Nominal Flexural Strength of High Strength Fiber Reinforced Concrete Beams

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1 Nominal Flexural Strength o High Strength Fier Reinorced Concrete Beam F.B.A. Behara, I.G. Shaaan, and.s. Mutaa Civil Engineering Department Banha Univerity, Faculty o Engineering at Shora Cairo Egypt ABSRAC: hi paper preent the development o imple emi-empirical ormulae or the analyi o nominal lexural trength o high trength teel ier reinorced concrete (HSFRC) eam. Such developed ormulae were aed on train compatiility and equilirium condition or ully and partially HSFRC ection in joint with uitale idealized compreion and tenion tre lock. he tre lock were given y uitale empirical unction or the compreive and pot-cracking trength o HSFRC. he enhancement in compreive trength due to ier incluion i propoed a a unction o concrete matrix trength and ier reinorcing index. o account or the pullout reitance o ier in tenion, the pot-cracking trength wa evaluated a a unction o ier reinorcing index and ond trength. he ier reinorcing index wa conidered a a unction o volume content, apect ratio, orientation and length eiciency actor o the ier. In view o the degenerative nature o the pullout reitance o the ier with the increae o crack width, a limit wa placed on the ueul tenile train extent; depending on ier length and crack pacing. It wa ound that there i a good agreement etween the lexural trength or HSFRC eam predicted y the propoed ormulae and the experimental reult reported in the literature, while the predicted lexural trength a computed y ACI committee (544) were very conervative. he parametric tudie indicate that the nominal moment ection capacity increae with the increae o ier content and ier apect ratio. KEY WORDS: Flexural trength, High trength concrete, Steel ier, Reinorced concrete eam. 1- INRODUCION Nowaday, dierent tructural application uch a eam, column, and connection are eing contructed uing teel ier reinorced concrete (SFRC) in comination with conventional teel reinorcing ar. When concrete crack, the randomly oriented ier arret the internal micro-cracking mechanim and limit crack propagation, and in turn, improve trength and ductility under dierent loading cheme (Shah et al., 1989). Several experimental program have een worked out (Daniel et al, 22; Altun et al; 26, Mutaa, 27) to identiy the lexural ehavior o SFRC eam. It wa ound that SFRC eam exhiit higher lexural trength, ductility and toughne propertie or longer ier and higher ier content. A hown in Fig. (1) & (2), the moment-delection curve o SFRC eam ha longer plateau at the peak load, and the decending part o curve i le teep compared to non-irou concrete eam. Moment (KN.m) v =.% v =.5% v = 1.% v = 2.% Delection (mm) Fig. 1. Eect o teel ier content on the loaddelection repone (Mutaa, 27) Moment (KN.m) l/φ=. l/φ=5. l/φ=6. l/φ= Delection (mm) Fig. 2. Eect o teel ier apect ratio on the loaddelection repone (Mutaa, 27) he exiting lexural deign approache or SFRC are aed on conventional deign method upplemented y pecial procedure or ier contriution (ACI Committee544, 1997; Altun et al; 26). Such method are oten empirical, and they may apply only to certain cae where limited upporting tet data have een otained. In (ACI Committee544, 1988; 1997), the lexural trength o SFRC ection i predicted on the ai o an equivalent rectangular compreion and rectangular tenion lock. he compreion lock i deined in term o the compreive trength o cylinder o concrete matrix while the tenion lock depend only on the ond trength o teel ier ( ). he ond trength i evaluated a 4. Mpa. A hown in Fig. (3), the aic equation or calculating the nominal moment trength (M n ) are a ollow:

