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"OwW|t x@U=Lt Oqwi =@ xOWKrUt uD@ |=Q@

M = Cosh(0 0022Ldrr f0c

db) (4)

|WywSB QO "OQ=O |oDU@ =yOQor}t G; |UOvy C=YNWt x@ r QDt=Q=B u; QO xm=@ Q@=Q@ Q=OH; |Oqwi |=yOQor}t |=Q@ 4 |x]@=Q QO r Q=Okt [13]'1998 p=U QO|x]@=Q R= xO=iDU= =@ xrYw pw] QO |oDUw}B Ctw=kt "CU= xOW xDiQo Q_v QO 3

%O};|t CUOx@ 5 |x]@=Q R= [14]'2005 p=U QO |Qo}O VywSBuEsf = T

�dbLd= uc

1 + 1=M1 85 + 0 024pM �

(0 88 + 0 12CMed

C) (1 + 0 015 fRAtAbCS

) (5)

s=ovy QO p=mU=B=ot ?UL Q@ |a[wt |oDUw}B VvD |xv}W}@ uc 'x]@=Q u}= QO%OwW|t x@U=Lt 6 |x]@=Q R= xm 'CU= CUmW

uc = 2 7C=db + 0 5C=db + 3 6

pf 0c (6)

|y=oW}=tR; |xH}Dv 284 j} Q] R= |Oqwi |=yOQor}t |=Q@ 5 |x]@=Q |DUQOx@ |y=oW}=tR; |oDUw}B Ctw=kt u}ov=}t 'j}kLD u}= QO [14]"CU= xOW |@=} RQ=|x]@=Q |q=@ CkO Q@ xm CU= 0 128 u; Q=}at h=QLv= w 1 021 Q@=Q@ |D=@U=LtR= QDtm |r}N GFRP |=yOQor}t |v=UWm pwOt xm =Hv; R= [14]"OQ=O CrqO 5`} RwD |ovwoJ 'CU= Cw=iDt R}v =yv; |@v=H K]U w CU= |Oqwi |=yOQor}t|x]@=Q w Ovm|t Q}}eD |Oqwi |=yOQor}t x@ C@Uv xrYw pw] QO |oDUw}B VvD|oDUw}B VvD xm CU= xOW xO=O u=Wv =yVywSB |NQ@ QO "OwW KqY= O}=@ 4x@ |oDUw}B VvD Vy=m w [18]'CU= |Oqwi |=yOQor}t R= QDtm FRP |=yOQor}txOWv x�=Q= |}x]@=Q uwvm =D |rw 'CU= |Qt}rB |=yOQor}t sm |v=UWm pwOt p}rO"Ovm OQ=w FRP |=yOQor}t |oDUw}B Ctw=kt QO =Q |v=UWm pwOt QF= xm CU=

[13]"O};|t CUOx@ 7 |x]@=Q R= xrYw pw] QO |oDUw}B VvD C=Q}}eDu(x) = a:Cosh(jx) (7)

|xv}W}@ Q=Okt "CU= xOW ?=NDv= xrYw \Uw QO x VHvU -=O@t 'x]@=Q u}= QO"OyO|t MQ u; \Uw QO |oDUw}B VvD |xv}tm w xrYw |=yDv= QO |oDUw}B VvD

%OwW|t x@U=Lt 9 w 8 |=yx]@=Q R= M 'u}W}B VywSB G}=Dv j@]uMax:(x = Ld

2 ) = a:Cosh( j:Ld2 ); uMin:(x = 0) = a (8)

M = uMax

uMin= Cosh( j:Ld2 ) (9)

%O};|t CUOx@ 10 |x]@=Q R= xm CU= |DNU pt=a j '\@=wQ u}= QO

jFRP =

srff 0c�dbAbEf

=

srff 0cdb

: 4Ef

(10)

CUOx@ FRP |=yOQor}t |=Q@ M QDt=Q=B '9 |x]@=Q QO 10 |x]@=Q |v} Ro}=H R="�11 |x]@=Q� O};|t

