Damage-BasedSeismicRetrofittingApproachforNonductile ...downloads.hindawi.com/journals/ace/2020/7564684.pdf · 2020-06-09 · ResearchArticle Damage-BasedSeismicRetrofittingApproachforNonductile

Research ArticleDamage-Based Seismic Retrofitting Approach for NonductileReinforced Concrete Structures Using FRP Composite Wraps

Vui Van Cao and Son Quang Pham

Faculty of Civil Engineering Ho Chi Minh City University of Technology (HCMUT)ndashVietnam National University268 Ly uong Kiet Street District 10 Ho Chi Minh Vietnam

Correspondence should be addressed to Vui Van Cao cvvuihcmuteduvn

Received 4 November 2019 Revised 16 March 2020 Accepted 16 May 2020 Published 30 May 2020

Academic Editor Filippo Ubertini

Copyright copy 2020 Vui Van Cao and Son Quang Pham +is is an open access article distributed under the Creative CommonsAttribution License which permits unrestricted use distribution and reproduction in anymedium provided the original work isproperly cited

Applying similar amount of fibre reinforced polymer (FRP) for all plastic hinge locations in a structure is not an ideal approach asdamage occurring at these critical locations may vary considerably Building owners also always want to keep FRP retrofitting costand associated interruption to a minimum In this context the current paper proposes an FRP retrofitting approach in which FRPis selectively distributed based on the distribution of seismic damage in structures +e proposed approach characterized by bothquantitative and qualitative criteria is simple but very effective in simultaneously reducing the seismic damage amount of FRP tobe used and time of installation For the considered cases of low- and mid-rise nonductile building structures the FRP amountreduced approximately by 31 compared to the cases in which FRP was evenly distributed leading to lower installation cost andless interruption time Interestingly although 31 FRP was saved the damage indices of the FRP retrofitted frames weresignificantly lower than those in cases of even FRP distribution because FRP effectively served for critical locations Due to itssimplicity and technicaleconomical effectiveness the proposed FRP retrofitting approach can be useful for engineering practice

1 Introduction

Many existing reinforced concrete (RC) building structuresaround the world designed and built based on old codes havebeen identified to be deficient compared with currentseismic codes [1] One of the common deficiencies is ofstirrups leading to nonductile behaviour and low lateralload resistance of structures [1 2] Consequently the weakbeam-strong column mechanism is not achieved and severedamage or collapse of buildings have been evident in the pastearthquake events [1 3] +us mitigating the seismic risk byretrofitting these structures to meet the requirement ofcurrent seismic provisions instead of demolishing and re-building has been a solution of choice because of economicand social reasons Extensive research has been devoted tothe investigations of fibre reinforced polymer (FRP) appli-cations in the past few decades and FRP has been widelyrecognized as an economical engineering solution for ret-rofitting RC structures Compared with conventional

methods such as steel brace system cross section enlarge-ment or steel jacketing FRP retrofit does not change thearchitecture or occupy the living space of buildings Inaddition FRP retrofit is much easier and quicker to installwhile FRP imposes almost no additional load on structuresdue to its lightweight +e high tensile strength and highcorrosive resistance are also good characteristics makingFRP become the material of choice to retrofit beams [4ndash10]columns [11ndash16] joints [17ndash21] and structures [22ndash24]

FRP retrofitting aims at increasing the ductility strengthandor stiffness of existing structures For structures withdeficiency of transverse reinforcement increasing theductility should be taken as priority FRP wraps provideconfinement conditions which significantly increase thecompressive strength and ultimate strain for concrete[25ndash28] Consequently the strength [29 30] ductility[29 30] and energy absorption capacity [29 31] of columnsretrofitted by FRP wraps greatly improved Studies onminimizing the amount of FRP and thus the cost for

HindawiAdvances in Civil EngineeringVolume 2020 Article ID 7564684 21 pageshttpsdoiorg10115520207564684

retrofitting of columns were also conducted by researchers[32 33] For frame structures similar beneficial effects ofFRP retrofitting have been confirmed by researchers FRPretrofitting successfully prevented soft storey [1] and col-umn-sway [34] mechanisms for structures FRP retrofittingsignificantly increased the seismic capacity [3 35ndash38] andconsiderably improved deformation capacity [34 37] butreduced damage [34 37 39] for structures

+e above studies on FRP retrofitting of RC framesconfirmed the effectiveness of FRP confinement applied tocritical locations of plastic hinges to improve the seismicperformance of RC structures however less attention hasbeen paid for the cost of FRP retrofitting Along with re-ducing to a predefined damage level for structures the leastamount of FRP and the shortest FRP installation time tominimize the cost are of major concerns by not onlybuilding owners but also structuralretrofitting engineersObviously these concerns are not appropriately addressedby evenly distributing FRP for critical locations of plastichinges because the seismic damage is unevenly distributed tothese locations To the best of the authorsrsquo knowledge thenumber of studies aiming at addressing these concerns isquite limited in the literature as reviewed in the following+ermou et al [40] developed a methodology for upgradingdeficient RC buildings in which the distribution of the inter-storey drift is optimized by intervening the stiffness dis-tribution in the vertical direction of the building Zou et al[41] optimized the performance-based design of FRP con-finement at plastic hinges of columns for seismic retrofittingof existing RC structures +e optimization objective was tominimize the thickness of FRP confinement while the op-timization process was subjected to the criterion of inelasticinter-storey drift Choi et al [42] proposed a seismic ret-rofitting method for shear-critical RC frames using FRPwraps withmultiobjectives+e two objective functions wereto minimize the amount of FRP and variation coefficient ofthe inter-storey drift while the constraint functions were theallowable inter-storey drift the shear failure and themaximum compressive strength of concrete +e optimalmethod was illustrated by the retrofitting of a three-storeyframe

Only limited number of studies [40ndash42] in which inter-storey drift was employed as the main criterion to distributeFRP together with no clear guidelines in current codesapplied for FRP distribution in frames have inspired theauthors to carry out this study An attempt aiming at helpingengineers to address the practical concern of FRP retrofittingcost raise by building owners and to improve the effec-tiveness of the FRP retrofitting is presented in this paper Toachieve this aim an FRP retrofitting approach of RCstructures in which FRP is distributed based on the seismicdamage distribution (instead of inter-storey drift) instructures was proposed Because the damage indices ofplastic hinges (element damage level) are more specific thaninter-storey drifts (storey damage level) the distribution ofFRP based on damage indices is logically more appropriate+e technical and economical effectiveness proposed ap-proach was demonstrated for the two FRP retrofitting casesof 4- and 8-storey nonductile RC frames representing for

low- and mid-rise building structures +e frames wereretrofitted by the proposed approach and then by evenlydistributing the FRP for comparison Conclusions are madebased on the comparison

2 The Proposed Damage-Based FRPRetrofitting Approach

Figure 1 shows the proposed FRP retrofitting approach forexisting structures based on seismic damage distributionBased on the design of a structure the seismic damagedistribution in structures is analysed +e obtained damagedistribution is used to distribute the FRP In this proposedFRP retrofitting approach FRP is only applied to the lo-cations of plastic hinges where the damage indices (DI) arelarger than the allowable damage index [DI] while the lo-cations with no or minor damage are not applied by FRP+is step is simple but very effective in appropriately dis-tributing FRP Two criteria are applied in the proposedretrofitting approach +e first criterion is quantitatively setby the condition DI le [DI] while the second criterion isqualitatively set by the damage distribution +e proposedFRP retrofitting approach is described in Figure 1 followedby the general descriptions of steps Some steps with longdetails are described in Sections 3 and 4 It is worth em-phasizing that the details of long steps presented in thesesections are of several methods that can be used For ex-ample the selection of seismic records can be different basedon the seismic design codes or the analysis method can bedifferent provided the target is achieved

(i) Step 1 existing structures+e design of building structures is collected pro-viding information for analyses and FRP retrofitting

(ii) Step 2 design earthquakes and the allowabledamage index [DI]+e design earthquake intensity is based on thecurrent seismic code for the region where theretrofitted building is located +e characteristicsof earthquakes occurring in the region are alsocollected if applicable +e design response spec-trum regulated in current seismic codes for theregion is constructed and earthquake groundmotions are then selected +ese selected groundmotions are scaled to match the design responsespectrum in order to obtain the scaled seismicrecords which are then used for inelastic timehistory (ITH) analyses+e other task of this step is to determine thedamage level for the retrofitted structures such aslight damage moderate damage or severe damagewhen the retrofitted structure experiences thedesign earthquakes +e target damage level isestablished by the owners managers or investorsunder being consulted by structural engineers witha reference to current seismic codes +e targetdamage level is then used to determine the al-lowable damage index [DI] +is [DI] is used as a

2 Advances in Civil Engineering

quantitative control criterion for the FRP retro-fitting design followed by the qualitative criterionof damage distribution

(iii) Step 3 ITH analyses of RC frame+e structure is modelled for ITH analyses +eseITH analyses are performed for the structuresubjected to the selected ground motions corre-sponding to the design seismic intensity estab-lished in Step 2 +e details of ITH analyses arepresented in Section 31

(iv) Step 4 damage analyses+e results of hysteretic behaviours of plastichinges obtained from ITH analyses in step 3 areexported in the form of Excel data files +en thesedata served for damage analyses conducted inMATLAB [43] expressed by damage indices +eobtained damage indices are then used to plot thedamage distribution in structures +e details ofdamage analyses are presented in Section 32

(v) Step 5 FRP retrofit based on damage distributionDue to the deficiency of internal confinement FRPwraps are applied to the plastic hinge locations to

provide external confinement +e design of FRPconfinement is presented in Section 41 +edamage distribution in the frame is then used todistribute the FRP in amanner that one or two FRPplies are applied for severe damage locations wherethe damage indices are larger than the allowabledamage index [DI] No FRP is applied for thelocations with no or minor damage +is simpleFRP distribution directly aims at severe andmoderate damage locations making the retrofit-ting approach become more effective

(vi) Step 6 ITH analyses of the FRP retrofitted frame+is step is similar to Step 3 however the FRPconfinement is included +e analyses for prop-erties of FRP-confined RC plastic hinges are pre-sented in Section 42 while ITH analyses of the FRPretrofitted frames are presented in Section 31

(vii) Step 7 damage analyses of the FRP retrofittedframesSimilar to Step 4 the hysteretic behaviours ofplastic hinges are exported in the form of Exceldata files which are then processed in MATLAB[43] and the damage of plastic hinges is quan-tified by the damage index +e damage indicesare plotted to obtain the damage distribution inthe frame Evaluation of damage distribution iscarried out to provide information for FRP re-distribution and adjustment in the frame +edetails of damage analyses are presented inSection 32

(viii) Step 8 check the quantitative condition DIle [DI](quantitative criterion)+e quantitative condition DIle [DI] is checked forall plastic hinge locations If there are plastic hingelocations whose damage indices are not satisfiedthis condition the FRP retrofitting for those lo-cations is redesigned by applying one additionalFRP ply thus go back to Step 5 Otherwise go toStep 9For special situations of finance the redesignshould aim at not only at the locations whosedamage index is larger than the allowable damageindex but also the locations whose damage indicesare too small A simple rule can be applied de-crease one ply for plastic hinge where the damageindex is much smaller than the [DI] and increaseone ply for plastic hinges where DIgt [DI]

(ix) Step 9 evaluating the damage distribution (qual-itative criterion)When the quantitative condition DIle [DI] issatisfied the distribution of damage in the frame isqualitatively evaluated +is step is conductedbased on the importance of storeys and elementsFor example the storey i is more important thanstorey i+ (the above storeys) while it is less im-portant than the storey i minus (the below storeys) +elowest storey can be the most important while the

Damage analyses

Evaluation of damage distribution(qualitative criterion)

End

DI le [DI](quantitative criterion)

Notreasonable

Reasonable

No

Yes

Existing structures

Inelastic time history analyses

Damage analysesof the FRP retrofitted structure

Inelastic time history analysesof the FRP retrofitted structure

Start

Design earthquakesand allowable damage level [DI]

FRP retrofitbased on damage distribution

Figure 1 +e proposed damage-based FRP retrofitting approach

Advances in Civil Engineering 3

top storey is the least important Within a storeycolumns should be more important than beamsIdeally the damage index of the storey one issmallest and the damage index of the top storey islargest

3 ITH and Damage Analyses

31 ITH Analyses Under earthquake excitations inelasticdeformation is often developed at the critical regions ofplastic hinges +e lump plasticity technique was employedfor nonlinear modelling in this study +e details of themodelling were described in [22] thus only brief de-scription is presented herein for convenience to readersLinear and nonlinear elements were employed for themodelling+e nonlinear elements were used to capture thenonlinear and hysteretic behaviours of plastic hinges +elocations of nonlinear elements are at the centers of plastichinges of beams and columns Figure 2(a) shows the modelof a four-storey three-bay frame +e locations of inelasticelements of beams are located at (hcolumn + lpbeam)2 wherelpbeam is the plastic hinge lengths of beams and hcolumn is theheight of the column sections Similarly the locations ofinelastic elements of columns are located at(hbeam + lpcolumn)2 where lpcolumn is the plastic hingelengths of columns and hbeam is the height of the beamsections

+e inelastic behaviours of plastic hinges are capturedusing a hysteretic model Several hysteretic models areavailable in the literature however majority of thesemodels excludes the crack of concrete in tension zone whilethe Takeda hysteretic model [44] includes the concretecracking +us the Takeda model is selected for damageanalyses in this paper because the crack of concrete can beconsidered as the onset of damage Figure 2(b) shows theTakeda hysteretic model [44] developed based on the force-deformation curve including the crack point (Dcr Pcr) andthe yield point (Dy Py) Details of this model can be foundelsewhere [44]

+e properties of nonlinear elements are moment-ro-tation curves of plastic hinges +ese moment-rotationcurves are obtained using the moment-curvature curves andthe plastic hinge lengths In this paper the simple model ofplastic hinge length lp h proposed by Sheikh and Khoury[45] is adopted while the moment-curvature curves areobtained using fibre model In moment-curvature analysesusing fibre model the cross section is discretized into manyfibres as shown in Figure 3(a) which are assumed to ex-perience pure longitudinal deformation +e distribution ofstrain in a cross section is assumed to be linear as shown inFigure 3(b) +e maximum compressive strain εm and theposition of the neutral axis Zn are used to determine thestrain distribution in the section Correspondingly thecurvature is computed as φ εmZn

+e position of neutral axis Zn is found when the forceequilibrium is attained +e force equilibrium is establishedbased on the fibre forces which are the products of fibre stressesand the fibre cross-sectional areas and the axial force N actingon the section For each fibre the strain at the fibre centroid is

used to compute the fibre stress using the stress-strain be-haviour of fibre material Amongst several stress-strain models[46ndash52] proposed for concrete Park et alrsquos [52] model takesinto account the enhancement of the maximum stress and thestrain at maximum stress due to the confinement effects thusthis model is used in this paper Equations (1) and (2) show therelationship between the stress fc and the strain εc of concrete+e parameters of themodel are shown in equations (3)ndash(6) inwhich ρs is the ratio of the volume of transverse reinforcementto that of the concrete surrounded by the transverse rein-forcement fc

prime (MPa) is the strength of concrete bPrime denotes theconcrete core width measured to the outside of transversereinforcement sh denotes the spacing of transversereinforcement

fc fcPrime 2εc

εo

minusεc

εo

1113888 1113889

2⎡⎣ ⎤⎦ if εc le εo (1)

fc fcPrime 1 minus Z εc minus εo( 11138571113858 1113859ge 02fc

Prime if εc ge εo (2)

fcPrime Kfc

Prime (3)

εo 0002K (4)

Z 05

3 + 029fcprime145fcprime minus 1000( 1113857 +(34)ρs

bPrimesh( 1113857

1113969

minus 0002K

(5)

K 1 +ρsfyh

fcprime

(6)

After the neutral axis Zn is determined the moment M

1113936nf

i1 Fidi with respected to the sectional mid-height axis inwhich di is the distance from the centroid of the fibre i to thesectional mid-height axis Fi is the force of fibre i which isequal to the product of the stress and the area of that fibreand nf is the number of fibres Moment-curvature analyseswere carried out in Matlab [43] up to the ultimate as plottedin Figure 3(d) +en the moment-curvature curves areconverted to moment-rotation curves by multiplying theplastic hinge lengths

32 Damage Analyses +e hysteretic behaviours of non-linear elements obtained from ITH analyses are exportedfor damage analyses using a damage model Comparedwith noncumulative damage models cumulative damagemodels are more appropriate for damage analyses ofstructures subjected to earthquake excitations because theduration number of cycles and frequency content of theground motions play important roles in damaging struc-tures In addition the magnitude of damage index shouldvary from 0 to 1 DI 0 refers to the state of no damagewhile DI 1 refers to the state of collapse +e damagemodel proposed by Cao et al [53] shown in equation (7)satisfied the just-mentioned characteristics and is used inthis paper


