seismic performance evaluation of special rc frames with

Research ArticleSeismic Performance Evaluation of Special RC Frames withGravity Steel Columns under the Base Level

Amin Zaherdannak1 Amirhosein Shabani 12 and Saeed Erfani 1

1Department of Civil and Environmental Engineering Amirkabir University of Technology (Tehran Polytechnic) Tehran Iran2Department of Civil Engineering and Energy Technology Oslo Metropolitan University Oslo Norway

Correspondence should be addressed to Saeed Erfani sderfaniautacir

Received 4 March 2020 Revised 12 April 2020 Accepted 13 May 2020 Published 30 June 2020

Academic Editor Roberto Palma

Copyright copy 2020 Amin Zaherdannak et al (is is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work isproperly cited

In manymultistory buildings basement levels are used as parking spaces However dimensions of reinforced concrete columns atthese levels cause them to be unideal parking spaces An alternative is to replace the RC columns in middle frames with steelcolumns that are not a part of seismic force resisting system and only support vertical loads therefore have smaller sections Usingsimply supported steel columns under the base level is beneficial not only because they have smaller cross-sections which lead toincreasing the parking space but also these steel columns are easier to be replaced after any possible damages and can beconsidered as convenient alternatives compared to ordinary RC columns in construction In this research seismic performance ofstructures implementing the suggested alternative is evaluated using nonlinear static and dynamic analyses and compared to thatof regular counterparts Results show that these structures pass the acceptability tests proposed by FEMA P695 methodologyMoreover seismic performance factors of these two structural systems have been calculated and proposed

1 Introduction

To minimize casualties in large earthquakes building codesprovide structural engineers with seismic design require-ments (is goal can be generally achieved by limiting theprobability of global structural collapse of buildings torelatively low levels However not even total satisfaction of abuilding code provisions can necessarily mean that abuilding will meet certain performance objectives duringlarge earthquakes Compared to the intended performanceobjective of the building code the performance exhibited bythe building may or may not be adequate (erefore amethodology is needed for evaluating the performance ofany given building designed based on requirements of abuilding code (e methodology introduced in FEMA P695satisfies this need and it has been used in this study

In the system the performance of which is evaluated inthis study the upper part consists of special RC momentframes Several research efforts have focused on developingmethods to improve seismic design procedure of RC frames

beyond minimum code requirements [1ndash3] and perfor-mance-based earthquake engineering is used to assess theeffectiveness of these improvements [4 5] Seismic collapsesafety of ductile moment frames has been assessed byHaselton [6] and seismic collapse capacity of nonductile RCframes is evaluated and compared with ductile momentframes by Abbie et al [7]

FEMA P695 introduces a methodology for quantifica-tion of building seismic performance factors used in seismicdesign and for specifying whether a structure satisfies theseismic performance objectives of building codes using theprobabilistic assessment of collapse risk [8]

According to FEMA P695 methodology Archetypes fornonlinear analyses must be selected so that they covernormal variations of key characteristics of structures [8]characteristics capable of affecting the overall seismic be-havior of structures such as height and bay length (enarchetypes with similarities in their structural behaviors andcharacteristics are classified into distinct performancegroups

HindawiShock and VibrationVolume 2020 Article ID 8825258 11 pageshttpsdoiorg10115520208825258

According to the ASCE 07-10 the base level location forthe structures with basement walls without any openingsand with compacted soil surrounding the walls is consideredfrom ground floor where the basement wall ends [9 10]

(is effort focuses on evaluating and comparing theperformance of two types of structural systems varying inone aspect At stories above the base level both types consistof special RC moment frames and dual systems (special RCmoment frames and special RC shear walls) on perimeterframes (e difference between two types is that in one themiddle frames in basement levels are special RC momentframes similar to stories above but on the other the col-umns in these middle frames are replaced with steel columnsthat are not a part of the SFRS In this article these two typesof buildings will be referred to as RCT (Typical RC system)and RCN (New RC system) respectively

Seismic performance of RC basement walls has beenevaluated alone [11] and research studies about combiningRC basement walls with special steel moment resistingframes have been conducted [12 13] but seismic perfor-mance of RC frames with basement walls should be per-formed as a prevalent construction method

Basement stories are often used as parking spaces and therelatively large dimensions of the RC columns in these levelsespecially in buildings with shorter bay lengths couldprevent these levels from being ideal parking spaces (eseRC columns can be replaced with gravity steel columns Notbeing a part of SFRS and only bearing vertical loads allowsthe steel columns in middle frames to have sections withrelatively smaller dimensions and making these levels idealfor the intended use

Moreover in this paper an innovative connection hasbeen introduced for steel column-to-RC beam connectionsRequiring only bolts and not any reinforcements or rebarsand being relatively faster-to-fasten connections comparedto traditional counterparts could make this connectionpreferable Using only bolts this connection can be easilydetached or replaced after any damages

Seismic performance factors for RCT and RCN modelsare not included in ASCE 07 Table 12-21 For designingstructures with two structural systems in which the uppersystem is more flexible than the lower ASCE 07 recom-mends a two-stage analysis In this paper the entirestructure has been designed using only the seismic per-formance factors of special RC moment resisting framesinstead of the recommended two-stage analysis Resultsshow that based on the FEMA P695 method this alternativedesign does not negatively affect the performance of thestructures [11]

For nonlinear models lumped plasticity approach isused to model frame elements Frame elements plastichinges are modeled using a stiffness and strength degradingmodel developed by Ibarra et al and modified by Lignos[14 15]

2 Designing Models

A set of archetypical structures are employed in the as-sessment (ese structures represent engineering design and

practice for RCT and RCN systems in high seismic regions16 structural designs encompass key structural design pa-rameters including building heights from 3 to 15 storiesabove the base level and from 2 to 5 basement levels and baywidths of 4 and 7m (1312 to 2297 ft) As summarized inTable 1 for both RCN and RCT archetypes this table isidentical All structures are space frame systems (ese ar-chetypes are classified into performance groups each ofwhich includes structures with relatively similar configu-ration and therefore structural behavior Table 1 includes thefundamental period (CuTa defined by Equation (5)-(5) ofFEMA P695) T the seismic base shear coefficient Cs and themaximum considered earthquake MCE-level spectral ac-celeration SMT [8]

All Archetypes are designed using response spectrumanalysis procedure for seismic design category Dmax Deadand live loads are applied to stories and static and dynamicsoil loads are applied to basement walls according to ASCE07-10 [9 16] A simplified method for considering the soil-structure interaction is used for designing the models thatthe soil is neglected but the wall is modeled Each buildingis designed according to the provisions of ASCE 7-10 ACI318-14 and AISC 360-10 [9 17 18] and all applicablerequirements for detailing stiffness strength and capacitydesign are met except for two-stage analysis procedure Asmentioned in ASCE 7-10 for structures having a flexibleupper portion above a rigid lower portion a two-stageanalysis procedure can be used (is study intentionallydoes not implement this requirement and uses seismicdesign coefficients of RC SMFs for designing both upperand lower portions of the building (e validity of thisassumption is put to test by FEMA P695 methodologyAccording to Table 122-1 in ASCE 07ndash10 design coeffi-cient and factors are R 8 Cd 55 and Ωo 3 for RCSMFs and R 7 Cd 55 and Ωo 25 for special RCshear walls [9]

