Evaluation of minimum shear reinforcement in reinforced concrete beams

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1 Ealuation o minimum shear reinorement in reinored onrete beams G. ppa Rao ssoiate Proessor, Department o Ciil Engineering Indian Institute o Tehnolog Madras, Chennai , India garao@iitm.a.in S.S. Injaganeri Researh Sholar, Department o Ciil Engineering Indian Institute o Tehnolog Madras, Chennai , India bstrat Failures in reinored onrete (RC) strutures under shear loads are proed to be brittle with the presene o web reinorement. The minimum web reinorement speiied b man odes o pratie is intended to maintain adequate resere strength and dutilit ater the diagonal raking and to ontrol widening o diagonal raking. Howeer, the expressions or estimating the minimum shear reinorement in odes o pratie are based on the experimental data base obsered on small beam depth made o normal strength onrete (NSC). Hene, these proisions need to be reassessed and altered or large size members made o high strength onrete (HSC). Further, there has been no onsensus on the amount o shear reinorement to be proided b dierent odes o pratie, as the dier signiiantl in respet o HSC members. In this paper, man ators inluening the minimum shear reinorement in RC beams has been inorporated. n expression has been proposed inorporating a wide range o onrete strengths. omparison o the minimum shear reinorement predited b the proposed expression has been made with the odes o pratie. Ke words: Shear reinorement, reinored onrete beam, dutilit, high strength onrete.

2 1. Introdution It is belieed that the web reinorement in the orm o ertial stirrups does not aet the diagonal raking strength signiiantl. Howeer, the presene o shear reinorement tends to alter the behaiour o reinored onrete (RC) beams and enhanes the shear apait b improing the shear transer mehanisms through better dowel ation, restraining rak propagation, minimising bond splitting ailure and enhaning the ontribution o unraked onrete in the ompression zone. In RC strutures, proision o minimum shear reinorement is mandated when the atored shear ore exeeds one-hal the design shear strength o onrete. The intension o proiding minimum shear reinorement in RC elements b the odes o pratie is (i). to preent sudden brittle ailure as soon as reahing the irst diagonal raking load, (ii). to ontrol widening o raks at serie loads and (iii). also to impart adequate dutilit beore ailure. Seeral national odes o pratie suh as CI 318, Canadian ode and SHTO spei the minimum shear reinorement aring with the ompressie strength o onrete, while it is aring with the ield strength o shear reinorement onl as per IS and BS odes o pratie. 2. Literature reiew The reiew o literature on the minimum shear reinorement is reported. Lin and Lee (2001) reported that the inrease in the quantit o tension reinorement inreases the shear strength but dereases the dutilit o the beams. Further an inrease in the perentage o ompression reinorement and the strength o onrete improes the dutilit o the beams eetiel. Beams with high strength shear reinorement exhibit the same rak ontrol abilit as ompared to the beams with normal strength shear reinorement. In another stud, Lin and Lee (2003) onluded that the ators aeting dutilit are shear span-to-depth (a/d) ratio, spaing o stirrups and strength o shear reinorement. lso it was obsered that b inreasing the quantit and the strength o shear reinorement does not show apparent inluene on the diagonal raking strength o beams. Howeer, inreasing the strength o onrete and strength o shear reinorement inreases the ultimate strength, while the derease in the shear-span-depth ratio and the spaing o stirrups inreases the ultimate strength. In beams with low a/d ratio, the eetieness o shear reinorement is muh low. Xie et al. (1994) arried out experimental stud on dutilit o reinored onrete beams in shear with and without web reinorement, in whih the ollowing ariables were aried; strength o onrete rom 40 MPa to 109 MPa, shear span-to-depth ratio rom 1.0 to 4.0 and the perentage shear reinorement rom 0.0 to In this stud, the post-peak response was quantiied through shear dutilit. Based on the omparison o tests on two large size beams b Johnson and Ramirez (1989) and the tests on redued size beams, Frosh (2000) reported that the size o the beam did not aet the post raking behaiour or the shear strength proided b the stirrups. Howeer, rom the ealuation o test results and preious studies, Johnson and Ramirez (1989) demonstrated that the oerall resere strength beond diagonal tension raking diminished with the inrease in ompressie strength, or the beams designed with the urrent proisions o minimum shear reinorement. This situation would be more ritial or beams with large a/d ratios at small perentage o longitudinal reinorement. Yoon et al. (1996) onluded that or HSC members the rak spaing is a untion o spaing o longitudinal and transerse reinorement. The spaing o shear raks inreases as the size

