Analytical model for axial stress-strain behavior of welded reinforcement grid confined concrete columns

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1 Journal of Asian Conrete Federation Vol. 1, No. 1, pp. 1-1, Sep. 215 ISSN / eissn Analytial model for axial stress-strain behavior of welded reinforement grid onfined onrete olumns Tavio* and B. Kusuma (Reeived: February 16, 215; Aepted: August 13, 215; Published online: September 3, 215) Abstrat: In a previous study by the authors, the innovative tehnology of applying welded reinforement grids (WRG) as onfining steel of reinfored onrete olumns (instead of traditional ties) under ompression loading was experimentally investigated. A stress-strain model of onrete whih takes onfinement effets into aount is developed based on the results of ompression loading tests of reinfored onrete olumn speimens. The stress-strain model is formulated by evaluating the relationship between several key parameters (effetive onfining pressure, peak stress, strain, and dutility) and the stress-strain behavior observed in the experiments. Analytial results are then ompared to experimental values available in the literature. It is shown that the predited stress-strain relation provides better agreement with the experimental results than existing models. Keywords: onfined onrete, lateral reinforement, reinfored onrete olumn, stress-strain model, welded reinforement grids (WRG). 1. Introdution Corresponding author Tavio is a Professor of the Department of Civil Engineering, Sepuluh Nopember Institute of Tehnology (ITS), Surabaya, Indonesia. B. Kusuma is a Ph.D. andidate of the Department of Civil Engineering, Sepuluh Nopember Institute of Tehnology (ITS), Surabaya, Indonesia. Column onfinement is an important omponent of the seismi design of reinfored onrete olumns [1-5]. The onfinement of ore onrete improves the overall strength and stability of the struture subjeted to large seismi lateral fores [6-12]. The harateristis of onfined onrete have been researhed extensively, and the primary parameters of onfinement have been identified both experimentally and analytially [13-19]. Various studies on the onfinement effets of lateral reinforement in olumn have already been onduted [2-24]. It is now well reognized that both the strength and dutility of onrete ompressive members an be greatly enhaned using welded reinforement grids (WRG) [25-29]. Very few experimental and analytial studies are available for ompressed members onfined by WRG. WRG an be flexibly prefabriated to meet the required size and volumetri ratio of transverse steel. The volumetri ratio is defined as the volume of the onfinement steel with respet to the volume of olumn, obtained by multiplying the gross ross-setional area and the spaing of onfining elements. These grids when used as olumn transverse reinforement, ould potentially lead to savings assoiated with easy and fast age assembly, and redution in steel onsumption sine the overlapping reinforement, bends and bend extensions are eliminated. Furthermore, the preision of welded grid orners, as ompared to bent onventional hoop orners, provides better and onsistent support to longitudinal reinforement, also improving olumn behavior. The grid orners may also provide additional onfinement pressure peaks without any longitudinal reinforement, improving the uniformity of pressure. The objetives of this study are as follows: 1) to study the appliability of existing onfinement models, and 2) to propose a stress-strain model of onfined onrete whih is appliable to a wider range of WRG ratios than the existing models. 2. Assessment of existing stress-strain onfinement models Several analytial stress-strain relations for retilinearly onfined onrete have been proposed. Among these, the relations presented by Hoshikuma et al. [3] and Legeron and Paultre [31] will be studied to determine the appliability to the speimens. Details of Hoshikuma s and Legeron s 1

