PARAMETRIC STUDY ON MOMENT REDISTRIBUTION IN CONTINUOUS RC BEAMS USING DUCTILITY DEMAND AND DUCTILITY CAPACITY CONCEPT *

Transcription

1 Iranian Journal of Science & Technolog, Tranacion B, Engineering, Vol. 31, No. B, Prined in The Ilamic Reublic of Iran, 7 Shiraz Univeri PARAMETRIC STUDY ON MOMENT REDISTRIBUTION IN CONTINUOUS RC BEAMS USING DUCTILITY DEMAND AND DUCTILITY CAPACITY CONCEPT * D. MOSTOFINEJAD ** AND F. FARAHBOD De. of Civil Engineering, Ifahan Univeri of Technolog, Ifahan, , I. R. of Iran dmoofi@cc.iu.ac.ir Abrac Exerimenal udie how ha an indeerminae rucure or a coninuou concree beam doe no fail when criical ecion reach heir ulimae rengh. Therefore, if a rucure ha adequae ducili, re and momen rediribuion will ake lace in he flexural member b develoing laic hinge a criical ecion. Thi caue he oher oin of beam o achieve heir ulimae rengh and caaciie. Beide, momen rediribuion allow deigner o adju he bending momen diagram comued b elaic anali. The uual reul i a reducion in he value of negaive momen a he uor face a well a an increae in he value of oiive momen along he an. In he curren inveigaion, a arameric ud on momen rediribuion in coninuou RC beam wih equal an under uniform loading wa erformed. Fir, he governing equaion for he allowable ercen of momen rediribuion wa exraced uing ducili demand and ducili caaci conce. The effec of differen arameer uch a he concree comreive rengh, he amoun and he rengh of reinforcing eel, he magniude of elaic momen a he uor and he raio of he lengh o he effecive deh of he coninuou beam on momen rediribuion were hen inveigaed. Furhermore, he allowable momen rediribuion were calculaed according o he regulaion of differen code in each cae. The reul howed ha, wherea he ermiible momen rediribuion in coninuou reinforced concree beam baed on he relevan rule in he curren code i no in a afe margin in ome cae, i i raher conervaive in mo cae. Keword Momen rediribuion, reinforced concree, ducili demand, ducili caaci 1. INTRODUCTION Elaic anali of coninuou reinforced concree beam i no able o demonrae a realiic behavior of he rucure a ulimae load. According o he code, coninuou member mu be deigned o rei more han one configuraion of live load. An elaic anali i erformed for each loading arrangemen and an enveloe momen value i obained for he deign of each ecion. Therefore, for an loading aern, cerain ecion in a given an will reach he ulimae momen, while he full caaci in he oher ecion i no uilized. Exerimenal e have hown ha a rucure can carr ome addiional load in exce o i elaic caaci if he ecion ha reach heir momen caaciie coninue o roae a laic hinge and rediribue he momen o oher ecion unil a collae mechanim form. Such addiional load caaci rovide he oibili of momen rediribuion in concree rucure [1]. Momen rediribuion ermi deigner o ue he bending momen diagram comued b elaic anali and modif i o accoun for laic behavior. Uuall hi rediribuion i carried ou b decreaing he negaive momen a he fir laic hinge region, wih correonding change in he oiive momen required b he equilibrium. The change in momen ma be uch a o reduce boh he Received b he edior Aril 16, 6; final revied form December 16, 6. Correonding auhor

