SIMULATION OF BEHAVIOR OF REINFORCED CONCRETE COLUMNS SUBJECTED TO CYCLIC LATERAL LOADS

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1 SIMULATION OF BEHAVIOR OF REINFORCED CONCRETE COLUMNS SUBJECTED TO CYCLIC LATERAL LOADS H. Sezen 1, M.S. Lodhi 2, E. Setzler 3, and T. Chowdhury 4 1,2 Department of Civil and Environmental Engineering and Geodeti Siene, The Ohio State University, Columbus, Ohio 3 Burgess and Niple, Painesville, Ohio 4 Skidmore Owings and Merrill, Chiago, Illinois ABSTRACT Reinfored onrete (RC) olumns with insuffiient transverse reinforement and non-seismi reinforement details are vulnerable to shear failure and loss of axial load arrying apaity. With an aim of developing a maro model to simulate yli lateral load-deformation performane, the behavior of non-dutile RC olumns is modeled by ombining deformation omponents due to flexure, reinforement slip and shear. Individual deformation omponent models developed for monotoni lateral loads serve as envelopes or primary urves for respetive yli responses. Based on a omparison of their predited shear and flexural strengths, the olumns are lassified into five general ategories and total monotoni and yli response is obtained by ombing the three deformation omponents aording to a set of rules speified for eah ategory. The proposed monotoni and yli response models are ompared with the data from various experimental studies on olumns having flexural failure with very limited or no shear effets, flexure and/or shear failure following the flexural yielding, and shear failure prior to flexural yielding. The predited and experimental response of olumns failing primarily in shear and flexure were omparable. Similarly, the hystereti response of the olumn with axial load failure was aptured reasonably well by foring the monotoni response envelopes to degrade linearly between the peak strength and the point of axial load failure. Although, the researh is foused on modeling the behavior of shear ritial olumns under seismi loads, the developed model is appliable to all RC olumns. KEYWORDS: Reinfored onrete olumns, monotoni and yli load, shear failure, axial load failure, loaddeformation behavior. 1. INTRODUCTION There is a large inventory of reinfored onrete buildings in US and other parts of the world that are not designed aording to modern seismi design provisions. These buildings are often haraterized by low lateral displaement apaity and rapid degradation of shear strength and hene are vulnerable to severe damage or even ollapse during strong ground motions. The need to assess their vulnerability to earthquake damage and hene suggesting the desired level of retrofit requires evaluation of the expeted behavior in terms of strength and deformation apaity. Reonnaissane of damage observed during the past earthquakes suggests that poorly designed reinfored onrete olumns are the most ritial elements to sustain damage leading to a potential building ollapse (Sezen et al. 23). Typially, these olumns have insuffiient and widely spaed transverse reinforement and lak essential seismi reinforement details resulting in non dutile behavior. The researh reported here is aimed at developing a model that an predit monotoni and yli response of a lightly reinfored onrete olumn subjeted to lateral loading. A typial fixed-ended reinfored onrete olumn, when subjeted to earthquake loading, undergoes lateral deformation whih is omprised of three omponents; flexural deformations, reinforement slip deformations and 1

2 shear deformations (Fig 1a). Eah of these deformation omponents are modeled separately and then ombined under a set of rules to obtain total monotoni and yli lateral response. Component deformation models and total response model under monotonially inreasing lateral load serve as response envelope or primary urve for respetive omponent and yli responses. The proposed model is tested against the experimental data reported by various researhers and is found to perform well with suffiient auray. Although, the researh is foused on modeling lightly reinfored onrete olumns that experiene flexural yielding followed by the shear failure, the model is appliable to the olumns failing in shear suh as very short olumns or well reinfored olumns that develop plasti hinges and eventually fail in flexure. 