Predicting Nonlinear Behavior and Stress-Strain Relationship of Rectangular Confined Reinforced Concrete Columns with ANSYS

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1 Civil Engineering Dimension, Vol. 11, No. 1, Marh 2009, ISSN print / ISSN X online Prediting Nonlinear Behavior and Stress-Strain Relationship of Retangular Confined Reinfored Conrete Columns with ANSYS avio,. 1 and ata, A. 2 Abstrat: his paper presents a nonlinear finite element modeling and analysis of retangular normal-strength reinfored onrete olumns onfined with transverse steel under axial ompressive loading. In this study, the olumns were modeled as disrete elements using ANSYS nonlinear finite element software. Conrete was modeled with 8-noded SOLID65 elements that an translate either in the x-, y-, or z-axis diretions from ANSYS element library. Longitudinal and transverse steels were modeled as disrete elements using 3D-LINK8 bar elements available in the ANSYS element library. he nonlinear onstitutive law of eah material was also implemented in the model. he results indiate that the stress-strain relationships obtained from the analytial model using ANSYS are in good agreement with the experimental data. his has been onfirmed with the insignifiant differene between the analytial and experimental, i.e and 2.80 perent for the peak stress and the strain at the peak stress, respetively. he omparison shows that the ANSYS nonlinear finite element program is apable of modeling and prediting the atual nonlinear behavior of onfined onrete olumn under axial loading. he atual stress-strain relationship, the strength gain and dutility improvement have also been onfirmed to be satisfatorily. Keywords: ANSYS; onfinement; dutility; stress-strain relationship; nonlinear finite element analysis; nonlinear behavior; reinfored onrete olumns; strength. Introdution One of several reasons that ause the ollapse of a multi-story building or bridge struture is the failure of the supporting members to withstand the earthquake loading. he failure of these members is mostly due to the lak of shear-resisting apaity and insuffiient dutility provided by little amount of transverse steel. It is well known that the dutility of a reinfored onrete olumn plays a very important role in preventing suh a failure. hat is why the study on the dutility of a reinfored onrete olumn has been developing at a fast pae in the last two deades in many ountries worldwide. One of the effetive ways to improve the dutility of a olumn is by introduing suffiient transverse steel as onfining steel for onrete ore in a olumn. his effort is primarily intended to delay the sudden ollapse of a olumn and fore it further to fail in a dutile manner. 1 Department of Civil Engineering, Sepuluh Nopember Institute of ehnology (IS), Surabaya, Indonesia tavio@its.a.id 2 Department of Civil Engineering, Khairun University, ernate, Maluku Utara, Indonesia Note: Disussion is expeted before June, 1st 2009, and will be published in the Civil Engineering Dimension volume 11, number 2, September Reeived 20 Otober 2008; revised 17 November 2008; aepted January Ineffetive onfined region Effetive onfined region Figur 1. Effetive and ineffetive onfined regions in a onrete ore of a square olumn ross setion produed by the arhing ation due to the existene of retilinear onfinement he effetiveness of onfinement depends on the uniformity of the stress ourred around the perimeter interfae between the onfining steel and onrete ore. In retilinear olumn setion, the most effetive onfined regions are only loated at the four orners of the onfining steel as shown in Fig. 1. Fig. 1 also shows the ineffetive and effetive regions produed by the arhing ation due to the existene of retilinear onfining steel in a onrete ore of a square olumn setion. he effet of onfinement in a reinfored onrete olumn an be onsiderably inreased if: (1) the spaing of transverse steel is denser; 23

2 avio,., et. al / Retangular Confined Reinfored Conrete Columns / CED, Vol. 11, No. 1, Marh 2009, pp (2) more number and well distributed longitudinal steel is used around the perimeter of the olumn setion; and (3) more number and well-distributed rossties are provided in the onrete ore. Numerous researhes have been onduted earlier to study the effetiveness of onfinement in improving the dutility of reinfored onrete olumns. Some experimental tests arried out by several previous researhers inlude the studies onduted by Cusson and Paultre [1], Saatioglu and Razvi [2], and Assa, Nishiyama, and Watanabe [3]. Cusson and Paultre [1] arried through the experimental tests on square short olumns with high-strength onrete and proposed a stress-strain model of