DI Eh

Eh + Erec1113890 1113891

α(Nminus i)

(7)

in which Eh is the cumulative hysteretic energy Erec is thecumulative recoverable energy N Eh1collapseEh1y is theequivalent number of yielding cycles to collapse i EhEh1y

is the equivalent number of yielding cycles at the currenttime of loading (ileN) Eh1collapse and Eh1y are respectivelythe hysteretic energy of one complete ultimate and oneyielding cycle and α 006 is a modification factor Table 1shows the damage levels with the legends corresponding totheir damage indices and damage descriptions +e legendsof damage are used to plot the damage states of frames inSections 5ndash7

4 Design and Analyses of FRPRetrofitted Frames

41 Design of FRP Confinement Providing external con-finement using FRP wraps is an appropriate retrofittingsolution applied to structures whose transverse steel inad-equately confines the concrete FRP wraps are applied to theplastic hinges of columns in the orientation of transversereinforcement to confine concrete leading to the

enhancement of strength and ductility for concrete +elength of columns on which FRP wraps are applied isassumed to be twice the plastic hinge length lp

+e effectiveness of FRP retrofitting depends on severalfactors such as the mechanical properties of FRP the di-mensions and shapes of cross sections and the strength ofunconfined concrete For a given FRP type and the crosssection the total thickness of FRP is of importance in FRPretrofitting which governs the strength and ductility of FRP-confined concrete [41] as can be apparent in the Lam andTeng model [25 54] +e thickness of one FRP ply is pro-duced by manufacturers and is a constant +erefore thenumber of FRP plies is considered as a variable for theretrofitting design In this study the cost of FRP retrofittingis directly inferred from the amount of FRP It should be

Non

linea

r lin

k el

emen

ts

(a) (b)

A

B

C

Pγ

DγDcr

Pcr

1

1

2

2

3

34

4

5

5

6

6

7

7

8

8

9

9

10

10a

10b

11

11

12

12

13

13

14

15

16

171819

20

Figure 2 Modelling for inelastic analyses (a) modelling and (b) hysteretic behaviour [44]

(b)(a) (c) (d)

fs1

fc

fs2

fs3

fs4

fs5

εs1

εs2

εs3

εs4

εs5

εc Zn

εm

MN

Ultimate

Curvature

Mom

ent

YieldIdealized

Crack

O

Real

Figure 3 Section analysis using fibre model (a) discretization (b) strain (c) stresses and (d) moment-curvature

Table 1 Damage levels

Legend Damage index Description 0ndash005 No or minor+ 005ndash025 Lightx 025ndash050 Moderate 050ndash075 Severe 075ndash100 Collapse


mentioned herein that the cost of FRP retrofitting alsodepends on the number of plastic hinges retrofitted by FRPdue to the labour work and time of FRP installation Forexample with a similar amount of FRP the retrofittingsolution with fewer locations of FRP installation could beless labour work and shorter installation time and such asolution is therefore cheaper

+e effectiveness of FRPwraps to improve the compressivestrength and ductility of concrete has been widely confirmed inthe literature +e tensile strength and modulus of GFRP aremuch lower than those of CFRP providing larger displacementductility for concrete consequently the aims of confinementand ductility improvement are better achieved by GFRP thanCFRP as confirmed in [22 55] Additionally GFRP is muchcheaper than CFRP+erefore GFRP is used in this paper+etensile strength and modulus of GFRP unidirectional fibresheets provided by the manufacturers are 3241MPa and72397MPa respectively [56] while the thickness is 0589mm[56] Figure 4 shows the design of GFRP wraps in which theplastic hinges of columns are wrapped by a number of GFRPplies To avoid stress concentration leading to early failure ofGFRP at corners rounding corners of columns should beconducted before applying the GFRP wraps [57] Rounding50mm at column corners [23 41] is adopted in this study andis shown in Figure 4

42 Inelastic Analyses of RC Frame Retrofitted by FRPConfinement Because the FRP wraps is in the orientation ofthe transverse reinforcement the strength and stiffness of FRPin the longitudinal direction of columns (axial axis of col-umns) can be neglected [41]+e effect of FRPwraps results inthe improvement of stress-strain behaviour of concrete thusthe moment-curvature analyses of sections confined by FRPare almost similar to moment-curvature analyses presentedSection 31 +e difference is that the stress-strain model ofFRP-confined concrete is taken into account +e confine-ment effect of GFRP wraps increases the compressive strengthand ultimate strain of concrete thus it has marginal effect onthe plastic hinge locations of FRP-confined columns asproven in [29] +erefore the locations of plastic hinges inbeams and columns of the retrofitted frame are unchangedcompared with those of the original frame

+e stress-strain behaviour of FRP-confined concretehas been studied by many researchers [25 26 54 58ndash60] andit is concluded that the strength and ductility of concreteincrease significantly Review on FRP-confined concretemodels has been performed by Ozbakkaloglu et al [61] forcircular sections and Rocca et al [62] for noncircular sec-tions Overall the available models of FRP-confined con-crete can be categorized into two types with and withoutincluding the internal effect of transverse reinforcementBoth transverse reinforcement and FRP provides confine-ment for the concrete core surrounded by transverse rein-forcement while only FRP provides confinement to thecover concrete +e models of FRP-confined concrete si-multaneously considering both confinement effects of FRPand transverse reinforcement are often complex due to theinteraction between the internal and external confinements

Additionally the external confinement caused by FRP ismuch stronger than the poor internal confinement caused bythe deficient transverse reinforcement +is stronger con-finement of FRP can be proven by the fact that after thestrain 0002 (approximately) the stress-strain branch of theFRP-confined concrete model ascends while that of thetransverse-reinforcement confined concrete model de-scends In addition the purpose of FRP wraps is to provideadditional confinement to poorly confined RC members+erefore for simplification the poor internal confinementof transverse reinforcement is neglected in this study

+ere are several stress-strain models [25 54 63ndash65] forconcrete confined by FRP wraps available in the literatureAmongst these Lam and Teng [25 54] model is simple butadequately accurate and is adopted in ACI code [66] Inaddition this model was the most appropriate for circularand rectangular columns as proven by Rocca et al [67] andhas been used by many researchers [23 55 67] +us theLam and Teng [25 54] stress-strain model for FRP-confinedconcrete is selected to use in this paper Figure 5 illustratesthe Lam and Teng [25 54] model which includes two partsthe parabolic curve (branch OA) expressed by equation (8)and the linear branch (AB) expressed by equation (9) +eparameters of the model are defined in equations (10)ndash(19)

for 0le εc le εt fc Ecεc minusEc minus E2( 1113857

2

4fcprime

ε2c (8)

for εt le εc le εu fc fcprime + E2εc (9)

in which

εt 2fcprime

Ec minus E2 (10)

E2 fcuprime minus fcprime

εu

(11)

For rectangular columns the ultimate stress fcuprime is

computed using equation (12) or (13) and the ultimate strainεu is expressed by using equation (14) +e parameters ofthese equations are described in equations (15)ndash(19) where

A A

FRP wrap

GFRP wraps r = 50mm

A-A

Figure 4 FRP wraps at locations of plastic hinges


tf is the total thickness of FRP wraps εhrup is the rupturestrain of FRP Ef is the modulus of FRP and D is theequivalent diameter of circular column ks1 and ks1 are shapefactors described in equations (17) and (18) respectively inwhich b is the width and h is the depth of the cross section ris the corner radius and ρs is the ratio of longitudinal steelarea to the cross sectional area

fcuprime fcprime 1 + 33ks1

fla

fcprime1113890 1113891 if

fla

fcprimege 007 (12)

fcuprime fcprime if

fla

fcprimelt 007 (13)

εu εo 175 + 12ks2fla

fcprime

εhrup

εo

1113888 1113889

045⎡⎣ ⎤⎦ (14)

fla Eftf

Rεhrup

2Eftf

Dεhrup (15)

D h2 + b2

radic (16)

ks1 b

h1113888 1113889

2Ae

Ac

(17)

ks2 h

b1113888 1113889

05Ae

Ac

(18)

Ae

Ac

1 minus (bh)(h minus 2r)2 +(hb)(b minus 2r)21113872 1113873 3Ag1113872 1113873 minus ρs

1 minus ρs

(19)+e rupture strain of FRP is defined as εhrup kεεfrp in

which kε is the ldquostrain efficiency factorrdquo which is muchsmaller than 1 Researchers have proposed different values ofkε for GFRP 0624 by Lam and Teng [25] 068 by Realfonzoand Napoli [68] and 066 by Baji et al [69] +ese valueswere of GFRP wraps for circular specimens subjected tomonotonic axial compressive loading In case of rectangularcolumns subjected to seismic loading the value of kε should

be smaller due to the higher stress concentration at cornersand the effect of cyclic loading Recently Baji [70] analysedthe test results of 184 GFRP-confined cylinder specimenssubjected to axial loading and the average value 062 for kε isobtained+is smallest value of 062 which is close to the oneproposed by Lam and Teng [25] was adopted in this paper

5 Verifications

Verifications were conducted using different aspects ofanalyses ITH analysis presented in Section 51 pushoveranalysis presented in Section 52 and damage analysispresented in Section 53

51 Verification Using Time History Analysis +e analyticalresults of time history analyses were verified using the timehistory results of [34 71] which were experimentally ob-tained from the shaking table tests of full-scale two-storeyframe +e general view of the frame is shown in Figure 6(a)while the cross sections and the arrangement of steel areshown in Figure 6(b) Only brief descriptions are presentedherein for convenience while the details can be foundelsewhere [34 71] +e vertical load for the shaking testincluded 45 kN of the steel plates attached to the floors andthe self-weight of the frame and slabs +e compressive andtensile strengths of concrete were 20MPa and 2MPa re-spectively while its unit weight was 24 kNm3 and the elasticmodulus was 255 GPa +e yield and ultimate strengths ofsteel were 551MPa and 656MPa respectively while theelastic modulus was 200GPa Steel ϕ6mm and ϕ8mm wererespectively used for stirrups of columns and beams

+e modelling technique described in Section 3 wasemployed to model the above full-scale tested frame usingSAP2000 Version 19 software [72] +e periods of the firstand second modes obtained from SAP2000 modal analysisare 054 s and 018 s which agree well with the experimentalvalues 053 s and 018 s [34 71] +e first and second modeshapes of the SAP2000 frame model are shown in Figure 7

+e SAP2000 [72] model of the frame was then subjectedto seismic motions of the shaking table [34 71] and timehistory nonlinear analyses were carried out +e historydisplacements of the first and second storeys obtained fromanalyses are compared with those obtained from the ex-periments showing a good agreement as can be visible inFigure 8

52 Verification Using Pushover Analysis +e 8-storey RCframe [55 73] with its typical column and beam sectionsshown in Figure 9 is revisited for verification using pushoveranalysis +e dimensions are in mm the steel is Grade 60(fy 420MPa) and the compressive strength of concrete was25MPa +e transverse reinforcement was Φ10mm +eload on beams included 10 kNm live load 30 kNm deadload and the self-weight of the structure +e frame wasdesigned based on UBC 1994 [74] however the spacing oftransverse reinforcement is large leading to nonductilebehaviour of the frame which needs to be retrofitted

Stre

ss

O

f primec

Ec = tanα

A

Bf primecu

Unconfined

FRP confined

αε0 εt εu Strain

Figure 5 Stress-strain model of FRP-confined concrete proposedby Lam and Teng [25 54]


+e frame under 100 dead load and 25 live load asrecommended in many seismic codes was modelled inSAP2000 [72] +e fundamental period T was determined as

124 s which agrees with the value 128 s analysed by Ronaghand Eslami [73] Pushover analysis of the frame based onUBCcode [74] is carried out In this analysis the equivalent lateralstatic seismic load Fi acting on each storey i and the additionalforce Ft acting on the top storey are computed using equations(20) and (21) [74] respectively in which Wi is the seismicweight of storey i hi is the height of storey i andV is the shearforce +e analytical pushover curve compared with the curveanalysed by Ronagh and Eslami [73] is shown in Figure 10which indicates an overall approximation

Fi V minus Ft( 1113857Wihi

1113936 Wihi

(20)

Ft 007TVle 025V (21)

53 Verification Using Damage Mode +e tested three-storey RC building structure represented for buildings

Beam

BeamSteel plates

Steel plates

Slabs 12mm thick

Steel box to fixthe frame

4260 times 4260

3300

3300

(a)

ϕ6mm200 ϕ6mm200

ϕ6m

m2

00

ϕ8mm300 ϕ8mm300

ϕ6m

m2

00

ϕ6m

m2

00ϕ8mm300

260

260

260 260

260

400

400

400

380

260 2601st floor 8ϕ14mm 2nd floor 4ϕ14mm

Reinforcement of columns

Reinforcement of beams(dimensions in mm)

8ϕ14mm

8ϕ14mm 8ϕ14mm

8ϕ14mm

4ϕ14mm

4ϕ14mm

(b)

Figure 6 Full-scale 2-storey frame [34 71] (a) General view (b) Cross sections and reinforcement arrangement

Figure 7 +e first (left) and second mode shapes of the two-storeyframe


designed based only on gravity load shown in Figure 11[75 76] is used for verification of damage analysis +eaverage compressive strength of concrete fcprime was 272MPawhile its modulus was 242GPa +e properties of steel areshown in Table 2 +e total gravity load of each floor whichincluded the self-weight of the structure and the attachedweights was approximately 120 kN More details can befound elsewhere [75 76]

+e frame was modelled in SAP2000 with the modellingdetails described in Section 3 +e SAP2000 model was thensubjected to the N21 E component with PGA 020g of theTaft earthquake occurring on 21 July 1952 at the LincolnSchool Tunnel site California which was used in the tableshaking experiment +e hysteretic behaviours of nonlinearelements were then exported to MATLAB [43] to computedamage indices using Cao et al [53] damage model +edamage indices were then used to plot the damage modes ofthe frame to compare with the experimental damage states

+e legends shown in Table 1 are used to read the analyticaldamage levels shown in Figure 12 +e comparisons pre-sented in Figure 12 show overall agreements between theanalytical and experimental damage states

6 Case Study 1 Four-Storey RC Frame

(i) Step 1 existing structure+e 4-storey frame shown in Figure 13 [23] is usedas a case study to demonstrate the proposed FRPretrofitting approach +e dead load included thedistributed load 30 kNm on beams and the self-weight of the frame while the live load was 10 kNm +e tensile strength of steel fy was 420MPa andthe compressive strength of concrete fc

prime was25MPa +e modulus of concrete Ec 4700

fcprime

1113969

[78] is adopted Steel Φ10mm was used for stir-rups +e frame was located in seismic zone 3 and

ndash20

ndash15

ndash10

ndash5

0

5

10

15

Disp

lace

men

t (m

m)

5 10 15 20 25 30 35 400Time (s)

ExperimentAnalysis

(a)

ndash20

ndash15

ndash10

ndash5

0

5

10

15

20

Disp

lace

men

t (m

m)

5 10 15 20 25 30 35 400Time (s)

ExperimentAnalysis

(b)

Figure 8 Comparison of the analytical and experimental [34 71] history displacements (a) Displacements of the 1st storey (b) Dis-placements of the 2nd storey


was designed in accordance with UBC 1994 [74]however the large spacing of stirrups leads tononductile behaviour of the frame and the need of

retrofitting More details of the design can befound in [23]

(ii) Step 2 design earthquake ground motions andallowable damage index [DI]+e building is assumed to be located in the seismiczone 3 based on UBC code [74] thus the seismiczone factor Z 03 and the seismic coefficientsCa 036 and Cv 054 are determined based onUBC code [74] +is is a standard occupancystructure of which the seismic important factor is1 while the importance factor of the building is 85[74] +e building is assumed to be located in stiffsoil D which is similar to type D in FEMA code[79] +e building is not located in near-fault re-gion thus near-source factors Na 1 and Nv 1+e seismic source type is B with the earthquakemagnitude larger than 65 +e design responsespectrumPGA is established as shown inFigure 14+e model was then analysed and the fundamentalperiod (T) of the frame was determined as 0764 s

Section b h d dprime Ast As Aprimes Shear steel spacing (mm)

A-A

B-B

C-C

D-D

E-E

F-F

600

600

600

600

600

600

600

600

600

600

600

600

540

540

440

440

440

440

60

60

60

60

60

60

16ϕ25

6ϕ25 4ϕ25

4ϕ226ϕ22

6ϕ18 3ϕ18

16ϕ18

16ϕ16

450

450

450

140

175

250

-

-

-

-

-

-

-

-

-

C C C C

C C

C C

C C

C C

C C

C C

B B

B B

A A

A A

B B

B B

A A

A A

FF

FF

FF

FF

EE

EE

EE

EE

DD

DD

DD

DD

DD

DD

DD

DD

CL8

3

m

3 5m

b b

h h

d d

d prime dprime

Ast

As

Aprimes

Typical beam sectionTypical column section

Figure 9 Eight-storey frame [55 73]