2 t d' d A N.A. c d-c tu.3 e a.85c' Strain ditriution Stre ditriution Fig. 3. ACI approach (ACI committee, 1988) M n = (d a/2) + (t/2 + c/2 a/2) (1) = (t e) (2) he ditance (e) i meaured rom extreme compreion ier to top o tenile tre lock o irou concrete. hi paper preent a more realitic and emi-empirical approach or predicting the nominal lexural trength on the ai o uitale idealized tre lock and ectional analyi procedure. he theoretical prediction o the ultimate moment capacity are compared with the meaured repone or many teted eam in other reearch program mentioned in the literature. 2- EVALUAION OF HSFRC PARAMEERS o develop the propoed lexural trength tate or HSFRC eam, the compreive trength and potcracking trength o HSFRC are empirically evaluated. 2-1 COMPRESSIVE SRENGH OF HSFRC Many experimental program or SFRC under uni-axial compreive loading were worked out (Balaguru et al., 1992; ACI Committee544, 1988) to tudy the eect o teel ier addition to normal and high trength concrete matrix. ypical tre-train curve o SFRC in compreion are given in Fig. (4) where the eect o increaing ier content i hown to increae the area under the decending ranch o the curve. he eect o increaing ier apect ratio ollow the ame trend a hown in Fig. (5). he main contriution o ier incluion i ound to increae toughne, integrity and ductility o the compoite in compreion. Compreive Stre, Mpa C ontrol v = 1. % Cc v = 3. % v = 2. % Axial Strain, millionth Fig. 4. Eect o ier volume raction on compreive tre-train curve (ACI committee, 1997) Compreive Stre, Mpa Control Axial Strain, millionth l/? l/φ=1 = l/φ=6 l/? = l/? l/φ=47 Fig. 5. Inluence o ier apect ratio on compreive tre-train curve (ACI committee, 1997) o evaluate the gain in compreive trength due to ier incluion in the preent work, nine HSC cue and eighteen HSFRC cue with dierent ier content were teted ater 28 day uing the tandard compreion machine. he trength value or dierent concrete cue are given in ale (1). It i clear that the compreive trength o the compoite HSFRC ha a light increae than that o HSC matrix. hi enhancement in uniaxial trength i due to the internal paive coninement o the matrix y teel ier which alo delay the crack preading and propagation (ACI committee544, 1997). ale 1. Summery o experimental reult o tandard cue (Mutaa, 27) No. o cue Fier volume (%) Average trength (Mpa) o determine the trength gain o HSFRC, analytical expreion wa ought in term o the ier reinorcing parameter and compreive trength o HSC matrix. For thi purpoe, thee key parameter were tatitically related to the experimental data o HSFRC cue. It wa generally oerved that the leat quare itting linear relation wa quite acceptale and imple. he ollowing general orm wa ued: cu = cu ( a + I ) (3) Where cu and cu are repectively the compreive trength o HSFRC compoite and HSC matrix. he contant a and are the lope and intercept parameter o the linear itting equation. In order to account or the random patial ditriution o dicrete hort teel ier and or the ier matrix interaction, the ier reinorcing index I i conidered a a unction o ier volume content v, ier apect ratio (l /Φ), orientation and length eiciency actor η oc, η lc I = 2 η lc η oc v (l /Φ) (4)