M = Cosh(Ld2srff 0cdb

: 4Ef

) = Cosh(Ld2sEsEf

4Es

rrff 0cdb

)

(11)

27

"""|=yOQ

or}t=@xO

WKrUt

Q=OxrYw

|=yQ}DQ

=DiQ|U

QQ@"|y=oW}=tR; |=yxvwtv |=Q@ |@v=H |=yOQor}t O=OaD w =yxrYw pw] C=}�RH "1 pwOH

|@v=H |=yOQor}t At=SM

Ld f 0ca

db CMed C u=wvaxrYw pw] QO mm mm MPa mm mm mm xvwtv

{ { { 180 39 7* 38 18 10 30 30 B-18�8@21 2 369 2 036 180 38 0* 38 18 10 30 30 B-25�8@55 0 902 2 679 279 38 8* 42 5 16 30 21 B-3

{ { { { 37 6* { 10 { 30 B-45�8@28 1 793 1 913 125 70 6** 38 18 10 30 30 B-57�12@24 4 642 2 642 161 69 8** 38 18 10 30 30 B-6

{ { { { 63 7** { 10 { 30 B-7"OwW|t xDiQo Q_v QO p=mU=B=ot 38 uD@ Ctw=kt \UwDt Qw] x@ *

"OwW|t xDiQo Q_v QO p=mU=B=ot 68 uD@ Ctw=kt \UwDt Qw] x@ **

"|m}D=DU= V}=tR; |=yx=oDUO "1 pmW

"=yxvwtv |m}D=DU= |Q=PoQ=@ |=ys=o "2 pwOHL3 L2 L1 L0 |m}D=DU= |Q=PoQ=@ |=ys=o30 20 10 Q}D uRw uDw}vwr}m ?UL Q@ |m}D=DU= Q=@

|@ QHD p=Owt V}=tR; QO "OvwW CW=OQ@ |y=oW}=tR; |m}t=v}O |=yxYNWt =Dl} QDmr=wR}B GvU?=DW R= w xR=U x@ lQLt |wQ}v p=ta= |=Q@ x@ Q[ VmJ R=|xHQO 23 'xOWs=Hv= |=yV}=tR; QO "OwW|t xO=iDU= xR=U MU=B Ci=} QO |=Q@sDWy |O=R; |xHQO QO GvU?=DW "CU= xOW xDiQo Q_v QO |vD@ Q}D |=Q@ |O=R;"OvwW|t l} QLD x@ Q[ VmJ =@ |O=R; C=HQO s=tD w OQ}o|t Q=Qk C@=F CQwYx@C@Uv =D OvwW|t pkDvt 4xr=v=m wO Qop}rLD l} x@ =yMU=B w =yl} QLD 'TBU`@=D x@ 'Ot=U@ |xRwL QO C@Uv u}= "OwW |Q}oxR=Ov= xOWp=ta= |wQ}v x@ MU=B?Yv w |O=R; C=HQO R= |m} l} QLD =@ xm =Hv; R= [4]"CU= swUwt 5|Ot=U@ MU=BQiY Q}e u; |=yOwt CmQL |xvt=O xm Qo}O |O=R; |xHQO l} QO GvU?=DWu=wvax@ sDWy |O=R; |xHQO 'OQm CW=OQ@ =Q =yOt=U@ |DL=Q x@ u=wD|t 'CU=

p=Owt V}=tR; R= hOy w CU= CQ=UN O=H}= w |Q}PBpmW '|oDUw}B Ctw=kt|=ys=o QO xrYw |=yxYNWt w |W=aDQ= |=yxYNWt C=Q}}eD u}@ |x]@=Q |UQQ@KQW p=Owt w |m}D=DU= |=yV}=tR; |ovwoJ 'xt=O= QO "CU= CQ=UN hrDNt