Base

shea

r for

ce (k

N)

0

250

500

750

1000

1250

1500

200 400 600 8000Roof displacement(mm)

SAP2000Ronagh and Eslami [73]

Figure 10 Comparison of pushover curves


Seismic records are then selected and scaled tomatch the design response spectrum +e criterionfor scaling the seismic records suggested by ASCEcode [80] is adopted in this paper Based on ASCE

code [80] the mean value of the 5 damped re-sponse spectra of the selected scaled seismic rec-ords is not less than the target response spectrumover the range [02T-15T] +e scaling result using

(a)

Int columnExt column8Prime8Prime 6prime-0Prime 6prime-0Prime

8prime-0Prime

4prime-0Prime

6prime-0Prime

W-ga114Primecolumn

ties (typ)

W-ga112Primesplice andext joint

(typ)

8Prime

4Prime

3Prime

6Prime2Prime4Prime

4Prime

12prime-0Prime

Y Y Y Y

Frames at 6primecenters

2Prime slab(typ)

All columns4Prime times 4Prime

All beams3Prime times 6Prime

Floor plan4Prime times 4Prime (typ)3Prime times 6Prime (typ)

t = 2Prime 12 ga2Prime(sqrs)

A

A

B

B

C

C

C

D

D D

D

2D5

2D42D4 1D41D4

2D4

2prime

2prime

6prime 10prime

Section Y-Y

W-ga11267Prime

4D4

W-ga11

C-C

B-BA-A

D-DBeam sections

3D4

3D4

2D4

2D4 2D4 1D5

2D5 2D5

W-ga11(typ)

1

Elevation

6prime-0Prime 3prime-0PrimeW-ga11267Prime

Beam steel

1 1-

(b)

Figure 11 +ree storey frame [75] (a) General view (b) Details (note 1 in 254mm)


PEER database software [77] is shown in Figure 15Two horizontal components of each earthquakestation were used for the scaling as employed in thePEER database software [77] Eight seismic recordsof four stations were selected scaled and used for

analyses+e information and scale factors of these8 seismic records are shown in Table 3 in whichRSN is the record sequence number As regulatedin ASCE code [80] if the number of seismicrecords is equal or larger than 7 the average output

Table 2 Steel properties

Steel Diameter (mm) Yield strength (MPa) Ultimate strength (MPa) Modulus (MPa) Ultimate strainD4 5715 46886 50334 214090 015D5 6401 26201 37233 214090 01512 ga 2770 39991 44128 206161 01311 ga 3048 38612 48265 205471 013

CrackedYielded

Note 2nd story beams and abovewere not quantitatively observed

(a)

++

+

++

++ +

++

(b)

Figure 12 Comparison of damage modes (a) Experiment [76] and (b) analysis

Section Spacing of stirrups (mm)

A-A 16ϕ18 - - 450

B-B - 6ϕ22 4ϕ22 175

C-C

500

500

500

60

60

60 - 6ϕ18 3ϕ18 250

440

440

440

500

500

500

Aprimes(mm2)

As(mm2)

Ast(mm2)

dprime(mm)

d(mm)

h(mm)

b(mm)

4

3m

3 5m

A

A

A

A

A

A

A

A

A

A

A

A

C

CC

C

B

BB

B

Figure 13 Four-storey frame [23]


parameters are used thus the damage index of aplastic hinge is the average damage index of 8damage indicesIn this case study minor damage is assumed as thelimit damage for the FRP retrofitted frame Toachieve this damage state the allowable damageindex [DI] is set as 025

(iii) Step 3 ITH analyses100 dead load and 25 live load are used for ITHanalyses of the frame subjected to the selected

ground motions +e moment-curvature analyses ofsections and moment-rotation curves of plastichinges were performed in MATLAB [43] using fibremodel described in Section 31+emoment-rotationcurves of plastic hinges were then assigned for thenonlinear elements in SAP2000 [72] When theSAP2000 model of the frame was built ITH analysesare conducted +e results from ITH analyses arethen used for damage analyses in Step 4

(iv) Step 4 damage analyses

Spec

tral

acce

lera

tion

PGA

00

05

10

15

20

25

30

1 2 3 40T (sec)

Figure 14 Spectral accelerationPGA

Target spectrumSuite mean

300 400100 200 500000 600Period (sec)

000

020

040

060

080

100

120

pSa (

g)

Figure 15 Scaling records to match the target spectrum [77]

Table 3 Selected records and scale factors

Number RSN Scale factor Event Year Station Magnitude1 861 6440 Landers 1992 Barstow 7282 859 7265 Landers 1992 Hacienda Height-Colima 7283 1215 5822 Chi Chi Taiwan 1999 CHY058 7624 1488 3303 Chi Chi Taiwan 1999 TCU048 762


+e hysteretic moment-rotation behaviours ob-tained from the ITH analyses in Step 3 are exportedto Excel and processed in MATLAB [43] tocompute the demand parameters and damageindices using Cao et al [53] damage model +ecomputation of damage index was applied forevery nonlinear element of plastic hinges and foreach ground motion As a result 56 damage in-dices of 56 plastic hinges were obtained when theframe subjected to a ground motion +e proce-dure was carried out for 8 ground motions of thedesign intensity thus each plastic hinge had 8damage indices For each plastic hinge the averageof these 8 damage indices was the damage index ofthat hinge Consequently the 56 average damageindices were obtained for the frame subjected tothe design seismic intensity +ese 56 averagedamage indices were then used to plot the damagedistribution in the frame as shown in Figure 16(a)+e damage mode in Figure 16(a) is used fordamage evaluation providing useful informationfor the adjustment of FRP distribution It should bementioned that for comparison the damage statesof the frames retrofitted by the proposed approach(Figures 16(b) and 16(c)) and by even distributionof FRP (Figure 16(d)) are also plotted in the samefigure Details of these Figures 16(b)ndash16(d) arepresented in the following steps

(v) Step 5 retrofit of structures based on damagedistribution+e damage distribution shown in Figure 16(a)provides a clear picture of damage mode whichis useful to distribute the FRP correspondinglyin which the larger amount of FRP is saved forthe locations with severe damage while no FRPis applied to the locations with no or minordamage By observing the damage distributionin Figure 16(a) the two inner columns of thefirst storey suffered severe damage () whilethe two outer columns of the first storey and thetwo inner columns of the second storey expe-rienced light damage (+) Two FRP ply wasapplied to these locations Other locations in theframe such as beams of all storeys and columnsof the third and the fourth storey have minordamage () thus FRP was not applied to theseminor damage locations +is FRP retrofittedframe is called RS1 which stands for retrofittedstructure in the first time using the proposedapproach

(vi) Step 6 ITH analyses of the retrofitted framesAfter the frame was retrofitted in Step 5 using theproposed retrofitting approach ITH analyses of thisFRP retrofitted frame (RS1) subjected to the selected8 ground motions were carried out +e analyticaldetails of the retrofitted frame are presented inSection 3 with the inclusion of the FRP confinement

(vii) Step 7 damage analyses of the retrofitted frames+e hysteretic behaviours of nonlinear elementsobtained in Step 6 were then exported to Excel andprocessed in MATLAB [43] to compute damageindices +e damage mode of RS1 is plotted inFigure 16(b)

(viii) Step 8 evaluate the damage using the damageindex criterion DIle [DI]+e quantitative condition DIle [DI] is checked forall plastic hinges of the RS1 All plastic hinge lo-cations satisfy this condition so go to Step 9

(ix) Step 9 evaluate the damage distribution in thestructureWhen the quantitative criterion DI le [DI] issatisfied for all plastic hinges the qualitativecriterion on the damage distribution in the frameis evaluated +e damage mode shown inFigure 16(b) is used to evaluate the damagedistribution in the frame For storey 1 the damageindices of the two inner columns are much largerthan those of the two outer columns +e FRPadjustment can be made so that the damage in-dices of columns in the same storey should besimilar Ideally the damage indices of the lowerstoreys should be less or equal than those of thehigher storey because the lower storeys are moreimportant than the higher storeysAdditional redesign of FRP by adding one ply toplastic hinges at the bottom ends of the innercolumns of the first storey is conducted +is FRPretrofitted structure is called RS2 +e procedure issimilar and the result is shown in Figure 16(c) +edamage index decreases from 0107 to 0077For comparison the frame retrofitted by evendistribution of FRP was also carried out One FRPply was applied for all plastic hinges and thisretrofitted frame is called RS0 +e number 0denotes that the frame is retrofitted without usingthe proposed retrofitting approach ITH anddamage analyses of this frame RS0 were performedand the damage state is plotted in Figure 16(d)Although all plastic hinges of the frame were ap-plied by two FRP plies the damage state of RS0 isworse than the damage states of RS1 and RS2For further comparison the maximum damageindex of each storey was used to plot the damagedistribution of storeys +e storey damage distri-butions of the original RS0 RS1 and RS2 areshown in Figure 17 +e damage state of the frameusing the proposed retrofitting approach is sig-nificantly improved showing the technical effec-tiveness of the proposed approach+e comparison in terms of retrofitting cost is alsocarried as follows +e amount of FRP used for theretrofitted frame RS0 RS1 and RS2 were com-puted and plotted in Figure 18 In order to plot the


Storey 4

Storey 3

Storey 2

Storey 1

(a)

Storey 4

Storey 3

Storey 2

Storey 1

(b)

Storey 4

Storey 3

Storey 2

Storey 1

(c)

Storey 4

Storey 3

Storey 2

Storey 1

(d)

Figure 16 Damage distribution in frames (a) Original (b) RS1 (c) RS2 and (d) RS0

0587

0140

0030

0000

0419

0077

0002

0107

0008

0077

025 050 075 100000Maximum damage index

OriginalRS0

RS1RS2

1

2

3

4

Stor

ey

Figure 17 Distribution of storey damage of 4-storey frame


damage indices whose magnitudes vary from 0 to 1and the amount of FRP of retrofitted frames RS0RS1 and RS2 in the same figure (the same verticalaxis) for visual comparison the amount of FRP isnormalized +e normalization is conducted bydividing the FRP amount by that of the RS0Figure 18 shows that the original frame has a largedamage index 0587 which shows the severedamage of the original frame With one ply appliedfor all plastic hinge locations the damage indexof RS0 decreases to 0419 When the proposedFRP retrofitting approach is applied the damageindex and the amount of FRP significantly de-crease Particularly the damage index decreasesto 0107 and the amount of FRP decreases 375(decrease to 625) With further adjustment ofthe FRP design (the frame RS2) the damageindex further decreases and the FRP ratio slightlyincreasesWith the proposed FRP retrofitting approach notonly the amount of FRP but also the damage indexreduces compared with the case of even distri-bution of FRP +us the cost reduces and theretrofitting becomes more effective by reducing alarger amount of damage index It is worthmentioning that with the proposed retrofittingapproach several locations of plastic hinges areidentified to be no or minor damage and thusFRP retrofitting is not needed +is is conse-quently helpful in shortening the FRP installationand interruption time additionally reducing theretrofitting cost and bringing social benefit

7 Case Study 2 8-Storey Frame

+e steps in this case study are similar to Case Study 1+erefore only the results and brief discussions are pre-sented to avoid repeating the information of Case Study 1

Steps 1ndash2 existing structures the design earthquakeground motions and the allowable damage index [DI]+e eight-storey frame described in Section 52 wasused for Case Study 2 +e ground motions were se-lected and scaled to match the design response spec-trum +e building was assumed to be located inseismic region with PGA 030g Table 4 shows therecords of four earthquakes with the scale factor andthe record sequence number (RSN)Steps 3ndash4 ITH and damage analyses of the originalframeITH and damage analyses were performed for theframe subjected to the selected ground motions +edamage distributions are shown in Figure 19(a)Steps 5ndash8 retrofit of structures based on damagedistribution dynamic and damage analysesSteps 5ndash8 were carried out for the frames retrofitted bythe proposed approach (RS1) +e frame RS1 wasretrofitted by applying 2 FRP plies to moderate damagelocations (times) and one FRP ply was applied to locationswith light damage (+) ITH and damage analyses ofthese frames were performed for the above frames +edamage state of the frame RS1 is shown in Figure 19(b)Step 9 evaluate the damage distribution in thestructure

0587

0419

0107 00770

1

06250688

Dam

age i

ndex

ratio

of F

RP

RS0 RS1 RS2OriginalOriginal and retrofitted structures

0

025

05

075

1

Damage indexFRP ratio

Figure 18 Variations of damage index and FRP ratio

Table 4 Records and scale factor

Number RSN Scale factor for intensity of Event Year Station Magnitude1 1155 3119 Kocaeli Turkey 1999 Bursa Tofas 7512 1604 21851 Duzce Turkey 1999 Cekmece 7143 2095 20320 Denali Alaska 2002 Anchorage-DOI Off of Aircraft 794 5824 15521 El Mayor-Cucapah Mexico 2010 CICESE 72


Based on the damage distribution of the frame RS1 andthe importance of lower storeys the frame RS1 wasretrofitted by adding 1 FRP ply to plastic hinges at thebottom ends of storey 1 inner columns and the plastichinges of inner columns of storey 3 making the

number of FRP plies respectively increase to 3 and 2for these locations and this frame is called RS2 +edamage state of the frame RS2 is shown in Figure 19(c)+ese analyses were also performed for the frameretrofitted by 1 FRP ply for all plastic hinges +is

Storey 8

Storey 7

Storey 6

Storey 5

Storey 4

Storey 3

Storey 2

Storey 1

(a)

Storey 8

Storey 7

Storey 6

Storey 5

Storey 4

Storey 3

Storey 2

Storey 1

(b)

Storey 8

Storey 7

Storey 6

Storey 5

Storey 4

Storey 2

Storey 3

Storey 1

(c)

Storey 8

Storey 7

Storey 6

Storey 5

Storey 4

Storey 3

Storey 2

Storey 1

(d)

Figure 19 Damage of the 8-storey frame (a) original (b) RS1 (c) RS2 and (d) RS0


retrofitted frame is called RS0 +e damage state of theretrofitted frame is shown in Figure 19(d) +e dis-tributions of storey damage indices of the original RS0RS1 and RS2 are plotted in Figure 20 Figure 21 showsthe variations of damage index and the FRP ratios forthe frames As can be visible in Figures 20 and 21 of theframe RS2 the damage index is significantly reduced

from 0396 (moderate damage) to 0238 (light damage)and the FRP ratio reduced to 688 when comparedwith that of the frame RS0 By coincidence the value688 is similar to the FRP ratio of the 4-storey frame

8 Conclusions

+is current paper presents the proposed FRP retrofittingapproach to address building ownersrsquo concern on reducing theFRP cost and installationinterruption time +e FRP retrofit-ting approach is proposed based on the seismic damage dis-tribution in structures using both quantitative and qualitativecriteria +e quantitative criterion is set by the condition DIle[DI] and the qualitative criterion is evaluated by the damagedistribution +e advantages of the proposed approach can belisted as follows (1) the damage index and the damage mode ofretrofitted structures are controlled (2) the amount of FRP isreduced because FRP is effectively redistributed based on thedamage distribution in structures and (3) FRP installationinterruption time is reduced since only critical locations un-dergo retrofitting +e second advantage directly reduces theFRP material cost while the third advantage indirectly reducesthe total retrofitting cost

+e proposed FRP retrofitting approach was used toretrofit low- and mid-rise nonductile RC frame structuresWith a similar predefined target of damage level the amountof FRP used for low- and mid-rise frames reduced to 688+is resulted in 312 saving in FRP when compared withthe traditional approach where FRP is evenly distributed Inaddition the damage indices of the considered low- andmid-rise FRP-retrofitted frames using the proposed retro-fitting approach were much lower than those of the framesretrofitted using traditional approach +us the proposedretrofitting approach not only reduced the cost but also wasvery effective in reducing the seismic damage Due to itssimplicity and technicaleconomical effectiveness the pro-posed FRP retrofitting approach can be useful for engi-neering practice in retrofitting structures

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

Acknowledgments

+is research was funded by Vietnam National Foundationfor Science and Technology Development (NAFOSTED)under Grant no 10702ndash201718

References

[1] J Shin D W Scott L K Stewart C-S Yang T R Wrightand R DesRoches ldquoDynamic response of a full-scale rein-forced concrete building frame retrofitted with FRP columnjacketsrdquo Engineering Structures vol 125 pp 244ndash253 2016