2 Table 1 Details of speimens tested by Tavio et al. [33] Column speimen ID Grid onfiguration Dia. (mm) Transverse reinforement s (mm) (%) f yh (MPa) Number (bars) Longitudinal reinforement Dia. (mm) g (%) f y (MPa) N1-3W N1-45W N1-6W N1-72W N1-9W N1-12W N2-3W N2-45W N2-72W N1-3W N1-45W N1-6W N1-72W N1-9W N1-12W N2-3W N2-45W N2-72W onfinement models an be found in the literature [3,31] and will not be given here. Hoshikuma s model is appliable to normalstrength onrete. It inorporates all the relevant parameters of onfinement, inluding the type, volumetri ratio, and spaing of transverse reinforement as well as setion geometry. The developed model an be used for onrete onfined by different types of setion geometry inluding irular, square, and wall-type setions. It an also be used for bridge olumns whih have larger onrete setions and, thus, lower volumetri ratios of transverse reinforement. Legeron s model is appliable for normal- and high-strength onrete olumns based on the large number of test results of irular, square, and retangular olumns tested under various researh studies that inluded the studies undertaken by themselves and a number of other researhers. The strengths ranged from 2 to 14 MPa and the tie yield strengths ranged from 3 to 14 MPa. The model inorporates almost all the parameters of onfinement. The stress-strain relationship was basially same as proposed by Cusson and Paultre [32], but the parameters of the model were realibrated on the basis of large number of test data olleted by the authors. 3. Modeling of stress-strain relation The stress-strain model has been proposed based on test data by Tavio et al. [33]. This model is appliable to olumns with square setions made of normal strength onrete and welded reinforement grids (WRG). In this setion, the equations used in the stress-strain model are modified by performing regression analysis on all test results of the speimens listed in a paper reported by Tavio et al. [33] exept for olumns laterally reinfored with onventional ties. Table 1 summarizes the details of speimens tested by Tavio et al. [33]. The ross setions of the tested speimens an be seen in Fig. 1. The perspetive view of the appliation of WRG 2

3 36 (14.2) Test Region Configuration 1 Configuration 2 Grids longitudinal bars Grids longitudinal bars Configuration 3 Configuration 4 where r E E f ; f is the ompressive strength of onfined onrete; is the axial strain at peak strength of onfined onrete; x is the normalized strain; f is the onrete stress orresponding to strain and E is the modulus of elastiity of unonfined onrete. 1 (.39) Grids (7.1) mm Grids (7.1) Configuration 4 longitudinal bars 5 12 Configuration longitudinal bars 6 Fig. 1 Cross setions of speimens tested by Tavio et al. [33] 18 mm The following expression, originally proposed by Carrasquillo et al. [35] is found to produe good agreement with experimentally obtained values, where f is in Mega Pasal. E 332 f 69 (2) The linear portion of the desending urve, extends to the level of the stress drop after maximum stress to be 2 perent of the peak stress and is based on the expression proposed by Martinez et al. [36] as desribed below. f f 1.15 (3) 85 Eq. (3), represented by a straight line, passes the strain orresponding to 85 perent of the maximum stress of the desending part, 85, for the onfined onrete. The proposed stress-strain relationship onsists of a nonlinear asending branh up to onfined peak stress and a linear desending branh beyond the peak, as illustrated in Fig. 3. Fig. 2 Perspetive view of appliation of WRG as transverse reinforement in RC olumn as transverse reinforement in RC olumn is shown in Fig. 2. The mathematial expressions of the asending part were originally proposed by Popovis [34], and later used by Cusson and Paultre [32] for high strength onrete. They are expressed by Eq. (1). In this researh, all parameters (r, x, f ) in Eq. (1) are modified based on experimental results as follows: f rf x r 1 x r (1) Fig. 3 Proposed model 3.1 Effetive onfining pressure In this study, the effetive onfining pressure, P, is defined aording to Eq. (4) [21,22]. e P d s t e 1 t f yh (4) i b 3