"OW Ovy=wN xO=O

|m}D=DU= V}=tR; "1"4|WtN |}x]kv 4 |m}D=DU= Q=@ CLD FRP =@ xOWKrUt |=yQ}D 'V}=tR; u}= QO|Q}oxR=Ov= Vm\N =@ Q}D \Uw u=mtQ}}eD "OvQ}o|t Q=Qk xO=U |=yx=ox}mD |wQ Q@w OvwW|t pkDvt 3xO=O C@F x=oDUO x@ 2GvUwQ}v =@ wQ}v w �LVDT� u=mtQ}}eDu=mtQ}}eD� Q=@ Q=Owtv R= xO=iDU= =@ "OwW|t CW=OQ@ xv=yO \Uw QO Q}D |@ QHD R}N|=yQ}D |Q}PBpmWXN=W w |oDUw}B Ctw=kt '|m}D=DU= V}=tR; R= xOt;CUO x@C=Oy=Wt '|Q=PoQ=@hrDNtpL=Qt QOu}vJty "OwW|t x@U=LtFRP =@ xOWKrUtXNWt Q}D CUmW |ovwoJ =D &OwW|t s}UQD =ylQD VQDUo |ovwoJ w C@Fu=Wv Q}D |wQ Q@ =Q u=mtQ}}eD w wQ}v VHvU sR=wr Q=QkDU= |ovwoJ '1 pmW "OwW

"OyO|t|Q=PoQ=@ |=ys=o "OwW|t OQ=w xR=U |wQ Q@ CQ=UN O=H}= hOy =@|m}D=DU= Q=@u=wD|t |Q=PoQ=@ |=ys=o u}= ?=NDv= =@ "Ov=xOW xO=O u=Wv 2 pwOH QO |m}D=DU=

"OQm |UQQ@ |Q=DiQ hrDNt |=yCr=L QO =Q xR=U

p=Owt V}=tR; "2"4|xR=U |wQ Q@ |Q=PoQ=@ |=ys=o u}@ QO w sr=U |xR=U |wQ Q@ =OD@= QO V}=tR; u}=s=Hv= hrDNt |=yCr=L QO xR=U |W=aDQ= Q=DiQ |UQQ@ Qw_vt x@ 'xO}OCQ=UNxm |]}=QW QO w OwW|t s=Hv= |Q=OQ@ Q=@ '|Q=PoQ=@ s=o Qy R= Oa@ u}=Q@=v@ "CU= xOWOQ}o|t CQwY p=OwtV}=tR; 'CU= xOW xOQw; QO u=R} w; CQwYx@ |}=yQvi =@ xvwtv

28

"""w|v=y

iY==[Q

OtLt'|

wUwt""

"=KwQO}

U

|y=oW}=tR; G}=Dv "5|y=oW}=tR; |=yxvwtv CUmW |ovwoJ "1"5

QO =yxvwtv CUmW |ovwoJ w |Q=PoQ=@ hrDNt pL=Qt QO =ylQD VQDUo |xwLv|=yOQor}t =@ xrYw pLt B-1 |xvwtv QO "CU= xOW xO=O u=Wv 4 pmWVWwB 6|oO}mQD w Ci=mW CUmW Owt 'u}=Q@=v@ 'CU= xOWv Q=yt |@v=H|=yDv= wO QO x}rw= |=ylQD 'xvwtv u}= V}=tR; s=ovy QO "Ow@ Oy=wN uD@=yOQor}t Q@ s�=k |U=tD VvD |xir-wt '|Q=PoQ=@ V}=Ri= =@ "Ov=xOW O=H}= xrYwV}=Ri= =@ |Q=PoQ=@ |xt=O= QO 'OwW|t OQor}t |=DU=Q QO |}=ylQD RwQ@ ?Hwt=@ w V}=Ri= xrYw |=yDv= wO |=ylQD ZQa '=yOQor}t VRer w |U=tD VvDCi= COW x@ Q=@ w s=Hv= |}=yv CUmW 'xrYw |x}L=v QO uD@ VWwB |oO}mQD

