INTERNATIONAL JOURNAL OF CIVIL AND STRUCTURAL ENGINEERING Volume 2, No 4, 2012

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1 INTERNATIONAL JOURNAL OF CIVIL AND STRUCTURAL ENGINEERING Volme 2, No 4, 2012 Copright 2010 All rights reserved Integrated Pblishing services Research article ISSN Dctilit of Prefabricated Cage Reinforced Concrete Beams: Analtical Std Chithra.R 1, Thenmozhi. R 2, Ravathi.M.C 3 1- Asst. Professor in Civil Engineering, Government College of Technolog, Coimbatore Associate Professor in Civil Engineering, Thanthai Periar Government Institte of Technolog, Vellore PG Scholar, Government College of Technolog, Coimbatore chithrajothin@gmail.com doi: /ijcser ABSTRACT Experimental stdies have reported that confinement provided b Prefabricated Cage effectivel improves the flexral strength, dctilit and deformation characteristics of Prefabricated Cage Reinforced Composite (PCRC) Beams. This paper presents an analtical soltion to predict the crvatre dctilit of PCRC beams. An eqation for dctilit is proposed in terms of ltimate concrete strain and ield strength of steel. Experimental reslts from literatre were emploed to validate the analtical reslts. The findings show that the theoretical analses are in good agreement with the test data. The theoretical crvatre dctilit factor has a reasonabl good agreement with the experimental reslts, which demonstrates the present closed-form soltion is simple et accrate. The analses also show the deformation characteristics of PCRC beams is significantl inflenced b the percentage of tension steel. Kewords: PCRC Beam; crvatre dctilit factor; prefabricated cage; eqilibrim eqations; strain compatibilit. 1. Introdction A strctral member is to be designed with sfficient dctilit capacit to avoid brittle failre in flexre and insre a dctile behavior, especiall for seismic design. The crrent philosoph of seismic design of moment-resisting reinforced concrete frames is based on the formation of plastic hinges at the critical sections of the frame nder the effect of sbstantial load reversals in the inelastic range. The abilit of the plastic hinge to ndergo several ccles of inelastic deformations withot significant loss in its strength capacit is sall assessed in terms of the available dctilit of the particlar section. The dctilit capacit of a section can be expressed in the form of crvatre dctilit factor (µ φ ). The moment-crvatre analsis of performed nder monotonicall increasing load represents onl the first qarter-ccle of the actal hsteretic behavior of the plastic hinge rotation nder the earthqake loading. Therefore, µ φ of a section calclated nder sch an assmption is considered a theoretical estimate of the actal dctilit that can be spplied b the section when sbjected to an actal earthqake loading. However, the theoretical estimation of µ φ nder monotonic loading is widel sed as an appropriate indicator of the adeqac of the earthqake resistant design of RC members. It is even sed for prediction of the damage level in frames nder earthqake loading. Althogh the actal response of frame sbjected to severe earthqakes is complex and involves large Received on March, 2012 Pblished on Ma

2 Dctilit of Prefabricated Cage Reinforced Concrete Beams: Analtical Std ncertainties, prediction of damage is sall made in terms of dctilit demand on individal members. Improving the dctilit of the materials generall leads to an improvement in the dctilit of the section. Based on a closer examination of pblished literatre, dctilit of concrete is being improved at present b confining it in steel binders, as ties in compression members and as closel spaced stirrps in beams (Shamim A Sheikh 1982, Mohamed Saafi et al. 1999, Mohamad M Ziara et al. 1995, Sharim A.Sheikh et al. 1994, Esneder Montoa et al. 2006, Gne Ozcebe et al. 1987, Soliman et al. 1967). The dctilit of strctres can be improved b adding compression steel in the concrete section or b confining the compression zone which leads to an improvement in the dctilit of the material. The concrete confined in sch a wa is called confined concrete or dctile concrete. Prefabricated cage proposed b Halil Sezen et al. (2006) to reinforce the strctral members and to confine the concrete core. Since the se of prefabricated cage for confinement of concrete is a relativel a new approach, theoretical work in this area is still limited and the models originall developed for transverse steel reinforcement are not necessaril applicable to prefabricated cage reinforcement. In beams reinforced with prefabricated cage known as Prefabricated Cage Reinforced Concrete (PCRC) Beams, the compression zone is partiall confined b prefabricated cage. This aids in confinement which helps to increase dctilit factor. The paper presents analtical model for crvatre dctilit factor for the PCRC beams. The analtical reslts are validated with the available experimental reslts. 2. Experimental Program Nine beam specimens were made in this std were 150mm x 200mm x 2500mm in size. The geometrical details of beams are shown in Table 1. The parameters considered in the std are the thickness of the sheet and Grade of Concrete. The ield strength of cold formed steel sed for making the Prefabricated Cage and compressive strength of concrete are given in Table 2. The details of the Prefabricated Cage beams are shown in Figre 1. Table 1: Geometrical Details of Beam Specimens Sl. No Beam Id t mm B mm D mm Length m Yield Strength of Steel (N/mm 2 ) Ast (mm 2 ) Grade of concrete 1 A M20 Profile of the Cage 2 A M20 3 A M20 4 B M25 5 B M25 6 B M25 7 C M30 8 C M30 P1 1027

