Seismic performance of repaired hollow-bridge piers

Construction and Building Materials 17(2003) 339–351

0950-0618/03/$ - see front matter� 2002 Elsevier Science Ltd. All rights reserved.PII: S0950-0618Ž02.00119-8

Seismic performance of repaired hollow-bridge piers

Chin-Tung Cheng *, Jyh-Csyang Yang , Yeong-Kae Yeh , Shen-En Chena, a b c

Department of Construction Engineering, National Kaohsiung First University of Science and Technology, 1 University Road, Yenchao,a

Kaohsiung 824, Taiwan, ROCNational Center on Research of Earthquake Engineering, 200, Section 3, Thin-high Road, Taipei 106, Taiwan, ROCb

Department of Civil and Environmental Engineering, University of Alabama at Birmingham, Birmingham, AL 35294-4440, USAc

Received 3 January 2002; received in revised form 2 October 2002; accepted 25 October 2002

Abstract

To develop an effective repair technique for rapid bridge restoration after an earthquake, four hollow bridge columns werecyclically loaded to failure, repaired and retested. The repair process includes using dog-bone shape bars to replace the fracturedlongitudinal bars in plastic hinges and using FRP(Fiber Reinforced Plastic) wraps to enhance the deformation capacity ofcolumns. The repair aims to restore seismic capacity in terms of strength and ductility. Test results indicate that the fracturedlongitudinal bars can be completely repaired and the deformation capacities of the columns were enhanced by FRP wraps.However, due to concrete deterioration and the buckling of the longitudinal bars in the inner layer of the hollow sections, the testresults also indicate the repaired column strengths are less than anticipated.� 2002 Elsevier Science Ltd. All rights reserved.

Keywords: Hollow-columns; Repair; FRP; Seismic performance; Flexure; Shear; Lap splice

1. Introduction

In order to cross the boundary of mountains in Taiwan,high elevation bridges with large-size columns are con-structed to accommodate the high moment demand inplastic hinges. In practice, hollow-bridge columns maybe used to reduce their self-weights and the high bearingdemand on pile foundations. Literatures on hollow-columns are rare with some notable works from Tylorand Breenw1x and Manderw2x. Unlike solid sectionsreinforced with longitudinal bars along the perimeter,hollow sections are reinforced with two layers of lon-gitudinal bars along column walls to achieve desiredductility. Since 1997, several researchers in Taiwanjoined forces to investigate the seismic flexural andshear capacities of these hollow-bridge piers, developretrofit techniques, and establish numerical models.Series of full-size hollow-bridge piers were subsequentlyconstructed and tested within a 3-year period. After thetests, the damaged columns were repaired according to

*Corresponding author. Tel.:q886-7-6011000x2118; fax:q886-7-6011017.

E-mail address: [email protected](C.-T. Cheng).

the concept developed in this research, and the resultsare reported herein.Bridge piers designed in accordance with old design

codes may suffer severe damage during seismic attacks.Even though safety of lives is ensured, damage incurredmay terminate the bridge function after earthquake. Thiswas evident in the 1999 Chi-Chi earthquake. The com-monly seen deficiency of damaged bridge columns maybe characterized as insufficient shear strength or ductil-ity, inadequate anchorage or bonding, and insufficientflexural strength or ductility. To mitigate column damagefor future earthquake, many retrofit techniques havebeen proposed such as steel jacketing, concrete jacket-ing, and composite jacketing. These jackets are primarilyused to provide confinement for columns. Currently,fiber reinforced plastics(FRP) are common for retro-fitting structures as proposed by many researchers suchas Seible et al.w3x and Saadamanesh et al.w4x. However,it is uncertain as to how these FRP jackets may performin the repair of hollow sections after an earthquake. Itis also unclear how the inner layer reinforcement mayaffect the performance of repair. The objective of thisresearch is to propose an effective repair technique forhollow bridge columns so that bridge function can be

340 C.-T. Cheng et al. / Construction and Building Materials 17 (2003) 339–351

quickly restored after an earthquake. The repair aims torestore seismic capacity of bridge columns in terms ofstrength and ductility without altering its strong beam-weak column design principle.

