length of the brace E is the elasticmodulus θ is the angle of inclination Lc is the length ofelement without connections c is the relation between Lcand L η is the relation between average axial strains ofoutside and inside the core and LRF is a factor that considersthe region of higher axial stiffness at the ends of the braceTeran-Gilmore and Ruiz-Garcıa [30] determined that underthe consideration of Lc it is equal to half value of L and thatthe average area outside the core is three times the area ofcore LRF is equal to 0667 erefore the actual stiffness thatBRB brings to the system depends on the difference betweenthe core and connection areas rough this type ofmechanism the reinforced concrete braced and unbracedbuildings were designed using the NSGA-II approach asexplained below Finally the seismic reliability when bothstructural systems are subjected to narrow-band motionsrecorded in Mexico City is compared

3 Methodology

31 Seismic Design of the RC Models Using NSGA-IICurrently there are a large number of studies on the ap-plication of optimization techniques for structural design











F1 IMIDC5slabC

3dCconC

110s (2)

F2 C13

C5slabC

3dCconC

110s (3)


IMID TDMID

(4)



segment



Unbonding material

L

Lc

Steel jacket

ConcreteSteel core






No

Building properties


population




Mutation


Yes

No


Plot results



C Cr + Cc + Cl (5)








middot dλIM(im)1113868111386811138681113868

1113868111386811138681113868

(6)





middot dλSa T1( ) sa( 111385711138681113868111386811138681113868

11138681113868111386811138681113868

(7)


P MIDgtmid|Sa T1( 1113857 sa( 1113857



⎛⎝ ⎞⎠

(8)
















05

04

03

02

0

01

0 500 1000 1500 2000Sa (T1) (cms2)

Max

imum

inte

rsto

ry d

ri

(a)

0 500 1000 1500 2000Sa (T1) (cms2)

05

04

03

02

0

01Max

imum

inte

rsto

ry d

ri

(b)

0 500 1000 1500 2000Sa (T1) (cms2)

05

04

03

02

0

01Max

imum

inte

rsto

ry d

ri

(c)

0 500 1000 1500 2000Sa (T1) (cms2)

05

04

03

02

0

01Max

imum

inte

rsto

ry d

ri

(d)

0 500 1000 1500 2000Sa (T1) (cms2)

05

04

03

02

0

01Max

imum

inte

rsto

ry d

ri

(e)

0 500 1000 1500 2000Sa (T1) (cms2)

05

04

03

02

0

01Max

imum

inte

rsto

ry d

ri

(f )






0

02

04

06

08

1

Stan

dard

dev

iatio

n

RC3-BRBRC3




ForceDisp

lace

men

t

ForceDisp

lace

men

t

Force

Disp

lace

men

t

Force

Disp

lace

men

t



500 1000 1500 20000Sa (T1) (cms2)

0

02

04

06

08

1P

[MID

gt 0

02

| Sa]

RC3RC3-BRB

(a)

500 1000 1500 20000Sa (T1) (cms2)

0

02

04

06

08

1

P [M

ID gt

00

2 | Sa]

RC6RC6-BRB

(b)

500 1000 1500 20000Sa (T1) (cms2)

0

02

04

06

08

1

P [M

ID gt

00

2 | Sa]

RC9RC9-BRB

(c)



10ndash7

10ndash6

10ndash5

10ndash4

10ndash3

10ndash2

Mea

n an

nual

rate

of e

xcee

danc

e

RC3RC3-BRB

(a)


10ndash7

10ndash6

10ndash5

10ndash4

10ndash3

10ndash2

Mea

n an

nual

rate

of e

xcee

danc

e

RC6RC6-BRB

(b)

Figure 8 Continued



5 Conclusions


Data Availability




Acknowledgments


References






10ndash7

10ndash6

10ndash5

10ndash4

10ndash3

10ndash2

Mea

n an

nual

rate

of e

xcee

danc

e

RC9RC9-BRB

(c)


























































F1 IMIDC5slabC

3dCconC

110s (2)