2 46 D. Moofinejad / F. Farahbod maximum oiive and negaive momen in he final enveloe diagram. Accordingl, momen rediribuion ma avoid reinforcemen congeion in he negaive momen region wihou an increae in he reinforcemen of he oiive momen region. The rimar exerimen regarding he momen rediribuion in coninuou reinforced concree beam were erformed b Maock in 199, and Cohn in 1964 [, 3]. Their work indicaed ha he rediribuion of he deign bending momen u o ercen doe no ignificanl change he curvaure and he crack widh in a coninuou RC beam deigned b he elaic heor. In 1993 Scholz inveigaed and verified he influence of he varing beam lenderne and iffne on he momen rediribuion in coninuou RC beam uing he ducili conce. He comared hi rooed mehod wih he allowable momen rediribuion given in he Canadian code, and concluded ha hi mehod redic more realiic reul for momen rediribuion comared o he reul of he Canadian code (CAN3-A3.3) [4]. In Lin and Chien udied he effec of longiudinal and ranvere reinforcemen on he ducili and momen rediribuion of 6 coninuou RC beam. The concluded ha he ranvere reinforcemen confine he concree and increae he ducili and momen rediribuion in he coninuou flexural member []. The aim of he curren ud i o deermine he allowable momen rediribuion uing ducili demand and ducili caaci conce. Furhermore, he influence of differen variable on he allowable momen rediribuion are inveigaed and dicued. The reul of hi ud how ha he allowable value exraced from he ducili-baed relaionhi are le han hoe ermied b code in ome cae.. RESEARCH SCOPE The curren andard in he world ae he ermiible momen rediribuion in variou form. Some of he code, i.e. CAN-A3., AS 36, BS 81 and CEB-FIP, define he allowable momen rediribuion direcl on he bai of he raio of he deh of he neural axi, c, o he effecive deh of beam, d [6-9]. ACI have limied he ercenage of he momen rediribuion o he maximum value of { 1 ( ρ ρ ) ρb }%, where ρ, ρ and ρb are he raio of he enile reinforcemen, ρ = A bd he raio of he comreive reinforcemen, ρ = A bd, and he reinforcemen raio correonding o he balance condiion, reecivel; while he rediribuion i limied o he condiion ha ρ or ρ ρ are no greaer han.ρb []. However he ACI 318- define he allowable momen rediribuion in erm of ne enile rain in exreme enile eel, ε, and exree i a ε ercen. According o hi code, he momen rediribuion i ermied if he criical ecion have adequae ducili; i.e. ε i equal or greaer han.7 a he ecion under conideraion [11]. Uing equilibrium equaion in a beam ecion, he ermiible momen rediribuion in an code could be exreed a a funcion of c / d. Such relaionhi are hown in Fig. 1 for ix differen code. I could be oberved from hi figure ha ACI 318 and CAN-A3. have limied he maximum rediribuion o he value of %, while he oher 4 code have limied he rediribuion of he momen o he maximum value of 3%. On he oher hand, he raio of c / d could be eail exreed a a funcion of he ne enile rain in he exreme enile reinforcemen, ε, uing he comaibili equaion in he rain diagram of a beam ecion. Such relaionhi are hown in Fig. for he relevan exreion in he aforemenioned 6 code. I could be een from hi figure ha ACI 318 and CAN-A3. have conidered a more conervaive afe margin for momen rediribuion comared o he oher 4 code. Iranian Journal of Science & Technolog, Volume 31, Number B Ocober 7