4 Strength Ratio, (f' /f' o )-1 where d t and i are the wire size and the length of one grid ell of welded reinforement grids (WRG), respetively; s is the longitudinal spaing of transverse reinforement; b is the shortest dimension of the olumn setion; and f are the volumetri ratio and yield strength of yh welded reinforement grids (WRG), respetively. 3.2 Peak stress, strain, and dutility A regression analysis was performed on all test results to formulate the peak strength, f, the strain at peak strength,, and the strain orresponding to 85 perent of the peak strength of the desending branh, 85. Figure 4 shows the relationship between the enhanement strength of onfined onrete and the effetive onfinement index, Pe f o, whereas Figure 5 shows the relationship between the strain gain and the effetive onfinement index, Pe fo. The results of regression analysis are as follows:.49 P e f fo (5) fo where fo is the ompressive strength of unonfined onrete. t Gain, /o R 2 =.861 P e o 1.31 EXP24.63 fo Effetive Confinement Index, P e /f' o Fig. 5 Effet of onfinement on peak strain of onrete Figure 6 shows the relationship between the dutility gain and the effetive onfinement index. The dutility gain is defined as the differene between the strains at whih the stress drops to 85 perent of the peak strength of onfined onrete, 85, and of unonfined onrete, o. Based on the results of regression analysis shown in Fig. 5, the expression for 85 an be derived as.7 P e 85 o. 13 (7) f o where the peak strain of the unonfined onrete, o, is expressed as per the reommendation of Foster and Gilbert [37] R 2 =.914 f 2 o.2.1 (8) P e f fo fo Effetive Confinement Index, P e /f' o Fig. 4 Effet of onfinement on peak onrete strength P e o1.31exp (6) fo The in-plae strength of unonfined onrete, fo, was taken to be.85f for all olumns. Similar values were used for olumns tested by others [26,27]. Dutility Gain, 85 -o R 2 = P e o fo Effetive Confinement Index, P e /f' o Fig. 6 Effet of onfinement on dutility of onrete 4

5 4. Comparison of preditions and experimental results The omparisons between the analytial onfined onrete strength values obtained from the proposed onfinement model and the experimental strength values are presented in Fig. 7. Strong orrelation between the analytial strength and the experimental strength is apparent. For the peak strain ε and strain at 85 perent of the peak strength, agreements between the measured and analytial results are also quite good as shown in Figs. 8 and 9. Comparisons were made between the preditions of the models and the experimental results of reinfored onrete olumns onfined with WRG. The study arried out by Holland [26] and Hong [27] inluded the olumn speimens with volumetri ratio ranged from 1. to 4. perent as given in Table 2. The omparisons of the model to the experimental results of all eighteen onfined speimens are shown in Figs Curves obtained from the models of Hoshikuma et al. [3] and Legeron and Paultre [31] are also shown in eah figure. In all ases, the stress-strain relation proposed by this researh aurately reprodues the experiment result. It ould be stated that the proposed model generally provides better agreement with the stress-strain relation of onfined onrete over a wider range of welded reinforement grids (WRG) ratios than previous onventional onfine-ment models. The inaurate preditions of both Legeron and Paultre and Hoshikuma et al. models on the peak stress and strain dutility are mainly due to the derivations of these models from the experimental results of traditionally-onfined olumns. Hene, the models are not appliable to WRG-onfined olumns. Table 2 Details of speimens tested by others [26, 27] Referene Label Grid onfiguration fo, MPa (ksi) d t, mm (in.) Transverse reinforement s, mm (in.) t, f yh, MPa % (ksi) Grid arrangement W (6.1) 3. (.118) 25.4 (1.) (54.) 2 2 W (5.7) 4.1 (.161) 19.1 (.75) (83.5) Holland [26] W (6.3) 2.4 (.94) 31.8 (1.25) (63.2) 3 3 W (5.6) 2.4 (.94) 12.7 (.5) (63.2) W (5.4) 2. (.79) 25.4 (1.) (41.7) W (6.9) 4.1 (.161) 19.1 (.75) (71.9) Hong [27] W (6.9) 2.5 (.98) 19.1 (.75) (63.2) W (6.9) 2. (.79) 25.4 (1.) (41.7) W (6.9) 2.7 (.16) 25.4 (1.) (57.5) W (6.9) 2.7 (.16) 19.1 (.75) (57.5) 5