3 In the preent work, ier length wa le than the critical ier length and wa much le than the dimenion o cue pecimen. In addition, the teting reult o SFRC conirm the act that teel ier exhiited only pull-out mechanim at increaing train. A a reult, the value o η oc and η lc a. and.5 repectively have een applied in the preent work or HSFRC in compreion. he ier reinorcing index I wa given y: I =. v (l /Φ) (5) From the tatitical analyi o the experimental reult (Mutaa, 27), the ollowing linear regreion equation wa derived to predict compreive trength o HSFRC compoite a: cu = cu ( v l /Φ) (6) 2-2 POS-CRACKING SRENGH OF HSFRC he exiting tudie on the tenile repone o SFRC in literature (ACI Committee544, 1988; Shah, 1989; Barro et al., 25), howed that the contriution o teel ier to the rittle matrix can e imulated a: igniicant increae in material ductility and toughne, and teady tate crack-width control mechanim. ypical example o the tre-crack width curve i hown in Fig. (6). It i clear that the tre-diplacement curve conit o a mall acending part ollowed y long decending otening part. Applied Load, KN Applied Load, KN V = 1%, l / = 42, l = 6mm v =1%, l/φ=42, l =6mm.5 Actual enile Repone From X - Y Recorder Diplacement, mm Actual enile Repone From X-Y Recorder Fig. 6. enile load-diplacement relationhip o SFRC Ater compoite cracking, the load i tranerred immediately to the ier at the crack interace. Due to ier deonding, the tenile tre repone in the meaured load-extenion curve aruptly drop and i arreted at a certain level y the pullout reitance o ier. hi tre level i deined a the pot-cracking trength pp. From the tenion tet on irou concrete, the pot-cracking trength i related (Lim et al., 1987) to the ond trength (τ u ), ier volume content v, ier apect ratio (l /Φ), ier length and orientation eiciency actor (η lt, η ot ) in tenion pp = 2 η lt η ot v (l /Φ) τ u (7) Diplacement, mm For the preent cae when the ier length wa le than the dimenion o eam ection, the value o η lt and η ot are.5 and.41 repectively. For the ultimate ond trength τ u, a value o 4. Mpa i adapted here (ACI Committee544, 1997). he pullout reitance pp, i given in Mpa a pp = 1.64 v (l /Φ) (8) It wa ound (Lim et al., 1987, Barro et al., 25) that the pot-cracking tre drop approximately to zero at crack extenion equal to hal the ier length. 3- PROPOSED NOMINAL FLEXURAL SRENGH APPROACH FOR HSFRC BEAMS Baed on the train compatiility & equilirium condition and uitale aumption or HSFRC eam ection, the ormulation o propoed approach are preented. According to ACI code (ACI Committee318, 25), the ultimate moment trength (M u ) i a ollow: M u = trength reduction actor x M n (9) 3-1 BASIC ASSUMPIONS OF HE APPROACH he propoed approach or lexure o HSFRC eam i aed on the ollowing aumption: Plane ection remain plane ater ending, and conequently the train ditriution i linear. he train in the reinorcement i equal to the train in concrete at the ame level which implie perect ond etween concrete and teel. For teel reinorcement in compreion and tenion, the ilinear elato-platic idealization i ued. For HSFRC in compreion, the tre ditriution i idealized y the equivalent rectangular tre lock o ACI code (ACI Committee318, 25). A uniorm tre o.67 cu i aumed to e ditriuted over an equivalent compreion zone o depth = a, given a a unction o the neutral axi depth c a = β c (1) β = ( cu / 6.9).85 β.65 (11) Baed on the tudy o platic hinge, concrete i aumed to cruh when the compreion train reache a limiting uale train which i taken a.3 (ACI Committee544, 1988). It hould e noted that much higher limiting train have een meaured in HSFRC memer. Uing a perectly platic idealization or the ehavior o HSFRC in tenion, the tenile tre rectangular ditriution i repreented y a uniorm tre which equal the pot-cracking trength pp and acting over