Detailing and in some cases sections of RC frame ele-ments above the base level are different in RCN archetypescompared to RCT counterparts (e reason is the incapa-bility of RCN buildings to transfer moments to stories belowthe base level using RC columns of middle frames since thesteel columns located at basement levels are not a part ofSFRS and can only provide support for gravity loads(erefore there is a different distribution of forces in RCNbuildings In middle frames moments at both ends of RCcolumns at the first story above the base level have smallervalues in RCN compared to their counterparts in RCTbuildings On the contrary beams located at the first storyand frame elements (both beam and column) and located atupper stories have larger moments in RCN buildings (edifferent distribution of forces leads to different detailingand section dimensions

Steel columns have box sections and are connected tobeams with simple connections Figure 1 shows a schematicof these simple connections By comparing the cross-sectionareas of the steel and RC middle columns under the baselevel it has resulted that this substitution leads to approx-imately 84 (as a mean value for all the archetypes) of cross-section area reduction

2 Shock and Vibration

3 Nonlinear Model Development

Figure 2 shows the nonlinear models created using OpenSeesstructural analysis platform Having shear walls in basementlevels the outer frames display a different structural be-havior compared to inner frames therefore neither canrepresent the behavior of the entire structure One solutioncan be used to model two frames side-by-side to capture thebehavior of both types of frames and their interactions (issolution eliminates the need for modeling leaning columnsthat capture the destabilizing P minus Δ effects since the gravitysystem (ie steel columns in basement levels) is directlymodeled and the other frames are space frames [19] (esetwo adjacent frames in the OpenSees model are connectedwith hinged rigid elements (ie elastic element with a veryhigh Youngrsquos modulus) that represent the slab connectingthese frames together

Damage reports of earthquakes including (1971) SanFernando and (1994) Northridge show that building base-ment walls have never been damaged due to soil seismicpressures [20] Based on these reports basement walls do notexhibit a nonlinear behavior in earthquakes therefore thebasement walls are modeled as elastic elements using planestress for node quadrilateral elements in OpenSees namedQUAD with Youngrsquos modulus of concrete (e results alsoshow that these levels undergo extremely small drifts duringIDAs compared with nonbasement stories Furthermore formodeling segments of basement walls that can contribute tothe response of modeled frames (ie parts of basement wallsperpendicular to directly modeled basement walls) aremodeled as elastic columns [21]

In this study for models subjected to dynamic loadsalthough the soil surrounding the retaining walls is not

directly modeled the effect of soil on the behavior of thestructure is accounted for using another method Based onthis method the soil is not modeled and since the horizontalresistance of soil is ignored the masses in subterraneanfloors are ignored as well [22ndash24]

(e lumped plasticity models have gained more popu-larity for seismic response simulation of RC buildings[8 25 26] Lumped plasticity elements were used because oftheir ability to capture rebar buckling and strain softeningwhich are critical for simulating the collapse of RC frames(e plastic hinges of frame elements (ie beams and col-umns) are modeled using a stiffness and strength degradingmodel with a peak-oriented hysteretic response developedby Ibarra et al (2005) and modified by Lignos [14 15 25]

Figure 3 illustrates the backbone curve and cyclic be-havior of the modified IMK (Ibarra Medina Krawinkler) interms of a moment-rotation relationship (e backbonecurve has three key parameters namely the elastic stiffnesspostyield stiffness and postcapping stiffness (strain soft-ening) Postcapping stiffness and the displacement (ductilitycapacity) at which this softening occurs are the most im-portant contributors affecting the seismic collapse capacity[6] In the cyclic behavior of this model the rate of cyclicdeterioration depends on the deterioration parameter whichdefines a reference energy-dissipation capacity for thecomponent denoting the cumulative plastic rotation ca-pacity [15 27 28] Parameters for RC frame elements modelsare calibrated based on test data for RC columns with ductiledetailing and low to moderate axial loads ATC 72 [24]

Modeling nonlinear behavior using plastic hingeswhen used in combination with Rayleigh damping couldlead to unrealistically large damping forces in plastichinges [29] One solution for this problem is the approachtaken by Ibarra and Media In this approach each beamelement is modeled as a combination of an elastic beamand rotational end spring(s) (ese zero-length springswhich do not have damping assigned to them are where theplastic hinging is concentrated In this model the ratio ofthe initial stiffness of end springs to the stiffness of elasticbeam element is defined by the parameter n Relativelylarge values of n are chosen and therefore most of elasticdeformation occurs in the elastic beam All the damping isassigned to the elastic beam as an equivalent stiffness-proportional damping [30] In this solution relativelylarge values of n are suggested [29] Larger values of n canmake the numerical convergence in nonlinear analyses a

Table 1 Archetypersquos configuration development and design properties for SBCC and RBCC archetypes

No of performancegroups

Archetype design IDnumber

No of SMFstories

No of stories under thebase level

No ofspans

Bay length(m)

T(sec)

SMT(g) Cs

1 3U2B3B4mBL 3 2 3 4 055 15 01252 3U2B3B7mBL 3 2 3 7 055 15 0125

37U2B3B4mBL 7 3 3 4 116 078 006511U4B3B4mBL 11 4 3 4 172 053 004415U5B3B4mBL 15 5 3 4 227 053 0044


BoltSteelplateSteel

column

RC beam

Figure 1 Schematic diagram of simple connections of steel col-umns in RCN archetypes

Shock and Vibration 3

more time-consuming and sometimes impossible processAnother issue is the assumption of end moments (in theoriginal frame element) that are equal in value and signwhich is not the case in earthquakes [30]

F Zareian and H Krawinkler (2009) have asserted by usingelastic frame elements with stiffness modifiers moment gra-dient problem is eliminated and considerably smaller values ofn can be used leading to less time-consuming numericalconvergences in nonlinear analyses [30] (erefore in thisstudy all elements are modeled by elastic frame elements withstiffness modifiers and n value equal to one

Rayleigh damping is applied equal to 5 of criticaldamping in the first and third modes of the models (eRayleigh damping stiffness-proportional term is assignedonly to the elastic frame elements with stiffness modifierswhile the mass-proportional term is assigned to all the framenodes with mass [6 31ndash33]

(e nonlinear models of structures employ a two-di-mensional joint model which was added to OpenSeesframework by Altoontash (e joint model accounts for thefinite joint size and includes a system of constraints androtational springs for direct modeling of the shear panel andbond-slip behavior [8] Figure 4 shows a schematic diagramof this model

4 Nonlinear Analyses

41 Nonlinear Static Analysis (Pushover) Nonlinear staticanalysis (pushover) is performed for all archetypes by using afirst mode lateral load pattern in accordance with Section63 FEMA P695 in order to compute the system over-strength factor (Ω0) and period-based ductility microT For agiven index archetype the overstrength factor Ω is definedas the ratio of maximum shear resistance Vmax to the designbase shear V For a given index archetype the period-basedductility μT is defined as the ratio of ultimate roof driftdisplacement δu to the effective yield roof drift displace-ment δyeff (ese parameters are shown in an idealizedpushover curve in Figure 5 In order to quantify these valuesthe lateral loads are increasingly applied until a loss of 20 ofthe base shear capacity is achieved [8]

Pushover analysis provides insight into some of thenonlinear behavior aspects of structures However since theclassical pushover analysis relies on constant lateral loadspatterns it is incapable of capturing the effects of highermodes (erefore it has been found to exhibit considerabledeviations from inelastic demands during dynamic analysesand seismic events [34]