2. DEVELOPMENT OF MONOTONIC LATERAL RESPONSE ENVELOPE 2.1. Flexural Deformations Flexural response of reinfored onrete elements an aurately be determined by performing setion analysis on a fiber model onsidering the atual onstitutive material properties in one dimensional stress field. In this study, the onstitutive laws for onrete in ompression are defined onsidering the effets of onfinement on onrete ore as per the onfinement model by Mander et al. (1988). However, in order to represent the expeted post-peak onrete behavior in shear ritial olumns, the desending branh is modeled by the relation developed by Roy and Sozen (1964). The reinforing steel behavior is modeled onsidering a linear elasti behavior, a yield plateau, and a nonlinear strain-hardening region. To be as realisti as possible and to apture non-linearity in atual urvature distribution, flexural deformations are alulated by integrating urvatures up to the yield point and by a plasti hinge model after the yielding as per Eqn and respetively. L f, y ( x) xdx (2.1.1) f f, y L (2.1.2) p y L p a 2 where f,y is the flexural displaement at yield, (x) is the setion urvature at distane x measured along olumn axis, L is the height of the olumn, is the urvature at the olumn end, y is the urvature at yield, and a is the shear span. The plasti hinge length, L p, is taken as one half of the total setion depth per the reommendations of Moehle (1992). Complete details of the flexural deformation model, inluding the material onstitutive laws and moment-urvature analysis, an be found in Setzler (25) and Chowdhury (27) Reinforement Slip Deformation The flexural deformations as determined through onventional fiber setion analysis do not aount for the rotations that are aused by reinforement slip. This results in lateral displaement that an be as large as 25 to 4% of the total lateral deformations (Sezen, 22). Therefore, slip deformations must be aounted for separately and added to the other deformation omponents (flexure and shear) to aurately model total drift of a olumn. Lateral displaements due to reinforement slip are alulated in this study through a model whih was originally developed by Sezen and Moehle (23) and further developed by Sezen and Setzler (28). The model, as shown in Fig 2a, approximates the bond stress as bi-uniform funtion with different values for elasti and inelasti steel behavior, whih allows for the effiient omputation of the reinforement slip and eliminates the need for the nested 2

3 iteration loops that are required in some of the existing bond stress-slip models. The value for the bond stress in the elasti range is taken as u 1 f (MPa) based on a study by Sezen (22) on 12 test olumns. For the inelasti b range, the value for bond stress is adopted from the study by Lehman and Moehle (2) as u. 5 f (MPa) where f is onrete ompressive strength. Slip at the loaded end of the reinforing bar an be alulated by integrating bi-linear strain distribution over the development length as follows: where l f d s b d and 4ub l d ( f s f b y 4u ) d b slip l d l d ( x) dx (2.2.1) orrespond to the development lengths for elasti and inelasti portions of the bar, respetively. f s is stress at loaded end of the bar, f y and d b are yield stress and diameter of the bar, respetively. The reinforement slip is assumed to our in tension bars only and ause the rotation about the neutral axis. Hene, slip rotation an be alulated from the following equation: slip s (2.2.2) d where d and are the distanes from the extreme ompression fiber to the entroid of the tension steel and the neutral axis, respetively. The lateral displaement at the free end of a antilever olumn an be alulated as the produt of this slip rotation and length of the olumn. b 2.3. Shear Deformations The basis of the shear model used in this researh is the model developed by Patwardhan (25), whih uses Modified Compression Field Theory, MCFT (Vehio and Collins, 1986). Patwardhan (25) proposed a pieewise linear model defining key points in the lateral fore-shear deformation envelope through a parametri study implementing MCFT through a omputer program Response-2. In this study, pre-peak non linear shear foreshear deformation response is obtained indiretly from Response-2 by integrating shear strain distribution over the height of the olumn for eah load step as following: v L ( x) dx (2.3.1) where is the average shear strain over the ross-setion at eah loation x along the height, L of the olumn, and v is the shear displaement. After the peak strength has reahed, the shear strength is assumed to remain onstant at its peak value until the onset of shear strength degradation. By modifying the equation proposed by Gerin and Adebar (24), the shear displaement at the onset of shear degradation, v,u, an be alulated as: vn v, u 4 12 v, n f (2.3.2) 3