0004

0024

0018

0238

0185

0215

0218

0059

0135

0090 0208 0396 0431

0155

0322

0290

0494

0242

0418

0376

0092

1

2

3

4

5

6

7

8

Stor

ey


OriginalRS0

RS1RS2


04940396

0242 02380

1

05940688

Original RS0 RS1 RS2Original and retrofitted structures


0

025

05

075

1

Dam

age i

ndex

FRP

ratio



[2] P Paultre and F Legeron ldquoConfinement reinforcement de-sign for reinforced concrete columnsrdquo Journal of StructuralEngineering vol 134 no 5 pp 738ndash749 2008

[3] I Erdem U Akyuz U Ersoy and G Ozcebe ldquoAn experi-mental study on two different strengthening techniques forRC framesrdquo Engineering Structures vol 28 no 13pp 1843ndash1851 2006

[4] J W Schmidt C O Christensen P Goltermann andK D Hertz ldquoShared CFRP activation anchoring methodapplied to NSMR strengthening of RC beamsrdquo CompositeStructures vol 230 p 111487 2019

[5] B Fu J G Teng GM Chen J F Chen and Y C Guo ldquoEffectof load distribution on IC debonding in FRP-strengthened RCbeams full-scale experimentsrdquo Composite Structures vol 188pp 483ndash496 2018

[6] Y Liu and Y Fan ldquoExperimental study on flexural behavior ofprestressed concrete beams reinforced by CFRP underchloride environmentrdquo Advances in Civil Engineeringvol 2019 Article ID 2424518 14 pages 2019

[7] A M H Kadhim H A Numan and M Ozakccedila ldquoFlexuralstrengthening and rehabilitation of reinforced concrete beamusing BFRP composites finite element approachrdquo Advancesin Civil Engineering vol 2019 Article ID 4981750 17 pages2019

[8] N Askandar and A Mahmood ldquoComparative investigationon torsional behaviour of RC beam strengthened with CFRPfabric wrapping and near-surface mounted (NSM) steel barrdquoAdvances in Civil Engineering vol 2019 Article ID 906170315 pages 2019

[9] N Basa M Ulicevic and R Zejak ldquoExperimental research ofcontinuous concrete beams with GFRP reinforcementrdquo Ad-vances in Civil Engineering vol 2018 Article ID 653272316 pages 2018

[10] K Chansawat T Potisuk T H Miller S C Yim andD I Kachlakev ldquoFEmodels of GFRP and CFRP strengtheningof reinforced concrete beamsrdquo Advances in Civil Engineeringvol 2009 Article ID 152196 pp 1ndash13 2009

[11] E del Rey Castillo M Griffith and J Ingham ldquoSeismic be-havior of RC columns flexurally strengthened with FRP sheetsand FRP anchorsrdquo Composite Structures vol 203 pp 382ndash395 2018

[12] J-J Zeng Y-C Guo W-Y Gao W-P Chen and L-J LildquoStress-strain behavior of concrete in circular concrete col-umns partially wrapped with FRP stripsrdquo Composite Struc-tures vol 200 pp 810ndash828 2018

[13] M T Jameel M N Sheikh and M N S Hadi ldquoBehaviour ofcircularized and FRP wrapped hollow concrete specimensunder axial compressive loadrdquo Composite Structures vol 171pp 538ndash548 2017

[14] Y Li M-F Xie and J-B Liu ldquoExperimental study on theseismic behaviour of reinforced concrete bridge piersstrengthened by BFRP sheetsrdquo Advances in Civil Engineeringvol 2019 Article ID 4169421 11 pages 2019

[15] A Raza Q u Z Khan and A Ahmad ldquoNumerical inves-tigation of load-carrying capacity of GFRP-reinforced rect-angular concrete members using CDP model in ABAQUSrdquoAdvances in Civil Engineering vol 2019 Article ID 174534121 pages 2019

[16] M Fossetti F Basone G DrsquoArenzo G Macaluso andA F Siciliano ldquoFRP-confined concrete columns a newprocedure for evaluating the performance of square andcircular sectionsrdquo Advances in Civil Engineering vol 2018Article ID 2543850 15 pages 2018

[17] C Del Vecchio M Di Ludovico A Prota and G ManfredildquoModelling beam-column joints and FRP strengthening in theseismic performance assessment of RC existing framesrdquoComposite Structures vol 142 pp 107ndash116 2016

[18] M Lesani M R Bahaari and M M Shokrieh ldquoNumericalinvestigation of FRP-strengthened tubular T-joints underaxial compressive loadsrdquo Composite Structures vol 100pp 71ndash78 2013

[19] E Esmaeeli F Danesh K F Tee and S Eshghi ldquoA com-bination of GFRP sheets and steel cage for seismicstrengthening of shear-deficient corner RC beam-columnjointsrdquo Composite Structures vol 159 no Supplement Cpp 206ndash219 2017

[20] S S Mahini and H R Ronagh ldquoStrength and ductility of FRPweb-bonded RC beams for the assessment of retrofitted beam-column jointsrdquo Composite Structures vol 92 no 6pp 1325ndash1332 2010

[21] A Mukherjee andM Joshi ldquoFRPC reinforced concrete beam-column joints under cyclic excitationrdquo Composite Structuresvol 70 no 2 pp 185ndash199 2005

[22] V V Cao and H R Ronagh ldquoReducing the seismic damage ofreinforced concrete frames using FRP confinementrdquo Com-posite Structures vol 118 pp 403ndash415 2014

[23] V V Cao and S Q Pham ldquoComparison of CFRP and GFRPwraps on reducing seismic damage of deficient reinforcedconcrete structuresrdquo International Journal of Civil Engi-neering vol 17 no 11 pp 1667ndash1681 2019

[24] E I Saqan H A Rasheed and T Alkhrdaji ldquoEvaluation ofthe seismic performance of reinforced concrete framesstrengthened with CFRP fabric and NSM barsrdquo CompositeStructures vol 184 no C pp 839ndash847 2018

[25] L Lam and J G Teng ldquoDesign-oriented stress-strain modelfor FRP-confined concreterdquo Construction and Building Ma-terials vol 17 no 6-7 pp 471ndash489 2003

[26] Y-Y Wei and Y-F Wu ldquoUnified stress-strain model ofconcrete for FRP-confined columnsrdquo Construction andBuilding Materials vol 26 no 1 pp 381ndash392 2012

[27] M Samaan A Mirmiran and M Shahawy ldquoModel ofconcrete confined by fiber compositesrdquo Journal of StructuralEngineering vol 124 no 9 pp 1025ndash1031 1998

[28] C Pellegrino and C Modena ldquoAnalytical model for FRPconfinement of concrete columns with and without internalsteel reinforcementrdquo Journal of Composites for Constructionvol 14 no 6 pp 693ndash705 2010

[29] S A Sheikh and G Yau ldquoSeismic behavior of concretecolumns confined with steel and fiber-reinforced polymersrdquoACI Structural Journal vol 99 no 1 pp 72ndash80 2002

[30] A Rahai and H Akbarpour ldquoExperimental investigation onrectangular RC columns strengthened with CFRP compositesunder axial load and biaxial bendingrdquo Composite Structuresvol 108 pp 538ndash546 2014

[31] M H Harajli and A A Rteil ldquoEffect of confinement usingfiber-reinforced polymer or fiber-reinforced concrete onseismic performance of gravity load-designed columnsrdquo ACIStructural Journal vol 101 no 1 pp 47ndash56 2004

[32] M K Zaki ldquoOptimal performance of FRP strengthenedconcrete columns under combined axial-flexural loadingrdquoEngineering Structures vol 46 pp 14ndash27 2013

[33] A Fam and J-K Son ldquoFinite element modeling of hollow andconcrete-filled fiber composite tubes in flexure optimizationof partial filling and a design method for polesrdquo EngineeringStructures vol 30 no 10 pp 2667ndash2676 2008

[34] R Garcia I Hajirasouliha and K Pilakoutas ldquoSeismic be-haviour of deficient RC frames strengthened with CFRP


compositesrdquo Engineering Structures vol 32 no 10pp 3075ndash3085 2010

[35] A Balsamo A Colombo GManfredi P Negro and A ProtaldquoSeismic behavior of a full-scale RC frame repaired usingCFRP laminatesrdquo Engineering Structures vol 27 no 5pp 769ndash780 2005

[36] M D Ludovico A Prota G Manfredi and E CosenzaldquoSeismic strengthening of an under-designed RC structurewith FRPrdquo Earthquake Engineering amp Structural Dynamicsvol 37 pp 141ndash162 2008

[37] M D Ludovico G Manfredi E Mola P Negro and A ProtaldquoSeismic behavior of a full-scale RC structure retrofitted usingGFRP laminatesrdquo Journal of Structural Engineering vol 134no 5 pp 810ndash821 2008

[38] A Mortezaei H R Ronagh and A Kheyroddin ldquoSeismicevaluation of FRP strengthened RC buildings subjected tonear-fault ground motions having fling steprdquo CompositeStructures vol 92 no 5 pp 1200ndash1211 2010

[39] H Ozkaynak E Yuksel O Buyukozturk C Yalcin andA A Dindar ldquoQuasi-static and pseudo-dynamic testing ofinfilled RC frames retrofitted with CFRP materialrdquo Com-posites Part B Engineering vol 42 no 2 pp 238ndash263 2011

[40] G E +ermou S J Pantazopoulou and A S ElnashaildquoGlobal interventions for seismic upgrading of substandardRC buildingsrdquo Journal of Structural Engineering vol 138no 3 pp 387ndash401 2012

[41] X K Zou J G Teng L De Lorenzis and S H Xia ldquoOptimalperformance-based design of FRP jackets for seismic retrofitof reinforced concrete framesrdquo Composites Part B Engi-neering vol 38 no 5-6 pp 584ndash597 2007

[42] S W Choi Y Kim and H S Park ldquoMulti-objective seismicretrofit method for using FRP jackets in shear-critical rein-forced concrete framesrdquo Composites Part B Engineeringvol 56 pp 207ndash216 2014

[43] +e MathWorks I (2014) MATLAB Version R2014a[44] T Takeda M A Sozen and N N Nielsen ldquoReinforced

concrete response to simulated earthquakesrdquo Journal of theStructural Division vol 96 pp 2557ndash2573 1970

[45] S A Sheikh and S S Khoury ldquoConfined concrete columnswith stubsrdquoACI Structural Journal vol 90 no 4 pp 414ndash4311993

[46] W W L Chan ldquo+e ultimate strength and deformation ofplastic hinges in reinforced concrete frameworksrdquo Magazineof Concrete Research vol 7 no 21 pp 121ndash132 1955

[47] A L L Baker and A M N Amarakone ldquoInelastic hyperstaticframes analysisrdquo in Proceedings of the International Sympo-sium on the Flexural Mechanics of Reinforced Concrete ASCE-ACI Miami FL USA pp 85ndash142 October 1964

[48] H E H Roy and M A Sozen ldquoDuctility of concreterdquo inProceedings of the International Symposium on the FlexuralMechanics of Reinforced Concrete ASCE-ACI Miami FLUSA pp 213ndash224 October 1964

[49] M T M Soliman and C W Yu ldquo+e flexural stress-strainrelationship of concrete confined by rectangular transversereinforcementrdquo Magazine of Concrete Research vol 19no 61 pp 223ndash238 1967

[50] M Sargin S K Ghosh and V K Handa ldquoEffects of lateralreinforcement upon the strength and deformation propertiesof concreterdquo Magazine of Concrete Research vol 23 no 75-76 pp 99ndash110 1971

[51] D C Kent and R Park ldquoFlexural members with confinedconcreterdquo Journal of the Structural Division vol 97 no 7pp 1969ndash1990 1971

[52] R Park M J N Priestley andW D Gill ldquoDuctility of square-confined concrete columnsrdquo Journal of the Structural Divi-sion vol 108 pp 929ndash950 1982

[53] V V Cao H R Ronagh M Ashraf and H Baji ldquoA newdamage index for reinforced concrete structuresrdquo Earth-quakes and Structures vol 6 no 6 pp 581ndash609 2014

[54] L Lam and J G Teng ldquoDesign-Oriented stress-strain modelfor FRP-confined concrete in rectangular columnsrdquo Journal ofReinforced Plastics and Composites vol 22 no 13pp 1149ndash1186 2003

[55] A Eslami and H R Ronagh ldquoEffect of FRP wrapping inseismic performance of RC buildings with and without specialdetailing - a case studyrdquo Composites Part B Engineeringvol 45 no 1 pp 1265ndash1274 2013

[56] A D Luca F Nardone F Matta A Nanni G P Lignola andA Prota ldquoStructural evaluation of full-scale FRP-confinedreinforced concrete columnsrdquo Journal of Composites forConstruction vol 15 no 1 pp 112ndash123 2011

[57] L-M Wang and Y-F Wu ldquoEffect of corner radius on theperformance of CFRP-confined square concrete columnsTestrdquo Engineering Structures vol 30 no 2 pp 493ndash505 2008

[58] M H Harajli E Hantouche and K Soudki ldquoStress-strainmodel for Fiber-Reinforced Polymer jacketed concrete col-umnsrdquo ACI Structural Journal vol 103 no 5 pp 672ndash6822006

[59] G Wu Z S Wu and Z T Lu ldquoDesign-oriented stress-strainmodel for concrete prisms confined with FRP compositesrdquoConstruction and Building Materials vol 21 no 5pp 1107ndash1121 2007

[60] M N Youssef M Q Feng and A S Mosallam ldquoStress-strainmodel for concrete confined by FRP compositesrdquo CompositesPart B Engineering vol 38 no 5-6 pp 614ndash628 2007

[61] T Ozbakkaloglu J C Lim and T Vincent ldquoFRP-confinedconcrete in circular sections review and assessment of stress-strain modelsrdquo Engineering Structures vol 49 pp 1068ndash10882013

[62] S Rocca N Galati and A Nanni ldquoReview of designguidelines for FRP confinement of reinforced concrete col-umns of noncircular cross sectionsrdquo Journal of Composites forConstruction vol 12 no 1 pp 80ndash92 2008

[63] A Mirmiran M Samaan S Cabrera and M ShahawyldquoDesign manufacture and testing of a new hybrid columnrdquoConstruction and Building Materials vol 12 no 1 pp 39ndash491998

[64] A Mirmiran M Shahawy M Samaan H E EcharyJ C Mastrapa and O Pico ldquoEffect of column parameters onFRP-confined concreterdquo Journal of Composites for Con-struction vol 2 no 4 pp 175ndash185 1998

[65] M N Fardis and H H Khalili ldquoFRP-encased concrete as astructural materialrdquo Magazine of Concrete Research vol 34no 121 pp 191ndash202 1982

[66] ACI (2008) Guide for the Design and Construction of Ex-ternally Bonded FRP Systems for Strengthening ConcreteStructures (ACI 4402R-08)

[67] S Rocca N Galati and A Nanni ldquoInteraction diagrammethodology for design of FRP-confined reinforced concretecolumnsrdquo Construction and Building Materials vol 23 no 4pp 1508ndash1520 2009

[68] R Realfonzo and A Napoli ldquoConfining concrete memberswith FRP systems predictive vs design strain modelsrdquoComposite Structures vol 104 pp 304ndash319 2013

[69] H Baji H R Ronagh and C Q Li ldquoProbabilistic designmodels for ultimate strength and strain of FRP-confined


concreterdquo Journal of Composites for Construction vol 20no 6 Article ID 04016051 2016

[70] H Baji ldquoCalibration of the FRP resistance reduction factor forFRP-confined reinforced concrete building columnsrdquo Journalof Composites for Construction vol 21 no 3 Article ID04016107 2017

[71] T Chaudat C Garnier S Cvejic S Poupin M Le Corre andM Mahe ECOLEADER Project no 2 Seismic Tests On AReinforced Concrete Bare Frame with FRP retrofitting-TestsReport CEA Saclay France 2005

[72] Computers and Structures Inc (2017) SAP2000 Version1920

[73] H R Ronagh and A Eslami ldquoFlexural retrofitting of RCbuildings using GFRPCFRP - a comparative studyrdquo Com-posites Part B Engineering vol 46 pp 188ndash196 2013 httpdxdoiorg101016jcompositesb201209072

[74] ICBO ldquoUniform building coderdquo International Conference ofBuilding Officials ICBO Whittier CA USA 1994

[75] J M Bracci A M Reinhorn and J B Mander ldquoSeismicresistance of reinforced concrete frame structures designedfor gravity loads performance of structural systemrdquo ACIStructural Journal vol 92 no 5 pp 597ndash608 1995

[76] J M Bracci Experimental and Analytical Study of SeismicDamage and Retrofit of Lightly Reinforced Concrete Structuresin Low Seismicity Zones PhD+esis State University of NewYork at Buffalo New York NY USA 1992