"Ovm|t'u}=Q@=v@ "CU= xOW Q=yt |@v=H |=yOQor}t =@ xrYw pLt 'B-2 |xvwtv QOw OwW|t Q=yt |@v=H |=yOQor}t =@ =yOQor}t Q@ s�=k |U=tD VvD |xir-wt'xvwtv u}= QO "ODi=|t j=iD= =yOQor}t VWwB |oO}mQD uwO@ OQor}t VRerV}=Ri= =@ "CU= QDW}@ B-1 |xvwtv x@ C@Uv pmW Q}}eD w =ylQD O=OaDu; R= TB w OwW|t wQW OQor}t VRer 'Q}D QO =ylQD `} RwD w |Q=PoQ=@|=yDv= lQD |oOWR=@ w OQor}t VRer =@ "O@=}|t VQDUo xrYw |=yDv= lQDQ=@ |Q=Wi |x}L=v QO uD@ uOWOQN =@ xQN-q=@ w V}=Ri= Q}D |=vLv= 'xrYwx@ OQor}t VRer '|oOWQwYLt Cra x@ 'xvwtv u}= QO "Ovm|t Ci= COW x@B-2 |xvwtv QO "OwW|t |Q}PBpmW V}=Ri= Ea=@ xm OwW|t s=Hv= |OvmxOWv xOy=Wt Q}D Q} R w wryB QO |rw] |=yOQor}t O=ODt= QO |mQD xvwoI}yxOw@ OQor}t 7|oO}WmuwQ}@ CUmW Owt R= |W=v OQor}t VRer 'u}=Q@=v@ "CU=

"CU=QO xm Cw=iD u}= =@ 'CU= B-1 |xvwtv x@=Wt ,=@} QkD B-3 |xvwtv CUmWxrYw O=ODt= QO lQD VQDUo '|@v=H |=yOQor}t OwHw Cra x@ B-3 |xvwtvxrYw |=yDv= wO R= x}rw= |=ylQD 'xvwtv u}= QO "OQ}o|t s=Hv= |H} QOD CQwYx@

"|y=oW}=tR; |=yxvwtv CUmW w |oOQwNlQD |ovwoJ "4 pmW

sDWy |O=R; |xHQO CmQL |xvt=O xm CU= sRq QmPD u}= "CU= xOW x�=Q= xvwtv|xHQO u}= |xvt=O 'u}vJty "OW Oy=wNv QiY u=Uwv pw= Owt 5 R= l}I}y QO

"CU= QDW}@ |O=R; C=HQO Q}=U R= sHvB w swO Owt QO |O=R;"OwW|t u;|}=Q}tV}=Ri= w|DNUVy=m?@U 'xR=U QO CQ=UN w lQD OwHwR= "Ot=Hv=|t xR=U |v=Uwv |=yOwt Q}}eD w |a}@] |=yOt=U@ Vy=m x@ |oS} w u}=|}=yv pmWQ}}eD =DT} wQU OL pmWQ}}eD u}@ |xrY=i 'Q}PBpmW Q}Dl} QO xm =Hv;xm OyO|t MQ |}xOWpQDvm w xOQDUo |=ylQD xrY=i u}= QO 'CU= O=} R CUmW