3 Parameric ud on momen rediribuion in 461 Momen rediribuion % 3 ACI [1 1] ACI [1 ] CAN-A3. [6] BS 811 [8] CEB-FIP [9] AS 36 [7] c / d Fig. 1. Permiible momen rediribuion veru he raio of c/d baed on differen code 3 Percen Change in Momen 3 ACI 318- [11] ACI [] CAN-A3. [6] BS 811 [8] CEB-FIP [9] AS 36 [7] Ne Tenile Srain Fig.. Permiible momen rediribuion veru he ne enile rain baed on differen code In he curren reearch, i i inended o ud he influence of differen arameer on momen rediribuion, i.e. he effec of he comreive rengh of concree, ield rengh of eel, he amoun of enile and comreive eel, he magniude of he elaic momen of he uor and he raio of he an o he effecive deh of he beam. To do o, he governing equaion of he allowable momen rediribuion in coninuou RC beam i obained wih regard o he minimum roaional caaci and he required ducili in he laic hinge region. Aferward, he effec of he aforemenioned arameer on he amoun of momen rediribuion are inveigaed and he reul are comared wih he limiaion of he momen rediribuion rovided b ACI 318- and he relevan requiremen in ome oher code. 3. CONVENTIONAL MOMENT REDISTRIBUTION Figure 3 illurae an inernal an of a coninuou reinforced concree beam wih lengh L, ubjeced o uniforml diribued load W. The maximum momen a he uor and he mid-an of he beam obained from he elaic anali for a aricular loading configuraion are M e, and M e, reecivel. A hown in Fig. 3 hee value will be reecivel changed o M u and M u afer comleion of rediribuion. The ercenage of momen rediribuion in he negaive momen region, R, i defined a follow: R = M M / M (1) ( e u ) e From Eq. (1), M u can be exreed in erm of he ercenage of momen rediribuion, R, and he elaic momen a he uor, M ; e M u = M ( 1 R ) () e Ocober 7 Iranian Journal of Science & Technolog, Volume 31, Number B

4 46 D. Moofinejad / F. Farahbod Plaic Hinge W Plaic Hinge EI L θ L P φu z φ Fig. 3. Elaic and inelaic momen 4. DUCTILITY DEMAND Aume ha he coninuou beam in Fig. 4 ha a conan iffne EI, and rimaril he laic hinge ake lace a he uor; alo aume an elao-laic bilinear momen-curvaure for he beam. Therefore, he demand value of laic hinge roaion uing he momen area mehod a hown in Fig. can be exreed b; d L WL θ = = ( θ θ ) M u EI (3) 1 where E i he modulu of elaici, I i he momen of ineria of he beam, and θ P and θ P are illuraed in Fig.. W Mu Me M ' e M ' u z L Fig. 4. Plaic hinge roaion and curvaure Mu W θ d Mu W = + θ 'P Mu θ '' Mu WL /8EI L L/ Mu /EI L L/ Fig.. Demand roaion uing momen area mehod The relaionhi beween he available laic hinge roaion and he curvaure of a criical ecion i given b [1]; a θ = ( φ φ ) L (4) where φ u i he curvaure a ulimae, φ i he curvaure a ield, and LP i he effecive lengh of he laic hinge (Fig. 4). Beide, baed on he bi-linear momen-curvaure diagram for he beam ecion, i i oible o exre he ecion curvaure a ield a; Iranian Journal of Science & Technolog, Volume 31, Number B Ocober 7 u

5 Parameric ud on momen rediribuion in 463 φ = M u EI () To have ufficien ducili for he occurrence of full momen rediribuion in a coninuou beam, θ mu be equal or greaer hanθ d. To mee hi requiremen and ubiuing he EI value from Eq. () ino Eq. (3), i can be aed; L WL φ ( φ u φ ) L φ (6) 1M u a Subiuing φ u L WL 1+ 1 φ L 1M u M u from Eq. () ino Eq. (7) will reul in: where φ φ i he ducili demand curvaure. u φ u L ( WL 1) 1+ 1 φ L M e(1 R ) (7) (8). DUCTILITY CAPACITY The curvaure of a beam ecion a i ulimae behavior wih reec o he rain diagram a failure i; φ = c (9) u ε cu wih ε. 3 a he ulimae rain of concree. The curvaure a ield i obained a; cu ( f E ) [ d( 1 k) ] φ = () where f and E are ield re and modulu of elaici of eel, reecivel; d i