2. Repair technique

As mentioned above, columns may fail in severalmodes such as flexural, shear, or bond failures. Forcolumns failing in flexural mode, the damages may besuperficial like cracking or spalling of concrete cover,or they may be severe such as reinforcement bucklingor even fracturing. Currently, there is no cure for barfracture except techniques proposed by Dutta et al.w5xand Leman et al.w6x. In Dutta’s research, one highstrength bar(f s1030 MPa) was used to replace twoy

fractured ordinary G60 reinforcements by welding thesebars on the same steel plate. In Leman’s research, thecross-section in a plastic hinge was enlarged to encasethe existing column, and new longitudinal bars wereplanted into the foundation.In this research, dog-bone shape bars(f s410 MPa)y

are proposed to replace each fractured bar in order torestore the flexural strength of the columns. The cross-section of the dog-bone bar is designed in a way thatits tensile strength is less than that of the originalreinforcement to avoid damage from penetration intothe foundation. The central length of the dog-bone barscan be designed proportional to the plastic length sug-gested by Priestley et al.w7x asL s0.008Lq4400́ d ,p y b

where L splastic-hinge length,Ls shear span,́ sp y

yield strain of longitudinal bars, andd slongitudinalb

bar diameter. In Cheng and Mander’sw8x study, thecentral length of the dog-bone bar can be tuned basedon seismic demand in order to get appropriate low cyclefatigue life for the columns. They also showed that thelonger the central length of the dog-bone bar, the longerthe fatigue life will be, which of course, also meanshigher repair costs.After the repair of longitudinal reinforcements, FRP

is then wrapped around the columns to enhance thedeformation capacity. Seible et al.w3x recommendedusing the thickness,t (cm), of the FRP wraps to achievef

the required flexural ductility, which can be calculatedas:

D ´ y0.004f9Ž .cu cct s0.09 (1)f

ff ´ju ju

where ´ sf =C andB E Bf Lu pC F Cm s1q3 y1 = 1ycu u u DD G Df Ly

and Dsthe column dimension in the loadingELpF0.5GL

direction (cm), f 9 the confined compressive strengthcc

of concrete(MPa), fsthe reduction factor for flexure

(taken as 0.9), f sultimate strength of FRP(MPa),ju

´ sultimate compressive strain of concrete(%), ´ scu ju

deformation capacity of FRP(%), C sneutral depthu

under ultimate curvature(cm), f sultimate curvatureu

of column, f syield curvature of column, andm sy D

displacement ductility factor.For lap-splice columns, damages such as spalling of

cover concrete and bond slip in lap-splice may occur.FRP wraps can then be used to confine the lap-splices.Seible et al.w3x indicate that bond slip at lap-splicewould initiate as circumferential strain, which hasreached the 1000–2000m´ range. Therefore, to limitthe circumferential strain to be under 1000m´, thethickness of the FRP wraps is calculated as

D f yfŽ .l ht s500 (2)f Ej

where andpsthe perimeterA fs yf sl B Ep

C Fq2(d qC ) Lb c sD G2n

along the lap-spliced bars(cm), nsthe number ofspliced bars along the perimeter,C sthe concrete coverc

to the center of main column reinforcement(cm), L sslap-splices length(cm), A sarea of one main columns

reinforcement(cm ), f syield strength of main rein-2y

forcement(MPa), and f sthe horizontal stress providedh

by the existing hoops(MPa). It is shown through thisequation that the shorter the lap-splice length, the thickerthe wraps are needed, such that bond slippage may becontrolled.For column failures due to insufficient shear strength,

only cracking damage may be reparable. Damage up tohoop fracture would result in large deformations andhence, it is beyond the scope of this research. Due tothe inner hole, direct injection of epoxy into cracks isineffective for hollow sections. Hence, minor crackswere left without repair. Loose concretes, however, wereremoved and replaced by non-shrinkage concrete. FRPwraps were then applied to the column to upgrade itsshear capacity to the demand level. Seible et al.w3xrecommended the thickness of FRP wrap for columnshear reinforcement to be:

Vyf yVŽ . n

t s (for circular column) (3a)jpy2 0.004E DŽ . j

Vyf yVŽ . n

t s (for rectangular column) (3b)j 2=0.004=E Dj

whereVsshear demand with the case of full flexuraloverstrength in plastic hinges(kN), fsreduction factor

341C.-T. Cheng et al. / Construction and Building Materials 17 (2003) 339–351

Fig. 1. Detail of original hollow bridge columns.