Figure 6 compares pushover curves for two models ofRCN and RCT In these figures the base shear and roof driftare normalized by design base shear and building heightrespectively

RCN models exhibit higher maximum shear resistancescompared to RCT models (e reason is different detailingand in some models different sections Figure 7 showsplastic hinge distribution in somemodels when the structureis pushed to the ultimate roof drift displacement as definedin FEMA P695 (e colors assigned to these plastic hingesindicate the severity of plastic hinging at these points (ecolor cyan for example indicates that a plastic hinge hasundergone a rotation between 1 to 5 times larger than itsyield rotation Absence of a circle indicates a rotation smallerthan the yield rotation

As shown in Figure 7 RC beams located precisely abovethe topmost steel columns in RCN models undergo con-siderably more severe rotations Since moments cannot betransferred from RC columns to the simply connected steelcolumns these beams transfer the moments to outer framesthus undergo larger forces and rotations Moreover in RCN

4m4m

4m

Figure 2 Plan view of archetypes and schematic nonlinear model of them

Chord rotation θ

Mom

ent M

Reloading stiffnessdeterioration

Unloading stiffnessdeterioration

Postcapping strength deterioration

θr

θp θpc

θu

Strength deterioration

Mndashr = xMndash

y

M+r = xM+

y

Figure 3 Backbone curve and cyclic behavior of the RC beam-column plastic hinge model [15]


building compared to RCT counterparts plastic hingingoccurs in more beams and in most cases it is more severewhich reflects a different distribution of forces in frameelements

42 Incremental Dynamic Analysis (IDA) IDA procedurerecommended by FEMA P695 involves performing a seriesof nonlinear dynamic time-history analyses using 22 pairs ofground motion records [35] Individual ground motions arescaled to increasing intensities until the structural modelreaches a global collapse point (e lowest intensity at whichhalf of the ground motions cause the structural modelto collapse is the median collapse capacity SCT (e ratio ofSCT to maximum considered earthquake (MCE) spectralacceleration at the fundamental period of each model (SMT)defines the collapse margin ratio (CMR) of that model [8]

(e results of these time-history analyses for one groundmotion create a single IDA curve An IDA curve is a diagramof the ground motion intensity measure (IM) against anengineering demand parameter (EDP) (e spectral accel-eration corresponding to the first mode elastic vibrationperiod of the structure Sa(T1) is a widely used groundmotion IM and the chosen EDP is the maximum interstorydrift [36ndash38]

For each archetype a collapse fragility curve is definedusing a cumulative distribution function which relates theprobability of collapse to the ground motion IM [39] (estandard deviation of natural logarithm and the mediancollapse capacity SCT are the parameters which define thecollapse capacity [40]

Figure 8 shows IDA and 16 50 and 84 percent fractilecurves for some of the archetypes with RCN and RCTstructural models as samples

Figure 9 exhibits a comparison of the fragility curves ofthese two models Results show that fragility curves ofcounterpart RCTand RCNmodels bear a close resemblance

(ese fragility curves suggest that substituting RC col-umns with simply supported steel columns at basementstories does not negatively impact the seismic behavior of thestructure [41]

5 Performance Evaluation

(emost important parameter in FEMA P695 methodologyis the adjusted collapse margin ratio (ACMR) Whether ornot a specific structure satisfies the seismic performanceobjectives set by codes is determined using ACMR (isparameter is obtained by multiplying the CMR by spectralshape factor (SSF) for each structural model

ACMR SSF times CMR (1)

Baker and Cornell (2006) showed that rare groundmotions in the western United States have a distinctivespectral shape that is different from the shape of the designspectrum in ASCE 7-10 (e shape of these rare groundmotions is peaked at the period of interest rapidly and dropsat shorter and longer periods Selecting a unique set ofground motions that have the appropriate shape for eachsite hazard level and structural period of interest is notfeasible hence FEMA P695 recommends using SSFmdashwhichis a function of fundamental period and period-basedductilitymdashto remove this conservative bias [8]

Acceptable values of ACMR are based on total systemcollapse uncertainty βTOT and established acceptable values

Panel zone

Beam-endzone

Column-endzone

Figure 4 Schematic diagram of joint2D [8]

Roof displacementδyeff δu

08Vmax

V

Vmax

Baseshear

Figure 5 Idealized pushover curve [8]


for probability of collapse (e total system collapse un-certainty is obtained using the following formula

βTOT

β2RTR + β2DR + β2TD + β2MLD

1113969

(2)

According to FEMA P695 in the performance evalua-tion of the systems with relatively large period-based duc-tilities (μT ge 3) the constant value of 04 is considered forrecord-to-record uncertainty (βRTR) [8]

3

25

2

15

1

05

00 002 004 006 008 01

Base

shea

rde

sign

base

shea

r

Roof dri ratio

3U2B3B4mBL

RCTRCN

(a)

0 002001 003 004 005 006 007Roof dri ratio

Base

shea

rde

sign

base

shea

r 25

2

15

1

05

0

7U3B3B4mBL

RCTRCN

(b)

Base

shea

rde

sign

base

shea

r

0 001 002 003 004 005 006Roof dri ratio

3

25

2

15

1

05

0

11U4B3B7mBL

RCTRCN

(c)

0 002001 003 004 005Roof dri ratio

Base

shea

rde

sign

base

shea

r 3

25

2

15

1

05

0

15U5B3B7mBL

RCTRCN

(d)

Figure 6 Normalized pushover curves comparison for some of the archetypes as samples for both RCN and RCT models

15 story [RCT] 15 story [RCN] 11 story [RCT] 11 story [RCN]

Ratio of maximum rotation to yield rotation

01ndash05 05ndash10 10ndash15 15ndash20 20ndash25

Figure 7 Sideway collapse mechanism of archetype 11 and 15-story buildings with 4m-long bay lengths under pushover analysis to δu


002 004 006 008 010Maximum interstory dri


Sa (T

5

) (g)

6

5

4

3

2

1

0

Sa (T

5

) (g)

6

5

4

3

2

1

0

84

50

16

84

50

16

RCT RCN

(a)



Sa (T

5

) (g)

3

2

1

0

Sa (T

5

) (g)

3

2

1

0

84

50

16

84

50

16

RCT RCN

(b)



Sa (T

5

) (g)

3

2

1

0

Sa (T

5

) (g)

3

2

1

0

84

50

16

84

50

16

RCT RCN

(c)

Figure 8 IDA and fractile curves of (a) 7U2B3B4mBL (b) 11U4B3B7mBL and (c) 15U5B3B7mBL for RCT and RCN models


00

02

04

06

08

10

12C

olla

pse p

roba

bilit

y

2 4 6 8 100Sa (T1 5) (g)

3U2B3B4mBL

RCTRCN

(a)

00

02

04

06

08

10

12

Col

laps

e pro

babi

lity

2 4 6 8 100Sa (T1 5) (g)

3U2B3B7mBL

RCTRCN

(b)

00

02

04

06

08

10

12

Col

laps

e pro

babi

lity

05 1 15 2 25 30Sa (T1 5) (g)

11U4B3B4mBL

RCTRCN

(c)

00

02

04

06

08

10

12

Col

laps

e pro

babi

lity

05 1 15 2 25 30Sa (T1 5) (g)

11U4B3B7mBL

RCTRCN

(d)