effecive deh. The value of k, he raio of he deh of he neural axi o an effecive deh of a beam ecion a he verge of he ield of reinforcemen could be obained a follow [1]: d 1 k = [( ρ + ρ ) n + ( ρ + ρ ) n ( ) n d ] ρ + ρ (11) wih n = E Ec and d equal o he diance from comreion eel o he exreme comreion fiber. Dividing Eq. (9) b Eq. (), he ducili caaci index will be calculaed a follow: The relaionhi beween indicaed a; φu ε cu (1 k) η φ = = (1) φ ( f E )( c d) c d and ε uing comaibili equaion of rain, a hown in Fig. 6, can be c d = ε ( ε + ε cu ) (13) where d i he diance from he exreme comreion fiber o he exreme enion eel. Furhermore, he raio of c d could be obained a follow: c d = d d)[ ε ( ε + ε )] (14) cu ( cu cu Subiuing he value of c d in Eq. (1), he raio of φ u φ will be found o be a follow: φu ( ε + ε cu )(1 k) η φ = = () φ ( d d)( f E ) Ocober 7 Iranian Journal of Science & Technolog, Volume 31, Number B

6 464 D. Moofinejad / F. Farahbod Fig. 6. Sre and rain diribuion of beam ecion a ulimae 6. ALLOWABLE MOMENT REDISTRIBUTION Sufficien roaional caaci and adequae ducili for momen rediribuion of flexural member will be rovided, if ducili caaci would be a lea equal o ducili demand. Equaing he righ ide of inequali (8) and Eq. (), he allowable momen rediribuion R i exraced a: R = 1 L M e L WL 1 ( ε + ε cu )(1 k) ( d )( ) d f E The variaion in he allowable momen rediribuion veru he ne enile rain in exreme enile eel of he beam ecion i hown in Fig. 7. For a coninuou beam wih equal an, L L P = 38, f = 4 MPa, ε cu =. 3, d = d and he elaic momen of uor M e = WL 1. Figure 7 illurae adequae agreemen beween he momen rediribuion curve obained from Eq. (16) and reference [13]. I could be een from hi figure ha he ACI 318- code rovide an adequae margin of momen rediribuion, while he oher andard reen exceive and higher value of rediribuion; for examle AS 36 and CEB-FIP how high value of momen rediribuion for ε =.1. and ε =.., reecivel. Noe ha Eq. (16) could alo be direcl ued for momen rediribuion in coninuou reinforced concree beam rovided for he conrol of erviceabili requiremen. (16) Percen Change in Momen ACI 318- [1 1] ACI [1 ] CAN-A3. [6] CEB-FIP [9] AS 36 [7] Eq. 1 6 & L/L=38 Reference [1 3] Ne Tenile Srain Fig. 7. Variaion of ermiible momen rediribuion veru ne enile rain in exreme enile eel baed on differen code 7. EFFECT OF L d RATIO ON MOMENT REDISTRIBUTION A indicaed in Eq. (16), he ermiible momen rediribuion i relaed o L L. To inveigae he effec of he raio of he beam an o he effecive deh of he beam, L d, on he amoun of he momen rediribuion in a coninuou beam, he lengh of he laic hinge, L, mu be quanified. Iranian Journal of Science & Technolog, Volume 31, Number B Ocober 7

7 Parameric ud on momen rediribuion in 46 a) The laic hinge lengh Variou exreion have been rooed for deermining he equivalen lengh of he laic hinge; ome of hem are ummarized a follow [1]: Baker, 1964: 1 4 L P = k k ( z d d [mm] (17) 1 3 ) where k 1 i aken equal o.7 for mild eel, k 3 i aken equal o.6 when f = 3. MPa, and.9 when fc = 11.7 MPa; d i he effecive deh of he beam; and z i he diance of criical ecion from he oin of inflecion in he bending momen diagram. Sawer, 1964 L P =.7z +. d [mm] (18) Maock, 1967 L =.z +. d [mm] (19) Paula and Priele, 199 [14]: f i he ield rengh of eel and where Leman e al, 1998 []: P L =.8z +. f d. 44 f d [mm] () b d b i he diameer of longiudinal eel. L =.