4 a depth o (t c). he pot-cracking trength account or the pullout reitance o teel ier. In view o the degenerative nature o the pullout reitance o teel ier with the increae o crack width, a limit i placed on the ueul tenile train extent. Hence, ε tu i et a a unction o the ier length l and the crack pacing S cr (Lim et al., 1987) ε tu = l / 8 S cr (12) Approximate value wa evaluated or crack pacing a.5t to.8t (Lim et al., 1987; Laura C., 27). he compreive and pot-cracking trength o HSFRC are evaluated y the empirical unction given eore in Section FORMULAIONS OF HE APPROACH t d d' d d' t A N.A. d-c c cu=.3 tu k cu 3 k c 2 Cc pp t-c c a=b1 c.67 pp cu Cc=.67 a a/2 Strain Actual Stre Idealized Stre Ditriution Ditriution Ditriution a) Fully Reinorced SFRC Section A N.A. d-c c cu=.3 Strain Ditriution c t a=b1 c.67 pp cu a/2 Idealized Stre Ditriution ) Partially Reinorced SFRC Section Fig. 7. Ultimate tre and train ditriution cu Cc= Baed on the aove aumption, the ultimate train and tre ditriution i hown in Fig. (7-a) or the ully reinorced HSFRC ection, and in Fig. (7-) or the partially reinorced HSFRC ection; where the teel ier i included only in the tenion ide over a depth o t, From the orce equilirium condition and train compatiility condition, the depth o the compreion lock can e determined a ollow: C c = + (13) = A () ε =.3(βd / a 1) (15) = E ε ε < ε y (16) = y ε ε y (17) cu For ully reinorced HSFRC ection, the orce C c and are given y: C c =.67 cu a (18) = 1.64 v (l / Φ) (t c) (19) For the partially reinorced HSFRC ection, the orce are given y: C c =.67 cu a (2) = 1.64 v (l /Φ) t (21) From the equilirium condition o moment, the nominal moment capacity o the ully reinorced HSFRC ection i expreed y: M n = (d βc/2) + [(t + c - βc) / 2] (22) he correponding nominal moment capacity o partially reinorced HSFRC ection i: M n = (d βc/2) + [t (t + βc)/2] (23) 4- VALIDAION AND PARAMERIC SUDIES 4-1 VERIFICAION SUDIES Uing the propoed approach, the nominal moment o everal SFRC eam are computed and compared with the experimental reult rom eight ource o literature. In ale (2), the predicted moment are compared with the teting reult or thirty nine eam. In addition, the examination o all teted and computed trength are hown in Fig. (8). he tudy o the reult lited in the tale and the igure howed that atiactory reult were otained rom the comparion o meaured and computed lexural trength. he mean value o the ratio etween the meaured and calculated trength i 1.17 and the tandard deviation i.9. he approach yield ae prediction or nominal moment capacity or normal trength and high trength irou concrete eam. Mn (tet), KN.m Mn (theoretical), KN.m Fig. 8. Correlation o the experimental and deign lexural trength or the propoed Method

5 Depite the dierence in tet pecimen, ale (2) and Figure (8) how that the propoed approach predict the lexural trength o tet pecimen reaonaly well. Data cover a road pectrum o irou eam including variation in concrete trength (34 cu 9 Mpa), teel yield tre (36 y 437 Mpa), tenile teel area (25 A 628 mm 2 ), compreion teel area ( A ' 1 mm 2 ), eam width (11 25 mm), eam depth (1 t 3 mm), ier volume content (. v 2.%), ier apect ratio (3 l /Φ 8), and ier zoning (Full, Partial). Moreover, ale (2) how that the ultimate moment capacity or irou eam increae with the increae o concrete trength, yield tre o teel, tenion teel ratio, and compreion teel ratio. he tenile train wa monitored at the extreme tenion ide and the computed value were in the range o.6 to.5. hee value have not exceeded the tenile train limit a given y Equation (12); ε tu = l / 4t. In ale (2), the lexural trength o the dierent experimental reult o irou eam are recalculated uing ACI equation. In addition, the examination o all teted and computed trength are hown in Fig. (9). he mean value o the