Title. Author(s)TUE, N. V.; TUNG, N. Đ. Issue Date Doc URL. Type. Note. File Information IN R/C MEMBERS.

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1 Title DEFORMATION-BASED APPROACH FOR DETERMINATION OF THE IN R/C MEMBERS Author()TUE, N. V.; TUNG, N. Đ. Iue Date Doc URL Type proceeding Note The Thirteenth Eat Aia-Paciic Conerence on Struc 13, 13, Sapporo, Japan. File Inormation eaec13-b-6-1.pd Intruction or ue Hokkaido Univerity Collection o Scholarly and Aca

2 DEFORMATION-BASED APPROACH FOR DETERMINATION OF THE EFFICIENCY OF THE CONFINEMENT IN R/C MEMBERS N. V. TUE 1, and N. Đ. TUNG 1* 1 Intitute o Structural Concrete, Graz Univerity o Technology, Autria ABSTRACT Currently, or the determination o the ultimate trength o conined concrete core in reinorced concrete member ubjected to compreion, the yielding o the conining reinorcement i uually aumed. Thi aumption may in many cae be on the unae ide, particularly by the ue o high-trength concrete or high-trength teel or conining reinorcement. Furthermore, the quetion about the poible palling o the concrete cover in a conined member under the ervice load i till open. In thi paper, the development o a model or lateral train o concrete in triaxial compreion i preented. With the propoed model, both the actual tre in conining reinorcement and the rik o the early palling o concrete cover can be etimated. Baed on the invetigation, lower and upper bound o the ratio o conining reinorcement or the eective coninement are propoed. Keyword: coninement, lateral train, compreive trength, reinorcement ratio 1. INTRODUCTION Reearch on the behavior o concrete under active coninement began at the early o th Century (Richart et al. 198), where a linear relation between the trength o conined concrete cc and the lateral tre σ l wa introduced a: cc c σ l = 1. + k c Where the coeicient k wa choen to be 4,1. The coninement can alo be obtained in R/C member through the ue o the lateral reinorcement in the orm o tie or tirrup (Fig. 1). In contrat to the triaxial compreion tet, the coninement in R/C member i a paive phenomenon, the actual conining tre σ le thu depend deciively on the hape o the cro-ection, the amount o lateral reinorcement and the deormation capacity o concrete in triaxial tre tate. Until now the interdependence between the lateral reinorcement and the conined concrete core i not yet clear. It i uually aumed that the conining reinorcement yield when the triaxial compreive trength cc i reached, e.g. in Model Code 1 (1) * Correponding author: n.tung@tugraz.at 1

3 (1). Thi aumption i rom the mechanical point o view inconitent and cannot be conirmed by experimental invetigation with low ratio o conining reinorcement or with high-trength concrete (Nagahima et al. 199; Cuon and Paultre 1995). ac a bc b wi ac a Figure 1: Stirrup und tie a conining reinorcement in R/C member Due to the coninement the lateral train o conined core i maller than that o concrete cover. An early palling o concrete cover may occur. Experimental invetigation hown that the longitudinal train at the cover palling ε c,a can be lower than the peak-train o concrete under uniaxial compreion ε co (Razvi 1996). Becaue o the act that the maximum trength o the conined concrete core cc can be everal time higher than the compreive trength o unconined concrete in member co, the concrete cover can ail even under the ervice load. To aure the durability o the tructure the coninement mut not exceed an upper boundary. For thi the determination o the train ε ca o the cover palling and the correponding load i o importance. Baed on the urther development o an exiting model or lateral train o concrete in triaxial compreion (Montoya et al. 6), the interaction between and the material propertie and the coninement conidering the tructural detailing o RC member are preented.. CONFINEMENT IN R/C MEMBERS.1. Lateral train o concrete in triaxial tre tate Baed on the reult o the experimental tudy on cylinder under triaxial compreion o Imran and Pantazoloulou (1996) a imple parabolic relation between the lateral train ε cl and the normalized longitudinal train ε c /ε cc wa propoed by Montoya et al. (6): ε cl ε c = ( Ie ) εcc () With thi model the lateral train in triaxial tre tate can be directly etimated in dependence o the coninement index I e = σ l / c. However thi model doen t conider the act that the lateral train decreae with the compreive trength. To improve thi, urther experimental data (Candappa et