"CU= xDU@=w |a}@] |=yOt=U@ Vy=m =@C=YNWt 'u}=Q@=v@ "CU= pYDt Vi=Q]= \}Lt x@ |ak=w |xR=U l} ,qwtat|Dkw "OQ=O |oDU@ R}v u; |RQt \}=QW x@ xR=U OwN Q@ xwqa xR=U |m}t=v}O|R=UxO=t; |}xvwo x@ xR=U ,qwtat 'OW=@ Q_vOt x=oW}=tR; QO FRF |Q}oxR=Ov=pt=m |R=UxO=}B "OwW |R=Ux}@W u; |=Q@ Q=OQ}o =} w O=R; |RQt \}=QW =D OwW|tCkO =@ u=wD|t =Q \}=QW u}= "CU}v umtt ,qta Q=OQ}o =} w O=R; |RQt \}=QWQO Q=OQ}o |RQt \}=QW O=H}= "OQm xO=}B |@} QkD CQwYx@ x=oW}=tR; QO |rwkatOvv=t sQv x=ox}mD R= xR=U j}raD =@ O=R; |RQt \}=QW |rw 'CU= pmWt x=oW}=tR;O}rwD R}v ?rY sUH CmQL Owt OvJ =} l} Cr=L u}= QO "OwW|t |R=Ux}@W QvixR=U u=UWm Owt u}rw= R= |i=m |xR=Ov= x@ ?rY |=yOwt |a}@] Ot=U@ "OwW|tQ=Owtv xm |DQwY QO Owt Qy 'Ot=U@ CUQO X}NWD |=Q@ [20]"OvDUy QDlJwm\w@ Qt Owt pmW STAR Q=Ri=sQv R= xO=iDU= =@ 'OW=@ xOW |}xN=W OvJ FRF

Oy=wN XNWt xOWs}UQD Owt pmW |wQ R= "OwW|t G=QNDU= O}OWD |xrk Qy x@|=yx=oDUO 3 w 2 |=ypmW "CU= Owt s=Om x@ \w@ Qt |Ot=U@ |xrk Qy xm OW

"OvyO|t u=Wv =Q VHvU sR=wr \=@DQ= |ovwoJ w p=Owt V}=tR;

"xr=v=m wO Qop}rLD x@ MU=B w wQ}v p=kDv= |ovwoJ "2 pmW

"p=Owt V}=tR; |=yx=oDUO "3 pmW

29

"""|=yOQ

or}t=@xO

WKrUt

Q=OxrYw

|=yQ}DQ

=DiQ|U

QQ@|}=yxvwtv xm CU= QmP p@=k "OyO|t u=Wv FRP |=yOQor}t uOWxQ=B x@ C@Uv|QDq=@ |Q}PBpmW 'CU= xOW xO=iDU= |@v=H OQor}t R= =yv; |xrYw |x}L=v QO xm

"Ov=xDW=O xrYw uwO@ |=yxvwtv x@ C@Uvw CU= xOW x@U=Lt �utest� =yxvwtv |y=oW}=tR; |oDUw}B Ctw=kt 'xt=O= QO[22]'ACI440 1R-03 w 5 |x]@=Q R= xOWx@U=Lt|oDUw}B |=yCtw=kt =@TBU=yxvwtv |=Q@ �utest�|oDUw}BCtw=kt "OvwW|t xU}=kt �uACI w uEsf ?}DQD x@�

%O};|t CUOx@ 14 |xrO=at R=

utest = Abftest�dbLd

(14)

QDlJwm xQ=wty =yOQor}tVvD xmCU= xOW u}}aD |Qw] xrYw pw] xmv}= x@ xHwD =@VvD u=wD|t 'OyO |wQ |WRer |oDN}Uo w OW=@ |Q=Wi CUmW pO=at VvD R=u}= "OQw; CUOx@ KrUt uD@ |WtN `]=kt |Q}tN� u=UWm \@=wQ R= =Q =yOQor}t

[13w12]"Ov=xOQm x}YwD w xO=iDU= u=QoWywSB ,q@k =Q xr�Ut

ftest = Mtest

Af jd(15)

"CU=Mtest = 0 7Ptest=2 =@ Q@=Q@ w CUmW |�=yv QovrMtest 'x]@=Q u}= QO`]kt sw=kt Qovr |wR=@ jd w FRP |WWm |=yOQor}t `]kt K]U Af 'u}vJty