ratio etween the meaured and calculated trength i 1.5 and the tandard deviation i.3. he tudy o the reult lited in the tale and the igure howed that ACI prediction o nominal moment capacity o SFRC ection are very conervative in comparion with the propoed method. Mn(tet), KN.m Mn(ACI), KN.m Fig. 9. Correlation o the experimental and deign lexural trength or the ACI equation 4-2 PARAMERIC AND DESIGN SUDIES Several cae tudie were perormed to demontrate the variation in the calculated lexural trength o HSFRC eam caued y the ier reinorcing parameter. he eam with v = 1.%, teted in (Mutaa, 27), wa taken a the datum eam or the parametric deign tudie. he eect o ier volume content, ier apect ratio, and ier zoning on the nominal moment i hown in Fig. (1).he tudy o the reult in thi igure indicate that or contant ier apect ratio =5, the increae o v rom.% to 2.% increae the moment capacity y 3.% or ully reinorced HSFRC eam. For the cae l /Φ = 8, the correponding increae in lexural trength i 47.%. It can alo e een rom Fig. (1) that the increae o ier apect ratio l /Φ rom 5 to 8 lead to 7.7% increae in lexure trength i v = 1.%, and to 13.5% increae in lexure trength i v = 2.%. In addition, the predicted lexural trength or partially reinorced HSFRC eam i lightly le than that o ully reinorced HSFRC eam. Mnth, KN.m FULL-l/Φ=5 PARIAL-l/Φ=5 FULL-l/Φ= v % Fig. 1. Eect o ier volume, apect ratio, and ier zoning on the predicted nominal moment o develop a lexural deign chart or ully reinorced HSFRC ection, the governing equilirium equation are rearranged and the ollowing dimenionle ormula wa derived or all grade o concrete and teel and with dierent ier reinorcing index. M n /(d 2 cu ) = µ ( y / cu ) (1-βc/2d) + ( pp / cu )[(t- c)/d][(t+c- βc)/2d] (24) he deign chart i plotted in Fig.(11). It i clear that the nominal moment capacity or a given ection increae with the increae o longitudinal teel ratio (µ) or with the increae o ier reinorcing index (I ). R=Mn/(d 2 cu ) ` W=A y / ( cu d) I=. I=.1 I=.2 I=.3 Fig. 11. Deign chart or all grade o concrete and teel with dierent ier reinorcing indice I

6 ale 2. Comparion etween experimental reult and pr INPU DAA Predicted ACI REF. x t (mm) A (mm 2 ) y Mpa v % l /Φ cu Mpa M nexp KN.m M np KN.m M nexp / M np M naci KN.m M nexp / M naci (Mutaa, 27) 12x (Mutaa, 27) 12x (Mutaa, 27) 12x (Mutaa, 27) 12x (Mutaa, 27) 12x (Mutaa, 27) 12x (Mutaa, 27) 12x (Mutaa, 27) 12x (Mutaa, 27) 12x (Mutaa, 27) 12x (Mutaa, 27) 12x (Ahour, 1997) 1x (Ahour, 1997) 1x (Lim, 1987) 1x (Lim, 1987) 1x (Lim, 1987) 1x (an, 1994) 1x (an, 1994) 1x (an, 1994) 1x (an, 1994) 1x (Al Sayed, 1993) 25x (Al Sayed, 1993) 25x (Al Sayed, 1993) 25x (Al Sayed, 1993) 25x (Ahour, 1997) 17x (Ahour, 1997) 17x (Ahour, 1997) 17x (Ahour, 1997) 17x (Ahour, 1997) 17x (Ahour, 1997) 17x (Kormeling, 198) 1x (Kormeling, 198) 1x (Kormeling, 198) 1x (Kormeling, 198) 1x (Craig, 1987) 175x (Craig, 1987) 175x (Craig, 1987) 175x (Craig, 1987) 175x (Craig, 1987) 175x OVERALL AVERAAGE OVERALL SANDARD DEVIAION.9.3

7 5- CONCLUSIONS here i a good agreement etween the computed lexural trength y the propoed ultimate trength tate or HSFRC eam, and the experimental reult o everal ource o literature. Depite the dierence in tet pecimen, concrete trength, reinorcement detail, and ier parameter, the propoed approach predict the lexural trength reaonaly well and prove the uitaility a a deign and analyi tool. he mean value o the ratio etween the meaured and calculated trength i 1.17 and the tandard deviation i.9. he predicted lexural trength a computed y (ACI committee544, 1988) are very conervative where the mean value o the ratio etween