4 al. 1; Dahl 199) were analyzed (Tung 9). Through a regreion analyi, a relation between the lateral train and the normalized longitudinal train wa propoed:,85 ε c ε cl = (, 176 +, 77 Ie c ) εcc (3) Calculated value ε ccl [ ] Imran/Pantazopoulou Candappa et al. Dahl Meaured value ε ccl [ ] Figure : Comparion the lateral train ε ccl between experimental tet and tet prediction A comparion o the lateral train ε ccl at triaxial compreive trength cc calculated with Eq. (3) to the tet reult (Imran and Pantazoloulou 1996; Candappa et al. 1; Dahl 199) i given in Fig.. The comparion how a good agreement between experiment and prediction, with an average value o 1,16 and a coeicient o variation o 1,5 %... Stre in conining reinorcement at maximum load Conidering a geometric coeicient o coninement eectivene K e, the conining tre in concrete core at maximum load σ ccl can be calculated rom the tre in conining reinorcement σ cc and the geometric ratio o reinorcement ρ = A /(a c ) according to Eq. (4): σ = K ρ σ (4) ccl e cc In thi contribution the widely-accepted propoal or K e o Mander et al. (1988) i adopted. Taking a a bai o the compatibility o deormation between conined concrete core in lateral direction and conining reinorcement (ε ccl = ε cc ) the train in conining reinorcement at maximum load (ε c /ε cc = 1) can be determined by ubtitution Eq. (4) into Eq. (3): 1 ε =, 176 +, 77 K ρ σ (5) cc e 1,85 cc co Where co =,85 c the compreive trength o unconined concrete in member. Aumed that the tre-train relation o conining reinorcement i ideal elato-platic, the tre and train o reinorcement at maximum load can be calculated uing Eq. (5) a: 3

5 , 176 ε = ; σ = E ε E cc cc cc 1,77 Ke ρ 1,85 co (6) I the calculated train according to Eq. (6) exceed the yielding limit o the conining reinorcement (ε cc ε ), then Eq. (5) i impliied a: ε =, 176 +, 77 K ρ ; σ = (7) cc e 1,85 cc co.3. Stre and train o concrete core at maximum load With the actual tre in conining reinorcement σ cc the maximum trength o the conined concrete core cc can be etimated uing Eq. (1). The coeicient k i determined to be 4,. Baed on the relation between the crack ormation and the aborbed energy (Tung 9) the train o concrete core at maximum loading ε cc can be determined a ollow: αc co ε ccl.1 εco cc εcc = ε co + αcc Ec.4 ε co Ec (8) Where α c =,815+,5. co ; α cc =,665+,5. I e the olidity actor o the tre-train curve o concrete under uniaxial and triaxial compreion (Tung 9). Calculated value cc [MPa] Nagahima et al. Cuon/Paultre Hong et al. Han et al. Razvi Li Calculated value ε cc [ ] Nagahima et al. Cuon/Paultre Hong et al. Han et al Meaured value cc [MPa] Meaured value ε cc [ ] Figure 3: Comparion the triaxial trength and correponding train between tet and model A comparion o the maximum trength o the conined concrete core cc and the correponding train ε cc uing Eq. (1) and (8) to the tet reult o 144 column perormed by dierent author (Nagahima et al. 199; Cuon and Paultre 1995; Hong et al. 6; Han and Sihn 3; Razvi 1996; Li 1994) i given in Fig. 3. The comparion how a good agreement between experiment and prediction. For the prediction o the maximum trength cc an average value o 1,3 and a coeicient o variation o 1,7 % are obtained, the prediction o the correpondent train ε cc give an average value o 1,7 and a coeicient o variation o,8 %. 4