dutile onfined onrete. Saatioglu and Razvi [2] tested and observed the dutile behavior of onfined onrete olumns with the strength up to 120 MPa. Assa, Nishiyama, and Watanabe [3] also onduted similar tests on onfined irular and square short olumns and examined their dutile behaviors, and there are still many more studies onduted by others [4-11]. he numerial approahes onduted by previous researhers were mostly developed on empirial basis. his is due to the omplex parameters involved in deriving the onstitutive law of onfined onrete. hough, some researhers had made many attempts to ome up with an aurate analytial stress-strain model of onfined onrete, they always ended up with a fine-tuning measure in mathing up the analytial results with the experimental data obtained from their tests. he authors fully realize that the experimental program is one of the best ways to adjust a model in order to ahieve an aeptable auray for pratial usage. his sort of effort, however, is often very ostly and time onsuming; besides it still depends on the availability and auray of the test apparatus and instrument. In addition, the use of the proposed model is often limited to a ertain extent of the test data where they are alibrated with. In this paper, the authors propose to use ANSYS [12], whih is apable of modeling the nonlinear behavior of reinfored onrete beams [13-15], for prediting the atual stress-strain relationship of both unonfined and onfined retangular onrete olumns with various spaings of transverse steel under axial onentri loading. However, none of the works [13-15] onduted previously using ANSYS inludes reinfored onrete olumns onfined by transverse steel or stirrups. he proposed proedure has been verified with four olumn speimens onfined by various spaing of stirrups representing light to heavy onfinement tested by Hoshikuma [16]. he analytial stress-strain urves obtained from the proposed proedure are shown to be in lose agreement with the experimental data from Hoshikuma [16]. Researh Signifiane Modeling the onstitutive law of onfined reinfored onrete olumns based on the empirial approah an sometimes be inaurate or limited to a narrow range of available experimental data. he tests are also very expensive and sometimes time onsuming. he appliability of the test data mainly depends on the auray of the test apparatus and the supporting instruments implemented during the test. Hene, it is deemed neessary to have another option of modeling the stress-strain relationship of onfined onrete without deploying an empirial approah in the modeling. One of the suitable software that an be utilized to desribe the atual nonlinear behavior of onfined onrete olumns under axial loading is ANSYS [12]. his is beause ANSYS is apable of analyzing the nonlinear behavior of a ombination between 3D SOLID and LINK elements in a struture based on the finite element proedure. With this option, researhers or design engineers an onfidently predit in advane the atual behavior of various onfined onrete olumns not only in the linear-elasti region, but furthermore also in the nonlinear post-elasti region. he authors wish that this eonomial proedure an be used to provide an alternative tool for researhers or strutural engineers in investigating various types of strutural onrete elements in the future. Finite Element Proedure he finite element proedure implemented in this study is developed using the available element types from ANSYS element library [12]. he onrete is modeled using SOLID65 element type, whereas the steel for longitudinal and transverse reinforements is modeled with LINK8 element type. SOLID65 is seleted beause this onrete material model an predit the failure of brittle materials by adopting the onstitutive model of onrete [12]. Both raking and rushing failure modes an be aounted for [12]. LINK8 in ANSYS is seleted beause this steel material model an take into aount the omplete stress-strain relations of materials [12]. Both yielding and strain-harderning failure modes an be aounted for [12]. he onepts used are diretly appliable to 3D SOLID elements [12]. By adopting and ombining these two element types, the reinfored onrete olumn model was developed. he olumn model was subjeted to an axial ompressive loading on their top fae simulating the atual loading applied in the tests [16], while the 24