Table 1Detail of original specimens

Specimen f 9c L P Longitudinal bar Stirrup barno. (MPa) (m) (kN)

Diameter fy Diameter Spacing fy

(mm) (MPa) (mm) (mm) (MPa)

PS1-C 31.7 5.5 3600 22 418.2 13 100 410PI1-C 33.8 5.5 3600 22 418.2 13 300 410PI2 32.6 3.5 3600 22 423.3 10 200 392PI2-C 33.2 3.5 3600 22 423.3 10 200 392

for shear (typical taken as 0.85), V sshear capacityn

(kN), andE sthe elastic modulus of FRP(MPa).j

The repair strategy is summarized as follows:

1. All damaged areas should be sandblasted.2. All fractured, buckled reinforcement bars are to bereplaced with dog-bone shape bars.

3. Ties are reinstalled and the cracked sections of thecolumn are then filled with repair concrete.

4. FRP is then wrapped around the columns.5. Depending on the location and purpose of application,the number of FRP layers should be determined.

3. Experiments

In order to validate the proposed repair techniques,one square and three circular full-size columns, designedto have distinguished failure modes such as lap-splice

failure (PI1-C), flexure-shear failure(PI2-C), shearfailure (PI2), and flexure failure(PS1-C), are construct-ed. The suffix letter C in the specimen number indicatescircular hollow column with 150 cm outer diameter and90 cm inner diameter. The square column has a150=150 cm cross-section with 90=90 cm hole in thecenter. The column heights are 6 m for specimens PS1-C and PI1-C, and 4 m for specimens PI2 and PI2-C.All columns are longitudinally reinforced with 64D22bars(as shown in Fig. 1). Measured material strengthsand other details are presented in Table 1, whereLrepresents the height to the applied lateral load from thefoundation surface. The longitudinal reinforcement ofthe specimen PI1-C is spliced in 50 cm(23d ) lengthb

from the foundation surface and is provided with onlyfour cross-ties(Fig. 1). This lap length is typical for thepre-1987 design of bridge columns in Taiwan.


Fig. 2. Test apparatus.

The four specimens were then tested under constantaxial load 3600 kN, representing 0.08f 9 A for rectan-c g

gular sections and 0.1f 9 A for circular sections. Subse-c g

quently, a cyclic lateral load was applied by three1000-kN actuators, as shown in Fig. 2, with sequentialdisplacement increments. A test was performed underdisplacement control in the form of triangular waveswith two cycles at each displacement increment: 0.5D ,y1D , 3D , 4D , 5D , etc., whereD is the calculatedy y y y y

effective yield displacement of columns. Test results

show that the failure modes of the four specimens areall different as intended.Flexural damage in plastic hinge of specimen PS1-C

was severe and concentrated so that the outer layerlongitudinal bars are fractured and the inner layerreinforcements are buckled, and the concrete is crushedinto the hollow section to form a big hole at the columnwall. For specimen PI2-C, the outer layer bars fracturedat the column hinge and diagonal shear cracks acrossthe mid-height of column wall occurred at the same


Fig. 3. Schematic drawing showing repair of fractured bars with dog bone bars.