6 3. EFFECTIVITY OF THE CONFINEMENT 3.1. Minimum reinorcement ratio To utilize the trength capacity o reinorcement or an eective coninement the tre in the conining reinorcement hould at leat reach it yield trength at maximum load. That mean:, 176 +, 77 Ke ρ (9) E 1,85 co With a certain yield trength o the ued conining reinorcement the minimum geometric ratio o reinorcement ρ,min can be determined a: ρ,min, 176 E = E,77 Ke 1,85 co (1) Reinorcement ratio ρ,min [%] _=1 MPa _=8 MPa _=6 MPa _=5 MPa _=4 MPa Strength o unconined concrete co [MPa] Figure 4: Minimum reinorcement ratio ρ,min Fig. 4 illutrate the minimum reinorcement ratio according to Eq. (1) with K e =,65 or dierent yield trength o conining reinorcement and compreive trength. Conidering the act, that the arrangement o tie or tirrup with the reinorcement ratio more than 3 % i practically not poible, the ue o high-trength teel or conining reinorcement or compreive member with HSC i not reaonable. Uing yield trength to calculate the conining tree or member with the reinorcement ratio lower than ρ,min will lead to an unae deign. 3.. Maximum reinorcement ratio to avoid the cover palling under ervice load With the conining tre σ ccl the maximum trength o the conined concrete core cc and the correpondent train ε cc can be etimated. The lateral train ε cl or conined concrete core with two dierent reinorcement ratio in comparion with the lateral train o the concrete cover are qualitatively depicted in Fig. 5. It can be een that up to a longitudinal train o ε 1 ~,5 ε co the lateral train dierent between core and cover i inigniicant. Ater that the lateral train o cover increae diproportionately until the uniaxial compreive trength co i reached, while the lateral 5

7 train o core remain lower due to the coninement. The lateral train dierent between core and cover ε cl depend on the reinorcement ratio. Lateral train ε cl ε ccl, ε ccl,1 ε col ε cl, Concrete cover Concrete core 1 Concrete core ρ,1 ε cl,1 ρ, ρ,1 <ρ, ε cl,1 < ε cl, ε 1l ε 1 ε co ε cc,1 ε cc, Longitudinal train ε c Figure 5: Schematic repreentation o the lateral train or the concrete cover and core I the train dierent ε cl exceed a tenile train ε ct o approx.,15 a plitting crack at the ace between concrete core and cover arie, it crack width can be etimated a ollow: ( ) w = a ε ε (11) 1 c cl ct The load traner at the crack can be decribed with a model according to MC 1 in which rom a crack width w t = G F / ctm downward the poible tenile tre i negligible. It i aumed that at thi crack width the palling o concrete cover occur completely. 1,,95 (a) 1,,95 (b) σ co,a / co [-],9,85 C4/5 σco,a/co [-],9,85 C9/15 ρ=,5% ρ=,5% Eq.(1),8 ρ=1,% ρ=1,% Eq.(1) ρ=,% ρ=,% Eq.(1), Width o concrete core [mm],8 ρ=,5% ρ=,5% Eq.(1) ρ=1,% ρ=1,% Eq.(1) ρ=,% ρ=,% Eq.(1) ρ=3,% ρ=3,% Eq.(1), Width o concrete core [mm] Figure 6: Relative tre o the concrete cover at palling: (a) co = 34 MPa; (b) co = 76,5 MPa With thi aumption the train o concrete cover at palling can be calculated with the Eq. (3, 11). Baed on the tre-train relation according to MC 1, the tre in the concrete cover can be alo determined. Fig. 6 how the reached tre in cover at the palling two trength clae o concrete (continuou line). It can be een that the tre σ co,a depend on the reinorcement ratio ρ, the compreive trength co and the width o concrete core. Conidering thee inluencing parameter a 6