3 avio,., et. al / Retangular Confined Reinfored Conrete Columns / CED, Vol. 11, No. 1, Marh 2009, pp bottom side was restrained. he loading proedure an be elaborated in the following sequene: (1) for the asending branh (up to peak stress): the olumn model is subjeted to a step-by-step inremental axial pressure on its entire top surfae; then (2) for the desending portion (beyond the peak stress): the loading was then swithed into the displaementmode ontrol by applying a step-by-step inremental displaement on its top surfae. o obtain an effiient solution, the olumn was modeled in a quarter following the symmetrial lines of its ross setion as shown in Fig. 2. he two sides along the symmetrial lines of a quarter were restrained to simulate the atual behavior of the fullsize olumn, and thus, maintaining the auray of analysis of the model. Symmetrial line Axially loaded Rest rained Symmetrial lines Figur 2. Boundary onditions of a symmetrial quarter of a olumn model: (a) elevation; (b) ross setion Determination of Model he analytial models were onstruted aording to the atual olumn speimens in literature [16] as shown in Fig. 3. he olumn models had a typial ross setion of 500 mm 500 mm with the height of 1500 mm as listed in able 1. he onrete over was 20 mm. he first olumn speimen was made from plain onrete, namely speimen LS0 (Fig. 3). he three remaining olumn speimens had various spaings and diameters of transverse steel, i.e. speimens LS1, LS2, and LS3 (see Fig. 3). he mehanial properties of eah speimen used for validation in this study were adopted in developing the analytial models to better reflet the atual behavior of eah olumn speimen. Material Properties he onstitutive laws used in the proposed analytial model were developed for two materials of olumn speimens, namely onrete and steel. Sine the proposed proedure is intended as an alternative way for prediting the atual nonlinear behavior of both unonfined and onfined reinfored onrete olumns prior to onduting the experimental program, the following analytial models are seleted in lieu of the atual experimental data. he experimental data is assumed unavailable at this stage, even though it might produe better predition to the atual behavior of the olumn speimens. he analytial model proposed by Popovis [17,18] to represent the stress-strain relationship of onrete was adopted in this study. For reinforing steel, the analytial model was that proposed by Park and Paulay [19]. he element type used to model eah material is those from the ANSYS element library [12] and summarized in able 2. he onrete is modeled using SOLID65 element, whereas the steel reinforement is modeled with LINK8 element. o develop the proposed analytial model in the ANSYS software, the following data is required to be prepared for the input data prior to the analysis. he material properties of eah element type an be elaborated in the following details to reflet the able 1. Summary of geometrial and mehanial properties of the olumn speimens Column Cross Setion Height f ρ fy l fyh Spaing,s Volumetri ratio ID (mm) (mm) (MPa) (%) (MPa) (MPa) (mm) (%) (1) (2) (3) (4) (5) (6) (7) (8) (9) LS LS LS LS Note: f = ompressive strength of onrete; ρ = ratio of longitudinal steel; fy l = yield strength of longitudinal steel; fyh = yield strength of transverse steel. able 2. Material types for modeling the olumn speimens Material Conrete Steel Reinforement ANSYS Elemen ype Solid65 Link8

4 avio,., et. al / Retangular Confined Reinfored Conrete Columns / CED, Vol. 11, No. 1, Marh 2009, pp Weld Weld Weld Weld Weld Weld Figure 3. Geometrial properties of olumn speimens LS0, LS1, LS2, and S3 used for model validation atual mehanial and physial properties of the olumn speimens. Following is the summary of the onrete properties required for input data: 1) stress-strain relationship of onrete (σ ); 2) modulus of elastiity of onrete (E); 3) speified ompressive strength of onrete (f = 24.3 MPa); 4) modulus of rupture of onrete (fr); 5) poisson ratio of onrete (ν = 0.2) ; 6) onrete density (γ); and for the reinforing steel, it an also be summarized as follows: 1) stress-strain relationship of reinforing steel (σs s); 2) speified yield strength of longitudinal steel (fy l = 295 MPa); 3) speified yield strength of transverse steel (fyh = 235 MPa); 4) modulus of elastiity of reinforing steel (Es); 5) Poisson ration of reinforing steel (νs = 0.3); 6) steel density (γs). he stress-strain relationship of onrete proposed by Popovis [17,18] as a part of the onstitutive laws adopted in the proposed model an be desribed by the following equations: Stress, f' f o f 0.5 A B o Strain, Desending Branh C u Figure 4. Stress-strain relationship of onrete proposed by Popovis [17,18] f nfo o = n 1+ o nk For region AB (0 o), k = 1 if o (1) 1 (2) 26