[77] PEER (2019) PEER Ground Motion Database httpsngawest2berkeleyedusite

[78] ACI Building Code Requirements for Structural Concrete (ACI318M-08) and Commentary American Concrete InstituteFarmington Hills MI USA 2008

[79] ASCE Prestandard and Commentary for the Seismic Reha-bilitation of Buildings Federal Emergency ManagementAgency Washington DC USA 2000

[80] ASCE Minimum Design Loads for Buildings and OtherStructures American Society of Civil Engineers FarmingtonHills MI USA 2010


retrofitting of columns were also conducted by researchers[32 33] For frame structures similar beneficial effects ofFRP retrofitting have been confirmed by researchers FRPretrofitting successfully prevented soft storey [1] and col-umn-sway [34] mechanisms for structures FRP retrofittingsignificantly increased the seismic capacity [3 35ndash38] andconsiderably improved deformation capacity [34 37] butreduced damage [34 37 39] for structures

+e above studies on FRP retrofitting of RC framesconfirmed the effectiveness of FRP confinement applied tocritical locations of plastic hinges to improve the seismicperformance of RC structures however less attention hasbeen paid for the cost of FRP retrofitting Along with re-ducing to a predefined damage level for structures the leastamount of FRP and the shortest FRP installation time tominimize the cost are of major concerns by not onlybuilding owners but also structuralretrofitting engineersObviously these concerns are not appropriately addressedby evenly distributing FRP for critical locations of plastichinges because the seismic damage is unevenly distributed tothese locations To the best of the authorsrsquo knowledge thenumber of studies aiming at addressing these concerns isquite limited in the literature as reviewed in the following+ermou et al [40] developed a methodology for upgradingdeficient RC buildings in which the distribution of the inter-storey drift is optimized by intervening the stiffness dis-tribution in the vertical direction of the building Zou et al[41] optimized the performance-based design of FRP con-finement at plastic hinges of columns for seismic retrofittingof existing RC structures +e optimization objective was tominimize the thickness of FRP confinement while the op-timization process was subjected to the criterion of inelasticinter-storey drift Choi et al [42] proposed a seismic ret-rofitting method for shear-critical RC frames using FRPwraps withmultiobjectives+e two objective functions wereto minimize the amount of FRP and variation coefficient ofthe inter-storey drift while the constraint functions were theallowable inter-storey drift the shear failure and themaximum compressive strength of concrete +e optimalmethod was illustrated by the retrofitting of a three-storeyframe

Only limited number of studies [40ndash42] in which inter-storey drift was employed as the main criterion to distributeFRP together with no clear guidelines in current codesapplied for FRP distribution in frames have inspired theauthors to carry out this study An attempt aiming at helpingengineers to address the practical concern of FRP retrofittingcost raise by building owners and to improve the effec-tiveness of the FRP retrofitting is presented in this paper Toachieve this aim an FRP retrofitting approach of RCstructures in which FRP is distributed based on the seismicdamage distribution (instead of inter-storey drift) instructures was proposed Because the damage indices ofplastic hinges (element damage level) are more specific thaninter-storey drifts (storey damage level) the distribution ofFRP based on damage indices is logically more appropriate+e technical and economical effectiveness proposed ap-proach was demonstrated for the two FRP retrofitting casesof 4- and 8-storey nonductile RC frames representing for

low- and mid-rise building structures +e frames wereretrofitted by the proposed approach and then by evenlydistributing the FRP for comparison Conclusions are madebased on the comparison

2 The Proposed Damage-Based FRPRetrofitting Approach

Figure 1 shows the proposed FRP retrofitting approach forexisting structures based on seismic damage distributionBased on the design of a structure the seismic damagedistribution in structures is analysed +e obtained damagedistribution is used to distribute the FRP In this proposedFRP retrofitting approach FRP is only applied to the lo-cations of plastic hinges where the damage indices (DI) arelarger than the allowable damage index [DI] while the lo-cations with no or minor damage are not applied by FRP+is step is simple but very effective in appropriately dis-tributing FRP Two criteria are applied in the proposedretrofitting approach +e first criterion is quantitatively setby the condition DI le [DI] while the second criterion isqualitatively set by the damage distribution +e proposedFRP retrofitting approach is described in Figure 1 followedby the general descriptions of steps Some steps with longdetails are described in Sections 3 and 4 It is worth em-phasizing that the details of long steps presented in thesesections are of several methods that can be used For ex-ample the selection of seismic records can be different basedon the seismic design codes or the analysis method can bedifferent provided the target is achieved

(i) Step 1 existing structures+e design of building structures is collected pro-viding information for analyses and FRP retrofitting

(ii) Step 2 design earthquakes and the allowabledamage index [DI]+e design earthquake intensity is based on thecurrent seismic code for the region where theretrofitted building is located +e characteristicsof earthquakes occurring in the region are alsocollected if applicable +e design response spec-trum regulated in current seismic codes for theregion is constructed and earthquake groundmotions are then selected +ese selected groundmotions are scaled to match the design responsespectrum in order to obtain the scaled seismicrecords which are then used for inelastic timehistory (ITH) analyses+e other task of this step is to determine thedamage level for the retrofitted structures such aslight damage moderate damage or severe damagewhen the retrofitted structure experiences thedesign earthquakes +e target damage level isestablished by the owners managers or investorsunder being consulted by structural engineers witha reference to current seismic codes +e targetdamage level is then used to determine the al-lowable damage index [DI] +is [DI] is used as a











Damage analyses


End


Notreasonable

Reasonable

No

Yes

Existing structures




Start













fc fcPrime 2εc

εo

minusεc

εo

1113888 1113889

2⎡⎣ ⎤⎦ if εc le εo (1)



fcPrime Kfc

Prime (3)

εo 0002K (4)

Z 05


bPrimesh( 1113857

1113969

minus 0002K

(5)

K 1 +ρsfyh

fcprime

(6)


1113936nf




DI Eh

Eh + Erec1113890 1113891

α(Nminus i)

(7)







Non

linea

r lin

k el

emen

ts

(a) (b)

A

B

C

Pγ

DγDcr

Pcr

1

1

2

2

3

34

4

5

5

6

6

7

7

8

8

9

9

10

10a

10b

11

11

12

12

13

13

14

15

16

171819

20


(b)(a) (c) (d)

fs1

fc

fs2

fs3

fs4

fs5

εs1

εs2

εs3

εs4

εs5

εc Zn

εm

MN

Ultimate

Curvature

Mom

ent

YieldIdealized

Crack

O

Real












2

4fcprime

ε2c (8)


in which

εt 2fcprime

Ec minus E2 (10)


εu

(11)



A A

FRP wrap

GFRP wraps r = 50mm

A-A





fla

fcprime1113890 1113891 if

fla

fcprimege 007 (12)

fcuprime fcprime if

fla

fcprimelt 007 (13)


fcprime

εhrup

εo

1113888 1113889

045⎡⎣ ⎤⎦ (14)

fla Eftf

Rεhrup

2Eftf

Dεhrup (15)

D h2 + b2

radic (16)

ks1 b

h1113888 1113889

2Ae

Ac

(17)

ks2 h

b1113888 1113889

05Ae

Ac

(18)

Ae

Ac


1 minus ρs




5 Verifications






Stre

ss

O

f primec

Ec = tanα

A

Bf primecu

Unconfined

FRP confined







1113936 Wihi

(20)

Ft 007TVle 025V (21)


Beam

BeamSteel plates

Steel plates

Slabs 12mm thick


4260 times 4260

3300

3300

(a)

ϕ6mm200 ϕ6mm200

ϕ6m

m2

00

ϕ8mm300 ϕ8mm300

ϕ6m

m2

00

ϕ6m

m2

00ϕ8mm300

260

260

260 260

260

400

400

400

380




8ϕ14mm

8ϕ14mm 8ϕ14mm

8ϕ14mm

4ϕ14mm

4ϕ14mm

(b)










fcprime

1113969


ndash20

ndash15

ndash10

ndash5

0

5

10

15

Disp

lace

men

t (m

m)

5 10 15 20 25 30 35 400Time (s)

ExperimentAnalysis

(a)

ndash20

ndash15

ndash10

ndash5

0

5

10

15

20

Disp

lace

men

t (m

m)

5 10 15 20 25 30 35 400Time (s)

ExperimentAnalysis

(b)







A-A

B-B

C-C

D-D

E-E

F-F

600

600

600

600

600

600

600

600

600

600

600

600

540

540

440

440

440

440

60

60

60

60

60

60

16ϕ25

6ϕ25 4ϕ25

4ϕ226ϕ22

6ϕ18 3ϕ18

16ϕ18

16ϕ16

450

450

450

140

175

250

-

-

-

-

-

-

-

-

-

C C C C

C C

C C

C C

C C

C C

C C

B B

B B

A A

A A

B B

B B

A A

A A

FF

FF

FF

FF

EE

EE

EE

EE

DD

DD

DD

DD

DD

DD

DD

DD

CL8

3

m

3 5m

b b

h h

d d

d prime dprime

Ast

As

Aprimes



Base

shea

r for

ce (k

N)

0

250

500

750

1000

1250

1500







(a)


8prime-0Prime

4prime-0Prime

6prime-0Prime

W-ga114Primecolumn

ties (typ)


(typ)

8Prime

4Prime

3Prime

6Prime2Prime4Prime

4Prime

12prime-0Prime

Y Y Y Y


2Prime slab(typ)





A

A

B

B

C

C

C

D

D D

D

2D5

2D42D4 1D41D4

2D4

2prime

2prime

6prime 10prime

Section Y-Y

W-ga11267Prime

4D4

W-ga11

C-C

B-BA-A

D-DBeam sections

3D4

3D4

2D4

2D4 2D4 1D5

2D5 2D5

W-ga11(typ)

1

Elevation


Beam steel

1 1-

(b)







CrackedYielded


(a)

++

+

++

++ +

++

(b)



A-A 16ϕ18 - - 450

B-B - 6ϕ22 4ϕ22 175

C-C

500

500

500

60

60

60 - 6ϕ18 3ϕ18 250

440

440

440

500

500

500

Aprimes(mm2)

As(mm2)

Ast(mm2)

dprime(mm)

d(mm)

h(mm)

b(mm)

4

3m

3 5m

A

A

A

A

A

A

A

A

A

A

A

A

C

CC

C

B

BB

B







Spec

tral

acce

lera

tion

PGA

00

05

10

15

20

25

30

1 2 3 40T (sec)



300 400100 200 500000 600Period (sec)

000

020

040

060

080

100

120

pSa (

g)












Storey 4

Storey 3

Storey 2

Storey 1

(a)

Storey 4

Storey 3

Storey 2

Storey 1

(b)

Storey 4

Storey 3

Storey 2

Storey 1

(c)

Storey 4

Storey 3

Storey 2

Storey 1

(d)


0587

0140

0030

0000

0419

0077

0002

0107

0008

0077


OriginalRS0

RS1RS2

1

2

3

4

Stor

ey







0587

0419

0107 00770

1

06250688

Dam

age i

ndex

ratio

of F

RP


0

025

05

075

1








Storey 8

Storey 7

Storey 6

Storey 5

Storey 4

Storey 3

Storey 2

Storey 1

(a)

Storey 8

Storey 7

Storey 6

Storey 5

Storey 4

Storey 3

Storey 2

Storey 1

(b)

Storey 8

Storey 7

Storey 6

Storey 5

Storey 4

Storey 2

Storey 3

Storey 1

(c)

Storey 8

Storey 7

Storey 6

Storey 5

Storey 4

Storey 3

Storey 2

Storey 1

(d)





8 Conclusions



Data Availability




Acknowledgments


References


0004

0024

0018

0238

0185

0215

0218

0059

0135

0090 0208 0396 0431

0155

0322

0290

0494

0242

0418

0376

0092

1

2

3

4

5

6

7

8

Stor

ey


OriginalRS0

RS1RS2


04940396

0242 02380

1

05940688



0

025

05

075

1

Dam

age i

ndex

FRP

ratio
































































































Damage analyses


End


Notreasonable

Reasonable

No

Yes

Existing structures




Start













fc fcPrime 2εc

εo

minusεc

εo

1113888 1113889

2⎡⎣ ⎤⎦ if εc le εo (1)



fcPrime Kfc

Prime (3)

εo 0002K (4)

Z 05


bPrimesh( 1113857

1113969

minus 0002K

(5)

K 1 +ρsfyh

fcprime

(6)


1113936nf




DI Eh

Eh + Erec1113890 1113891

α(Nminus i)

(7)







Non

linea

r lin

k el

emen

ts

(a) (b)

A

B

C

Pγ

DγDcr

Pcr

1

1

2

2

3

34

4

5

5

6

6

7

7

8

8

9

9

10

10a

10b

11

11

12

12

13

13

14

15

16

171819

20


(b)(a) (c) (d)

fs1

fc

fs2

fs3

fs4

fs5

εs1

εs2

εs3

εs4

εs5

εc Zn

εm

MN

Ultimate

Curvature

Mom

ent

YieldIdealized

Crack

O

Real












2

4fcprime

ε2c (8)


in which

εt 2fcprime

Ec minus E2 (10)


εu

(11)



A A

FRP wrap

GFRP wraps r = 50mm

A-A





fla

fcprime1113890 1113891 if

fla

fcprimege 007 (12)

fcuprime fcprime if

fla

fcprimelt 007 (13)


fcprime

εhrup

εo

1113888 1113889

045⎡⎣ ⎤⎦ (14)

fla Eftf

Rεhrup

2Eftf

Dεhrup (15)

D h2 + b2

radic (16)

ks1 b

h1113888 1113889

2Ae

Ac

(17)

ks2 h

b1113888 1113889

05Ae

Ac

(18)

Ae

Ac


1 minus ρs




5 Verifications






Stre

ss

O

f primec

Ec = tanα

A

Bf primecu

Unconfined

FRP confined







1113936 Wihi

(20)

Ft 007TVle 025V (21)


Beam

BeamSteel plates

Steel plates

Slabs 12mm thick


4260 times 4260

3300

3300

(a)

ϕ6mm200 ϕ6mm200

ϕ6m

m2

00

ϕ8mm300 ϕ8mm300

ϕ6m

m2

00

ϕ6m

m2

00ϕ8mm300

260

260

260 260

260

400

400

400

380




8ϕ14mm

8ϕ14mm 8ϕ14mm

8ϕ14mm

4ϕ14mm

4ϕ14mm

(b)










fcprime

1113969


ndash20

ndash15

ndash10

ndash5

0

5

10

15

Disp

lace

men

t (m

m)

5 10 15 20 25 30 35 400Time (s)

ExperimentAnalysis

(a)

ndash20

ndash15

ndash10

ndash5

0

5

10

15

20

Disp

lace

men

t (m

m)

5 10 15 20 25 30 35 400Time (s)

ExperimentAnalysis

(b)







A-A

B-B

C-C

D-D

E-E

F-F

600

600

600

600

600

600

600

600

600

600

600

600

540

540

440

440

440

440

60

60

60

60

60

60

16ϕ25

6ϕ25 4ϕ25

4ϕ226ϕ22

6ϕ18 3ϕ18

16ϕ18

16ϕ16

450

450

450

140

175

250

-

-

-

-

-

-

-

-

-

C C C C

C C

C C

C C

C C

C C

C C

B B

B B

A A

A A

B B

B B

A A

A A

FF

FF

FF

FF

EE

EE

EE

EE

DD

DD

DD

DD

DD

DD

DD

DD

CL8

3

m

3 5m

b b

h h

d d

d prime dprime

Ast

As

Aprimes



Base

shea

r for

ce (k

N)

0

250

500

750

1000

1250

1500







(a)


8prime-0Prime

4prime-0Prime

6prime-0Prime

W-ga114Primecolumn

ties (typ)


(typ)

8Prime

4Prime

3Prime

6Prime2Prime4Prime

4Prime

12prime-0Prime

Y Y Y Y


2Prime slab(typ)





A

A

B

B

C

C

C

D

D D

D

2D5

2D42D4 1D41D4

2D4

2prime

2prime

6prime 10prime

Section Y-Y

W-ga11267Prime

4D4

W-ga11

C-C

B-BA-A

D-DBeam sections

3D4

3D4

2D4

2D4 2D4 1D5

2D5 2D5

W-ga11(typ)

1

Elevation


Beam steel

1 1-

(b)







CrackedYielded


(a)

++

+

++

++ +

++

(b)



A-A 16ϕ18 - - 450

B-B - 6ϕ22 4ϕ22 175

C-C

500

500

500

60

60

60 - 6ϕ18 3ϕ18 250

440

440

440

500

500

500

Aprimes(mm2)

As(mm2)

Ast(mm2)

dprime(mm)

d(mm)

h(mm)

b(mm)