4 Where, v n is the shear stress at peak strength, f is the onrete ompressive strength, and v,n is the shear displaement at maximum strength determined from Response-2. The peak strength, V peak is the minimum of the shear strength of the olumn, V n, and shear fore orresponding to the maximum moment sustainable by the setion, V p. After the shear degradation is initiated, shear strength dereases linearly with inreasing shear deformations to the point of axial load failure, where lateral strength is assumed to be zero, as shown in Fig 2b. The displaement at axial load failure, v,f, is alulated as: (2.3.3) v, f ALF f, f s, f v, u where ALF is the total displaement at axial load failure, and f,f and s,f are the flexural and slip displaements, respetively, at the point of axial load failure. The drift at axial load failure is determined by the expression proposed by Elwood and Moehle (25a), whih is based on a shear frition model and an idealized shear failure plane as: L ALF tan tan P A sv f yv s d tan (2.3.4) where is the angle of the shear rak, P is the axial load, A sv is the area of transverse steel with yield strength f yv at spaing s, and d is the depth of the ore onrete, measured to the enterlines of the transverse reinforement. In the derivation, is assumed to be 65 degrees Total Monotoni Lateral Response The proposed proedure models eah of flexure, slip and shear deformation by a spring subjeted to the same fore and the total response is the sum of the responses of eah spring (Fig 1b). Eah of the deformation omponents an simply be added to obtain the total response up to the peak strength of the olumn. However, for post-peak behavior, the olumn is lassified into one of the five ategories based on a omparison of its shear, yield and flexural strengths and rules are speified for the ombination of the deformation omponents for eah ategory (Setzler and Sezen, 28). Yield strength, V y is defined as the lateral load orresponding to the first yielding of the tension bars in the olumn, flexural strength, V p is the lateral load orresponding to the peak moment sustainable by the olumn during flexural analysis. The shear strength of the olumn, V n is alulated by the expression developed by Sezen and Moehle (24) for lightly reinfored onrete olumns as: 6 f P Asv f yvd V n k( V Vs ) k 1. 8Ag (2.4.1) a 6 f A s g d where V is the onrete ontribution to shear strength, V s is the steel ontribution to shear strength. A sv is the area of transverse steel at spaing s, k is a fator related to the displaement dutility, whih is the ratio of the maximum displaement to the yield displaement. Classifiation of the olumn based on omparison of shear, yield and flexural strength determines expeted olumn behavior. The peak response is limited by the lesser of the shear strength (V n ) and the flexural strength (V p ), however post peak response is assumed to be governed by the limiting mehanism (i.e., flexure or shear). Category 4

5 I olumn (V n < V y ) fails in shear while the flexural behavior remains elasti. Category II olumn (V y V n <.95V p ) also fails in shear, however inelasti flexural deformation ourring prior to shear failure affets the post-peak behavior. Shear deformations ontinue to inrease after the peak shear strength is reahed, but the flexure and shear springs are loked at their peak strength values. In Category III olumn (.95V p V n 1.5 V p ), the shear and flexural strengths are nearly idential. It is not possible to predit onlusively whih mehanism will govern the peak response. Shear and flexural failure are assumed to our simultaneously, and both mehanisms ontribute to the post-peak behavior. Category IV olumn (1.5 V p < V n 1.4V p ) may potentially fail in the flexure, however inelasti shear deformations affet the post-peak behavior and shear failure may our as the displaements inrease. The shear strength in Category V olumn (V n > 1.4V p ) is muh greater than the flexural strength and olumn fails in flexure while shear behavior remains elasti Shear Failure at High Displaement Dutility Shear strength degrades as the displaement dutility inreases (Sezen and Moehle, 24), whih an ause shear failure in the olumns that are initially dominated by flexure. To apture suh behavior, as enountered in ategory- IV olumns, shear failure surfae defined by the empirial drift apaity model by Elwood and Moehle (25b) is imposed on the lateral load-total displaement behavior as per following equation: SF L v 1 P 1 4 v (2.5.1) 5 f 4 A f 1 g where SF is the drift at shear failure, v is the transverse reinforement ratio, and v is the nominal shear stress. f and v have units of psi. If the total lateral response envelope exeeds the alulated drift at shear failure, shear failure is assumed to have ourred (Elwood 24), and the model is modified to degrade linearly from the point of shear failure to strength of zero at the drift at axial load failure. 