8 relation or etimation o the tre σ co,a according to Eq. (1) i propoed, the tre σ co,a calculated with Eq. (1) i alo illutrated in Fig. 6. σ co, A ρ Ke.4 = ac 1 co co.5 a c in m (1) It i aumed that the tre in concrete core at the palling σ cc,a equal approximately to the tre in cover σ co,a. With the total cro-ectional area o the member, A tot, and the area o concrete core bounded by centerline o tie or tirrup, A cc, the load at palling can be calculated a: ( ) P = σ A A + σ A σ A (13) c, A co, A tot cc cc, A cc co, A tot To enure the durability the load at palling mut be larger than the ervice load calculated rom the maximum load P cc =. cc A cc. That i: Pc, A Pcc / ( γ E γ C ) = cc Acc / γ (14) Where γ E, γ C are the partial aety actor or action and the material concrete. ρ,max [%] 7,5 6 4,5 3 C6/75 C5/6 C4/5 C3/37 C5/3 1, Width o concrete core a c [mm] Figure 7: Maximum reinorcement ratio ρ,max Inerting Eq. (1), (1), (13) in Eq. (14) the maximum reinorcement ratio ρ,max can be drawn. 1 co.4 A tot Atot.4 Atot ρ,max =.5 ac γ γ 16.5 ac γ 64Ke Acc Acc A cc (15) The maximum reinorcement ratio ρ,max or a member with c nom = 5 mm, = 5 MPa and K e =,6 calculated with Eq. (15) i illutrated in Fig. 7. In the calculation a total aety actor γ = γ. E γ C =,1 i ued. It i clearly that maximum reinorcement ratio increae with the compreive trength and decreae with the width o the concrete core. In general, a lateral reinorcement ratio o more than 3% can hardly be arranged, o the rik o palling o the concrete cover under ervice load or member made o high-trength concrete i avoided. 7

9 4. CONCLUSION In contrat to the triaxial compreion tet, the coninement in R/C member depend trongly on the deormation capacity o the concrete in lateral direction, the reinorcement ratio and the material law o conining reinorcement. Baed on the compatibility o deormation between conined concrete core in lateral direction and conining reinorcement the actual tre in conining reinorcement can be determined. Conidering that the conining reinorcement hould at the latet yield when the triaxial compreive trength i reached or an eective coninement, the minimum ratio o the conining reinorcement i introduced. It i hown that high-trength teel are le uitable or conining reinorcement. By comparing the tranvere train in cover and core concrete, the phenomenon o palling o the concrete cover wa cleared. In view o the durability o the R/C member an upper limit or the ratio o conining reinorcement wa determined depending on the concrete trength and the cro-ectional width. REFERENCES Candappa, D. C., Sanjayan, J. G., & Setunge, S. (1). Complete triaxial tre-train curve o high-trength concrete. J. Mate. Civ. Eng., ASCE, 13, No. 3, pp Cuon, D., & Paultre, P. (1995). Stre-train model or conined high-trength concrete. J. Struct. Eng., ASCE, 11, No. 3 (S ). Dahl, K. (199). A Failure criterion or normal and high-trength concrete. Technical Univerity o Denmark, Department o Structural Engineering, Di. Han, B. S., & Sihn, S. W. (3). A model o conined concrete in high-trength reinorced concrete tied column. Magazine o Concrete Reearch, 55, No. 3, pp Hong, K., Akiyama, M., Yi, S., & Suzuki, M. (6). Stre-train behaviour o high-trength concrete column conined by low-volumetric ratio rectangular tie. Magazine o Concrete Reearch, 58, No., pp Imran, I., & Pantazoloulou, S. (1996). Experimental tudy o plain concrte under triaxial tre. ACI Mate. J., 93, No. 6, pp International Federation or Structural Concrete. (1). Model Code 1, Final drat. Lauanne. Li, B. (1994). Strength and ductility o reinorced concrete member and rame contructed uing high trength concrete. Chritchurch, New Zealand: Univerity o Canterbury. Mander, J., Prietley, M., & Park, R. (1988). Theoretical tre-train model or conined concrete. J. Struct. Eng., ASCE, 114, No. 8, pp Montoya, E., Vecchio, F., & Sheikh, S. (6). Compreion ield modeling o conined concrete: Contitutive model. J. Mate. Civ. Eng., ASCE, 18, No. 4, pp Nagahima, T., Sugano, S., Kimura, H., & Ichikawa, A. (199). Monotonic axial compreion tet on untra-high-trength concrete tied column. Madrid, Spain: 1th World Conerence on Earthquake Engineering. Razvi, S. (1996). Coninement o normal and high-trength concrete column. Univerity o Ottawa, Canada, Di. Richart, F. E., Brandtzaeg, A. L., & Brown, R. (198). A Study o the Failure o Concrete under Combined Compreive Stree. Engineering Experiment Station, Univerity o Illinoi. Tung, N. D. (9). Zum Einlu de Verormungvermögen von Stahl und Beton au die Umchnürungwirkung bei Stahlbetontützen. Univerität Leipzig, Di. 8