5 avio,., et. al / Retangular Confined Reinfored Conrete Columns / CED, Vol. 11, No. 1, Marh 2009, pp For region BC ( > o), f k = MPa 62 if o > 1 (3) E = 3320 f MPa (4) f n o = E n 1 (5) f n = MPa 17 (6) Stress f f su f y f s B A y tan θ= E s θ C sh Strain D su Figure 5. Stress-strain relationship for reinforing steel proposed by Park and Paulay [19] For reinforing steel, the adopted stress-strain relationship in the proposed model is that proposed by Park and Paulay [19]. he related equations used to develop the onstitutive laws in the model are as follows: For region AB (0 s y), fs = ses (7) f y y = (8) Es For region BC (y s sh), fs = fy (9) sh = 16y (10) For region CD (sh s su), m( fs = s sh) + 2 ( s sh)(60 m) f + 2 (11) y 60( s sh) + 2 2(r + 1) where: 2 ( fsu / f y )(r + 1) + 60r 1 m = (12) 2 15r r = su sh (13) Element Meshing After preparing all the input data of material and geometrial properties, the olumn models were divided into small ubial elements. he meshing results of all olumn speimens used for model validation are shown in Fig. 6. Column speimen s LS0 was also meshed with similar pattern as three other olumn speimens shown in Fig. 6. For olumns reinfored with steel rebar, it is worthwhile to notie that the meshing was reated aording to the loations of reinforing bars, either the longitudinal or transverse reinforement, as well as the olumn speimen ross-setional perimeter. By using sharing nodes option in ANSYS [12], SOLID65 and LINK8 elements an be interonneted one to another forming a single solid olumn model whih apable of simulating the atual behavior of reinfored onrete olumn. Loading Proedure o apply the axial load on the top of the olumn speimen, an axial pressure was implemented over the entire top surfae of the olumn model in the ANSYS software. he axial pressure an be simulated using the ANSYS load step option [12]. Load step option may be used when the inremental loading is onsidered. he number of load steps depends on the user s definition. In this ase, load steps were defined aording to the atual load steps applied during the test. A solution was obtained by solving several sub-steps in eah load step to attain onvergene. In eah sub-step, an iteration proedure was arried out until providing a onvergent solution before moving to the next sub-step. he number of the sub-steps taken in the analysis may improve the auray of the solution. It will, however, sometimes be very time-onsuming when too many sub-steps are taken. o avoid the problem, ANSYS offers an alternate automati time step option [12] to redue the omputational time required in the analysis. Due to this advantage, this option is seleted. When the automati time step option is seleted, it will automatially resize the number of the sub-steps in eah load step when it fails to reah a onvergent solution. his proess keeps repeating until it provides a onvergene value. When the load has reahed its peak value, the load ontrol mode was swithed into the displaement ontrol mode. he displaement ontrol mode was set into several displaement steps orresponding to the experimental data. Using the automati time steps, the olumn speimen was displaed until failure. he objetive of using this kind of mode is to obtain the desending branh of the stress-strain urve of the olumn speimens under axial loading. he inremental nonlinear equation an be written as follows: K( u) u = P (14) where u and P desribe the unknown inremental displaement and the given inremental applied load vetors, respetively. 27

6 avio,., et. al / Retangular Confined Reinfored Conrete Columns / CED, Vol. 11, No. 1, Marh 2009, pp o solve a nonlinear problem, ANSYS uses the Newton-Raphson (N-R) method [12] involving an iterative proedure. his method starts with a trial assumption: u = ui, to define the inremental of the next steps, ui = K 1 (ui) P, and the load vetor exists beyond the equilibrium, Ri = P K(ui) ui. here will always be a disrepany between the applied load and the load evaluated based on the assumption. o satisfy the state of equilibrium, the load vetor exists beyond the equilibrium should be zero. Sine the solution requires an iterative proedure, a tolerane value should be determined suh that a onvergent solution an be obtained. In eah iteration step, N-R method alulates the load vetor exists beyond the equilibrium and always heks if the onvergent solution under speified tolerane is obtained. If the value is still greater than the tolerane value, then the initial assumed value is updated with the inremental displaement, ui+1 = ui + ui. he next inremental solution vetor is determined with ui+1 = K 1 (ui+1) P, providing a new load vetor exists beyond the equilibrium Ri+1 = P K(ui+1) ui+1. his proedure is repeated until the onvergent solution is obtained. Numerial Impelementation he quantitative implementation of the finite element proedure used in the ANSYS software [12] is based on the priniples of virtual work or the postulation of minimum potential energy in the assembly of the elements as formulated the following equilibrium equation: [ K ]{ d} + { F} + { F} + { F} + { F } { R} = 0 (15) p g 0 σ 0 he stiffness matrix [K], K = B D B dv (16) [ ] [ ] [ ][ ] he nodal fore due to the surfae load, F N p dv (17) { } p = [ ] { } ele he nodal fore due to the body load, F N g dv (18) { } g = [ ] { } ele he nodal fore due to the initial strain, = B D dv { F} 0 [ ] [ ]{ 0} ele he nodal fore due to the initial stress, B D dv { F} σ 0 = [ ] [ ]{ σ 0} ele (20) (21) LS0 LS1 LS2 LS3 Figure 6. Element meshing of quarter olumn speimens LS0, LS1, LS2, and LS3 28