time—typical of a flexural-shear failure mode. Forspecimen PI2, two distinguished diagonal cracks acrossthe mid-height of the column wall resulted from insuf-ficient shear capacity. Spalling of cover concrete at thecolumn hinge and bond slip at lap-splices along theloading direction, were observed in the test of specimenPI1-C. Due to the limitation of paper length, somephotos showing pictures of failure for original columnscan be referred to the research of Yeh et al.w9,10x.All specimens were repaired following the technique

described in the previous section. To repair the fracturedlongitudinal reinforcements, loose concrete was firstremoved; the fractured or severely buckled bars in theouter layer of cross-section were cut and were replacedby the dog-bone bar as shown in Fig. 3. The centrallength of the dog-bone bar is equal to the plastic length

suggested by Priestley et al.w7x. The dog-bone bars forspecimens PS1-C are longer than that of specimen PI1-C due to its column height. Since the buckled bars inthe inner layer were difficult to reach, hence, they werenot replaced. Original stirrups were reinstalled beforethe quickset non-shrinkage concrete was poured. Toenhance the column ductility, FRP wraps were appliedto the columns. The thickness and coverage of the FRPwrap on the columns are shown in both Table 2 andFig. 4. The thickness of the FRP is 0.1375 mmylayersupplied by Advanced Group Co., Taiwan. Materialstrengths of FRP and steel are presented in Table 3 forcomparison. From Eq.(1), two layers of FRP arerequired to achieve a target displacement ductility of 6for specimen PS1-C. From Eq.(2), 27 layers of FRPwould be required to prevent bond slip at lap-splice due


Table 2Detail of repaired specimens

Specimen f 9 (MPa)c FRP wraps Replaced barno.

Original Repair Inside Height Outside Height Diameter fy

plastic (m) plastic (m) (mm) (MPa)hinge hinget (mm)f t (mm)f

RPS1-C 31.7 38.8 0.26 1.1 – – 20 471.3RPI1-C 33.8 34.6 0.78 0.75 0.26 5.0 – –RPI2 32.6 38.1 0.52 – 0.52 3.0 – –RPI2-C 33.2 41.2 0.52 – 0.52 3.0 20 484.3

Fig. 4. Applied FRP wraps in each specimen.

to a short lap length. However, since it is unrealistic toapply such thick FRP wrap to the damaged column, therepair strategy is set to increase the energy dissipationand the deformation capacity, instead of preventing bondslippage. Hence, only six layers of FRP at lap-splice

region were provided for a target ductility of 2.7 basedon 4% cumulative plastic drift from theoretical predic-tions(Fig. 9). In this way, the repair technique is limitedto columns in low to medium seismic activity regions.For the strengthening of specimens PI1-C and PI2, four


Table 3Comparison of material strengths between steel and carbon fiber

Type Tensile Tensile Ultimate Densitystrength modulus strain (Nycm )3

(MPa) (MPa)

Steel 280 2.06=105 0.06 0.025Carbon fiber 3560 2.35=105 0.015 0.019(FAW 250)

Fig. 5. Photo showing bars fracture after test for specimen RPI1-C.

Fig. 6. Photo showing deterioration of concrete wall after test forspecimen PI2.

layers of FRP wraps are required based on Eqs.(3a)and (3b). The proposed repair procedure for eachcolumn is estimated to be complete within 1 week.After repair, the four specimens were tested again

following the same procedure as the original tests.Failure modes of the repaired specimens are all identicalto their original counterparts except specimen PI2-Cwhere flexure-shear failure mode was upgraded to flex-ure-dominant mode. Visual observations show that theFRP in column hinge was separated in tension andbulged in compression between the fibers under firstcycle of 3D loading for specimen RPS1-C and 4Dy y

loading for specimen RPI2-C. Fracture of dog-bone barsoccurred in the first cycle of 4D loading for specimeny

RPS1-C and 5D loading for specimen RPI2-C, as showny

in Fig. 5. Throughout the test of RPI1-C, only separationof FRP fibers in the lap-splice region was observed. Forthe test of RPI2, the FRP bulged due to shear observedin the first cycle of 5D loading. In this case, the damagey

was so severe that a 90=50 cm empty hole in 1.5 mheight of column wall was formed after removal of theFRP and loose concrete as shown in Fig. 6.Hysteresis of all specimens is shown in Fig. 7, where