0

02

04

06

08

1

12

Col

laps

e pro

babi

lity

1 2 3 4 50Sa (T1 5) (g)

7U3B3B7mBL

RCTRCN

(e)

0

02

04

06

08

1

12

Col

laps

e pro

babi

lity

05 1 15 2 250Sa (T1 5) (g)

15U5B3B4mBL

RCTRCN

(f )

Figure 9 Fragility curves of some archetypes as samples for RCN and RCT models


ACI 318-14 design requirements have been utilized inthis study Since this code includes lessons learned fromrecent major earthquakes and represents many years ofexperiment and development for assessing uncertaintyaccording to FEMAP695methodology design requirementsare categorized as superior (A) and the value of 01 isconsidered for βDR

(e test data used in this article contain both cyclic andmonotonic loading protocols and cover a wide range ofcolumn design configurations Nevertheless a number ofthese loading protocols are not continued to deformationslarge enough to observe strength loss Moreover these testdata do not include beam elements with attached slabs Inaddition only column element tests were utilized for thecalibration of the element model while subassemblage testsand full-scale tests were not used Considering the aboveobservations the test data are categorized as Good (B) andthe value of 02 is assigned to βTD [8]

Many detailing and capacity design requirements con-trol RC frame buildings which limits possible modes offailure (e primary expected mode of failure is flexuralhinging leading to sideways collapse By capturing postpeakdegrading response under both cyclic and monotonicloading the modeling approach can simulate flexuralhinging and sideway collapse Furthermore the modelingapproach can simulate structural response directly up to

collapse point by simulating all expected modes of damagethat could lead to collapse However despite being calibratedusing column data the model was not well calibrated tobeam-slabs and it does not capture axial-flexural interactionin columns Additionally for modeling soil-structure in-teraction a simplified method is used and basement wallswere assumed to remain elastic up to global collapse of thestructure Consequently the modeling quality is categorizedas good (B) and the value of 05 is assigned to βMDL

Using values assigned to different sources of uncertaintydiscussed above the total system collapse uncertainty of thestructural models βTOT is calculated to 0675 For theevaluation of the response modification coefficient based onFEMA P695 methodology acceptable seismic performanceis achieved when the average value of ACMR for eachperformance group exceeds the acceptable value of theACMR corresponding to the collapse probability of 10(ACMR10) and individual value of ACMR for each ar-chetype exceeds the acceptable value of the ACMR corre-sponding to the collapse probability of 20 (ACMR20)Using Tables 7-3 in FEMA P695 and a total system collapseuncertainty ACMR20 and ACMR10 values are found to be176 and 238 respectively [8]

Tables 2 and 3 summarize the results obtained fromnumerous IDA and pushover analyses for both RCT andRCN structural models

Table 2 Collapse performance evaluation of RCT archetypes



No of SMFstories Ω μt Sct Smt CMR SSF ACMR Accept

ACMRPass orfail

1 3U2B3B4mBL 3 277 877 39 15 26 133 346 18 PGroup performance 277 346 245 P2 3U2B3B7mBL 3 265 788 333 15 222 133 296 18 P

Group performance3

265 296 245 P7U3B3B4mBL 7 219 768 214 078 275 149 409 18 P11U4B3B4mBL 11 208 753 117 053 221 16 354 18 P15U5B3B4mBL 15 172 828 098 053 185 15 277 18 P

Group performance 199 347 245 P

47U3B3B7mBL 7 238 823 18 078 231 149 345 18 P11U4B3B7mBL 11 262 974 123 053 232 16 371 18 P15U5B3B7mBL 15 227 7 109 053 206 15 309 18 P


Table 3 Collapse performance evaluation of RCN archetypes

No of performancegroup



ACMRPass orfail

1 3U2B3B4mBL 3 283 842 375 15 25 133 333 18 PGroup performance 283 333 245 P2 3U2B3B7mBL 3 27 859 345 15 23 133 306 18 PGroup performance 27 306 245 P






Results show that all archetypes pass the acceptabilitycheck for seismic performance (e value of the systemoverstrength factorΩo for use in design should not be takenless than the largest average value of overstrength Ω of anyperformance group Based on the results summarized intables above 283 is the highest average value for over-strength therefore the overstrength of the system can beconservatively considered 3 and the same value is specifiedin ASCE 7ndash10 for special RC moment frames [8]

6 Conclusions

In this study typical RC columns in middle frames atbasement levels are substituted with simply connected steelcolumns to make these levels more ideal parking spaces bydecreasing the space occupied by structural elements iecolumns Seismic performance of structures with RC col-umns (RCT) and those with the substituted steel columns atbasement levels (RCN) was evaluated based on the FEMAP695 method To evaluate the seismic performance of thesestructures 16 archetypical structures where designedaccording to building codes modeled in OpenSees platformand analyzed using pushover and IDA analyses

Both RCT and RCN structures can be designed usingresponse modification and overstrength factors 8 and 3respectively In order to design either RCN or RCT struc-tures seismic performance factors of special RC framesR 8 Cd 55 and Ωo 3 can be used for designing bothupper and lower parts (ie special RC frames and dualsystems) of the structure In other words the two-stageanalysis procedure recommended by ASCE 7-10 does notneed to be applied to neither RCN nor RCT structures Aregular one-stage analysis will suffice

Inspecting plastic hinging occurrences in structuralmodels when structures are pushed to effective yield drift inpushover analyses show that collector beams at the bottomof the first story above the base level of RCN archetypes aremore prone to plastic hinging compared to their RCTcounterparts (e reason is the different load paths in RCNbuildings and the role these beams play in transferring forcesfrom RC columns in middle frames to RC columns and wallsin lower levels

Because of different detailing and frame element sectionsin RC frames above the base level compared to RCTbuildings RCN structures have higher overstrength values

RCN structures exhibit a similar or improved seismicperformance compared to RCT building thereforesubstituting RC columns by simply connected steel columnsdoes not seem to negatively impact the overall behaviorseismic of the structure

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 they have no conflicts of interest

References

[1] I Hajirasouliha P Asadi and K Pilakoutas ldquoAn efficientperformance-based seismic design method for reinforcedconcrete framesrdquo Earthquake Engineering amp Structural Dy-namics vol 41 no 4 pp 663ndash679 2012

[2] J Bai S Jin C Zhang and J Ou ldquoSeismic optimizationdesign for uniform damage of reinforced concrete moment-resisting frames using consecutive modal pushover analysisrdquoAdvances in Structural Engineering vol 19 no 8 pp 1313ndash1327 2016

[3] M Ahmed S Tayyaba and M W Ashraf ldquoEffect of bucklingrestrained braces locations on seismic responses of high-riseRC core wall buildingsrdquo Shock and Vibration vol 2016Article ID 6808137 15 pages 2016

[4] O Arroyo A Liel and S Gutierrez ldquoA performance-basedevaluation of a seismic design method for reinforced concreteframesrdquo Journal of Earthquake Engineering vol 22 pp 1ndash182017

[5] D Tao Q Ma and S Li ldquoSeismic damage detection ofmoment resisting frame structures using time-frequencyfeaturesrdquo Shock and Vibration vol 2018 Article ID 108654018 pages 2018

[6] C B Haselton ldquoSeismic collapse safety of reinforced concretebuildings I assessment of ductile moment framesrdquo Journal ofStructural Engineering vol 137 no 4 pp 481ndash491 2010