3 o the member inreases. Hene the Canadian Standards ssoiation (CS) (1984) underestimates the shear strength o large size members at ailure. Roller and Russell (1990) reported that the minimum shear reinorement speiied in the odes o pratie needs to be inreased as the strength o onrete inreases. The equation proposed b Yoon et al. (1996) was realuated b Ozebe et al. (1999) and stated that the amount o shear reinorement ould be 20% smaller than that o the minimum shear reinorement required as per the proisions o CI ode (1999). Experimental inestigations b ngelakos (2001) showed that the minimum amount o reinorement in the orm o stirrups proided b CI ode (1999) exhibited inadequate saet margins. 3. Code proisions or minimum shear reinorement The proisions or minimum shear reinorement b arious odes o pratie are shown in Table 1. The ariation o the shear reinorement index (r* ) with ompressie strength o onrete is shown in igure 1 (r = s / ). It demonstrates that the minimum shear reinorement is a untion o the ompressie strength o onrete as per CI (1999), SHTO (2000) and CS (1984) odes. It is the untion o the strength o shear reinorement alone as per BS (1985) and IS (2000) odes. lso, the dierene is muh large or HSC beams ompared to NSC beams. Table 1. Proisions or Minimum Shear Reinorement b arious Codes o Pratie Sl. No Code Equation Equation 1 CI (1999) s (1) 2 SHTO [2000] s 12 (2) 3 CS(1984) s (3) 4 IS 456(2000) s (4) 4 BS 8110 (1985) s (4)

4 Figure 1. Shear reinorement index s. Compressie strength o onrete. 4. Estimation o minimum shear reinorement The minimum shear reinorement speiied b the odes o pratie is intended to ensure that the strength o a member ater raking exeeds the load at whih the diagonal raking ours or in other words or a beam with the gien geometr and materials the minimum shear reinorement is neessar to inrease the shearing strength o the beam to a alue V greater than that o the raking strength, V r. The studies arried out b Johnson and Ramirez (1989) showed that the resere strength dereases with the inrease in ompressie strength o onrete and that it would be more ritial with inrease in the shear span-to-depth ratio and derease in the quantit o the longitudinal reinorement. Thereore, the minimum shear reinorement must be a untion o the shear-span-todepth ratio and the longitudinal reinorement apart rom the ompressie strength o onrete. V V V r 0.17 Taking V and V bs (Injaganeri, 2007) s s s V u 0.5 s r ' ' d s u ' bd 3 a/d bd 1/6 2 3 a/d /6 (5) (6) (7) (8) (9)

5 Where a = shear span, a/d = shear span-to-depth ratio, s = area o tension reinorement, s = rea o shear reinorement, b = breadth o beam, d = eetie depth in mm, = lindrial ompressie strength in MPa, = ield strength o longitudinal steel, s = ield strength o shear reinorement, ρ l = longitudinal reinorement ratio, r = s /, S = Spaing o stirrups, r = diagonal raking strength, u = ultimate shear strength, V = shear apait o onrete, V s = shear strength o reinorement, V r = raking shear strength, and V ul = atored shear ore at ritial setion Using the relation obtained between the diagonal and the ultimate shear strength b Injaganeri (2007) and the ondition (V + V s ) > V r, an expression or the minimum shear reinorement has been established. The minimum shear reinorement is a untion o the ompressie strength o onrete, the shear span-to-depth ratio and the perentage o the lexural reinorement as shown in Eq. 9. Figure 2 demonstrates the ariation o the minimum shear reinorement as per Eq. 9 with the ompressie strength o onrete = 60 MPa = 40 MPa = 20 MPa r* a/d l Figure 2. Minimum Shear Reinorement with a/d ratio and longitudinal reinorement, ρ. 5. Results and disussion The minimum shear reinorement as per the CI and IS odes demands that the ultimate shear strength be equal to the shear strength o onrete 0.48 MPa and 0.4 MPa respetiel or = 60 MPa. Howeer, the proisions or shear reinorement b the odes o pratie are independent o the shear span-to-depth ratio and the perentage o longitudinal reinorement. Figure 2 shows the

6 ariation o shear reinorement with a/d ratio and ρ l or dierent strengths o onrete. It an be obsered that the web reinorement dereases with the inrease in ρ l and inreases with inrease in the a/d ratio. The odes o pratie spei the minimum shear reinorement to ensure minimum dutilit apart rom ensuring the shear strength greater than its diagonal raking strength. It is to note that the addition o een a small quantit o shear reinorement inreases the dutilit o a member. Howeer, the minimum dutilit needs to be deined or that member. In order to stud the minimum shear reinorement, six geometriall similar reinored onrete beams o two dierent sizes abriated with high strength onrete (HSC) were tested under threepoint loading using a displaement ontrol testing sstem o 500 kn apait. The spaing o stirrups was altered to stud the ariation o dutilit and ompare the minimum shear reinorement estimated rom the proisions o the odes o pratie. Details o the speimens are shown in Table 2. Table 2. Geometri and Material Properties with Reinorement Details Beam b d l e a/d st s r* s H #16 / H #16 / H #16 / H #20 / H #20 / H #20 / Figure 3. Load s. Deletion in beams (D = 200mm).