the dotted straight line represents the nominal strengthof the columns following ACI provisions with theconsideration ofPyD effect. ThePyD effect can becalculated based on the configuration of test set-up(Fig.2), where axial load was transferred by tendons anchoredto the steel beams at strong floor. For repaired columns,the inner layers of longitudinal rebar, which were notrepaired, are excluded from the calculation of nominalstrengths. Test results in terms of strength and ductilityare listed in Table 4, where yield and ultimate displace-ments have the same definition as in Priestley and Parkw11x. Ultimate displacement was defined as the displace-ment corresponding to the column strength reduced to80% of ultimate strength on the load displacementenvelop.As shown in Table 4, only 76% of strength and part

of the deformation capacity for specimen PS1-C arerestored, even though fractured bars in outer layer weresuccessfully repaired. The reason may be attributed tothe severe damage in previous test with ductility up to10. Besides, buckled bars in inner layer and cracksbeyond hinge region were all left without repair. It is

suggested that in addition to plastic hinge region, FRPwraps should be applied to the whole column height inorder to take care of the cracks that have gone beyondthe hinge region. For the repair of the lap-splice column,bond slip at the inner layer was left without repair sothat only 77% of strength is restored. However, the FRP


Fig. 7. Hysteresis of specimens before and after repair.

wraps did increase the ultimate column displacementsas expected.Shear damage in specimen PI2-C was less severe than

that in specimen PI2. Therefore, 85% of strength forspecimen PI2-C compared to only 58% for specimenPI2 have been recovered. Although the severely deteri-

orated concrete in the cracked region was replaced bynew concrete and wrapped with FRP, shear failure inspecimen PI2 cannot be avoided. Test results show thatthe shear damage in PI2 is much more severe thanexpected. The repair of damaged concrete was ineffec-tive and difficult due to the hollow section. However,


Table 4Test results of all specimens

Specimen Yielding Ultimate Ductility Ultimate moment Failureno. displacement displacement factor (kNØm) mode

Dy (mm) Du (mm) (DuyDy)Pull Push Average Ratio

Push Pull Push Pull(%)

PS1-COriginal 36.2 360.1 359.8 9.7 10.2 8470 8921 8696 100 FlexureRepair 72.7 150.0* 149.8* 2.0 2.1 6451 6806 6629 76 Flexure

PI1-COriginal 32.5 90.1 89.6 2.6 2.9 7473 8078 7775 100 BondRepair 48.9 120.1 115.3 2.4 2.4 5367 6671 6002 77 Bond

PI2Original 18.9 75.2 67.5 4.0 3.6 9277 9155 9216 100 ShearRepair 17.5 110.2 88.5 6.5 4.9 5209 5501 5355 58 Shear

PI2-COriginal 20.1 104.1 100* 5.3 4.9 8192 7844 8018 100 Flexure

-shearRepair 44.8 158.2 180.3 3.6 3.9 6866 6671 6768 85 Flexure

Maximum displacement recorded when test concluded with strength descended higher than 80% of ultimate strength.*

deformation capacities for both specimens PI2-C andPI2 are enhanced as shown in Table 4.In addition to the FRP wraps, to fill concrete into the

hollow section or to enlarge the cross-sections couldprovide other possible alternatives for the repairs. Theadvantages are increases in lateral stiffness and strength,and the decrease in yield displacement. However, theincreased weight due to concrete filling may also raisethe bearing demands on the pile foundations and increasethe inertial force during earthquake excitation.Displacement at the top of columns is attributed to

the deformations due to shear and flexure, and can beseparated into two components as shown in Fig. 8. Theflexural displacement at the top of the column can becalculated by the moment–curvature areas measuredfrom the displacement transducers installed at the col-umn hinge. The flexural displacements measured bytransducers for specimens PI1-C and RPI1-C, as shownin Fig. 8, include the bond slip at the lap splice. Theshear component can be obtained by deducting theflexural displacement from the total displacements. Asshown in Fig. 8, shear displacement in short columnsare low due to FRP wraps. It is especially true forspecimen RPI2-C where a similar proportion of sheardisplacement as in the test of the flexure-dominatedcolumn PS1-C was obtained.