[7] A B Liel C B Haselton and G G Deierlein ldquoSeismiccollapse safety of reinforced concrete buildings II compar-ative assessment of nonductile and ductile moment framesrdquoJournal of Structural Engineering vol 137 no 4 pp 492ndash5022010

[8] Fema Quantification of Building Seismic Performance Factors(FEMA P695) Federal Emergency Management AgencyWashington DC USA 2009

[9] ASCE Design Loads For Buildings And Other StructuresASCESEI 7-10 American Sociey of Civil Engineers RestonVA USA 2010

[10] M Tehranizadeh and M S Barkhordari ldquoEffect of peripheralwall openings in basement and number of basement floors onthe base level of braced framed tube systemrdquo InternationalJournal of Civil Engineering vol 16 2017

[11] J Lee and J Kim ldquoSeismic performance evaluation of stag-gered wall structures using Fema P695 procedurerdquo Magazineof Concrete Research vol 65 no 17 pp 1023ndash1033 2013

[12] A Shabani and S Erfani ldquoEvaluation of seismic performancefactors of special steel moment resisting frames with basementwallsrdquo in Proceedings of the 3rd International Conference ofSteel and Structure Tehran Iran December 2018

[13] A Shabani and S Erfani ldquoSeismic performance evaluation ofSSMF with simple beamndashcolumn connections under the baselevelrdquo International Journal of Steel Structures vol 20pp 1ndash12 2019

[14] L F Ibarra R A Medina and H Krawinkler ldquoHystereticmodels that incorporate strength and stiffness deteriorationrdquoEarthquake Engineering amp Structural Dynamics vol 34no 12 pp 1489ndash1511 2005

[15] D Lignos and H Krawinkler Sidesway Collapse of Deterio-rating Structural Systems under Seismic Excitations Stanforduniversity Stanford CA USA 2012

[16] N Sitar R G Mikola and G Candia ldquoSeismically inducedlateral earth pressures on retaining structures and basementwallsrdquo in Proceedings of the Geotechnical Engineering State ofthe Art and Practice Keynote Lectures from GeoCongresspp 335ndash358 Oakland CA USA 2012


[17] AISC Seismic Provisions for Structural Steel Buildings (ANSIAISC 341-10) American Institute of Steel ConstructionChicago IL USA 2010

[18] ACI Building Code Requirements for Structural Concrete ACI318-14 American Concrete Institute Farmington HillsMichigan USA 2014

[19] A Elkady and D G Lignos ldquoModeling of the compositeaction in fully restrained beam-to-column connections im-plications in the seismic design and collapse capacity of steelspecial moment framesrdquo Earthquake Engineering amp StructuralDynamics vol 43 no 13 pp 1935ndash1954 2014

[20] M Lew N Sitar L Al Atik M Pourzanjani andM B Hudson ldquoSeismic earth pressures on deep buildingbasementsrdquo in Proceedings of the Structural Engineers Asso-ciation of California Annual Convention Proceedings IndianWells CA USA 2010

[21] S Mazzoni OpenSees Command Language Manual OpenSystem for Earthquake Engineering Simulation (OpenSees)New York NY USA 2006

[22] Fema NEHRP Recommended Seismic Provisions for NewBuildings and Other Structures FEMA P-750 Federal Emer-gencey Management Agency Washington DC USA 2009

[23] TBI Guidelines for Performance-Based Seismic Design of TallBuildings Tall Building Initiative New York NY USA 2010

[24] PEERATC Modeling and Acceptance Criteria for SeismicDesign and Analysis of Tall Buildings (ATC 72-1) AppliedTechnology Council Pacific Earthquake Engineering Re-search Center Bekley CA USA 2010

[25] S Manie A S Moghadam and M Ghafory-AshtianyldquoCollapse behavior evaluation of asymmetric buildings sub-jected to bi-directional groundmotionrdquoGe Structural Designof Tall and Special Buildings vol 24 no 8 pp 607ndash628 2015

[26] M Surana Y Singh and D H Lang ldquoFragility analysis ofhillside buildings designed for modern seismic design codesrdquo(e Structural Design of Tall and Special Buildings Article IDe1500 2018

[27] B U Gokkaya J W Baker and G G Deierlein ldquoEstimationand impacts of model parameter correlation for seismicperformance assessment of reinforced concrete structuresrdquoStructural Safety vol 69 pp 68ndash78 2017

[28] D G Lignos and H Krawinkler ldquoDevelopment and utili-zation of structural component databases for performance-based earthquake engineeringrdquo Journal of Structural Engi-neering vol 139 no 8 pp 1382ndash1394 2012

[29] L F Ibarra and H Krawinkler Global Collapse of FrameStructures under Seismic Excitaions Stanford universityStanford CA USA 2005

[30] F Zareian and H Krawinkler Simplified Performance BasedEarthquake Engineering Stanford university Stanford CAUSA 2009

[31] F Zareian and R A Medina ldquoA practical method for propermodeling of structural damping in inelastic plane structuralsystemsrdquo Computers amp Structures vol 88 no 1-2 pp 45ndash532010

[32] A K Chopra and F McKenna ldquoModeling viscous damping innonlinear response history analysis of buildings for earth-quake excitationrdquo Earthquake Engineering amp Structural Dy-namics vol 45 no 2 pp 193ndash211 2016

[33] F A Charney ldquoUnintended consequences of modelingdamping in structuresrdquo Journal of Structural Engineeringvol 134 no 4 pp 581ndash592 2008

[34] M AlHamaydeh S Abdullah A Hamid and A MustaphaldquoSeismic design factors for RC special moment resisting

frames in Dubai UAErdquo Earthquake Engineering and Engi-neering Vibration vol 10 no 4 pp 495ndash506 2011

[35] Z He Z Wang and Y Zhang ldquoCollapse safety margin andseismic loss assessment of RC frames with equal materialcostrdquo Ge Structural Design of Tall and Special Buildingsvol 27 no 1 p e1407 2018

[36] D Vamvatsikos and C A Cornell ldquoApplied incrementaldynamic analysisrdquo Earthquake Spectra vol 20 no 2pp 523ndash553 2004

[37] D Vamvatsikos Seismic Performance Capacity and Reli-ability of Structures as Seen through Incremental DynamicAnalysis Stanford university Stanford CA USA 2012

[38] Y Jiang ldquoSeismic performance of composite structures madewith concrete-filled steel tubular membersrdquo in Proceedings ofthe 16ECEE- 16th European Conference on EarthquakeEngineering (essaloniki Greece June 2018

[39] F Zareian and H Krawinkler ldquoAssessment of probability ofcollapse and design for collapse safetyrdquo Earthquake Engi-neering amp Structural Dynamics vol 36 no 13 pp 1901ndash19142007

[40] K Porter ldquoBeginnerrsquos guide to fragility vulnerability andriskrdquo Encyclopedia of Earthquake Engineering pp 235ndash260Springer Berlin Germany 2015

[41] M Zaker Esteghamati M Banazadeh and Q Huang ldquo(eeffect of design drift limit on the seismic performance of RCdual high-rise buildingsrdquo Ge Structural Design of Tall andSpecial Buildings vol 27 no 8 Article ID e1464 2018


According to the ASCE 07-10 the base level location forthe structures with basement walls without any openingsand with compacted soil surrounding the walls is consideredfrom ground floor where the basement wall ends [9 10]