4

3m

3 5m

A

A

A

A

A

A

A

A

A

A

A

A

C

CC

C

B

BB

B







Spec

tral

acce

lera

tion

PGA

00

05

10

15

20

25

30

1 2 3 40T (sec)



300 400100 200 500000 600Period (sec)

000

020

040

060

080

100

120

pSa (

g)












Storey 4

Storey 3

Storey 2

Storey 1

(a)

Storey 4

Storey 3

Storey 2

Storey 1

(b)

Storey 4

Storey 3

Storey 2

Storey 1

(c)

Storey 4

Storey 3

Storey 2

Storey 1

(d)


0587

0140

0030

0000

0419

0077

0002

0107

0008

0077


OriginalRS0

RS1RS2

1

2

3

4

Stor

ey







0587

0419

0107 00770

1

06250688

Dam

age i

ndex

ratio

of F

RP


0

025

05

075

1








Storey 8

Storey 7

Storey 6

Storey 5

Storey 4

Storey 3

Storey 2

Storey 1

(a)

Storey 8

Storey 7

Storey 6

Storey 5

Storey 4

Storey 3

Storey 2

Storey 1

(b)

Storey 8

Storey 7

Storey 6

Storey 5

Storey 4

Storey 2

Storey 3

Storey 1

(c)

Storey 8

Storey 7

Storey 6

Storey 5

Storey 4

Storey 3

Storey 2

Storey 1

(d)





8 Conclusions



Data Availability




Acknowledgments


References


0004

0024

0018

0238

0185

0215

0218

0059

0135

0090 0208 0396 0431

0155

0322

0290

0494

0242

0418

0376

0092

1

2

3

4

5

6

7

8

Stor

ey


OriginalRS0

RS1RS2


04940396

0242 02380

1

05940688



0

025

05

075

1

Dam

age i

ndex

FRP

ratio































































































fc fcPrime 2εc

εo

minusεc

εo

1113888 1113889

2⎡⎣ ⎤⎦ if εc le εo (1)



fcPrime Kfc

Prime (3)

εo 0002K (4)

Z 05


bPrimesh( 1113857

1113969

minus 0002K

(5)

K 1 +ρsfyh

fcprime

(6)


1113936nf




DI Eh

Eh + Erec1113890 1113891

α(Nminus i)

(7)







Non

linea

r lin

k el

emen

ts

(a) (b)

A

B

C

Pγ

DγDcr

Pcr

1

1

2

2

3

34

4

5

5

6

6

7

7

8

8

9

9

10

10a

10b

11

11

12

12

13

13

14

15

16

171819

20


(b)(a) (c) (d)

fs1

fc

fs2

fs3

fs4

fs5

εs1

εs2

εs3

εs4

εs5

εc Zn

εm

MN

Ultimate

Curvature

Mom

ent

YieldIdealized

Crack

O

Real












2

4fcprime

ε2c (8)


in which

εt 2fcprime

Ec minus E2 (10)


εu

(11)



A A

FRP wrap

GFRP wraps r = 50mm

A-A





fla

fcprime1113890 1113891 if

fla

fcprimege 007 (12)

fcuprime fcprime if

fla

fcprimelt 007 (13)


fcprime

εhrup

εo

1113888 1113889

045⎡⎣ ⎤⎦ (14)

fla Eftf

Rεhrup

2Eftf

Dεhrup (15)

D h2 + b2

radic (16)

ks1 b

h1113888 1113889

2Ae

Ac

(17)

ks2 h

b1113888 1113889

05Ae

Ac

(18)

Ae

Ac


1 minus ρs




5 Verifications






Stre

ss

O

f primec

Ec = tanα

A

Bf primecu

Unconfined

FRP confined







1113936 Wihi

(20)

Ft 007TVle 025V (21)


Beam

BeamSteel plates

Steel plates

Slabs 12mm thick


4260 times 4260

3300

3300

(a)

ϕ6mm200 ϕ6mm200

ϕ6m

m2

00

ϕ8mm300 ϕ8mm300

ϕ6m

m2

00

ϕ6m

m2

00ϕ8mm300

260

260

260 260

260

400

400

400

380




8ϕ14mm

8ϕ14mm 8ϕ14mm

8ϕ14mm

4ϕ14mm

4ϕ14mm

(b)










fcprime

1113969


ndash20

ndash15

ndash10

ndash5

0

5

10

15

Disp

lace

men

t (m

m)

5 10 15 20 25 30 35 400Time (s)

ExperimentAnalysis

(a)

ndash20

ndash15

ndash10

ndash5

0

5

10

15

20

Disp

lace

men

t (m

m)

5 10 15 20 25 30 35 400Time (s)

ExperimentAnalysis

(b)







A-A

B-B

C-C

D-D

E-E

F-F

600

600

600

600

600

600

600

600

600

600

600

600

540

540

440

440

440

440

60

60

60

60

60

60

16ϕ25

6ϕ25 4ϕ25

4ϕ226ϕ22

6ϕ18 3ϕ18

16ϕ18

16ϕ16

450

450

450

140

175

250

-

-

-

-

-

-

-

-

-

C C C C

C C

C C

C C

C C

C C

C C

B B

B B

A A

A A

B B

B B

A A

A A

FF

FF

FF

FF

EE

EE

EE

EE

DD

DD

DD

DD

DD

DD

DD

DD

CL8

3

m

3 5m

b b

h h

d d

d prime dprime

Ast

As

Aprimes



Base

shea

r for

ce (k

N)

0

250

500

750

1000

1250

1500







(a)


8prime-0Prime

4prime-0Prime

6prime-0Prime

W-ga114Primecolumn

ties (typ)


(typ)

8Prime

4Prime

3Prime

6Prime2Prime4Prime

4Prime

12prime-0Prime

Y Y Y Y


2Prime slab(typ)





A

A

B

B

C

C

C

D

D D

D

2D5

2D42D4 1D41D4

2D4

2prime

2prime

6prime 10prime

Section Y-Y

W-ga11267Prime

4D4

W-ga11

C-C

B-BA-A

D-DBeam sections

3D4

3D4

2D4

2D4 2D4 1D5

2D5 2D5

W-ga11(typ)

1

Elevation


Beam steel

1 1-

(b)







CrackedYielded


(a)

++

+

++

++ +

++

(b)



A-A 16ϕ18 - - 450

B-B - 6ϕ22 4ϕ22 175

C-C

500

500

500

60

60

60 - 6ϕ18 3ϕ18 250

440

440

440

500

500

500

Aprimes(mm2)

As(mm2)

Ast(mm2)

dprime(mm)

d(mm)

h(mm)

b(mm)

4

3m

3 5m

A

A

A

A

A

A

A

A

A

A

A

A

C

CC

C

B

BB

B







Spec

tral

acce

lera

tion

PGA

00

05

10

15

20

25

30

1 2 3 40T (sec)



300 400100 200 500000 600Period (sec)

000

020

040

060

080

100

120

pSa (

g)












Storey 4

Storey 3

Storey 2

Storey 1

(a)

Storey 4

Storey 3

Storey 2

Storey 1

(b)

Storey 4

Storey 3

Storey 2

Storey 1

(c)

Storey 4

Storey 3

Storey 2

Storey 1

(d)


0587

0140

0030

0000

0419

0077

0002

0107

0008

0077


OriginalRS0

RS1RS2

1

2

3

4

Stor

ey







0587

0419

0107 00770

1

06250688

Dam

age i

ndex

ratio

of F

RP


0

025

05

075

1








Storey 8

Storey 7

Storey 6

Storey 5

Storey 4

Storey 3

Storey 2

Storey 1

(a)

Storey 8

Storey 7

Storey 6

Storey 5

Storey 4

Storey 3

Storey 2

Storey 1

(b)

Storey 8

Storey 7

Storey 6

Storey 5

Storey 4

Storey 2

Storey 3

Storey 1

(c)

Storey 8

Storey 7

Storey 6

Storey 5

Storey 4

Storey 3

Storey 2

Storey 1

(d)





8 Conclusions



Data Availability




Acknowledgments


References


0004

0024

0018

0238

0185

0215

0218

0059

0135

0090 0208 0396 0431

0155

0322

0290

0494

0242

0418

0376

0092

1

2

3

4

5

6

7

8

Stor

ey


OriginalRS0

RS1RS2


04940396

0242 02380

1

05940688



0

025

05

075

1

Dam

age i

ndex

FRP

ratio























































































DI Eh

Eh + Erec1113890 1113891

α(Nminus i)

(7)







Non

linea

r lin

k el

emen

ts

(a) (b)

A

B

C

Pγ

DγDcr

Pcr

1

1

2

2

3

34

4

5

5

6

6

7

7

8

8

9

9

10

10a

10b

11

11

12

12

13

13

14

15

16

171819

20


(b)(a) (c) (d)

fs1

fc

fs2

fs3

fs4

fs5

εs1

εs2

εs3

εs4

εs5

εc Zn

εm

MN

Ultimate

Curvature

Mom

ent

YieldIdealized

Crack

O

Real












2

4fcprime

ε2c (8)


in which

εt 2fcprime

Ec minus E2 (10)


εu

(11)



A A

FRP wrap

GFRP wraps r = 50mm

A-A





fla

fcprime1113890 1113891 if

fla

fcprimege 007 (12)

fcuprime fcprime if

fla

fcprimelt 007 (13)


fcprime

εhrup

εo

1113888 1113889

045⎡⎣ ⎤⎦ (14)

fla Eftf

Rεhrup

2Eftf

Dεhrup (15)

D h2 + b2

radic (16)

ks1 b

h1113888 1113889

2Ae

Ac

(17)

ks2 h

b1113888 1113889

05Ae

Ac

(18)

Ae

Ac


1 minus ρs




5 Verifications






Stre

ss

O

f primec

Ec = tanα

A

Bf primecu

Unconfined

FRP confined







1113936 Wihi

(20)

Ft 007TVle 025V (21)


Beam

BeamSteel plates

Steel plates

Slabs 12mm thick


4260 times 4260

3300

3300

(a)

ϕ6mm200 ϕ6mm200

ϕ6m

m2

00

ϕ8mm300 ϕ8mm300

ϕ6m

m2

00

ϕ6m

m2

00ϕ8mm300

260

260

260 260

260

400

400

400

380




8ϕ14mm

8ϕ14mm 8ϕ14mm

8ϕ14mm

4ϕ14mm

4ϕ14mm

(b)










fcprime

1113969


ndash20

ndash15

ndash10

ndash5

0

5

10

15

Disp

lace

men

t (m

m)

5 10 15 20 25 30 35 400Time (s)

ExperimentAnalysis

(a)

ndash20

ndash15

ndash10

ndash5

0

5

10

15

20

Disp

lace

men

t (m

m)

5 10 15 20 25 30 35 400Time (s)

ExperimentAnalysis

(b)







A-A

B-B

C-C

D-D

E-E

F-F

600

600

600

600

600

600

600

600

600

600

600

600

540

540

440

440

440

440

60

60

60

60

60

60

16ϕ25

6ϕ25 4ϕ25

4ϕ226ϕ22

6ϕ18 3ϕ18

16ϕ18

16ϕ16

450

450

450

140

175

250

-

-

-

-

-

-

-

-

-

C C C C

C C

C C

C C

C C

C C

C C

B B

B B

A A

A A

B B

B B

A A

A A

FF

FF

FF

FF

EE

EE

EE

EE

DD

DD

DD

DD

DD

DD

DD

DD

CL8

3

m

3 5m

b b

h h

d d

d prime dprime

Ast

As

Aprimes



Base

shea

r for

ce (k

N)

0

250

500

750

1000

1250

1500







(a)


8prime-0Prime

4prime-0Prime

6prime-0Prime

W-ga114Primecolumn

ties (typ)


(typ)

8Prime

4Prime

3Prime

6Prime2Prime4Prime

4Prime

12prime-0Prime

Y Y Y Y


2Prime slab(typ)





A

A

B

B

C

C

C

D

D D

D

2D5

2D42D4 1D41D4

2D4

2prime

2prime

6prime 10prime

Section Y-Y

W-ga11267Prime

4D4

W-ga11

C-C

B-BA-A

D-DBeam sections

3D4

3D4

2D4

2D4 2D4 1D5

2D5 2D5

W-ga11(typ)

1

Elevation


Beam steel

1 1-

(b)







CrackedYielded


(a)

++

+

++

++ +

++

(b)



A-A 16ϕ18 - - 450

B-B - 6ϕ22 4ϕ22 175

C-C

500

500

500

60

60

60 - 6ϕ18 3ϕ18 250

440

440

440

500

500

500

Aprimes(mm2)

As(mm2)

Ast(mm2)

dprime(mm)

d(mm)

h(mm)

b(mm)

4

3m

3 5m

A

A

A

A

A

A

A

A

A

A

A

A

C

CC

C

B

BB

B







Spec

tral

acce

lera

tion

PGA

00

05

10

15

20

25

30

1 2 3 40T (sec)



300 400100 200 500000 600Period (sec)

000

020

040

060

080

100

120

pSa (

g)












Storey 4

Storey 3

Storey 2

Storey 1

(a)

Storey 4

Storey 3

Storey 2

Storey 1

(b)

Storey 4

Storey 3

Storey 2

Storey 1

(c)

Storey 4

Storey 3

Storey 2

Storey 1

(d)


0587

0140

0030

0000

0419

0077

0002

0107

0008

0077


OriginalRS0

RS1RS2

1

2

3

4

Stor

ey







0587

0419

0107 00770

1

06250688

Dam

age i

ndex

ratio

of F

RP


0

025

05

075

1








Storey 8

Storey 7

Storey 6

Storey 5

Storey 4

Storey 3

Storey 2

Storey 1

(a)

Storey 8

Storey 7

Storey 6

Storey 5

Storey 4

Storey 3

Storey 2

Storey 1

(b)

Storey 8

Storey 7

Storey 6

Storey 5

Storey 4

Storey 2

Storey 3

Storey 1

(c)

Storey 8

Storey 7

Storey 6

Storey 5

Storey 4

Storey 3

Storey 2

Storey 1

(d)





8 Conclusions



Data Availability




Acknowledgments


References


0004

0024

0018

0238

0185

0215

0218

0059

0135

0090 0208 0396 0431

0155

0322

0290

0494

0242

0418

0376

0092

1

2

3

4

5

6

7

8

Stor

ey


OriginalRS0

RS1RS2


04940396

0242 02380

1

05940688



0

025

05

075

1

Dam

age i

ndex

FRP

ratio






























































































2

4fcprime

ε2c (8)


in which

εt 2fcprime

Ec minus E2 (10)


εu

(11)



A A

FRP wrap

GFRP wraps r = 50mm

A-A





fla

fcprime1113890 1113891 if

fla

fcprimege 007 (12)

fcuprime fcprime if

fla

fcprimelt 007 (13)


fcprime

εhrup

εo

1113888 1113889

045⎡⎣ ⎤⎦ (14)

fla Eftf

Rεhrup

2Eftf

Dεhrup (15)

D h2 + b2

radic (16)

ks1 b

h1113888 1113889

2Ae

Ac

(17)

ks2 h

b1113888 1113889

05Ae

Ac

(18)

Ae

Ac


1 minus ρs




5 Verifications






Stre

ss

O

f primec

Ec = tanα

A

Bf primecu

Unconfined

FRP confined







1113936 Wihi

(20)

Ft 007TVle 025V (21)


Beam

BeamSteel plates

Steel plates

Slabs 12mm thick


4260 times 4260

3300

3300

(a)

ϕ6mm200 ϕ6mm200

ϕ6m

m2

00

ϕ8mm300 ϕ8mm300

ϕ6m

m2

00

ϕ6m

m2

00ϕ8mm300

260

260

260 260

260

400

400

400

380




8ϕ14mm

8ϕ14mm 8ϕ14mm

8ϕ14mm

4ϕ14mm

4ϕ14mm

(b)










fcprime

1113969


ndash20

ndash15

ndash10

ndash5

0

5

10

15

Disp

lace

men

t (m

m)

5 10 15 20 25 30 35 400Time (s)

ExperimentAnalysis

(a)

ndash20

ndash15

ndash10

ndash5

0

5

10

15

20

Disp

lace

men

t (m

m)

5 10 15 20 25 30 35 400Time (s)

ExperimentAnalysis

(b)







A-A

B-B

C-C

D-D

E-E

F-F

600

600

600

600

600

600

600

600

600

600

600

600

540

540

440

440

440

440

60

60

60

60

60

60

16ϕ25

6ϕ25 4ϕ25

4ϕ226ϕ22

6ϕ18 3ϕ18

16ϕ18

16ϕ16

450

450

450

140

175

250

-

-

-

-

-

-

-

-

-

C C C C

C C

C C

C C

C C

C C

C C

B B

B B

A A

A A

B B

B B

A A

A A

FF

FF

FF

FF

EE

EE

EE

EE

DD

DD

DD

DD

DD

DD

DD

DD

CL8

3

m

3 5m

b b

h h

d d

d prime dprime

Ast

As

Aprimes



Base

shea

r for

ce (k

N)