6 f' Experimental (MPa) Experimental (x 1-3 mm/mm) R² = f' Analytial (MPa) Fig. 7 Correlation between experimental and analytial onfined onrete strength R² = Analytial (x 1-3 mm/mm) Fig. 8 Correlation between experimental and analytial peak strain of onfined onrete 85 Experimental (x 1-3 mm/mm) R² = Analytial (x 1-3 mm/mm) Fig. 9 Correlation between experimental and analytial strain at 85% of the peak strength of onfined onrete For verifiation of the proposed model, Figures 14 and 15 ompare the orresponding experimental and predited stress-strain urves of a few representative test speimens only listed in Table 2. It may be seen from these figures that the agreement between the preditions from the proposed model and the experimental stress-strain urves is very satisfatory. Figures 1-15 indiate that the proposed model predits the experimental results more aurately than the other models, espeially along the desending part of the stress-strain urve. This is beause suh previous models were developed for traditional tied and/or spiral olumns, whih are not as dutile as olumns transversely reinfored with WRG. It an also be onluded that the proposed model an predit the atual stress-strain urves 1 Experimental Proposed model 8 6 Legeron & Paultre Hoshikuma et al. s = 4.8% s = 3 mm s = 3.2% s = 45 mm s = 2.4% s = 6 mm s = 2.% s = 72 mm s = 1.6% s = 9 mm s = 1.2% s = 12 mm 4 2 N1-3W2-4.8 N1-45W2-3.2 N1-6W2-2.4 N1-72W2-2. N1-9W2-1.6 N1-12W % Fig. 1 Comparison between experimental and theoretial stress-strain urves of onfined onrete of 2 2 WRG with four longitudinal bars. 6

7 1 8 6 Experimental Legeron & Paultre Proposed model Hoshikuma et al. s = 4.8% s = 3 mm s = 3.2% s = 45 mm s = 2.% s = 72 mm 4 2 N2-3W2-4.8 N2-45W2-3.2 N2-72W2-2. 2% Fig. 11 Comparison between experimental and theoretial stress-strain urves of onfined onrete for 2 2 WRG with eight longitudinal bars s = 4.8% s = 3 mm Experimental Legeron & Paultre Proposed model Hoshikuma et al. s t = 3.2% s = 45 mm s = 2.4% s = 6 mm t s = 2.% t s = 72 mm s = 1.6% s = 9 mm s = 1.2% s = 12 mm 4 2 N1-3W3-4.8 N1-45W3-3.2 N1-6W3-2.4 N1-72W3-2. N1-9W3-1.6 N1-12W % Fig. 12 Comparison between experimental and theoretial stress-strain urves of onfined onrete for 3 3 WRG with four longitudinal bars s = 4.8% s = 3 mm Experimental Proposed model Legeron & Paultre Hoshikuma et al. s t = 3.2% s = 45 mm s = 2.% s = 72 mm 4 2 N2-3W3-4.8 N2-45W3-3.2 N2-72W3-2. 2% Fig. 13 Comparison between experimental and theoretial stress-strain urves of onfined onrete for 3 3 WRG with twelve longitudinal bars. 7

8 1 Experimental Proposed model 8 6 s = 1.36% s = 25.4 mm s = 3.13% s = 19.1 mm s = 2.38% s = 12.7 mm s =.99% s = 31.8 mm s = 1.% s = 25.4 mm 4 2 W-1 W-2 W-3 W-4 W-5 3%. Fig. 14 Predition of onfined onrete response of olumns of Holland [26] s t = 4.5% s = 19.1 mm s = 1.79% s = 19.1 mm s = 1.23% s = 25.4 mm Experimental s = 2.15% s = 25.4 mm Proposed model s = 2.87% s = 19.1 mm 4 2 W-6 W-7 W-8 W-9 W-1 3%. Fig. 15 Predition of onfined onrete response of olumns of Hong [27] more aurately for a wide range of experimental results [33] than the other models, partiularly in the desending branh of the urves. 5. Conlusions Based on the experimental results from eighteen RC olumn speimens tested by Tavio et al. [33], the onfinement effets of welded reinforement grids (WRG) on the stress-strain behavior of normal- and high-strength onrete were investigated and a stress-strain relationship model is proposed. The following onluding remarks an be drawn: (1) When the same amounts of welded reinforement grids (WRG) were used, the gains in the strength and dutility of normal strength onrete onfined by 3 3 welded reinforement grids (WRG) (9-ells) were predited higher by the proposed model than those of onrete onfined by 2 2 welded reinforement grids (WRG) (4-ells) only. (2) The dutility of olumns is shown to be dependent on onfinement index, f f. It is onluded that the strain dutility ratio inreases with an inrease in f f for a given welded reinforement grids (WRG). (3) The proposed model an predit the stressstrain urves more aurately for a wide range of experimental results [33] than the other models, partiularly in the desending branh of the urves. The proposed model has also been verified with other experimental data [26, 27]. It also provides a simple omputational proedure without requiring any iterative al- s yh s yh 8