α z + 1.α ( f 4 f ) d [mm] (1) u u c b b M u M α = () M where f u i he ulimae rengh of eel, f c i he comreive rengh of concree, a he fir ield of enile eel and M u i he ulimae momen of beam ecion. Panagioako and Fardi, 1 [16]: P b c M i he momen L =.1z f d [mm] (3) I could be een ha he lengh of he laic hinge in Eq. (17) o (19) i defined in erm of z and effecive beam deh, d ; while L in Eq. () o (3) i comried of he effec of he arameer z and he anchorage li of longiudinal reinforcing bar. b) The relaionhi beween L d and L L To deermine relaion beween L d and L L, i i required o fir calculae z. For racical cae, in a coninuou beam wih equal an under uniform loading, z varie from.l o.l for M u = WL 16 o M u = WL 1, reecivel. Beide, he ACI 318- code limi he raio of lengh o he effecive deh of he coninuou beam, L d, o he maximum value of 1 for deflecion. Since h varie from 1.1d o 1.d in convenional beam; herefore, L d will be limied o he maximum value of. Hence, for calculaing L baed on Eq. (17), ubiuing k1 =. 7 and auming z =. L and an average value of. 7 for k 3, he laic hinge lengh, L, will be equal o L P = (.)(.L) d (4) 3/ 4 L L P =.8483( L d) (Baker equaion) () Ocober 7 Iranian Journal of Science & Technolog, Volume 31, Number B

8 466 D. Moofinejad / F. Farahbod Furhermore, auming z =. L in Eq. (18) and (19), L L will be a follow for Sawer and Maock exreion, reecivel; L L P = 1 (. +. d L) (6) L L P = 1 (. +. d L) (7) Similar equaion could be obained for L L, wih he aumion of z =. L ; for inance uing Eq. (18), L L will equal o; L L P = 1 (.1 +.d L) (Sawer equaion) (8) The amoun of L L have been calculaed and reened in Table 1 for L d =, and, according o Baker, Sawer, and Maock equaion and for z =. L and.l. Furhermore, auming L = 8 mm, d b = mm and f = 4 MPa, he raio of L L ha been reened in hi able, baed on Eq. () and (3). A hown in Table 1, exce for Sawer equaion ha indicae higher value for L L, he oher redicion of L L are cloe ogeher. Table 1. Raio of L L for differen value of z z L/d L/L Eq. () L/L Eq. (6) L/L Eq. (7) L/L Eq. () L/L Eq. (3).L.L Figure 8 illurae he variaion of he ermiible momen rediribuion in erm of ε, baed on Eq. (16), auming f = 4 MPa and M e = WL 1, for z =. L and for differen value of L d. To draw Fig. 8, Eq. (6), which i baed on Sawer equaion, wa ued for he relaionhi of L L and L d. A hown in Fig. 8, he ermiible momen rediribuion decreae when he raio of L d increae. Furhermore, i could be oberved in hi figure ha CAN-A3. and AS 36 code iml exceive rediribuion for ε <. and ε =.1., reecivel. Percen Change in Momen 3 3 Eq. (6), L/d= & L/L=4 Eq. (6), L/d= & L/L=36 Eq. (6), L/d= & L/L=3 Eq. (8), L/d= & L/L=47 ACI 318- [11] CAN-A3. [6] AS 36 [7] Ne Tenile Sre Fig. 8. Allowable momen rediribuion for differen raio of L/d The variaion of ermiible momen rediribuion for z =. L, L d = and L L = 47, ha been alo indicaed in Fig. 8. I could be een from hi figure ha for high level of L L, e.g. Iranian Journal of Science & Technolog, Volume 31, Number B Ocober 7