F2 C13

C5slabC

3dCconC

110s (3)


IMID TDMID

(4)



segment



Unbonding material

L

Lc

Steel jacket

ConcreteSteel core






No

Building properties


population




Mutation


Yes

No


Plot results



C Cr + Cc + Cl (5)








middot dλIM(im)1113868111386811138681113868

1113868111386811138681113868

(6)





middot dλSa T1( ) sa( 111385711138681113868111386811138681113868

11138681113868111386811138681113868

(7)


P MIDgtmid|Sa T1( 1113857 sa( 1113857



⎛⎝ ⎞⎠

(8)
















05

04

03

02

0

01

0 500 1000 1500 2000Sa (T1) (cms2)

Max

imum

inte

rsto

ry d

ri

(a)

0 500 1000 1500 2000Sa (T1) (cms2)

05

04

03

02

0

01Max

imum

inte

rsto

ry d

ri

(b)

0 500 1000 1500 2000Sa (T1) (cms2)

05

04

03

02

0

01Max

imum

inte

rsto

ry d

ri

(c)

0 500 1000 1500 2000Sa (T1) (cms2)

05

04

03

02

0

01Max

imum

inte

rsto

ry d

ri

(d)

0 500 1000 1500 2000Sa (T1) (cms2)

05

04

03

02

0

01Max

imum

inte

rsto

ry d

ri

(e)

0 500 1000 1500 2000Sa (T1) (cms2)

05

04

03

02

0

01Max

imum

inte

rsto

ry d

ri

(f )






0

02

04

06

08

1

Stan

dard

dev

iatio

n

RC3-BRBRC3




ForceDisp

lace

men

t

ForceDisp

lace

men

t

Force

Disp

lace

men

t

Force

Disp

lace

men

t



500 1000 1500 20000Sa (T1) (cms2)

0

02

04

06

08

1P

[MID

gt 0

02

| Sa]

RC3RC3-BRB

(a)

500 1000 1500 20000Sa (T1) (cms2)

0

02

04

06

08

1

P [M

ID gt

00

2 | Sa]

RC6RC6-BRB

(b)

500 1000 1500 20000Sa (T1) (cms2)

0

02

04

06

08

1

P [M

ID gt

00

2 | Sa]

RC9RC9-BRB

(c)



10ndash7

10ndash6

10ndash5

10ndash4

10ndash3

10ndash2

Mea

n an

nual

rate

of e

xcee

danc

e

RC3RC3-BRB

(a)


10ndash7

10ndash6

10ndash5

10ndash4

10ndash3

10ndash2

Mea

n an

nual

rate

of e

xcee

danc

e

RC6RC6-BRB

(b)

Figure 8 Continued



5 Conclusions


Data Availability




Acknowledgments


References






10ndash7

10ndash6

10ndash5

10ndash4

10ndash3

10ndash2

Mea

n an

nual

rate

of e

xcee

danc

e

RC9RC9-BRB

(c)




















































No

Building properties


population




Mutation


Yes

No


Plot results



C Cr + Cc + Cl (5)








middot dλIM(im)1113868111386811138681113868

1113868111386811138681113868

(6)





middot dλSa T1( ) sa( 111385711138681113868111386811138681113868

11138681113868111386811138681113868

(7)


P MIDgtmid|Sa T1( 1113857 sa( 1113857



⎛⎝ ⎞⎠

(8)
















05

04

03

02

0

01

0 500 1000 1500 2000Sa (T1) (cms2)

Max

imum

inte

rsto

ry d

ri

(a)

0 500 1000 1500 2000Sa (T1) (cms2)

05

04

03

02

0

01Max

imum

inte

rsto

ry d

ri

(b)

0 500 1000 1500 2000Sa (T1) (cms2)

05

04

03

02

0

01Max

imum

inte

rsto

ry d

ri

(c)

0 500 1000 1500 2000Sa (T1) (cms2)

05

04

03

02

0

01Max

imum

inte

rsto

ry d

ri

(d)