3 Dctilit of Prefabricated Cage Reinforced Concrete Beams: Analtical Std 9 C M30 Series Material Table 2: Material Properties Properties (In N/ mm 2 ) f ck E c f t f E A Concrete x B x C x CR sheet (1.6mm) x 10 5 A, B,C CR sheet (2.0mm) x 10 5 CR sheet (2.5mm) x Testing of Specimens Figre 1: Details of Prefabricated Cage and PCRC beam All the specimens were tested in a 100ton capacit Reaction Frame. The test set p is shown in the Figre 2. In order to record the applied load precisel, a proving ring of 30ton capacit with a least cont of 0.01ton was sed. A special steel frame arrangement was fabricated for measring the longitdinal strains. Three dial gages having a travel of 50mm were sed to record the vertical deflection at the bottom of mid span and nder the loading points. The behavior of the beams was keenl observed from the beginning till the collapse. The appearance of the first crack, the development and propagation of cracks de to the increase of load were also recorded. The loading was contined pto the peak load. 1028

4 Dctilit of Prefabricated Cage Reinforced Concrete Beams: Analtical Std 3. Methods of Defining Dctilit Figre 2: Test setp over strong floor The term dctilit is generall, qantitativel described b a parameter called dctilit factor or dctilit ratio. The most common measres of dctilit are displacement Dctilit factor and crvatre dctilit factor. a) Displacement dctilit factor (µ = / ). where, is the displacement at ltimate load and is the displacement at which tension steel ields. b) Crvatre dctilit factor (µ Ø = Ø / Ø ) where, Ø is the crvatre corresponding to and Ø is the crvatre at which tension steel ields. 3.1 Cross sectional dctilit of PCRC beam The dctilit of beams ma be defined in terms of the behavior of individal cross sections or the behavior of entire beams. The cross sectional dctilit is widel sed as a measre of beam dctilit represented as dctilit factor Calclation of Yield and Ultimate Crvatres A tpical PCRC beam section with its corresponding strain distribtion at the ield and ltimate stages are shown in Figres 3 and 4. As all the beams exhibit nearl fll shear connection at ltimate, for the calclation of dctilit factor, slip in these beams is ignored. The crvatre calclations are given b the following eqations: a) At Yield Stage Yield Crvatre φ = (1) N 1029

5 Dctilit of Prefabricated Cage Reinforced Concrete Beams: Analtical Std where N can be determined b assming the linear stress distribtion and satisfing the eqilibrim condition of forces. This leads to: The netral axis (N ) at the ield state is obtained from the eqilibrim condition which is given in eqation 2. C = T ck s [ d b ] f BN = 2 f t + t t Figre 3: Stress-strain diagram at ield stage N 2ts f ( dt + bt = Bfck ) (2) Where, f ck - cbe compression strength at 28 th da in MPa f - ield stress of steel sheet in MPa At Ultimate Stage Ultimate Crvatre φ = (3) N where = Concrete compressive strain at crshing of concrete or at ltimate moment N = Depth of compression zone at ltimate, can be determined b satisfing eqilibrim eqation of forces. 1030