Howeer, it seems insuiient or large size beams, where beam depth exeeds 600 mm with HSC as the shear reinorement legs snapped ater reahing the ultimate load when the shear reinorement index r* = 0.

7 Load s. Central Deletions responses are shown in igures 3 and 4. Figures 3 and 4 demonstrate that the minimum shear reinorement proided b the odes o pratie looks suiient or small size beams as adequate dutilit has been obsered. Howeer, it seems insuiient or large size beams, where beam depth exeeds 600 mm with HSC as the shear reinorement legs snapped ater reahing the ultimate load when the shear reinorement index r* = 0.4 and 0.6. Figure 4. Load s. Deletion in beams (D = 600mm). 6. Conlusion The minimum amount o web reinorement speiied b IS and BS odes are independent o ompressie strength o onrete and seems to be inadequate or HSC beams. Howeer, CI, CS and SHTO proisions represent as a untion o ompressie strength o onrete but are independent o a/d ratio and perentage o longitudinal reinorement, ρ l. The model proposed in this stud predits reasonabl well the minimum shear reinorement in terms o the ariables ompressie strength o onrete, a/d ratio and perentage o the longitudinal reinorement, ρ l. Reerenes Lin, C.H., and Lee, F.S. (2001), Dutilit o High Perormane Conrete Beams with High Strength Lateral Reinorement, CI Str Jl, V. 98, N. 4, Jul-ug, pp Lin, C.H., and Lee, F.S. (2003), Shear Behaiour o High Workabilit Conrete Beams, CI Strutural Journal, V. 100, N. 5, Sep.-Ot., pp Xie. Y., hmad, S.H., Yu, T., and Chung, W. (1994), Shear Dutilit o RC Beams o Normal and High Strength Conrete CI Journal, V. 91 N.2, pp

8 Johnson, M.K., and Ramirez, J.. (1989), Minimum Shear Reinorement in Beams with HSC, CI Strutural Journal, V. 86 N. 4, Jul-ug, pp Frosh, R. (2000), Behaiour o large Sale Reinored Conrete Beams with Minimum Sear Reinorement, CI Strutural Journal, V. 97 N. 6, No.-De., pp Yoon, Y.S., Cook, W.D., and Mithell, D. (1996), Minimum Shear Reinorement in Normal Medium and HSC Beams, CI St Jl, V. 93 N. 5, Sep-Ot., pp CS, Rexdale, (1984), Design o Conrete Strutures or Buildings 1984 Roller, J.J., and Russell, H.G. (1990), Shear Strength o HSC Beams with Web Reinorement, CI Strutural Journal, V. 87 N. 2, Marh-pril, pp Ozebe, G., and Erso, U., and Tankut, T. (1999), Ealuation o Minimum Shear Reinorement Requirements or HSC, CI Journal, V. 96 N. 3, Ma-June, pp CI Committee 318, (1999), Building Code requirements or Strutural Conrete (CI ), merian Conrete institute, Mihigan. gelakos, D., Bentz, E.C., and Collins, M.P. (2001), Eet o onrete strength and Min. Stirrups on Shear Strength o Large Members CI St Jl, V.98, N. 3, pp SHTO LRFD (2000), Bridge Design Speiiations and Commentar, 2 nd ssoiation o State Highwa Transportation Oiial, Washington DC. Ed. merian IS 456, (2000), Code o Pratie or Plain and Reinored Conrete, 4 th Re, Bureau o Indian Standards, New Delhi. BS 8110 (Part 1), (1985), Code o Pratie or Design and Constrution, British Standards Injaganeri, S.S., (2007), Studies on size eet on design strength and dutilit o reinored onrete beams in shear, Ph.D. Thesis, Department o Ciil Engineering, Indian Institute o Tehnolog Madras.

MINIMUM SHEAR REINFORCEMENT FOR OPTIMUM DUCTILITY OF REINFORCED CONCRETE BEAMS

IJRET: International Journal o Researh in Engineering and Tehnolog eissn: 2319-1163 pissn: 2321-7308 MINIMUM SHEAR REINFORCEMENT FOR OPTIMUM DUCTILITY OF REINFORCED CONCRETE BEAMS Appa Rao. G 1, Injaganeri.