(is effort focuses on evaluating and comparing theperformance of two types of structural systems varying inone aspect At stories above the base level both types consistof special RC moment frames and dual systems (special RCmoment frames and special RC shear walls) on perimeterframes (e difference between two types is that in one themiddle frames in basement levels are special RC momentframes similar to stories above but on the other the col-umns in these middle frames are replaced with steel columnsthat are not a part of the SFRS In this article these two typesof buildings will be referred to as RCT (Typical RC system)and RCN (New RC system) respectively

Seismic performance of RC basement walls has beenevaluated alone [11] and research studies about combiningRC basement walls with special steel moment resistingframes have been conducted [12 13] but seismic perfor-mance of RC frames with basement walls should be per-formed as a prevalent construction method

Basement stories are often used as parking spaces and therelatively large dimensions of the RC columns in these levelsespecially in buildings with shorter bay lengths couldprevent these levels from being ideal parking spaces (eseRC columns can be replaced with gravity steel columns Notbeing a part of SFRS and only bearing vertical loads allowsthe steel columns in middle frames to have sections withrelatively smaller dimensions and making these levels idealfor the intended use

Moreover in this paper an innovative connection hasbeen introduced for steel column-to-RC beam connectionsRequiring only bolts and not any reinforcements or rebarsand being relatively faster-to-fasten connections comparedto traditional counterparts could make this connectionpreferable Using only bolts this connection can be easilydetached or replaced after any damages

Seismic performance factors for RCT and RCN modelsare not included in ASCE 07 Table 12-21 For designingstructures with two structural systems in which the uppersystem is more flexible than the lower ASCE 07 recom-mends a two-stage analysis In this paper the entirestructure has been designed using only the seismic per-formance factors of special RC moment resisting framesinstead of the recommended two-stage analysis Resultsshow that based on the FEMA P695 method this alternativedesign does not negatively affect the performance of thestructures [11]

For nonlinear models lumped plasticity approach isused to model frame elements Frame elements plastichinges are modeled using a stiffness and strength degradingmodel developed by Ibarra et al and modified by Lignos[14 15]

2 Designing Models

A set of archetypical structures are employed in the as-sessment (ese structures represent engineering design and

practice for RCT and RCN systems in high seismic regions16 structural designs encompass key structural design pa-rameters including building heights from 3 to 15 storiesabove the base level and from 2 to 5 basement levels and baywidths of 4 and 7m (1312 to 2297 ft) As summarized inTable 1 for both RCN and RCT archetypes this table isidentical All structures are space frame systems (ese ar-chetypes are classified into performance groups each ofwhich includes structures with relatively similar configu-ration and therefore structural behavior Table 1 includes thefundamental period (CuTa defined by Equation (5)-(5) ofFEMA P695) T the seismic base shear coefficient Cs and themaximum considered earthquake MCE-level spectral ac-celeration SMT [8]

All Archetypes are designed using response spectrumanalysis procedure for seismic design category Dmax Deadand live loads are applied to stories and static and dynamicsoil loads are applied to basement walls according to ASCE07-10 [9 16] A simplified method for considering the soil-structure interaction is used for designing the models thatthe soil is neglected but the wall is modeled Each buildingis designed according to the provisions of ASCE 7-10 ACI318-14 and AISC 360-10 [9 17 18] and all applicablerequirements for detailing stiffness strength and capacitydesign are met except for two-stage analysis procedure Asmentioned in ASCE 7-10 for structures having a flexibleupper portion above a rigid lower portion a two-stageanalysis procedure can be used (is study intentionallydoes not implement this requirement and uses seismicdesign coefficients of RC SMFs for designing both upperand lower portions of the building (e validity of thisassumption is put to test by FEMA P695 methodologyAccording to Table 122-1 in ASCE 07ndash10 design coeffi-cient and factors are R 8 Cd 55 and Ωo 3 for RCSMFs and R 7 Cd 55 and Ωo 25 for special RCshear walls [9]

Detailing and in some cases sections of RC frame ele-ments above the base level are different in RCN archetypescompared to RCT counterparts (e reason is the incapa-bility of RCN buildings to transfer moments to stories belowthe base level using RC columns of middle frames since thesteel columns located at basement levels are not a part ofSFRS and can only provide support for gravity loads(erefore there is a different distribution of forces in RCNbuildings In middle frames moments at both ends of RCcolumns at the first story above the base level have smallervalues in RCN compared to their counterparts in RCTbuildings On the contrary beams located at the first storyand frame elements (both beam and column) and located atupper stories have larger moments in RCN buildings (edifferent distribution of forces leads to different detailingand section dimensions

Steel columns have box sections and are connected tobeams with simple connections Figure 1 shows a schematicof these simple connections By comparing the cross-sectionareas of the steel and RC middle columns under the baselevel it has resulted that this substitution leads to approx-imately 84 (as a mean value for all the archetypes) of cross-section area reduction













No of SMFstories


No ofspans

Bay length(m)

T(sec)

SMT(g) Cs

1 3U2B3B4mBL 3 2 3 4 055 15 01252 3U2B3B7mBL 3 2 3 7 055 15 0125



BoltSteelplateSteel

column

RC beam













4m4m

4m


Chord rotation θ

Mom

ent M




θr

θp θpc

θu


Mndashr = xMndash

y

M+r = xM+

y















Panel zone

Beam-endzone

Column-endzone



08Vmax

V

Vmax

Baseshear




βTOT


1113969

(2)


3

25

2

15

1

05

00 002 004 006 008 01

Base

shea

rde

sign

base

shea

r

Roof dri ratio

3U2B3B4mBL

RCTRCN

(a)

0 002001 003 004 005 006 007Roof dri ratio

Base

shea

rde

sign

base

shea

r 25

2

15

1

05

0

7U3B3B4mBL

RCTRCN

(b)

Base

shea

rde

sign

base

shea

r

0 001 002 003 004 005 006Roof dri ratio

3

25

2

15

1

05

0

11U4B3B7mBL

RCTRCN

(c)

0 002001 003 004 005Roof dri ratio

Base

shea

rde

sign

base

shea

r 3

25

2

15

1

05

0

15U5B3B7mBL

RCTRCN

(d)









Sa (T

5

) (g)

6

5

4

3

2

1

0

Sa (T

5

) (g)

6

5

4

3

2

1

0

84

50

16

84

50

16

RCT RCN

(a)



Sa (T

5

) (g)

3

2

1

0

Sa (T

5

) (g)

3

2

1

0

84

50

16

84

50

16

RCT RCN

(b)



Sa (T

5

) (g)

3

2

1

0

Sa (T

5

) (g)

3

2

1

0

84

50

16

84

50

16

RCT RCN

(c)



00

02

04

06

08

10

12C

olla

pse p

roba

bilit

y

2 4 6 8 100Sa (T1 5) (g)

3U2B3B4mBL

RCTRCN

(a)

00

02

04

06

08

10

12

Col

laps

e pro

babi

lity

2 4 6 8 100Sa (T1 5) (g)

3U2B3B7mBL

RCTRCN

(b)

00

02

04

06

08

10

12

Col

laps

e pro

babi

lity

05 1 15 2 25 30Sa (T1 5) (g)

11U4B3B4mBL

RCTRCN

(c)

00

02

04

06

08

10

12

Col

laps

e pro

babi

lity

05 1 15 2 25 30Sa (T1 5) (g)