"CU=

|m}D=DU= V}=tR; G}=Dv "3"5QO "Ov=xOW GQO 3 pwOH QO =yxvwtv |oDUw}B Ctw=kt w |Q}PBpmW G}=Dv|oDUw}B VvD x@ |y=oW}=tR; |oDUw}B VvD C@Uv 'pwOH u}= 9 w 8 |=yuwDU|oDUw}B VvD x@ |y=oW}=tR; |oDUw}B VvD C@Uv w �utest=uEsf � |D=@U=Lt�utest=uEsf � C@Uv u}ov=}t "CU= xOt; �utest=uACI � =m} Qt; |xt=vu}};OvyO|t u=Wv Q}O=kt u}= "CU= 0 25 Q=}at R= h=QLv= w 1 15 =yxvwtv s=tD |=Q@[22]'ACI440 1R-03 R= QDy@ w |@ wN ,=D@Uv CkO =@ |O=yvW}B |x]@=Q xm'pwOH u}= 12 uwDU QO "Ovm|t |v}@V}B =Q FRP |=yOQor}t |oDUw}B Ctw=ktxHwD =@ "CU= xOt; VywSB u}= QO xOWV}=tR; |=yxvwtv |Q}PBpmW XN=WOQor}t uwO@ |xvwtv |Q}PBpmW xm OwW|t xOy=Wt '3 pwOH 12 uwDU x@Q@=Q@ B-2 |@v=H OQor}t |=Q=O |xvwtv |Q}PBpmW w 1 17 Q@=Q@ B-1 |@v=HV}=Ri= Ea=@ xrYw pw] QO |@v=H OQor}t xm OyO|t u=Wv w CU= 1 37CUmW Owt Q}}eD Ea=@ 'xrYw pw] QO |@v=H OQor}t "CU= xOW |Q}PBpmWB-2 |xvwtv QO OQor}t |oO}WmuwQ}@ x@ B-1 |xvwtv QO uD@ VWwB Ci=mW R=QO xOWpQDvm CQwYx@ OQor}t VRer O=H}= Ea=@ Owt Q}}eD u}= "CU= xOWxO=O V}=Ri= =Q u; |Q}PBpmW xm CU= xOW B-2 |@v=H OQor}t |=Q=O xvwtv

"CU==@ w OQD CUmW l} 'OQor}t |oQ=B Cra x@ �xrYw uwO@� B-7 |xvwtv QO^=Lr R= xm �Q=OxrYw� B-6 w B-5 |=yxvwtv QO "CU= xO=Di= j=iD= sm |Q}PBpmWs=ovy QO OQor}t VRer Cra x@ 'Ov=x@=Wt B-7 =@ uD@ Ctw=kt w OQor}t Q]k

"CU= xOt; CUOx@ |}q=@ |Q}PBpmW CUmW|Q}PBpmW xm OwW|t xOy=Wt 3 pwOH 12 uwDU w 5 pmW |=yQ=Owtv R=xrYw uwO@ |=yxvwtv R= 'xrYw pw] QO |@v=H OQor}t |=Q=O w Q=OxrYw |=yxvwtv|xvwtv |Q}PBpmW xm OwW|t x_Lqt 3 pwOH QO 12 uwDU x@ xHwD =@ "CU= QDy@pw] =@ B-5 |xvwtv |Q}PBpmW R= QDW}@ QDt|Dv=U 16 1 |xrYw pw] =@ B-6

|WtN |=ylQD '|H} QOD |=ylQD O=H}= w |Q=PoQ=@ V}=Ri= R= TB w Ov=xOW O=H}=Ci= Q=@ uD@ VWwB Ci=mW R= TB w Ov=xOW jLrt sy x@ xrYw pw] O=ODt= QO

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�References� `@=vt1. Cawley, P. and Adams, R.D. \The location of defects

in structures from measurements of natural frequen-cies", Journal of Strain Analysis for Engineering Design,14(2), pp. 49-57 (1979).

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16. Tighiouart, B., Benmokrane, B. and Mukhopadhyaya,D. \Bond strength of glass FRP rebar splices in beamsunder static loading", Construction and Building Mate-rials, 13(7), pp. 383-392 (1999).