0 500 1000 1500 2000Sa (T1) (cms2)

05

04

03

02

0

01Max

imum

inte

rsto

ry d

ri

(e)

0 500 1000 1500 2000Sa (T1) (cms2)

05

04

03

02

0

01Max

imum

inte

rsto

ry d

ri

(f )






0

02

04

06

08

1

Stan

dard

dev

iatio

n

RC3-BRBRC3




ForceDisp

lace

men

t

ForceDisp

lace

men

t

Force

Disp

lace

men

t

Force

Disp

lace

men

t



500 1000 1500 20000Sa (T1) (cms2)

0

02

04

06

08

1P

[MID

gt 0

02

| Sa]

RC3RC3-BRB

(a)

500 1000 1500 20000Sa (T1) (cms2)

0

02

04

06

08

1

P [M

ID gt

00

2 | Sa]

RC6RC6-BRB

(b)

500 1000 1500 20000Sa (T1) (cms2)

0

02

04

06

08

1

P [M

ID gt

00

2 | Sa]

RC9RC9-BRB

(c)



10ndash7

10ndash6

10ndash5

10ndash4

10ndash3

10ndash2

Mea

n an

nual

rate

of e

xcee

danc

e

RC3RC3-BRB

(a)


10ndash7

10ndash6

10ndash5

10ndash4

10ndash3

10ndash2

Mea

n an

nual

rate

of e

xcee

danc

e

RC6RC6-BRB

(b)

Figure 8 Continued



5 Conclusions


Data Availability




Acknowledgments


References






10ndash7

10ndash6

10ndash5

10ndash4

10ndash3

10ndash2

Mea

n an

nual

rate

of e

xcee

danc

e

RC9RC9-BRB

(c)

















































C Cr + Cc + Cl (5)








middot dλIM(im)1113868111386811138681113868

1113868111386811138681113868

(6)





middot dλSa T1( ) sa( 111385711138681113868111386811138681113868

11138681113868111386811138681113868

(7)


P MIDgtmid|Sa T1( 1113857 sa( 1113857



⎛⎝ ⎞⎠

(8)
















05

04

03

02

0

01

0 500 1000 1500 2000Sa (T1) (cms2)

Max

imum

inte

rsto

ry d

ri

(a)

0 500 1000 1500 2000Sa (T1) (cms2)

05

04

03

02

0

01Max

imum

inte

rsto

ry d

ri

(b)

0 500 1000 1500 2000Sa (T1) (cms2)

05

04

03

02

0

01Max

imum

inte

rsto

ry d

ri

(c)

0 500 1000 1500 2000Sa (T1) (cms2)

05

04

03

02

0

01Max

imum

inte

rsto

ry d

ri

(d)

0 500 1000 1500 2000Sa (T1) (cms2)

05

04

03

02

0

01Max

imum

inte

rsto

ry d

ri

(e)

0 500 1000 1500 2000Sa (T1) (cms2)

05

04

03

02

0

01Max

imum

inte

rsto

ry d

ri

(f )






0

02

04

06

08

1

Stan

dard

dev

iatio

n

RC3-BRBRC3




ForceDisp

lace

men

t

ForceDisp

lace

men

t

Force

Disp

lace

men

t

Force

Disp

lace

men

t



500 1000 1500 20000Sa (T1) (cms2)

0

02

04

06

08

1P

[MID

gt 0

02

| Sa]

RC3RC3-BRB

(a)

500 1000 1500 20000Sa (T1) (cms2)

0

02

04

06

08

1

P [M

ID gt

00

2 | Sa]

RC6RC6-BRB

(b)

500 1000 1500 20000Sa (T1) (cms2)

0

02

04

06

08

1

P [M

ID gt

00

2 | Sa]

RC9RC9-BRB

(c)



10ndash7

10ndash6

10ndash5

10ndash4

10ndash3

10ndash2

Mea

n an

nual

rate

of e

xcee

danc

e

RC3RC3-BRB

(a)