9 Parameric ud on momen rediribuion in 467 L L = 47, ACI 318- rovide a afe margin for momen rediribuion, while oher code like CAN-A3. and AS 36 give higher amoun of rediribuion in he ame condiion. 8. EFFECT OF CONCRETE COMPRESSIVE STRENGTH To evaluae he effec of he comreive rengh of concree on momen rediribuion in coninuou beam, i i required o deermine he relaion of ε and f c. A hown in Fig. 9, auming ρ = and uing he rain comaibili rincial, Eq. (14) can be rewrien a below: c d = d d)[ ε ( ε + ε )] = ( ρ f ) (.8 f β ) (9) ( cu cu c 1 ε + ε ) ( d d) = (.8β f ε ) ( ρ f ) (3) ( cu 1 c cu Subiuing Eq. (3) ino Eq. (16) and auming ε cu =.3 and momen rediribuion i obained in erm of f c ; MPa E =, he ermiible R = 1 M e L L ( WL 1) β 1 fc (1 k) ρ( f ) (31) Figure 9 how he ermiible momen rediribuion in erm of ε for variou amoun of f c, auming f = 4 MPa, L L = 38 and M e = WL 1. I could be een from Fig. 9 ha higher value of f c rovide higher amoun for oible momen rediribuion. Such a reul i alicable for concree rengh which coml wih he code aumion on comreion re block arameer. Furhermore, Fig. 9 how ha for low value of concree comreive rengh, i.e. f c = 17 MPa, ACI 318- overeimae he ermiible momen rediribuion; alo he oher curren code like CAN- A3.., AS 36 and CEB-FIP, allow for higher amoun of momen rediribuion, comared o he quaniie aken from heoreical anali. Percen Change in Momen 3 3 f ' c=3 & f=4 MPa f ' c= & f=4 MPa f ' c= & f=4 MPa f ' c=1 7 & f=4 MPa ACI [11] CAN-A3. [6] AS 36 [7] CEB-FIP [9] Ne Tenile Srain Fig. 9. Permiible momen rediribuion veru ne enile rain of eel for variou concree comreive rengh 9. EFFECT OF YIELD STRENGTH OF STEEL The ield rengh of eel i couned a an influenial arameer on momen rediribuion in RC coninuou beam. Auming M e = WL 1 and L d =, he ermiible momen rediribuion in erm of rain ε, for f = 4 and MPa i indicaed in Fig.. I could be een from Fig. ha a Ocober 7 Iranian Journal of Science & Technolog, Volume 31, Number B

10 468 D. Moofinejad / F. Farahbod long a he ield rengh of reinforcing eel i no greaer han ha of convenional eel, i.e. f 4 MPa, he ACI 318- code ermi for momen rediribuion in a afe margin, while he oher andard, i.e. CAN-A3. and AS 36 allow for higher amoun of rediribuion. However, for higher value of f, all code ma overeimae he amoun of ermiible momen rediribuion, eeciall when he beam i deigned in uch a wa ha i enile reinforcemen i no much enioned. Percen ercen Change Change in in Momen Momen f=4 M Pa & L/d= f= M Pa & L/d= 3 f= M Pa & L/d= 3 ACI 318- CAN-A3. [6] AS 36 [7] Ne Tenile Sre Fig.. Permiible momen rediribuion for differen value of ield rengh of reinforcing eel. EFFECT OF THE AMOUNT OF REINFORCING STEEL The amoun of enile and comreive reinforcing eel in a coninuou beam alo affec on he oible momen rediribuion. For an under-reinforced concree ecion which i hown in Fig. 6, uing equilibrium and comaibili equaion and olving he reuling equaion wih reec o he neural axi deh, c, he following equaion could be obained; c = ( ρf.3ρ de ) + ( ρf.3ρ E ) fc β1(.3ρ Ed / d ) d 1.7β f 1 c (3) where ρ and ρ are he enile and comreive reinforcemen raio, reecivel; and d and d are reecivel he diance of enile and comreive eel from he exreme comreion fiber in concree. fc 6 Subiuing c from Eq. (3) ino Eq. (14) and uing he balanced eel raio a ρ b =.8β1, f 6 + f he following equaion i exraced; ε + ε d d cu = ρb ( f + 6)( f 6) ( ρf.3ρ E ) + ( ρf.3ρ E ) f β (.3ρ E d d ) Equaion (33) accomanied b Eq. (16) can be ued o how he effec of he amoun of eel reinforcemen on he oible ercenage of momen rediribuion. Uing hee equaion and auming f = 4 MPa, L L = 38 and M e = WL 1, he ermiible momen rediribuion in erm of ρ ρ b i calculaed and illuraed in Fig. 11 for differen raio of