3. CYCLIC RESPONSE MODEL Lightly reinfored onrete olumns exhibit harateristi behavior under yli lateral loading assoiated with stiffness deterioration, strength deay, pinhing, and axial load effets. A realisti hystereti model must be able to simulate these harateristi features in order to suessfully predit the lateral deformation response of suh olumns. As was done for monotoni response, yli response for eah deformation omponent is predited using a set of hystereti rules and then ombined to obtain total yli response. Eah omponent and total monotoni response serves as an envelope or primary urve for the orresponding yli response omponent. The proposed yli response models are based on existing hystereti models that are either simplified for omputational effiieny or modified to better present the atual behavior of the olumns onsidered in this study Component Hystereti Models In order to aurately analyze the hystereti flexural response a shear ritial olumn, strength deay features must be inorporated into hystereti model alongwith stiffness degradation onsiderations. The proposed hystereti model for flexural response is based on a modified model by Takeda et al. (197), whih provides realisti lateral behavior of reinfored onrete olumn with a limited omputational effort and inorporates degradation of stiffness during reloading and unloading of hystereti fore-deformation behavior. In the proposed model, the reloading branhes of hystereti loops are aimed at previous maximum response points, thereby simulating stiffness degradation. The reloading slope (k 3 in Fig 4a) is dereased with inreasing maximum response deformation. 5

6 Unloading slopes (k 1 and k 2 in Fig 4a) are alulated as a funtion of the previous maximum deformation. The original unloading slope defined by Takeda et al. (197) is multiplied by a fator of 1.7 to predit realisti yli flexural response of a lightly reinfored onrete olumn. Hene, the proposed slope of the unloading branh is given by: k r D y ky( ) (3.1.1) D where k r is the slope of the unloading branh, k y is the slope of the line onneting the yield point in one diretion to the raking point in the other diretion, D is the maximum defletion attained in the diretion of the loading, and D y is the yield defletion. The strength deay feature is inorporated in the proposed yli flexural model by enveloping the response through monotoni flexural response whih exhibits deterioration of strength after reahing the peak strength. For simpliity, the alulated monotoni response envelope is represented by few seleted points on the envelope and extended linearly beyond the theoretial failure point. This envelope replaes tri-linear primary urve used in original Takeda et al. model. The proposed hystereti model for reinforement slip is based on the model by Alsiwat and Saatioglu (1992) whih inorporates pinhing of hysteresis loops and degradation of stiffness taking plae during reloading and unloading. The primary urve employed for the hystereti model by Alsiwat and Saatioglu is replaed with monotoni response envelope based on the bar slip model proposed by Sezen and Setzler (28). The slopes of the unloading and reloading branhes hange only at zero fore level, hene proposed hystereti slip model is similar to that of hystereti flexural model shown in Fig 4a. The monotoni slip model envelopes the hystereti model and fores strength deay beyond peak strength at larger deformations. Unlike flexural response, shear fore-shear deformation relationship shows pronouned pinhing of hysteresis loops due to sliding of two raked surfaes, developed during previous loadings, and is exhibited by a redution in load resistane during reloading. Shear ritial reinfored onrete olumns also exhibit prominent deterioration in stiffness and strength deay during reversed yli loading. The proposed hystereti shear model is based on the model by Ozebe and Saatioglu (1989) whih suessfully integrates strength deay, stiffness deterioration and pinhing of hysteresis loops in hystereti shear fore-shear deformation relationship in a omputationally effiient way. The pinhing of hysteresis loops is inorporated in the model by defining two separate lines for reloading branhes, with a hange of slope established at the raking point or V r in Fig 4b. The deterioration of the stiffness is simulated by aiming at previous maximum response points. The model by Ozebe and Saatioglu is modified to better simulate stiffness degradation and to apture response of the olumn with limited displaement dutility or with no flexural yielding. In this regard, it is suggested that the reloading branh be targeted at the previous peak displaement and load instead of a projeted point in the original model. Thus the reloading branh beyond V r follows a straight line and passes through the maximum displaement point reahed previously. Also, in order to apture response of the olumn with signifiant shear distress properly, the slope of the unloading branh between ' V r and zero lateral load ( k2 or k 2 in Fig 4b) is revised and redued to: k2 or ' k 2.2k y 1. 7 where is maximum displaement reahed during previous yle before unloading, k y is slope at yielding. y (3.3.1) y is defletion at yield, and 6