6 Dctilit of Prefabricated Cage Reinforced Concrete Beams: Analtical Std d = Effective depth of Beam (4) where, A st = Area of tension reinforcement t s = thickness of Prefabricated cage (a) (b) (c) Figre 4: Section at ltimate stage From strain compatibilit conditions, c s = N d N ) ( (5) (6) From eqilibrim conditions, C = T 1 + T

7 Dctilit of Prefabricated Cage Reinforced Concrete Beams: Analtical Std f BN = ck f A st (7) (8) 2 an + bn c = (9) Solving eqation 9, N can be obtained as The addition of compression reinforcement in the form of continos sheet to a beam will shift the netral axis pwards and increase the ltimate crvatre sbstantiall, althogh it has little effect on its ield strength or ield crvatre. Hence the crvatre dctilit factor is defined as, φ µ φ = (10) φ ( d N ) c µ φ = Es (11) N f s 4. Reslts and Discssions Using eq.11, crvatre dctilit factor (CDF) for the PCRC beams was evalated and are presented in Table 3. The experimental reslts (Chithra et. al, 2011) were sed to validate the theoretical predictions. The ratio between the experimental and theoretical dctilit factor shows the accrac of the eqation. Table 3: Theoretical and Experimental dctilit factor Sl.No Netral axis Crvatre dctilit factor Ratio Beam ID N N Theor Expt. µ φ, EXP (mm) (mm) ( µ φ, T ) ( µ φ, E ) µ φ, THE 1 A A A B B B C C C

8 5. Conclsions Dctilit of Prefabricated Cage Reinforced Concrete Beams: Analtical Std From the analtical investigations carried ot in the present std, the following major findings can be arrived at. 1. The flexral behavior and crvatre dctilit of PCRC beams made of materials of widel varing strengths have been stdied. 2. From eqilibrim forces and strain compatibilit conditions at ield and at ltimate the eqation for crvatre dctilit factor was arrived. 3. The experimental and theoretical dctilit factors are in good agreement. 4. From eqilibrim forces and strain compatibilit conditions at ield and at ltimate the eqation for crvatre dctilit factor was arrived. 6. References 1. Chithra R, Thenmozhi R., (2011), Stdies on prefabricated cage reinforced steel- concrete composite beams, Asian Jornal of Civil Engineering (Bilding and Hosing), 12(1), pp Esneder Montoa; Frank J. Vecchio; Shamim A. Sheikh., (2006), Compression Field modeling of Confined Concrete: Constittive Models, Jornal of Materials in Civil Engineering, 18(4), pp Gne Ozcebe; Mrat Saatciogl., (1987), Confinement of concrete colmns for seismic loading, ACI Strctral Jornal, 84(4), pp Halil Sezen; Mohammad Shamsai., (2006), Behavior of normal strength concrete colmns reinforced with prefabricated cage sstem, Strctres Congress 2006, p Halil Sezen; and Mohammad Shamsai., (2008), High-strength concrete colmns reinforced with prefabricated cage sstem, Jornal of Strctral Engineering, ASCE, 134(5), pp Mohamed M.Zaira; David Haldane; Atallah S.Kttab., (1995), Flexral Behavior of Beams with Confinement, ACI Strctral Jornal, 92(1), pp Mohamed Saafi; Hossam A. Totanji; Zongjin Li., (1999), Behavior of Concrete Colmns confined with Fiber Reinforced Polmer Tbes, ACI Strctral Jornal, 96(4), pp Shamim A. Sheikh., (1982), A Comparative Std of Confinement Models, ACI Strctral Jornal, 79(4), pp Sharim A.Sheikh, Dharmendra V.Shah, and Shafik S.Khor., (1994), Confinement of High-Strength concrete colmns, ACI Strctral Jornal, 91(1), pp

9 Dctilit of Prefabricated Cage Reinforced Concrete Beams: Analtical Std 10. Soliman.M.T.M.; Y.C.W., (1967), The flexral stress-strain relationship of concrete confined b rectanglar transverse reinforcement, Magazine of Concrete Research, 19(61), pp