10ndash7

10ndash6

10ndash5

10ndash4

10ndash3

10ndash2

Mea

n an

nual

rate

of e

xcee

danc

e

RC6RC6-BRB

(b)

Figure 8 Continued



5 Conclusions


Data Availability




Acknowledgments


References






10ndash7

10ndash6

10ndash5

10ndash4

10ndash3

10ndash2

Mea

n an

nual

rate

of e

xcee

danc

e

RC9RC9-BRB

(c)



























































05

04

03

02

0

01

0 500 1000 1500 2000Sa (T1) (cms2)

Max

imum

inte

rsto

ry d

ri

(a)

0 500 1000 1500 2000Sa (T1) (cms2)

05

04

03

02

0

01Max

imum

inte

rsto

ry d

ri

(b)

0 500 1000 1500 2000Sa (T1) (cms2)

05

04

03

02

0

01Max

imum

inte

rsto

ry d

ri

(c)

0 500 1000 1500 2000Sa (T1) (cms2)

05

04

03

02

0

01Max

imum

inte

rsto

ry d

ri

(d)

0 500 1000 1500 2000Sa (T1) (cms2)

05

04

03

02

0

01Max

imum

inte

rsto

ry d

ri

(e)

0 500 1000 1500 2000Sa (T1) (cms2)

05

04

03

02

0

01Max

imum

inte

rsto

ry d

ri

(f )






0

02

04

06

08

1

Stan

dard

dev

iatio

n

RC3-BRBRC3




ForceDisp

lace

men

t

ForceDisp

lace

men

t

Force

Disp

lace

men

t

Force

Disp

lace

men

t



500 1000 1500 20000Sa (T1) (cms2)

0

02

04

06

08

1P

[MID

gt 0

02

| Sa]

RC3RC3-BRB

(a)

500 1000 1500 20000Sa (T1) (cms2)

0

02

04

06

08

1

P [M

ID gt

00

2 | Sa]

RC6RC6-BRB

(b)

500 1000 1500 20000Sa (T1) (cms2)

0

02

04

06

08

1

P [M

ID gt

00

2 | Sa]

RC9RC9-BRB

(c)



10ndash7

10ndash6

10ndash5

10ndash4

10ndash3

10ndash2

Mea

n an

nual

rate

of e

xcee

danc

e

RC3RC3-BRB

(a)


10ndash7

10ndash6

10ndash5

10ndash4

10ndash3

10ndash2

Mea

n an

nual

rate

of e

xcee

danc

e

RC6RC6-BRB

(b)

Figure 8 Continued



5 Conclusions


Data Availability




Acknowledgments


References






10ndash7

10ndash6

10ndash5

10ndash4

10ndash3

10ndash2

Mea

n an

nual

rate

of e

xcee

danc

e

RC9RC9-BRB

(c)



















































05

04

03

02

0

01

0 500 1000 1500 2000Sa (T1) (cms2)

Max

imum

inte

rsto

ry d

ri

(a)

0 500 1000 1500 2000Sa (T1) (cms2)

05

04

03

02

0

01Max

imum

inte

rsto

ry d

ri

(b)

0 500 1000 1500 2000Sa (T1) (cms2)

05

04

03

02

0

01Max

imum

inte

rsto

ry d

ri

(c)

0 500 1000 1500 2000Sa (T1) (cms2)

05

04

03

02

0

01Max

imum

inte

rsto

ry d

ri

(d)

0 500 1000 1500 2000Sa (T1) (cms2)

05

04

03

02

0

01Max

imum

inte

rsto

ry d

ri

(e)

0 500 1000 1500 2000Sa (T1) (cms2)

05

04

03

02

0

01Max

imum

inte

rsto

ry d

ri

(f )






0

02

04

06

08

1

Stan

dard

dev

iatio

n

RC3-BRBRC3




ForceDisp

lace

men

t

ForceDisp

lace

men

t

Force

Disp

lace

men

t

Force

Disp

lace

men

t



500 1000 1500 20000Sa (T1) (cms2)