0

250

500

750

1000

1250

1500







(a)


8prime-0Prime

4prime-0Prime

6prime-0Prime

W-ga114Primecolumn

ties (typ)


(typ)

8Prime

4Prime

3Prime

6Prime2Prime4Prime

4Prime

12prime-0Prime

Y Y Y Y


2Prime slab(typ)





A

A

B

B

C

C

C

D

D D

D

2D5

2D42D4 1D41D4

2D4

2prime

2prime

6prime 10prime

Section Y-Y

W-ga11267Prime

4D4

W-ga11

C-C

B-BA-A

D-DBeam sections

3D4

3D4

2D4

2D4 2D4 1D5

2D5 2D5

W-ga11(typ)

1

Elevation


Beam steel

1 1-

(b)







CrackedYielded


(a)

++

+

++

++ +

++

(b)



A-A 16ϕ18 - - 450

B-B - 6ϕ22 4ϕ22 175

C-C

500

500

500

60

60

60 - 6ϕ18 3ϕ18 250

440

440

440

500

500

500

Aprimes(mm2)

As(mm2)

Ast(mm2)

dprime(mm)

d(mm)

h(mm)

b(mm)

4

3m

3 5m

A

A

A

A

A

A

A

A

A

A

A

A

C

CC

C

B

BB

B







Spec

tral

acce

lera

tion

PGA

00

05

10

15

20

25

30

1 2 3 40T (sec)



300 400100 200 500000 600Period (sec)

000

020

040

060

080

100

120

pSa (

g)












Storey 4

Storey 3

Storey 2

Storey 1

(a)

Storey 4

Storey 3

Storey 2

Storey 1

(b)

Storey 4

Storey 3

Storey 2

Storey 1

(c)

Storey 4

Storey 3

Storey 2

Storey 1

(d)


0587

0140

0030

0000

0419

0077

0002

0107

0008

0077


OriginalRS0

RS1RS2

1

2

3

4

Stor

ey







0587

0419

0107 00770

1

06250688

Dam

age i

ndex

ratio

of F

RP


0

025

05

075

1








Storey 8

Storey 7

Storey 6

Storey 5

Storey 4

Storey 3

Storey 2

Storey 1

(a)

Storey 8

Storey 7

Storey 6

Storey 5

Storey 4

Storey 3

Storey 2

Storey 1

(b)

Storey 8

Storey 7

Storey 6

Storey 5

Storey 4

Storey 2

Storey 3

Storey 1

(c)

Storey 8

Storey 7

Storey 6

Storey 5

Storey 4

Storey 3

Storey 2

Storey 1

(d)





8 Conclusions



Data Availability




Acknowledgments


References


0004

0024

0018

0238

0185

0215

0218

0059

0135

0090 0208 0396 0431

0155

0322

0290

0494

0242

0418

0376

0092

1

2

3

4

5

6

7

8

Stor

ey


OriginalRS0

RS1RS2


04940396

0242 02380

1

05940688



0

025

05

075

1

Dam

age i

ndex

FRP

ratio

























































































fla

fcprime1113890 1113891 if

fla

fcprimege 007 (12)

fcuprime fcprime if

fla

fcprimelt 007 (13)


fcprime

εhrup

εo

1113888 1113889

045⎡⎣ ⎤⎦ (14)

fla Eftf

Rεhrup

2Eftf

Dεhrup (15)

D h2 + b2

radic (16)

ks1 b

h1113888 1113889

2Ae

Ac

(17)

ks2 h

b1113888 1113889

05Ae

Ac

(18)

Ae

Ac


1 minus ρs




5 Verifications






Stre

ss

O

f primec

Ec = tanα

A

Bf primecu

Unconfined

FRP confined







1113936 Wihi

(20)

Ft 007TVle 025V (21)


Beam

BeamSteel plates

Steel plates

Slabs 12mm thick


4260 times 4260

3300

3300

(a)

ϕ6mm200 ϕ6mm200

ϕ6m

m2

00

ϕ8mm300 ϕ8mm300

ϕ6m

m2

00

ϕ6m

m2

00ϕ8mm300

260

260

260 260

260

400

400

400

380




8ϕ14mm

8ϕ14mm 8ϕ14mm

8ϕ14mm

4ϕ14mm

4ϕ14mm

(b)










fcprime

1113969


ndash20

ndash15

ndash10

ndash5

0

5

10

15

Disp

lace

men

t (m

m)

5 10 15 20 25 30 35 400Time (s)

ExperimentAnalysis

(a)

ndash20

ndash15

ndash10

ndash5

0

5

10

15

20

Disp

lace

men

t (m

m)

5 10 15 20 25 30 35 400Time (s)

ExperimentAnalysis

(b)







A-A

B-B

C-C

D-D

E-E

F-F

600

600

600

600

600

600

600

600

600

600

600

600

540

540

440

440

440

440

60

60

60

60

60

60

16ϕ25

6ϕ25 4ϕ25

4ϕ226ϕ22

6ϕ18 3ϕ18

16ϕ18

16ϕ16

450

450

450

140

175

250

-

-

-

-

-

-

-

-

-

C C C C

C C

C C

C C

C C

C C

C C

B B

B B

A A

A A

B B

B B

A A

A A

FF

FF

FF

FF

EE

EE

EE

EE

DD

DD

DD

DD

DD

DD

DD

DD

CL8

3

m

3 5m

b b

h h

d d

d prime dprime

Ast

As

Aprimes



Base

shea

r for

ce (k

N)

0

250

500

750

1000

1250

1500







(a)


8prime-0Prime

4prime-0Prime

6prime-0Prime

W-ga114Primecolumn

ties (typ)


(typ)

8Prime

4Prime

3Prime

6Prime2Prime4Prime

4Prime

12prime-0Prime

Y Y Y Y


2Prime slab(typ)





A

A

B

B

C

C

C

D

D D

D

2D5

2D42D4 1D41D4

2D4

2prime

2prime

6prime 10prime

Section Y-Y

W-ga11267Prime

4D4

W-ga11

C-C

B-BA-A

D-DBeam sections

3D4

3D4

2D4

2D4 2D4 1D5

2D5 2D5

W-ga11(typ)

1

Elevation


Beam steel

1 1-

(b)







CrackedYielded


(a)

++

+

++

++ +

++

(b)



A-A 16ϕ18 - - 450

B-B - 6ϕ22 4ϕ22 175

C-C

500

500

500

60

60

60 - 6ϕ18 3ϕ18 250

440

440

440

500

500

500

Aprimes(mm2)

As(mm2)

Ast(mm2)

dprime(mm)

d(mm)

h(mm)

b(mm)

4

3m

3 5m

A

A

A

A

A

A

A

A

A

A

A

A

C

CC

C

B

BB

B







Spec

tral

acce

lera

tion

PGA

00

05

10

15

20

25

30

1 2 3 40T (sec)



300 400100 200 500000 600Period (sec)

000

020

040

060

080

100

120

pSa (

g)












Storey 4

Storey 3

Storey 2

Storey 1

(a)

Storey 4

Storey 3

Storey 2

Storey 1

(b)

Storey 4

Storey 3

Storey 2

Storey 1

(c)

Storey 4

Storey 3

Storey 2

Storey 1

(d)


0587

0140

0030

0000

0419

0077

0002

0107

0008

0077


OriginalRS0

RS1RS2

1

2

3

4

Stor

ey







0587

0419

0107 00770

1

06250688

Dam

age i

ndex

ratio

of F

RP


0

025

05

075

1








Storey 8

Storey 7

Storey 6

Storey 5

Storey 4

Storey 3

Storey 2

Storey 1

(a)

Storey 8

Storey 7

Storey 6

Storey 5

Storey 4

Storey 3

Storey 2

Storey 1

(b)

Storey 8

Storey 7

Storey 6

Storey 5

Storey 4

Storey 2

Storey 3

Storey 1

(c)

Storey 8

Storey 7

Storey 6

Storey 5

Storey 4

Storey 3

Storey 2

Storey 1

(d)





8 Conclusions



Data Availability




Acknowledgments


References


0004

0024

0018

0238

0185

0215

0218

0059

0135

0090 0208 0396 0431

0155

0322

0290

0494

0242

0418

0376

0092

1

2

3

4

5

6

7

8

Stor

ey


OriginalRS0

RS1RS2


04940396

0242 02380

1

05940688



0

025

05

075

1

Dam

age i

ndex

FRP

ratio


























































































1113936 Wihi

(20)

Ft 007TVle 025V (21)


Beam

BeamSteel plates

Steel plates

Slabs 12mm thick


4260 times 4260

3300

3300

(a)

ϕ6mm200 ϕ6mm200

ϕ6m

m2

00

ϕ8mm300 ϕ8mm300

ϕ6m

m2

00

ϕ6m

m2

00ϕ8mm300

260

260

260 260

260

400

400

400

380




8ϕ14mm

8ϕ14mm 8ϕ14mm

8ϕ14mm

4ϕ14mm

4ϕ14mm

(b)










fcprime

1113969


ndash20

ndash15

ndash10

ndash5

0

5

10

15

Disp

lace

men

t (m

m)

5 10 15 20 25 30 35 400Time (s)

ExperimentAnalysis

(a)

ndash20

ndash15

ndash10

ndash5

0

5

10

15

20

Disp

lace

men

t (m

m)

5 10 15 20 25 30 35 400Time (s)

ExperimentAnalysis

(b)







A-A

B-B

C-C

D-D

E-E

F-F

600

600

600

600

600

600

600

600

600

600

600

600

540

540

440

440

440

440

60

60

60

60

60

60

16ϕ25

6ϕ25 4ϕ25

4ϕ226ϕ22

6ϕ18 3ϕ18

16ϕ18

16ϕ16

450

450

450

140

175

250

-

-

-

-

-

-

-

-

-

C C C C

C C

C C

C C

C C

C C

C C

B B

B B

A A

A A

B B

B B

A A

A A

FF

FF

FF

FF

EE

EE

EE

EE

DD

DD

DD

DD

DD

DD

DD

DD

CL8

3

m

3 5m

b b

h h

d d

d prime dprime

Ast

As

Aprimes



Base

shea

r for

ce (k

N)

0

250

500

750

1000

1250

1500







(a)


8prime-0Prime

4prime-0Prime

6prime-0Prime

W-ga114Primecolumn

ties (typ)


(typ)

8Prime

4Prime

3Prime

6Prime2Prime4Prime

4Prime

12prime-0Prime

Y Y Y Y


2Prime slab(typ)





A

A

B

B

C

C

C

D

D D

D

2D5

2D42D4 1D41D4

2D4

2prime

2prime

6prime 10prime

Section Y-Y

W-ga11267Prime

4D4

W-ga11

C-C

B-BA-A

D-DBeam sections

3D4

3D4

2D4

2D4 2D4 1D5

2D5 2D5

W-ga11(typ)

1

Elevation


Beam steel

1 1-

(b)







CrackedYielded


(a)

++

+

++

++ +

++

(b)



A-A 16ϕ18 - - 450

B-B - 6ϕ22 4ϕ22 175

C-C

500

500

500

60

60

60 - 6ϕ18 3ϕ18 250

440

440

440

500

500

500

Aprimes(mm2)

As(mm2)

Ast(mm2)

dprime(mm)

d(mm)

h(mm)

b(mm)

4

3m

3 5m

A

A

A

A

A

A

A

A

A

A

A

A

C

CC

C

B

BB

B







Spec

tral

acce

lera

tion

PGA

00

05

10

15

20

25

30

1 2 3 40T (sec)



300 400100 200 500000 600Period (sec)

000

020

040

060

080

100

120

pSa (

g)












Storey 4

Storey 3

Storey 2

Storey 1

(a)

Storey 4

Storey 3

Storey 2

Storey 1

(b)

Storey 4

Storey 3

Storey 2

Storey 1

(c)

Storey 4

Storey 3

Storey 2

Storey 1

(d)


0587

0140

0030

0000

0419

0077

0002

0107

0008

0077


OriginalRS0

RS1RS2

1

2

3

4

Stor

ey







0587

0419

0107 00770

1

06250688

Dam

age i

ndex

ratio

of F

RP


0

025

05

075

1








Storey 8

Storey 7

Storey 6

Storey 5

Storey 4

Storey 3

Storey 2

Storey 1

(a)

Storey 8

Storey 7

Storey 6

Storey 5

Storey 4

Storey 3

Storey 2

Storey 1

(b)

Storey 8

Storey 7

Storey 6

Storey 5

Storey 4

Storey 2

Storey 3

Storey 1

(c)

Storey 8

Storey 7

Storey 6

Storey 5

Storey 4

Storey 3

Storey 2

Storey 1

(d)





8 Conclusions



Data Availability




Acknowledgments


References


0004

0024

0018

0238

0185

0215

0218

0059

0135

0090 0208 0396 0431

0155

0322

0290

0494

0242

0418

0376

0092

1

2

3

4

5

6

7

8

Stor

ey


OriginalRS0

RS1RS2


04940396

0242 02380

1

05940688



0

025

05

075

1

Dam

age i

ndex

FRP

ratio





























































































fcprime

1113969


ndash20

ndash15

ndash10

ndash5

0

5

10

15

Disp

lace

men

t (m

m)

5 10 15 20 25 30 35 400Time (s)

ExperimentAnalysis

(a)

ndash20

ndash15

ndash10

ndash5

0

5

10

15

20

Disp

lace

men

t (m

m)

5 10 15 20 25 30 35 400Time (s)

ExperimentAnalysis

(b)







A-A

B-B

C-C

D-D

E-E

F-F

600

600

600

600

600

600

600

600

600

600

600

600

540

540

440

440

440

440

60

60

60

60

60

60

16ϕ25

6ϕ25 4ϕ25

4ϕ226ϕ22

6ϕ18 3ϕ18

16ϕ18

16ϕ16

450

450

450

140

175

250

-

-

-

-

-

-

-

-

-

C C C C

C C

C C

C C

C C

C C

C C

B B

B B

A A

A A

B B

B B

A A

A A

FF

FF

FF

FF

EE

EE

EE

EE

DD

DD

DD

DD

DD

DD

DD

DD

CL8

3

m

3 5m

b b

h h

d d

d prime dprime

Ast

As

Aprimes



Base

shea

r for

ce (k

N)

0

250

500

750

1000

1250

1500







(a)


8prime-0Prime

4prime-0Prime

6prime-0Prime

W-ga114Primecolumn

ties (typ)


(typ)

8Prime

4Prime

3Prime

6Prime2Prime4Prime

4Prime

12prime-0Prime

Y Y Y Y


2Prime slab(typ)





A

A

B

B

C

C

C

D

D D

D

2D5

2D42D4 1D41D4

2D4

2prime

2prime

6prime 10prime

Section Y-Y

W-ga11267Prime

4D4

W-ga11

C-C

B-BA-A

D-DBeam sections

3D4

3D4

2D4

2D4 2D4 1D5

2D5 2D5

W-ga11(typ)

1

Elevation


Beam steel

1 1-

(b)







CrackedYielded


(a)

++

+

++

++ +

++

(b)



A-A 16ϕ18 - - 450

B-B - 6ϕ22 4ϕ22 175

C-C

500

500

500

60

60

60 - 6ϕ18 3ϕ18 250

440

440

440

500

500

500

Aprimes(mm2)

As(mm2)

Ast(mm2)

dprime(mm)

d(mm)

h(mm)

b(mm)

4

3m

3 5m

A

A

A

A

A

A

A

A

A

A

A

A

C

CC

C

B

BB

B







Spec

tral

acce

lera

tion

PGA

00

05

10

15

20

25

30

1 2 3 40T (sec)



300 400100 200 500000 600Period (sec)

000

020

040

060

080

100

120

pSa (

g)












Storey 4

Storey 3

Storey 2

Storey 1

(a)

Storey 4

Storey 3

Storey 2

Storey 1

(b)

Storey 4

Storey 3

Storey 2

Storey 1

(c)

Storey 4

Storey 3

Storey 2

Storey 1

(d)


0587

0140

0030

0000

0419

0077

0002

0107

0008

0077


OriginalRS0

RS1RS2

1

2

3

4

Stor

ey







0587

0419

0107 00770

1

06250688

Dam

age i

ndex

ratio

of F

RP


0

025

05

075

1








Storey 8

Storey 7

Storey 6

Storey 5

Storey 4

Storey 3

Storey 2

Storey 1

(a)

Storey 8

Storey 7

Storey 6

Storey 5

Storey 4

Storey 3

Storey 2

Storey 1

(b)