comreive and enile eel. Figure 11 how ha increae in he raio of enile reinforcemen o he balanced reinforcemen, ρ ρ b, decreae he allowable momen rediribuion. Furhermore, increaing he amoun of comreive reinforcemen, ρ, increae he amoun of he momen rediribuion. I could be oberved from he figure ha ACI 318-, deie he oher code, rovide acceable amoun of momen rediribuion for differen combinaion of ρ ρ and ρ ρ. Neverhele, he rocedure of b c 1 (33) Iranian Journal of Science & Technolog, Volume 31, Number B Ocober 7

11 Parameric ud on momen rediribuion in 469 ACI 318- lead o ver conervaive value of momen rediribuion for low raio of raio of ρ ρ. Percen Change in Momen 3 ρ ' / ρ = 3 ρ ' / ρ =. ρ ' / ρ =. ρ ' / ρ =.7 ρ ' / ρ = 1. ACI 318- [11] CAN-A3. [6] AS 36 [7] Tenion Seel Raio ( ρ ρ b ) Fig. 11. Permiible momen rediribuion veru he enile eel raio, for differen value of comreive eel 11. EFFECT OF THE ELASTIC MOMENT OF SUPPORT ρ ρb and high To inveigae he effec of he amoun of elaic momen of uor on he momen rediribuion baed on Eq. (16), he variaion of he ermiible momen rediribuion in erm of ε for L L = 38, M e = WL 11 and M e = WL 1 i hown in Fig. 1. Noe ha in convenional coninuou beam, he negaive elaic momen a he face of inernal uor normall varie wihin WL 11 and WL 1. I could be een from Fig. 1 ha if he elaic momen in he uor region of a reinforced concree beam increae, he ermiible momen rediribuion in he beam would alo increae. Figure 1 how ha for a aricular ne enile rain of ε =., he ercenage of rediribuion in momen are 8% and 34% for elaic momen of he uor equal o WL 1 and WL 11, reecivel. However mo code including ACI 318- and CAN-3. limi he maximum ermiible momen rediribuion o %, robabl o reven he evere roagaion of he crack under erviceabili condiion. Neverhele, ome oher code including AS 36, BS 81 and CEB-FIP allow for rediribuion of he momen u o 3% [7-9]. 3 Percen change in momen 3 Eq. (16) & M e=wl /1 Eq. (16) & M e=wl /11 ACI 318- CAN-A3. [6] AS 36 [7] BS 81 [8] CEB-FIP [9] Ne enile rain Fig. 1. Permiible momen rediribuion for differen value of uor elaic momen 1. SUMMARY AND CONCLUSIONS In he curren ud, uing ducili demand and ducili caaci conce, he effec of differen arameer on he momen rediribuion of reinforced concree coninuou beam wih equal an, under uniform loading were inveigaed. Providing minimum roaional caaci in he laic hinge region of he beam, he coniuive equaion of ermiible momen rediribuion in erm of ne enile rain, ε, a well a in erm of raio of enile and comreive reinforcemen wa obained. The variaion of Ocober 7 Iranian Journal of Science & Technolog, Volume 31, Number B

12 47 D. Moofinejad / F. Farahbod ercen change in momen rediribuion wih regard o ome arameer were drawn and comared wih he roviion of ome curren andard including ACI 318-, CAN-A3., AS 36, BS 81 and CEB-FIP code in ome cae. The reul of hi ud wihin he aumion which were made in he anali are ummarized a follow: 1. Increaing he ne enile rain in exreme enile eel increae he ermiible momen rediribuion value.. Increaing he raio L d and L L, and uilizing he convenional equaion for he eimaion of he laic hinge lengh, decreae he ermiible momen rediribuion. 3. The ermiible momen rediribuion i decreaed b decreaing he concree comreive rengh; alo, i i decreaed b he increae of ield rengh of enile reinforcemen. Furhermore, increae in enile reinforcemen raio, decreae he value of ermiible momen rediribuion. 