11U4B3B7mBL

RCTRCN

(d)

0

02

04

06

08

1

12

Col

laps

e pro

babi

lity

1 2 3 4 50Sa (T1 5) (g)

7U3B3B7mBL

RCTRCN

(e)

0

02

04

06

08

1

12

Col

laps

e pro

babi

lity

05 1 15 2 250Sa (T1 5) (g)

15U5B3B4mBL

RCTRCN

(f )













ACMRPass orfail


Group performance3









ACMRPass orfail








6 Conclusions






Data Availability




References
























































No of SMFstories


No ofspans

Bay length(m)

T(sec)

SMT(g) Cs

1 3U2B3B4mBL 3 2 3 4 055 15 01252 3U2B3B7mBL 3 2 3 7 055 15 0125



BoltSteelplateSteel

column

RC beam













4m4m

4m


Chord rotation θ

Mom

ent M




θr

θp θpc

θu


Mndashr = xMndash

y

M+r = xM+

y















Panel zone

Beam-endzone

Column-endzone



08Vmax

V

Vmax

Baseshear




βTOT


1113969

(2)


3

25

2

15

1

05

00 002 004 006 008 01

Base

shea

rde

sign

base

shea

r

Roof dri ratio

3U2B3B4mBL

RCTRCN

(a)

0 002001 003 004 005 006 007Roof dri ratio

Base

shea

rde

sign

base

shea

r 25

2

15

1

05

0

7U3B3B4mBL

RCTRCN

(b)

Base

shea

rde

sign

base

shea

r

0 001 002 003 004 005 006Roof dri ratio

3

25

2

15

1

05

0

11U4B3B7mBL

RCTRCN

(c)

0 002001 003 004 005Roof dri ratio

Base

shea

rde

sign

base

shea

r 3

25

2

15

1

05

0

15U5B3B7mBL

RCTRCN

(d)









Sa (T

5

) (g)

6

5

4

3

2

1

0

Sa (T

5

) (g)

6

5

4

3

2

1

0

84

50

16

84

50

16

RCT RCN

(a)



Sa (T

5

) (g)

3

2

1

0

Sa (T

5

) (g)

3

2

1

0

84

50

16

84

50

16

RCT RCN

(b)



Sa (T

5

) (g)

3

2

1

0

Sa (T

5

) (g)

3

2

1

0

84

50

16

84

50

16

RCT RCN

(c)



00

02

04

06

08

10

12C

olla

pse p

roba

bilit

y

2 4 6 8 100Sa (T1 5) (g)

3U2B3B4mBL

RCTRCN

(a)

00

02

04

06

08

10

12

Col

laps

e pro

babi

lity

2 4 6 8 100Sa (T1 5) (g)

3U2B3B7mBL

RCTRCN

(b)

00

02

04

06

08

10

12

Col

laps

e pro

babi

lity

05 1 15 2 25 30Sa (T1 5) (g)

11U4B3B4mBL

RCTRCN

(c)

00

02

04

06

08

10

12

Col

laps

e pro

babi

lity

05 1 15 2 25 30Sa (T1 5) (g)

11U4B3B7mBL

RCTRCN

(d)

0

02

04

06

08

1

12

Col

laps

e pro

babi

lity

1 2 3 4 50Sa (T1 5) (g)

7U3B3B7mBL

RCTRCN

(e)

0

02

04

06

08

1

12

Col

laps

e pro

babi

lity

05 1 15 2 250Sa (T1 5) (g)

15U5B3B4mBL

RCTRCN

(f )













ACMRPass orfail


Group performance3









ACMRPass orfail








6 Conclusions






Data Availability




References























































4m4m

4m


Chord rotation θ

Mom

ent M




θr

θp θpc

θu


Mndashr = xMndash

y

M+r = xM+

y















Panel zone

Beam-endzone

Column-endzone



08Vmax

V

Vmax

Baseshear




βTOT


1113969

(2)


3

25

2

15

1

05

00 002 004 006 008 01

Base

shea

rde

sign

base

shea

r

Roof dri ratio

3U2B3B4mBL

RCTRCN

(a)

0 002001 003 004 005 006 007Roof dri ratio

Base

shea

rde

sign

base

shea

r 25

2

15

1

05

0

7U3B3B4mBL

RCTRCN

(b)

Base

shea

rde

sign

base

shea

r

0 001 002 003 004 005 006Roof dri ratio

3

25

2

15

1

05

0

11U4B3B7mBL

RCTRCN

(c)

0 002001 003 004 005Roof dri ratio

Base

shea

rde

sign

base

shea

r 3

25

2

15

1

05

0

15U5B3B7mBL

RCTRCN

(d)









Sa (T

5

) (g)

6

5

4

3

2

1

0

Sa (T

5

) (g)

6

5

4

3

2

1

0

84

50

16

84

50

16

RCT RCN

(a)



Sa (T

5

) (g)

3

2

1

0

Sa (T

5

) (g)

3

2

1

0

84

50

16

84

50

16

RCT RCN

(b)



Sa (T

5

) (g)

3

2

1

0

Sa (T

5

) (g)

3

2

1

0

84

50

16

84

50

16

RCT RCN

(c)



00

02

04

06

08

10

12C

olla

pse p

roba

bilit

y

2 4 6 8 100Sa (T1 5) (g)

3U2B3B4mBL

RCTRCN

(a)

00

02

04

06

08

10

12

Col

laps

e pro

babi

lity

2 4 6 8 100Sa (T1 5) (g)

3U2B3B7mBL

RCTRCN

(b)

00

02

04

06

08

10

12

Col

laps

e pro

babi

lity

05 1 15 2 25 30Sa (T1 5) (g)

11U4B3B4mBL

RCTRCN

(c)

00

02

04

06

08

10

12

Col

laps

e pro

babi

lity

05 1 15 2 25 30Sa (T1 5) (g)

11U4B3B7mBL

RCTRCN

(d)

0

02

04

06

08

1

12

Col

laps

e pro

babi

lity

1 2 3 4 50Sa (T1 5) (g)

7U3B3B7mBL

RCTRCN

(e)

0

02

04

06

08

1

12

Col

laps

e pro

babi

lity

05 1 15 2 250Sa (T1 5) (g)

15U5B3B4mBL

RCTRCN

(f )













ACMRPass orfail


Group performance3









ACMRPass orfail








6 Conclusions






Data Availability




References

























































Panel zone

Beam-endzone

Column-endzone



08Vmax

V

Vmax

Baseshear




βTOT


1113969

(2)


3

25

2

15

1

05

00 002 004 006 008 01

Base

shea

rde

sign

base

shea

r

Roof dri ratio

3U2B3B4mBL

RCTRCN

(a)

0 002001 003 004 005 006 007Roof dri ratio

Base

shea

rde

sign

base

shea

r 25

2

15

1

05

0

7U3B3B4mBL

RCTRCN

(b)

Base

shea

rde

sign

base

shea

r

0 001 002 003 004 005 006Roof dri ratio

3

25

2

15

1

05

0

11U4B3B7mBL

RCTRCN

(c)

0 002001 003 004 005Roof dri ratio

Base

shea

rde

sign

base

shea

r 3

25

2

15

1

05

0

15U5B3B7mBL

RCTRCN

(d)









Sa (T

5

) (g)