Storey 8

Storey 7

Storey 6

Storey 5

Storey 4

Storey 2

Storey 3

Storey 1

(c)

Storey 8

Storey 7

Storey 6

Storey 5

Storey 4

Storey 3

Storey 2

Storey 1

(d)





8 Conclusions



Data Availability




Acknowledgments


References


0004

0024

0018

0238

0185

0215

0218

0059

0135

0090 0208 0396 0431

0155

0322

0290

0494

0242

0418

0376

0092

1

2

3

4

5

6

7

8

Stor

ey


OriginalRS0

RS1RS2


04940396

0242 02380

1

05940688



0

025

05

075

1

Dam

age i

ndex

FRP

ratio



























































































A-A

B-B

C-C

D-D

E-E

F-F

600

600

600

600

600

600

600

600

600

600

600

600

540

540

440

440

440

440

60

60

60

60

60

60

16ϕ25

6ϕ25 4ϕ25

4ϕ226ϕ22

6ϕ18 3ϕ18

16ϕ18

16ϕ16

450

450

450

140

175

250

-

-

-

-

-

-

-

-

-

C C C C

C C

C C

C C

C C

C C

C C

B B

B B

A A

A A

B B

B B

A A

A A

FF

FF

FF

FF

EE

EE

EE

EE

DD

DD

DD

DD

DD

DD

DD

DD

CL8

3

m

3 5m

b b

h h

d d

d prime dprime

Ast

As

Aprimes



Base

shea

r for

ce (k

N)

0

250

500

750

1000

1250

1500







(a)


8prime-0Prime

4prime-0Prime

6prime-0Prime

W-ga114Primecolumn

ties (typ)


(typ)

8Prime

4Prime

3Prime

6Prime2Prime4Prime

4Prime

12prime-0Prime

Y Y Y Y


2Prime slab(typ)





A

A

B

B

C

C

C

D

D D

D

2D5

2D42D4 1D41D4

2D4

2prime

2prime

6prime 10prime

Section Y-Y

W-ga11267Prime

4D4

W-ga11

C-C

B-BA-A

D-DBeam sections

3D4

3D4

2D4

2D4 2D4 1D5

2D5 2D5

W-ga11(typ)

1

Elevation


Beam steel

1 1-

(b)







CrackedYielded


(a)

++

+

++

++ +

++

(b)



A-A 16ϕ18 - - 450

B-B - 6ϕ22 4ϕ22 175

C-C

500

500

500

60

60

60 - 6ϕ18 3ϕ18 250

440

440

440

500

500

500

Aprimes(mm2)

As(mm2)

Ast(mm2)

dprime(mm)

d(mm)

h(mm)

b(mm)

4

3m

3 5m

A

A

A

A

A

A

A

A

A

A

A

A

C

CC

C

B

BB

B







Spec

tral

acce

lera

tion

PGA

00

05

10

15

20

25

30

1 2 3 40T (sec)



300 400100 200 500000 600Period (sec)

000

020

040

060

080

100

120

pSa (

g)












Storey 4

Storey 3

Storey 2

Storey 1

(a)

Storey 4

Storey 3

Storey 2

Storey 1

(b)

Storey 4

Storey 3

Storey 2

Storey 1

(c)

Storey 4

Storey 3

Storey 2

Storey 1

(d)


0587

0140

0030

0000

0419

0077

0002

0107

0008

0077


OriginalRS0

RS1RS2

1

2

3

4

Stor

ey







0587

0419

0107 00770

1

06250688

Dam

age i

ndex

ratio

of F

RP


0

025

05

075

1








Storey 8

Storey 7

Storey 6

Storey 5

Storey 4

Storey 3

Storey 2

Storey 1

(a)

Storey 8

Storey 7

Storey 6

Storey 5

Storey 4

Storey 3

Storey 2

Storey 1

(b)

Storey 8

Storey 7

Storey 6

Storey 5

Storey 4

Storey 2

Storey 3

Storey 1

(c)

Storey 8

Storey 7

Storey 6

Storey 5

Storey 4

Storey 3

Storey 2

Storey 1

(d)





8 Conclusions



Data Availability




Acknowledgments


References


0004

0024

0018

0238

0185

0215

0218

0059

0135

0090 0208 0396 0431

0155

0322

0290

0494

0242

0418

0376

0092

1

2

3

4

5

6

7

8

Stor

ey


OriginalRS0

RS1RS2


04940396

0242 02380

1

05940688



0

025

05

075

1

Dam

age i

ndex

FRP

ratio

























































































(a)


8prime-0Prime

4prime-0Prime

6prime-0Prime

W-ga114Primecolumn

ties (typ)


(typ)

8Prime

4Prime

3Prime

6Prime2Prime4Prime

4Prime

12prime-0Prime

Y Y Y Y


2Prime slab(typ)





A

A

B

B

C

C

C

D

D D

D

2D5

2D42D4 1D41D4

2D4

2prime

2prime

6prime 10prime

Section Y-Y

W-ga11267Prime

4D4

W-ga11

C-C

B-BA-A

D-DBeam sections

3D4

3D4

2D4

2D4 2D4 1D5

2D5 2D5

W-ga11(typ)

1

Elevation


Beam steel

1 1-

(b)







CrackedYielded


(a)

++

+

++

++ +

++

(b)



A-A 16ϕ18 - - 450

B-B - 6ϕ22 4ϕ22 175

C-C

500

500

500

60

60

60 - 6ϕ18 3ϕ18 250

440

440

440

500

500

500

Aprimes(mm2)

As(mm2)

Ast(mm2)

dprime(mm)

d(mm)

h(mm)

b(mm)

4

3m

3 5m

A

A

A

A

A

A

A

A

A

A

A

A

C

CC

C

B

BB

B







Spec

tral

acce

lera

tion

PGA

00

05

10

15

20

25

30

1 2 3 40T (sec)



300 400100 200 500000 600Period (sec)

000

020

040

060

080

100

120

pSa (

g)












Storey 4

Storey 3

Storey 2

Storey 1

(a)

Storey 4

Storey 3

Storey 2

Storey 1

(b)

Storey 4

Storey 3

Storey 2

Storey 1

(c)

Storey 4

Storey 3

Storey 2

Storey 1

(d)


0587

0140

0030

0000

0419

0077

0002

0107

0008

0077


OriginalRS0

RS1RS2

1

2

3

4

Stor

ey







0587

0419

0107 00770

1

06250688

Dam

age i

ndex

ratio

of F

RP


0

025

05

075

1








Storey 8

Storey 7

Storey 6

Storey 5

Storey 4

Storey 3

Storey 2

Storey 1

(a)

Storey 8

Storey 7

Storey 6

Storey 5

Storey 4

Storey 3

Storey 2

Storey 1

(b)

Storey 8

Storey 7

Storey 6

Storey 5

Storey 4

Storey 2

Storey 3

Storey 1

(c)

Storey 8

Storey 7

Storey 6

Storey 5

Storey 4

Storey 3

Storey 2

Storey 1

(d)





8 Conclusions



Data Availability




Acknowledgments


References


0004

0024

0018

0238

0185

0215

0218

0059

0135

0090 0208 0396 0431

0155

0322

0290

0494

0242

0418

0376

0092

1

2

3

4

5

6

7

8

Stor

ey


OriginalRS0

RS1RS2


04940396

0242 02380

1

05940688



0

025

05

075

1

Dam

age i

ndex

FRP

ratio



























































































CrackedYielded


(a)

++

+

++

++ +

++

(b)



A-A 16ϕ18 - - 450

B-B - 6ϕ22 4ϕ22 175

C-C

500

500

500

60

60

60 - 6ϕ18 3ϕ18 250

440

440

440

500

500

500

Aprimes(mm2)

As(mm2)

Ast(mm2)

dprime(mm)

d(mm)

h(mm)

b(mm)

4

3m

3 5m

A

A

A

A

A

A

A

A

A

A

A

A

C

CC

C

B

BB

B







Spec

tral

acce

lera

tion

PGA

00

05

10

15

20

25

30

1 2 3 40T (sec)



300 400100 200 500000 600Period (sec)

000

020

040

060

080

100

120

pSa (

g)












Storey 4

Storey 3

Storey 2

Storey 1

(a)

Storey 4

Storey 3

Storey 2

Storey 1

(b)

Storey 4

Storey 3

Storey 2

Storey 1

(c)

Storey 4

Storey 3

Storey 2

Storey 1

(d)


0587

0140

0030

0000

0419

0077

0002

0107

0008

0077


OriginalRS0

RS1RS2

1

2

3

4

Stor

ey







0587

0419

0107 00770

1

06250688

Dam

age i

ndex

ratio

of F

RP


0

025

05

075

1








Storey 8

Storey 7

Storey 6

Storey 5

Storey 4

Storey 3

Storey 2

Storey 1

(a)

Storey 8

Storey 7

Storey 6

Storey 5

Storey 4

Storey 3

Storey 2

Storey 1

(b)

Storey 8

Storey 7

Storey 6

Storey 5

Storey 4

Storey 2

Storey 3

Storey 1

(c)

Storey 8

Storey 7

Storey 6

Storey 5

Storey 4

Storey 3

Storey 2

Storey 1

(d)





8 Conclusions



Data Availability




Acknowledgments


References


0004

0024

0018

0238

0185

0215

0218

0059

0135

0090 0208 0396 0431

0155

0322

0290

0494

0242

0418

0376

0092

1

2

3

4

5

6

7

8

Stor

ey


OriginalRS0

RS1RS2


04940396

0242 02380

1

05940688



0

025

05

075

1

Dam

age i

ndex

FRP

ratio



























































































Spec

tral

acce

lera

tion

PGA

00

05

10

15

20

25

30

1 2 3 40T (sec)



300 400100 200 500000 600Period (sec)

000

020

040

060

080

100

120

pSa (

g)












Storey 4

Storey 3

Storey 2

Storey 1

(a)

Storey 4

Storey 3

Storey 2

Storey 1

(b)

Storey 4

Storey 3

Storey 2

Storey 1

(c)

Storey 4

Storey 3

Storey 2

Storey 1

(d)


0587

0140

0030

0000

0419

0077

0002

0107

0008

0077


OriginalRS0

RS1RS2

1

2

3

4

Stor

ey







0587

0419

0107 00770

1

06250688

Dam

age i

ndex

ratio

of F

RP


0

025

05

075

1








Storey 8

Storey 7

Storey 6

Storey 5

Storey 4

Storey 3

Storey 2

Storey 1

(a)

Storey 8

Storey 7

Storey 6

Storey 5

Storey 4

Storey 3

Storey 2

Storey 1

(b)

Storey 8

Storey 7

Storey 6

Storey 5

Storey 4

Storey 2

Storey 3

Storey 1

(c)

Storey 8

Storey 7

Storey 6

Storey 5

Storey 4

Storey 3

Storey 2

Storey 1

(d)





8 Conclusions



Data Availability




Acknowledgments


References


0004

0024

0018

0238

0185

0215

0218

0059

0135

0090 0208 0396 0431

0155

0322

0290

0494

0242

0418

0376

0092

1

2

3

4

5

6

7

8

Stor

ey


OriginalRS0

RS1RS2


04940396

0242 02380

1

05940688



0

025

05

075

1

Dam

age i

ndex

FRP

ratio






























































































Storey 4

Storey 3

Storey 2

Storey 1

(a)

Storey 4

Storey 3

Storey 2

Storey 1

(b)

Storey 4

Storey 3

Storey 2

Storey 1

(c)

Storey 4

Storey 3

Storey 2

Storey 1

(d)


0587

0140

0030

0000

0419

0077

0002

0107

0008

0077


OriginalRS0

RS1RS2

1

2

3

4

Stor

ey







0587

0419

0107 00770

1

06250688

Dam

age i

ndex

ratio

of F

RP


0

025

05

075

1








Storey 8

Storey 7

Storey 6

Storey 5

Storey 4

Storey 3

Storey 2

Storey 1

(a)

Storey 8

Storey 7

Storey 6

Storey 5

Storey 4

Storey 3

Storey 2

Storey 1

(b)

Storey 8

Storey 7

Storey 6

Storey 5

Storey 4

Storey 2

Storey 3

Storey 1

(c)

Storey 8

Storey 7

Storey 6

Storey 5

Storey 4

Storey 3

Storey 2

Storey 1

(d)





8 Conclusions



Data Availability




Acknowledgments


References


0004

0024

0018

0238

0185

0215

0218

0059

0135

0090 0208 0396 0431

0155

0322

0290

0494

0242

0418

0376

0092

1

2

3

4

5

6

7

8

Stor

ey


OriginalRS0

RS1RS2


04940396

0242 02380

1

05940688



0

025

05

075

1

Dam

age i

ndex

FRP

ratio























































































Storey 4

Storey 3

Storey 2

Storey 1

(a)

Storey 4

Storey 3

Storey 2

Storey 1

(b)

Storey 4

Storey 3

Storey 2

Storey 1

(c)

Storey 4

Storey 3

Storey 2

Storey 1

(d)


0587

0140

0030

0000

0419

0077

0002

0107

0008

0077


OriginalRS0

RS1RS2

1

2

3

4

Stor

ey







0587

0419

0107 00770

1

06250688

Dam

age i

ndex

ratio

of F

RP


0

025

05

075

1








Storey 8

Storey 7

Storey 6

Storey 5

Storey 4

Storey 3

Storey 2

Storey 1

(a)

Storey 8

Storey 7

Storey 6

Storey 5

Storey 4

Storey 3

Storey 2

Storey 1

(b)

Storey 8

Storey 7

Storey 6

Storey 5

Storey 4

Storey 2

Storey 3

Storey 1

(c)

Storey 8

Storey 7

Storey 6

Storey 5

Storey 4

Storey 3

Storey 2

Storey 1

(d)





8 Conclusions



Data Availability




Acknowledgments


References


0004

0024

0018

0238

0185

0215

0218

0059

0135

0090 0208 0396 0431

0155

0322

0290

0494

0242

0418

0376

0092

1

2

3

4

5

6

7

8

Stor

ey


OriginalRS0

RS1RS2


04940396

0242 02380

1

05940688



0

025

05

075

1

Dam

age i

ndex

FRP

ratio



























































































0587

0419

0107 00770

1

06250688

Dam

age i

ndex

ratio

of F

RP


0

025

05

075

1








Storey 8

Storey 7

Storey 6

Storey 5

Storey 4

Storey 3

Storey 2

Storey 1

(a)

Storey 8

Storey 7

Storey 6

Storey 5

Storey 4

Storey 3

Storey 2

Storey 1

(b)

Storey 8

Storey 7

Storey 6

Storey 5

Storey 4

Storey 2

Storey 3

Storey 1

(c)

Storey 8

Storey 7

Storey 6

Storey 5

Storey 4

Storey 3

Storey 2

Storey 1

(d)





8 Conclusions



Data Availability




Acknowledgments


References


0004

0024

0018

0238

0185

0215

0218

0059

0135

0090 0208 0396 0431

0155

0322

0290

0494

0242

0418

0376

0092

1

2

3

4

5

6

7

8

Stor

ey


OriginalRS0

RS1RS2


04940396

0242 02380

1

05940688



0

025

05

075

1

Dam

age i

ndex

FRP

ratio

























































































Storey 8

Storey 7

Storey 6

Storey 5

Storey 4

Storey 3

Storey 2

Storey 1

(a)

Storey 8

Storey 7

Storey 6

Storey 5

Storey 4

Storey 3

Storey 2

Storey 1

(b)

Storey 8

Storey 7

Storey 6

Storey 5

Storey 4

Storey 2

Storey 3

Storey 1

(c)

Storey 8

Storey 7

Storey 6

Storey 5

Storey 4

Storey 3

Storey 2

Storey 1

(d)





8 Conclusions



Data Availability




Acknowledgments


References


0004

0024

0018

0238

0185

0215

0218

0059

0135

0090 0208 0396 0431

0155

0322

0290

0494

0242

0418

0376

0092

1

2

3

4

5

6

7

8

Stor

ey


OriginalRS0

RS1RS2


04940396

0242 02380

1

05940688



0

025

05

075

1

Dam

age i

ndex

FRP

ratio

























































































8 Conclusions



Data Availability




Acknowledgments


References


0004

0024

0018

0238

0185

0215

0218

0059

0135

0090 0208 0396 0431

0155

0322

0290

0494

0242

0418

0376

0092

1

2

3

4

5

6

7

8

Stor

ey


OriginalRS0

RS1RS2


04940396

0242 02380

1

05940688



0

025

05

075

1

Dam

age i

ndex

FRP

ratio










































































































































































































































Documents

Damage-BasedSeismicRetrofittingApproachforNonductile ...downloads.hindawi.com/journals/ace/2020/7564684.pdf · 2020-06-09 · ResearchArticle Damage-BasedSeismicRetrofittingApproachforNonductile