7 avio,., et. al / Retangular Confined Reinfored Conrete Columns / CED, Vol. 11, No. 1, Marh 2009, pp where [N] is the shape funtion; {d} is the vetor of nodal displaement; {R} is the vetor of applied nodal fore; {p} is the vetor of surfae load; and {g} is the vetor of body load. he ANSYS software uses Newton-Raphson (N-R) method [12] to obtain the onvergent solution of the nonlinear equilibrium iterative equation to develop the stiffness matrix of the olumn model. Results and Disussions Stress Distribution he axial stress distributions of olumn speimens LS0, LS1, LS2, and LS3 obtained from the ANSYS solution are shown in Fig. 7. As an be seen in the figure, for olumn speimens LS1, LS2, and LS3, the axial stress ontours over mid-height ross setions of the olumn speimens indiate similar axial stress distributions with various intensities of stress onentrations. he axial stress onentrations around the longitudinal reinforement also indiate similar axial stress distributions with the axial stress distribution in the atual olumn speimens. Column speimen LS0 has different axial stress ontour sine it does not ontain any reinforing bars (plain onrete). Higher axial stress onentration ours over the enter region of the olumn ross setion. his phenomenon desribes a orret mehanism of a plain onrete olumn speimen subjeted to axial loading. Stress-Strain Relationship he axial stress-strain urves obtained from the ANSYS solution are onfirmed by the experimental results [16]. From the omparisons shown in Fig. 8, it shows that the preditions are in lose agreement with the experimental urves. his indiates that the atual behavior of olumn speimens onfined by various volumetri ratios of transverse steel under axial ompressive loading an be aurately predited by the FEM approah. he auray of the proposed proedure is also onfirmed by the lose values of peak stress, strain at the peak stress as well as strain when the stress drops to 85 perent of the peak stress obtained from the FEM analysis and the experimental test. From the omparison values listed in able 3, it an be seen that the largest differenes of all olumn speimens onsidered in the study are only 2.80, LS0 LS1 LS2 LS3 Figure 7. Axial stress distributions over the mid-height ross setion of quarter olumn speimens LS0, LS1, LS2, and LS3 29

8 avio,., et. al / Retangular Confined Reinfored Conrete Columns / CED, Vol. 11, No. 1, Marh 2009, pp Stress, f (MPa) LS0 f = MPa = ,000 0,005 0,010 0,015 0,020 Stress, f (MPa) LS1 est HOSHIKUMA [16] f = MPa = est [16] f = MPa = Strain, Strain, Stress, f (MPa) 35 LS2 est HOSHIKUMA [16] f = MPa = est [16] 5 f = MPa = Stress, f (MPa) LS3 est HOSHIKUMA [16] f =.20 MPa = est [16] 5 f =.11 MPa = Strain, Strain, Figure 8. Stress-strain urves of olumn speimens LS0, LS1, LS2, and LS3 able 3. Comparison between the peak stress and strain at the peak stress obtained from FEM analysis and experimental test Column Speimen ID FEM f (MPa) est Diff. (%) FEM (%) est Diff. (%) FEM 85 (%) est Diff. (%) LS LS LS LS , and 5.38 perents for the peak stress, the strain at the peak stress, and the strain when the stress drops to 85 perent of the peak stress, respetively. hese values onfirmed the auray of the proposed proedure in prediting the atual nonlinear behavior of the olumns under axial loading shown in Fig. 8. Conlusions Based on the FEM analysis and disussion above, the following onlusions an be drawn: 1. ANSYS software is apable of prediting the atual stress-strain relationships of both unonfined and onfined reinfored onrete olumn speimens subjeted to axial loading. 2. From the axial stress ontours obtained from the FEM analysis, it an be onluded that the axial stress onentrations are in the enter regions of the olumn ross setions, partiularly in the onfined areas. 3. he auray of the proposed proedure has been well onfirmed by the lose values of peak stress, strain at the peak stress as well as strain when the stress drops to 85 perent of the peak stress obtained from the FEM analysis and the experimental test.