6

5

4

3

2

1

0

Sa (T

5

) (g)

6

5

4

3

2

1

0

84

50

16

84

50

16

RCT RCN

(a)



Sa (T

5

) (g)

3

2

1

0

Sa (T

5

) (g)

3

2

1

0

84

50

16

84

50

16

RCT RCN

(b)



Sa (T

5

) (g)

3

2

1

0

Sa (T

5

) (g)

3

2

1

0

84

50

16

84

50

16

RCT RCN

(c)



00

02

04

06

08

10

12C

olla

pse p

roba

bilit

y

2 4 6 8 100Sa (T1 5) (g)

3U2B3B4mBL

RCTRCN

(a)

00

02

04

06

08

10

12

Col

laps

e pro

babi

lity

2 4 6 8 100Sa (T1 5) (g)

3U2B3B7mBL

RCTRCN

(b)

00

02

04

06

08

10

12

Col

laps

e pro

babi

lity

05 1 15 2 25 30Sa (T1 5) (g)

11U4B3B4mBL

RCTRCN

(c)

00

02

04

06

08

10

12

Col

laps

e pro

babi

lity

05 1 15 2 25 30Sa (T1 5) (g)

11U4B3B7mBL

RCTRCN

(d)

0

02

04

06

08

1

12

Col

laps

e pro

babi

lity

1 2 3 4 50Sa (T1 5) (g)

7U3B3B7mBL

RCTRCN

(e)

0

02

04

06

08

1

12

Col

laps

e pro

babi

lity

05 1 15 2 250Sa (T1 5) (g)

15U5B3B4mBL

RCTRCN

(f )













ACMRPass orfail


Group performance3









ACMRPass orfail








6 Conclusions






Data Availability




References














































βTOT


1113969

(2)


3

25

2

15

1

05

00 002 004 006 008 01

Base

shea

rde

sign

base

shea

r

Roof dri ratio

3U2B3B4mBL

RCTRCN

(a)

0 002001 003 004 005 006 007Roof dri ratio

Base

shea

rde

sign

base

shea

r 25

2

15

1

05

0

7U3B3B4mBL

RCTRCN

(b)

Base

shea

rde

sign

base

shea

r

0 001 002 003 004 005 006Roof dri ratio

3

25

2

15

1

05

0

11U4B3B7mBL

RCTRCN

(c)

0 002001 003 004 005Roof dri ratio

Base

shea

rde

sign

base

shea

r 3

25

2

15

1

05

0

15U5B3B7mBL

RCTRCN

(d)









Sa (T

5

) (g)

6

5

4

3

2

1

0

Sa (T

5

) (g)

6

5

4

3

2

1

0

84

50

16

84

50

16

RCT RCN

(a)



Sa (T

5

) (g)

3

2

1

0

Sa (T

5

) (g)

3

2

1

0

84

50

16

84

50

16

RCT RCN

(b)



Sa (T

5

) (g)

3

2

1

0

Sa (T

5

) (g)

3

2

1

0

84

50

16

84

50

16

RCT RCN

(c)



00

02

04

06

08

10

12C

olla

pse p

roba

bilit

y

2 4 6 8 100Sa (T1 5) (g)

3U2B3B4mBL

RCTRCN

(a)

00

02

04

06

08

10

12

Col

laps

e pro

babi

lity

2 4 6 8 100Sa (T1 5) (g)

3U2B3B7mBL

RCTRCN

(b)

00

02

04

06

08

10

12

Col

laps

e pro

babi

lity

05 1 15 2 25 30Sa (T1 5) (g)

11U4B3B4mBL

RCTRCN

(c)

00

02

04

06

08

10

12

Col

laps

e pro

babi

lity

05 1 15 2 25 30Sa (T1 5) (g)

11U4B3B7mBL

RCTRCN

(d)

0

02

04

06

08

1

12

Col

laps

e pro

babi

lity

1 2 3 4 50Sa (T1 5) (g)

7U3B3B7mBL

RCTRCN

(e)

0

02

04

06

08

1

12

Col

laps

e pro

babi

lity

05 1 15 2 250Sa (T1 5) (g)

15U5B3B4mBL

RCTRCN

(f )













ACMRPass orfail


Group performance3









ACMRPass orfail








6 Conclusions






Data Availability




References















































Sa (T

5

) (g)

6

5

4

3

2

1

0

Sa (T

5

) (g)

6

5

4

3

2

1

0

84

50

16

84

50

16

RCT RCN

(a)



Sa (T

5

) (g)

3

2

1

0

Sa (T

5

) (g)

3

2

1

0

84

50

16

84

50

16

RCT RCN

(b)



Sa (T

5

) (g)

3

2

1

0

Sa (T

5

) (g)

3

2

1

0

84

50

16

84

50

16

RCT RCN

(c)



00

02

04

06

08

10

12C

olla

pse p

roba

bilit

y

2 4 6 8 100Sa (T1 5) (g)

3U2B3B4mBL

RCTRCN

(a)

00

02

04

06

08

10

12

Col

laps

e pro

babi

lity

2 4 6 8 100Sa (T1 5) (g)

3U2B3B7mBL

RCTRCN

(b)

00

02

04

06

08

10

12

Col

laps

e pro

babi

lity

05 1 15 2 25 30Sa (T1 5) (g)

11U4B3B4mBL

RCTRCN

(c)

00

02

04

06

08

10

12

Col

laps

e pro

babi

lity

05 1 15 2 25 30Sa (T1 5) (g)

11U4B3B7mBL

RCTRCN

(d)

0

02

04

06

08

1

12

Col

laps

e pro

babi

lity

1 2 3 4 50Sa (T1 5) (g)

7U3B3B7mBL

RCTRCN

(e)

0

02

04

06

08

1

12

Col

laps

e pro

babi

lity

05 1 15 2 250Sa (T1 5) (g)

15U5B3B4mBL

RCTRCN

(f )













ACMRPass orfail


Group performance3









ACMRPass orfail








6 Conclusions






Data Availability




References













































00

02

04

06

08

10

12C

olla

pse p

roba

bilit

y

2 4 6 8 100Sa (T1 5) (g)

3U2B3B4mBL

RCTRCN

(a)

00

02

04

06

08

10

12

Col

laps

e pro

babi

lity

2 4 6 8 100Sa (T1 5) (g)

3U2B3B7mBL

RCTRCN

(b)

00

02

04

06

08

10

12

Col

laps

e pro

babi

lity

05 1 15 2 25 30Sa (T1 5) (g)

11U4B3B4mBL

RCTRCN

(c)

00

02

04

06

08

10

12

Col

laps

e pro

babi

lity

05 1 15 2 25 30Sa (T1 5) (g)

11U4B3B7mBL

RCTRCN

(d)

0

02

04

06

08

1

12

Col

laps

e pro

babi

lity

1 2 3 4 50Sa (T1 5) (g)

7U3B3B7mBL

RCTRCN

(e)

0

02

04

06

08

1

12

Col

laps

e pro

babi

lity

05 1 15 2 250Sa (T1 5) (g)

15U5B3B4mBL

RCTRCN

(f )













ACMRPass orfail


Group performance3









ACMRPass orfail








6 Conclusions






Data Availability




References























































ACMRPass orfail


Group performance3









ACMRPass orfail








6 Conclusions






Data Availability




References














































6 Conclusions






Data Availability




References













































seismic performance evaluation of special rc frames with

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