the meaured and calculated trength i 1.5 and the tandard deviation i.3. he enitivity tudie o the governing ier parameter indicate that the nominal moment capacity or a given HSFRC ection increae with the increae o ier volume raction and ier apect ratio. For dierent ier content, the predicted lexural trength or partially reinorced SFRC eam are lightly le than that o ully reinorced SFRC eam. Alo, the validation tudie indicate the increae o nominal moment capacity with the increae o concrete trength, yield tre o teel, tenion teel ratio, and compreion teel ratio. 6- REFERENCES ACI Committee 544.4R (1988) (Reapproved 22). Deign Conideration or Steel Fier Reinorced Concrete. ACI Structural Journal, 85(5), ACI committee 544.1R (1997) (Reapproved 22). State-o-he-Art Report on Fier Reinorced Concrete. ACI Structural Journal, 94(1), ACI Committee 318 (25). Building Code Requirement or Structural Concrete (ACI 318M-5) and Commentary (ACI 318-R-99). ACI, Detroit. Al Sayed, S. H. (1993). Flexural Delection o Reinorced Firou Concrete Beam. ACI Structural Journal, 9(1), Altun, F., Haktanir,., and Ari, K. (26). Experimental Invetigation o Steel Fier Reinorced Concrete Box Beam Under Flexure. Material and Structure, 39, Ahour, S. A., and Waa, F. F. (1997), Flexural Behavior o High-Strength Fier Reinorced Concrete Beam. ACI Structural Journal, 9(3), Ahour, S. A., Mahmood, K., and Waa, F. F. (1997). Inluence o Steel Fier and Compreion Reinorcement on Delection o High Strength Concrete Beam. ACI Structural Journal, 94(6), Balaguru, P. N., and Shah, S. P. (1992). Fier Reinorced cement compoite. Mc Graw Hill, Inc. Balaguru, P., Rameh, N., and Mahendra, P. (1992). Flexural oughne o Steel Fier Reinorced Concrete. ACI Material Journal, 89(6), Barro, J. A., Cunha, V. M., and Antune, J. A. (25). Potcracking Behavior o Steel Fier Reinorced Concrete. Material and Structure, 38(1), Craig, R. (1987). Flexural Behavior and Deign o Reinorced Fier Concrete memer. Fier Reinorced Concrete Propertie and Application, SP-15, Daniel, L., and Loukili, A. (22). Behavior o High Strength Fier Reinorced Concrete Beam Under Cyclic Loading. ACI Structural Journal, 99(23), Dwarakanath, H. V., and Nagaraj,. S. (1991). Comparative Study o Flexural Strength o Steel Fier Concrete. ACI Structural Journal, 88(6), Haan, H. (1988). Flexural Behavior o Fier Reinorced Concrete Beam. Cairo Univerity (Faculty o Eng.), PhD. Hu, C.., He, R. L., and Ezeldin, A. S. (1992). Load- Deormation Behavior o Steel Fier Reinorced Concrete Beam. ACI Structural Journal, 89(6), Hugo, S. A., and Nemkumar, B. (1997). Predicting the Flexural Pot-Cracking Perormance o Steel Fier Reinorced Concrete rom the Pullout o Single Fier. ACI Material Journal, 94(1), Kormeling, H. A., Reinhadt, H. W., and Shah, S. P. (198). Static and Fatigue Propertie o Concrete Beam Reinorced with Bar and Fier. ACI Journal, 77(1), Lim,. Y., Paramaivam, P., and Lee, S. L. (1987). Bending Behavior o Steel Fier Concrete Beam. ACI Structural Journal, 84(5), Laura, C. (27). Cracking o Reinorced Concrete Element. Ovidui Univerity Ann. Serie, 1(9), Mutaa,. S. (27). Behavior o High Strength Fier Reinorced Concrete Beam. Banha Univerity (Faculty o Eng.), M.Sc hei. Roert, J. W., and Victor, C. L. (199). Dependence o Flexural Behavior o Fier Reinorced Mortar on Material Fracture Reitance and Beam Size. ACI Material Journal, 87(6), Shah, S. P., and Baton, G. B. (1989). Fier Reinorced Concrete: Propertie and Application. ACI, SP-15. an, K. H., Paramaivam, P., and an, K. C. (1994). Intantaneou and Long erm Delection o Steel Fier Reinorced Concrete Beam. ACI Structural Journal, 91(4),