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35

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19. Harajli, M. and Abouniaj, M. \Bond performance ofGFRP bars in tension: Experimental evaluation and as-sessment of ACI 440 guidelines", ASCE, J. Compos.Constr., 14(6), pp. 659-668 (2010).

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22. ACI Committee 440, Guide for the Design and Con-struction of Concrete Reinforced with FRP Bars. ACI440.1R-03, American Concrete Institute (ACI), Farm-ington Hills, Detroit, 42 pp, (2003).

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Abstract

Fiber-Reinforced Polymer (FRP) bars can be used as areinforcing material by nature corrosion resistant. Thesebars have high tensile strength and appropriate dura-bility but are linear elastic up to failure and not duc-tile. Also, the bond strengths of lap-spliced concretebeams reinforced with steel and GFRP bars are di�er-ent because of the elastic modulus and the surface con-ditions of these bars. These parameters a�ect the non-uniformity of bond stress along the spliced length of lap-spliced concrete beams reinforced with GFRP bars. Dif-ferent studies show that by using an appropriate amountof transverse reinforcement, satisfactory bond strengthand ductility response can be obtained. Some studiesconcluded that the bond strength of FRP bars is lessthan that of steel bars and the modulus of elasticity isthe most signi�cant parameter in the reduction of bondstrength. In this paper, a previous proposed equationwhich accounts for the modulus of elasticity of reinforc-ing bars in bond strength is modi�ed for FRP bars. Themodi�ed equation is compared with experimental resultsand ACI440.1R-03 provisions. The results show thatthe bond strengths calculated with the modi�ed equa-tion correlate well with the experimental values. In theexperimental part of the study, seven beam specimenswere manufactured and tested. Laboratory specimenswere designed with di�erent parameters of splice length,concrete compressive strength, amount of transverse re-inforcement along the splice length and the diameter oflongitudinal bars. Static test is carried out for caus-

ing damage in di�erent levels of loading. The cracks ofthe specimens were mapped and test observation wasrecorded during loading steps and at the time of fail-ure. Also, the relationships of force versus mid-span dis-placement were obtained using the static tests. Then thebond strength and the ductility of specimens were ana-lyzed. At each step of loading, a modal test was carriedout to obtain the dynamic parameters of the specimens.Changes in the dynamic parameters are evaluated bymodal test results between di�erent steps of loading.

The results show that the ductility is increased by in-creasing of transverse reinforcement and splice lengthand concrete compressive strength. The bond failuremode alters from splitting to pullout due to an appro-priate amount of transverse reinforcement. This alter-ation controls the slip of bars and increases the duc-tility. Frequency reduction of specimens with splittingfailure is lower than that of specimens with pullout fail-ure. Also, frequency reduction increases with increasein transverse reinforcement along splice length of lap-spliced beams. The spliced specimens with an appropri-ate amount of transverse reinforcement are more ductilethan non-spliced specimens. This is mainly due to theslip of spliced bars in the lap-spliced specimens. In ad-dition, frequency reduction of ductile specimens is morethan that of brittle specimens in di�erent loading steps.

Key Words: modal test, bond strength, ductility, splicelength, frequency, transverse reinforcement, GFRP bars.

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STUDY ON BEHAVIOR OFLAP-SPLICED CONCRETE BEAMSREINFORCED WITH GFRP BARS BYSTATIC AND MODAL TESTSS.R. Mousavise mu15@stu-mail.um.ac.irM.R. Esfahani(corresponding author)esfahani@um.ac.irB. Mohammadzadehmohamadzad@um.ac.irDept. of Civil EngineeringFerdowsi University of Mashhad

Sharif Civil Engineering JournalVolume 29, Issue 4, Page 25-36, Original Article

c Sharif University of Technology

� Received 11 April 2011; received in revised form 10 August2011; accepted 17 September 2011.