0

02

04

06

08

1P

[MID

gt 0

02

| Sa]

RC3RC3-BRB

(a)

500 1000 1500 20000Sa (T1) (cms2)

0

02

04

06

08

1

P [M

ID gt

00

2 | Sa]

RC6RC6-BRB

(b)

500 1000 1500 20000Sa (T1) (cms2)

0

02

04

06

08

1

P [M

ID gt

00

2 | Sa]

RC9RC9-BRB

(c)



10ndash7

10ndash6

10ndash5

10ndash4

10ndash3

10ndash2

Mea

n an

nual

rate

of e

xcee

danc

e

RC3RC3-BRB

(a)


10ndash7

10ndash6

10ndash5

10ndash4

10ndash3

10ndash2

Mea

n an

nual

rate

of e

xcee

danc

e

RC6RC6-BRB

(b)

Figure 8 Continued



5 Conclusions


Data Availability




Acknowledgments


References






10ndash7

10ndash6

10ndash5

10ndash4

10ndash3

10ndash2

Mea

n an

nual

rate

of e

xcee

danc

e

RC9RC9-BRB

(c)




















































0

02

04

06

08

1

Stan

dard

dev

iatio

n

RC3-BRBRC3




ForceDisp

lace

men

t

ForceDisp

lace

men

t

Force

Disp

lace

men

t

Force

Disp

lace

men

t



500 1000 1500 20000Sa (T1) (cms2)

0

02

04

06

08

1P

[MID

gt 0

02

| Sa]

RC3RC3-BRB

(a)

500 1000 1500 20000Sa (T1) (cms2)

0

02

04

06

08

1

P [M

ID gt

00

2 | Sa]

RC6RC6-BRB

(b)

500 1000 1500 20000Sa (T1) (cms2)

0

02

04

06

08

1

P [M

ID gt

00

2 | Sa]

RC9RC9-BRB

(c)



10ndash7

10ndash6

10ndash5

10ndash4

10ndash3

10ndash2

Mea

n an

nual

rate

of e

xcee

danc

e

RC3RC3-BRB

(a)


10ndash7

10ndash6

10ndash5

10ndash4

10ndash3

10ndash2

Mea

n an

nual

rate

of e

xcee

danc

e

RC6RC6-BRB

(b)

Figure 8 Continued



5 Conclusions


Data Availability




Acknowledgments


References






10ndash7

10ndash6

10ndash5

10ndash4

10ndash3

10ndash2

Mea

n an

nual

rate

of e

xcee

danc

e

RC9RC9-BRB

(c)

















































500 1000 1500 20000Sa (T1) (cms2)

0

02

04

06

08

1P

[MID

gt 0

02

| Sa]

RC3RC3-BRB

(a)

500 1000 1500 20000Sa (T1) (cms2)

0

02

04

06

08

1

P [M

ID gt

00

2 | Sa]

RC6RC6-BRB

(b)

500 1000 1500 20000Sa (T1) (cms2)

0

02

04

06

08

1

P [M

ID gt

00

2 | Sa]

RC9RC9-BRB

(c)



10ndash7

10ndash6

10ndash5

10ndash4

10ndash3

10ndash2

Mea

n an

nual

rate

of e

xcee

danc

e

RC3RC3-BRB

(a)


10ndash7

10ndash6

10ndash5

10ndash4

10ndash3

10ndash2

Mea

n an

nual

rate

of e

xcee

danc

e

RC6RC6-BRB

(b)

Figure 8 Continued



5 Conclusions


Data Availability




Acknowledgments


References






10ndash7

10ndash6

10ndash5

10ndash4

10ndash3

10ndash2

Mea

n an

nual

rate

of e

xcee

danc

e

RC9RC9-BRB

(c)


















































5 Conclusions


Data Availability




Acknowledgments


References






10ndash7

10ndash6

10ndash5

10ndash4

10ndash3

10ndash2

Mea

n an

nual

rate

of e

xcee

danc

e

RC9RC9-BRB

(c)










































































































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