4. Comreive eel advanageoul affec on momen rediribuion enhancemen. The higher raio of comreive o enile reinforcemen in he beam ecion augmen he oible momen rediribuion.. The ermiible momen rediribuion would enhance b increae in he elaic momen of uor. 6. Alhough he ACI 318- code exhibi a afe margin for ermiible momen rediribuion in mo cae: he code roviion lead o higher amoun of momen rediribuion in ome cae; for inance, in coninuou beam wih high raio of L d and eel ield rengh, or in beam wih low comreive rengh of concree. Furhermore, oher curren code, i.e. Canadian, Auralian and Euroean andard rovide exceive value of momen rediribuion for he cae whenε <., ε >. 1 and. < ε <., reecivel. 7. Proviion of he curren code including ACI 318-, CAN-A3. and AS 36 lead o ver conervaive value for momen rediribuion in ome cae, i.e. in coninuou reinforced concree beam wih enile and comreive reinforcemen wih he raio of ρ ρ >.. 8. Comared o he roviion of he code, higher value of momen rediribuion could be obained for coninuou reinforced concree beam wih high value of ε a ulimae; however, i ma no be adviable o uilize hee value due o evere crack roagaion a he erviceabili age. REFERENCES 1. Noe on ACI 318-, (). Building code requiremen for rucural concree wih deign alicaion. PCA, USA.. Maock, A. H. (199) Rediribuion of deign bending momen in reinforced concree coninuou beam, Proceeding, Iniuion of Civil Engineer (London), Vol. 13, Cohn, M. Z. (1964). Roaional comaibili in he limi deign of reinforced concree coninuou beam. Proceeding, Inernaional Smoium on he Flexural Mechanic of Reinforced Concree, ASCE-ACI, Miami, Scholz, H. (1993). Conribuion o rediribuion of momen in coninuou reinforced concree beam, ACI Sruc. J., Vol. 9, No.,. -.. Lin, Chien-Hung, & Chien, Yu-Min. (). Effec of ecion ducili on momen rediribuion of coninuou concree beam, Journal of Chinee Iniue of Engineer, Tranacion of he Chinee Iniue of Engineer, Vol. 3, No., CAN-A3.. (1994). Code for he deign of concree rucure for building, Canadian Sandard Aociaion. Iranian Journal of Science & Technolog, Volume 31, Number B Ocober 7

13 Parameric ud on momen rediribuion in AS 36, (1994). Auralian concree rucure andard. Sandard Auralia, Sdne, Auralia. 8. BS 81, (199) Srucural Ue of Concree-ar 1, Briih Sandard Iniuion. 9. CEB-FIP, (199). Inernaional em of unified andard code of racice for rucure. Model Code for Concree Srucure, Euroe.. ACI , (1999). Building code requiremen for rucural concree (ACI ) and commenar-aci 318 RM-99. ACI, Farmingon Hill, MI, USA. 11. ACI 318-, (). Building code requiremen for rucural concree (ACI 318-) and commenar-aci 318 R-. ACI, Farmingon Hill, MI, USA. 1. Park, R. & Paula, T. (197). Reinforced concree rucure. John Wile & Son. 13. Ma, R. F. (199). Unified deign roviion for reinforced and rereed concree flexural and comreion member. ACI Sruc. J., Vol. 89, No., Paula, T. & Priele, M. J. N. (199). Seimic deign of reinforced concree and maonar building. John Wile & Son, New York.. Leman, D. E., Calderone, A. J. & Moehle, J. P. (1998). Behavior and deign of lender column ubjeced o laeral loading. 6h US Naional Conference on Earhquake Engineering, EERI, Seale, Wahingon, Ma Panagioako, T. & Fardi, M. N. (1). Deformaion of RC member a eilding and uimae. ACI Sruc. J., Vol. 98, No., Ocober 7 Iranian Journal of Science & Technolog, Volume 31, Number B