9 ulation. Aknowledgements The authors would like to express their sinere gratitude to all the researh projet members on Innovative Development of WRG for Seismi-Resistant Strutures. Their generous ontributions are deeply appreiated. All opinions, findings, onlusions, and reommendations in the paper are those of the authors. Referenes 1. Tavio; and Teng, S. (24) Effetive Torsional Rigidity of Reinfored Conrete Members, ACI Strutural Journal, 11(2), pp Tavio (28) Building Code Requirements for Strutural Conrete (ACI 318-8) and Commentary (ACI 318R-8), Disussion and Closure, Conrete International, Amerian Conrete Institute (ACI), 3(4), pp Kusuma, B.; and Tavio (28) Unified Stress- Model for Confined Columns of Any Conrete and Steel Strengths, Proeedings of the 1 st International Conferene on Earthquake Engineering and Disaster Mitigation (ICEEDM-I), Jakarta, Indonesia. 4. Tavio; and Kusuma, B. 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10 26. Holland, J.M. (1995) Two-Dimensional Welded Wire Mesh as Confining Reinforement in Square Conrete Columns. MS Thesis, University of Houston, 118 pp. 27. Hong, L. (1997) Welded Wire Fabri as Confining Reinforement in Reinfored Conrete Columns. MS Thesis, University of Houston, 127 pp. 28. Saatioglu, M.; and Grira, M. (1999) Confinement of Reinfored Conrete Columns with Welded Reinforement Grids, ACI Strutural Journal, 96(1), pp Lambert, N.A.; and Tabsh, S.W. (1999) Confinement of High Strength Conrete with Welded Wire Reinforement, ACI Strutural Journal, 98(5), pp Hoshikuma, J.; Kawashima, K.; Nagaya, K.; and Taylor A.W. (1997) Stress- Model for Confined Reinfored Conrete in Bridge, Journal of Strutural Engineering, ASCE, 123(5), pp Legeron, F.; and Paultre, P. (23) Uniaxial Confinement Model for Normal-and High-Strength Conrete Columns, Journal of Strutural Engineering, ASCE, 129(2), pp Cusson, D.; and Paultre, P. (1994) High Strength Conrete Columns Confined by Retangular Ties, Journal of Strutural Engineering, ASCE, 12(3), pp Tavio; Kusuma, B.; and Suprobo, P. (212) Experimental Behavior of Conrete Columns Confined by Welded Wire Fabri as Transverse Reinforement under Axial Compression, ACI Strutural Journal, 19(3), pp Popovis, S. (1973) Analytial Approah to Complete Stress- Curves, Cement and Conrete Researh, 3(5), pp Carrasquillo, R.L.; Nilson, A.H.; and Slate F.O. (1981) Properties of High Strength Conrete Subjet to Short-Term Loads, ACI Journal, Proeedings, 78(3), pp Martinez, S.; Nilson, A.H.; and Slate, F.O. (1984) Spirally Reinfored High-Strength Conrete Columns, ACI Journal, Proeedings, 81(5), pp Foster, S.J.; and Gilbert, R.I. (1996) The Design of Non-flexural Members with Normal and High- Strength Conretes, ACI Strutural Journal, 93(1), pp