4. Seismic evaluation

Due to various failure mechanisms in columns, themethods of strength evaluation may differ. For example,the strength of the flexural dominant column can beestimated in accordance with ACI provisionsw12x

(inverse ofz-dotted line in Fig. 7), and the strength inthe lap-splice column can be evaluated by an energymodel proposed by Mander and Duttaw13x. The follow-ing are the descriptions of four shear models for columnswithout FRP wrap, as proposed by several researchers.The last model introduced here, is applied for columnswith FRP wraps.The first model is based on ACI shear design equa-

tion, which can be expressed as:

V sV qV (4)n c s

where and ,B EP A f dV yhC FyV s0.167 1q f9 b d V sc c w sD G14A Sg

V sshear resistance provided by concrete(kN), V sc s

shear resistance provided by hoops(kN), Psaxial loads(MN), A scolumn gross area(m ), f 9 sconcrete com-2

g c

pressive strength(MPa), f syield strength of hoopsyh

(MPa), Sshoop spacing(cm), b sweb width (cm),w

dseffective depth(cm), A shoops area(cm ). For2v

rectangular hollow sections,b is equal to the wholew

column width minus the hollow width. For circularhollow sections,b is equal to the outside diameterw

minus the inside diameter, and then multiplied by 0.886.d is also multiplied by 0.886 for circular sections. Inthis way (0.886spy4), shear area in circular sections2

can be transformed into shear area of a square sectionand applied in Eq.(4).The second model is proposed by Priestley et al.w14x

and is expressed as:

V sV qV qV (5)n c s a


Fig. 8. Displacement component at point of lateral loads application.

where yV sk f 9Ac c e

A f hv yh cV s cotus S

DyxV s Pa

2D MyVDŽ .whereV sshear resistance provided by axial load,ksa

deterioration factor for concrete,A s0.8 times b de w

(m ), h scentral distance between closed hoops(m),2c

usangle between cracks and vertical gravity lines,xsdepth of compressive zone in column(m), MyVsshearspan(m). The deterioration factor can be calculated as

ks0.29 for m -2.0D

ks0.29y0.095m y2 for 2.0Fm F4.0Ž .D D

ks0.1 for m )4.0D

wherem sdisplacement ductility factor.D

A third model, as proposed by Aschhiem et al.w15x,is expressed as:

V sV qV (6)n c S

where , , andB EP A f dV yhC FyV s0.29 kq f9 A V sc c e s 0D G14Ag Stan30

. The parametersf 9 and f are in SI4ymD1Gks G0 c yh3

units (MPa). The fourth model is proposed by Caltransw16x and is expressed as:

V sV qV (7)n c s

where ,y yV sfactor1=factor2= f9 A F1y3 f9 A V sc c e c e s

, ,A f h r0fV yh c yh0.3Gfactor1s q3.67ym G3.0 1.0FDS 1.034

, r0 volume ratio of hoops,B EPC Ffactor2s q1F1.5D G14Ag

and f 9 and f are in megaPaschals(MPa).c yh

For columns wrapped by FRP, a model proposed bySeible et al.w3x is used to evaluate its shear strength:

V sV qV qV qV (8)n c s a f

whereV , V and V are following the same definitionc s a

as in Priestley’s Modelw14x, and V shear resistancef

provided by FRP wraps(kN) is calculated as:

V s2=0.004=t E D for rectangular columnf j j

V spy2=0.004=t E D for circular columnf j j

Figs. 9 and 10 show the strength deterioration of thecolumns failed due to bond loss and shear, respectively.As shown in Fig. 9, it is noted that the analytical resultsare in good agreement with the experimental results.Analytical results show that bond loss for repairedcolumn is commenced earlier at cumulative plastic driftangle of 0.031(rad) than that of the original column at0.043(rad) due to ignoring the inner lap-splices. How-ever, the rate of strength deterioration for the repairedcolumn tends to mitigate due to the confinement of FRPwraps. As shown in Fig. 10, the Priestley model is thebest fit with experiments among models for originalcolumns in terms of strength as well as failure modepredictions, e.g. PI2 failed by shear and PI2-C failed byflexure-shear. For repair columns, Seible’s predictionshows that FRP should provide enough shear capacity


Fig. 9. Strength deterioration for lap-splice column.