7 3.2. Combined Hystereti Model/Total Cyli Response The total yli response of reinfored onrete olumn is predited by oupling the hystereti flexure, reinforement slip, and shear responses as springs in series. The fore in eah spring is always same and total displaement is sum of the displaements of eah spring. Up to the peak strength of the olumn and during unloading and reloading branhes, three deformation omponents are simply added to alulate total lateral displaement. After the peak response is obtained, either shear or flexure governs the olumn behavior. Post-peak total hystereti response is bounded by the total monotoni response based on olumn failure mode or lassifiation ategory. 4. COMPARISON OF MODELS AND TEST DATA 4.1. Monotoni Response Model In order to verify the proposed model and test its appliability to a wider range of shear and flexural strengths, material properties and olumn geometries, a database of 37 olumn tests from eight different researhers was omplied from Paifi Earthquake Engineering Researh Center s Strutural Performane Database. Lateral foredisplaement relationships are shown in Fig 3 for five of the 37 test olumns (one from eah ategory) modeled in this study. Comparisons for the other olumns an be found in Setzler (25). The plots ompare the response envelopes predited by the proposed model to yli test data for eah olumn. The model predits reasonable response envelopes for the olumns examined in the study. For olumns in Category IV (Fig 3d) the dashed lines show the proposed model before modifiation for delayed shear failure. The solid line is the final model predition, after onsideration of the Elwood shear failure surfae. The shear failure surfae was used suessfully in prediting the lateral response of Category IV olumns. As disussed previously, Category V olumns are those whose shear strengths are high enough suh that they are not expeted to experiene shear failure even at large displaements. The Elwood shear failure surfae and point of axial failure were omputed for these olumns for omparison purposes. However, for ategory V olumns, it is not appropriate to modify the model using the Elwood shear failure surfae as the proposed model predits the behavior of these olumns well without any shear failure modifiations Cyli Response Model Fig 5 shows the omparison of experimental and predited response of olumns tested by Sezen and Moehle (26). Speimen-1 is a Category III olumn. It should be noted that the range of experimental and predited displaement response is between -9 and +8 mm, however this olumn was able to arry its axial load at larger lateral displaements. The yli model had to be stopped at a lower displaement mainly beause the experimental flexure, bar slip, and shear displaements were not available beyond what is measured. The total experimental lateral displaement is measured by a single displaement potentiometer or LVDT attahed to the top of the olumn speimen. However, the omponent experimental hystereti displaements were obtained from up to 62 different displaement potentiometers. Thus, the sum of individual experimental displaements do not neessarily equal to the total experimental displaement. As a result of this disrepany in the experimental data, the maximum predited and experimental lateral displaements are sometimes not lose. If the sum of measured omponent displaements mathed the total lateral displaement, the predited hystereti response would improve greatly. To the authors knowledge, there is very limited or no experimental olumn studies reporting individual hystereti flexure, bar slip and shear displaements. Speimen-2 is lassified as a Category IV olumn, failing in flexure with limited ontributions from shear at failure. Speimen-3 was tested under variable axial load. In the positive loading 7

8 diretion it is a Category IV olumn, while in the negative diretion it is plaed in Category III. Speimen-4 is idential to Speimen-1, and belongs to Category III. It is evident that reasonable orrelation exists between analytial and experimental results. The proposed hystereti model aptures the strength deay in olumns. Although the strength of the olumns predited reasonably, the overall response was not predited well in many yles mainly beause the sum of experimental omponent displaements used in the model did not math the total experimental lateral displaement. Complete details of omparisons alongwith appliation of proposed hystereti model to other speimen an be found in Chowdhury (27). 