9 avio,., et. al / Retangular Confined Reinfored Conrete Columns / CED, Vol. 11, No. 1, Marh 2009, pp Referenes 1. Cusson, D. and Paultre, P., High-Strength Conrete Columns Confined by Retangular ies, Journal of Strutural Engineering, ASCE, V. 120, No. 3, Mar. 1994, pp Saatioglu, M. and Razvi, S., High-Strength Conrete Columns with Square Setion under Conentri Compression, Journal of Strutural Engineering, ASCE, V. 124, No. 12, De. 1998, pp Assa, B., Nishiyama, M., and Watanabe, F., New Approah for Modeling Confined Conrete Retangular Columns, Journal of Strutural Engineering, ASCE, V. 127, No. 7, July 2001, pp Fafitis, A. and Shah, P. S., Lateral Reinforement for High-Strength Conrete Columns, ACI Speial Publiation, SP-87, Detroit, USA, 1985, pp Nagashima,., Sugano, S., Kimura, H., and Ihikawa, A., Monotoni Axial Compression est on Ultra High Strength Conrete ied Columns, Proeedings of the 10th World Conferene on Earthquake Engineering, Madrid, Spain, July 19-24, 1992, V. 5, pp Cusson, D. and Paultre, P., Stress-Strain Model for Confined High-Strength Conrete, Journal of Strutural Engineering, ASCE, V. 121, No. 3, Mar. 1995, pp Sheikh, S. A. and Uzumeri, S. M., Analytial Model for Conrete Confinement in ied Columns, Journal of the Strutural Division, ASCE, V. 108, S12, De. 1982, pp Sheikh, S. A. and Uzumeri, S. M., Strength and Dutility of ied Conrete Columns, Journal of the Strutural Division, ASCE, V. 106, S5, May 1980, pp Sott, B. D., Park, R., and Priestley, M. J. N., Stress-Strain Behavior of Conrete Confined by Overlapping Hoops at Low and High Strain Rates, ACI Strutural Journal, V. 79, No. 1, Jan.-Feb. 1982, pp Nishiyama, M., Fukushima, I., Watanabe, F., and Muguruma, H., Axial Loading est on High-Strength Conrete Prisms Confined by Ordinary and High-Strength Steel, Pro. Symposium on High-Strength Conrete, 1993, pp Razvi, S. and Saatioglu, M., est of High- Strength Conrete Columns under Conentri Loading, Rep. No. OCEERC 96-03, Ottawa Carleton Earthquake Engineering Researh Centre, Ottawa, ON, Canada, ANSYS, ANSYS User s Manual Revision 5.6, ANSYS, In., Canonsburg, Pennsylvania, Santhakumar, R., Dhanaraj, R., and Chandrasekaran, E., Behaviour of Retrofitted Reinfored Conrete Beams under Combined Bending and orsion: A Numerial Study, Eletroni Journal of Strutural Engineering, V. 7, 2007, pp Wolanski, A. J., Flexural Behavior of Reinfored and Prestressed Conrete Beams using Finite Element Analysis, MS. hesis, Faulty of the Graduate Shool, Marquette University, Milwaukee, Wisonsin, May Barbosa, A. F., and Ribeiro, G. O., Analysis of Reinfored Conrete Strutures using ANSYS Nonlinear Conrete Model, Computational Mehanis, CIMNE, Barelona, Spain, 1998, pp Hoshikuma, J., Kawashima, K., Nagaya, K., and aylor, A. W., Stress-Strain Model for Confined Reinfored Conrete in Bridge, Journal of Strutural Engineering, ASCE, V. 123, No. 5, May 1997, pp Popovis, S., A Numerial Approah to the Complete Stress-Strain Curve of Conrete, Cement and Conrete Researh, V. 3, No. 5, May 1973, pp Collins, M. P., Mithell, D., and MaGregor, J. G., Strutural Design Consideration for High- Strength Conrete, Conrete International, ACI, V. 15, No. 5, May 1993, pp Park, R. and Paulay,., Reinfored Conrete Strutures, John Wiley and Sons, In., Canada, July