Fig. 10. Strength evaluation for specimens PI2-C and PI2 before and after repair.


for both specimens as evident in the test of anotherproject w17x where an identical undamaged specimenwas retrofitted with the same amount of FRP. However,test results show that shear capacity in specimen RPI2is severely deteriorated due to previous damage. Asshown in Fig. 10, column RPI2 may fail with theresistance of FRP(1466 kN) only. This means onlyresistance by FRP can be accounted for.

5. Conclusions

Bridge piers are designed to dissipate earthquake-induced energy and should behave in a strong beam-weak column fashion. If the traditional capacity designis considered alone, bridge piers will be vulnerableunder severe earthquake attack. This research aims todevelop a repair technique for damaged columns, inorder to restore quickly the bridge functions after earth-quakes. Different failure modes have been considered.The primary objectives are to enhance the columndeformation capacity and to restore their strength. Toachieve this objective, a newly designed dog-bone shapebar is applied to replace fractured longitudinal bars. FRPwraps are then utilized to enhance deformation capacityfor hollow-columns failed due to shear, bond loss andflexural damage.Test results of four full-size hollow bridge columns

show that the hollow columns reinforced with two layersof longitudinal rebar can achieve the desired strengthand with excellent ductility, provided sufficient hoopsare used. Test results also show that the flexural damagecaused by the fracture of outer layer longitudinal barswere successfully repaired by dog-bone shape bars.While buckled rebars in the inner layer, which were leftwithout repair due to construction feasibility, resulted inlower restored column strength. Test results indicate thatFRP wraps not only increase the ultimate displacementsfor the columns, but also reduce column shear defor-mation. In addition, flexural-shear failure mode in thecircular column was upgraded to flexural dominance.Among the models for columns without FRP, the

Priestley shear model is the best fit with experiments interms of strength and prediction of failure modes. Forrepaired columns, Seible’s evaluation overestimated theshear capacity due to the poor efficiency of concreterepair in the column wall. The energy model proposedby Dutta and Mander made a reasonable prediction ofstrength deterioration for the lap-splice column.

6. Nomenclature

A :e effective shear area equal to 0.8 times ,b dwA :g column gross areaA :v hoops area,A :s area of one main column-reinforcing bar,

C :c concrete cover to the center of main columnreinforcement,

C :u neutral depth under ultimate curvature,D: column dimension in the loading direction,E :j modulus of FRP,L: shear span,L :p plastic-hinge length,L :s lap-splices length,MyV: shear span,P: axial loads,S: hoops spacing,V: column shear demand on full flexural

overstrength in plastic hinges,V :a shear resistance provided by axial load,V :c shear resistance provided by concrete,V :n shear capacity,V :s shear resistance provided by hoops,V :f shear resistance provided by FRP wrapsb :w web width,d: effective depthd :b Longitudinal bar diameter,f 9 :c concrete compressive strength,f 9 :cc confined compressive strength of concrete,f :h horizontal stress level provided by existing

hoops,f :ju ultimate strength of FRP,f :y yield strength of main reinforcement,f :yh yield strength of hoops,h :c central distance between closed hoops,k: Deterioration factor for concrete,n: number of spliced bars alongp,p: perimeter along the lap-spliced bars,t :f FRP thickness,x: depth of compressive zone in column,´ :y yield strain of longitudinal bars,´ :cu ultimate compressive strain of concrete,´ :ju Deformation capacity of FRP,f: reduction factor,f :u ultimate curvature of column,f :y yield curvature of column,m :D Displacement ductility factor.u: angle between cracks and vertical gravity

lines,r0: volume ratio of hoops,

Acknowledgments

Financial support from the National Science Councilin Taiwan under grant NSC89-2625-Z-327-006 and tech-nical help from Mr Chih-Hsiung Chou in NationalCenter for Research on Earthquake Engineering aregratefully appreciated.


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Documents

Seismic performance of repaired hollow-bridge piers