5. CONCLUSIONS An analytial maro model is developed that an simulate non linear monotoni and yli response of reinfored onrete olumns. Although, the researh was foused on studying the behavior of shear ritial olumns, the proposed models an aurately predit the lateral fore-displaement response of well designed olumns as well. Deformation omponents due to flexure, reinforement slip and shear are first modeled individually for monotoni loading and then ombined depending upon omparison of their shear and flexural strength. The omponent and total monotoni response models envelop the orresponding yli behavior in the development of yli response models. The proposed monotoni and yli response models are tested against a database of test speimens. The omparison of monotoni response model with the test data shows reasonable agreement in prediting the maximum strength of the olumns and their failure mode. The average of the ratio of predited strength to experimental strength was.95 with a standard deviation of.1. Similarly, for yli response models, strength deay behavior was reasonably aptured by foring the response to follow the deterioration of strength in monotoni envelope after peak strength is ahieved. The lassifiation system used appears to identify the failure mode and represent the flexural and shear behavior for yli response as well. REFERANCES Alsiwat, J.M., Saatioglu, M. Reinforement Anhorage Slip under Monotoni Loading. ASCE Journal of Strutural Engineering. 1992; 118 (9) Chowdhury, T. Hystereti Modeling of Shear-Critial Reinfored Conrete Columns. M.S. Thesis. The Ohio State University, Columbus, Ohio, 27. Elwood, J.K., Moehle, J.P. Shake Table Tests and Analytial Studies on the Gravity Load Collapse of Reinfored Conrete Frames. PEER Report 23/1, Paifi Earthquake Engineering Researh Center, Univ. of California, Berkeley, 23. Elwood, K. J., Moehle, J.P. Drift Capaity of Reinfored Conrete Columns with Light Transverse Reinforement. Earthquake Spetra. 25; 21 (1), Elwood, K.J., Moehle J.P. Axial Capaity Model for Shear-Damaged Columns. ACI Strutural Journal. 25; 12 (4), Gerin, M., Adebar, P. Aounting for Shear in Seismi Analysis of Conrete Strutures. Proeedings of the 13 th World Conferene on Earthquake Engineering, Vanouver, 24. Paper No (last visited on Nov. 15, 27) 8

9 Lee, D.H., Elnashai, A.S. Seismi Analysis of RC Bridge Columns with Flexure- Shear Interation. ASCE Journal of Strutural Engineering 21; 127 (5): Lehman, D.E., Moehle, J.P. Seismi Performane of Well-Confined Conrete Bridge Columns. PEER Report 98/1, Paifi Earthquake Engineering Researh Center, Univ. of California, Berkeley, pp. Lynn, A.C., Moehle, J.P., Mahin, S.A., Holmes, W.T. Seismi Evaluation of Existing Reinfored Conrete Building Columns. Earthquake Spetra 1996; 124 (4) Mander, J.B., Priestley, J.N., Park, R. Theoretial Stress-Strain Model for Confined Conrete. ASCE Journal of Strutural Engineering. 1988; 114 (8), Ozebe, G., Saatioglu, M. Hystereti Shear Model for Reinfored Conrete Members. ASCE Journal of Strutural Engineering. 1989; 115 (1), Patwardhan, C. Strength and Deformation Modeling of Reinfored Conrete Columns. M.S. Thesis. The Ohio State University, Columbus, Ohio, 25. Petrangeli, M., Pinto P.E., Ciampi V. Fiber Element for Cyli Bending and Shear of RC Strutures. I: Theory. ASCE Journal of Engineering Mehanis 1999; 125 (9): Pinheira, J.A., Dotiwala, F.S., D Souza, J.T. Seismi Analysis of Older Reinfored Conrete Columns. Earthquake Spetra 1999; 15 (2): Riles, J.M., Yang, Y.S., Priestley, M.J.N. Modeling Nondutile R/C Columns for Seismi Analysis of Bridges. ASCE Journal of Strutural Engineering 1998; 124 (4): Roy, H.E.H., Sozen, M.A. Dutility of Conrete. International Symposium on Flexural Mehanis of Reinfored Conrete - Proeedings. Miami, Fla., Saatioglu, M., Ozebe, G. Response of Reinfored Conrete Columns to Simulated Seismi Loading. ACI Strutural Journal 1989; 86 (1) Saatioglu, M., Alsiwat, J.M., Ozebe, G. Hystereti Behavior of Anhorage Slip in R/C Members. ASCE Journal of Strutural Engineering. 1992; 118 (9) Setzler, E.J. Modeling the Behavior of Lightly Reinfored Conrete Columns Subjeted to Lateral Loads. M.S. Thesis. The Ohio State University, Columbus, Ohio, 25. Setzler, E.J., Sezen, H. Model for the Lateral Behavior of Reinfored Conrete Columns Inluding Shear Deformations. Earthquake Spetra. 28; 24(2) Sezen, H. Seismi Behavior and Modeling of Reinfored Conrete Building Columns. Ph.D. Dissertation. University of California, Berkeley, 22. Sezen, H., Whittaker, A.S., Elwood, K.J., Mosalam, K.M. Performane of Reinfored Conrete and Wall Buildings during the August 17, 1999 Koaeli, Turkey Earthquake, and Seismi Design and Constrution Pratie in Turkey. Engineering Strutures. 23; 25 (1):

10 lateral load Sezen, H., Moehle, J.P. Bond-Slip Behavior of Reinfored Conrete Members. fib-symposium: Conrete Strutures in Seismi Regions. CEB-FIP, Athens, Greee, 23. Sezen, H., Moehle J.P. Seismi Tests of Conrete Columns with Light Transverse Reinforement. ACI Strutural Journal 26; 13 (6) Sezen H., and Setzler E.J. Reinforement Slip in Reinfored Conrete Columns. ACI Strutural Journal. 28; 15(3) Takeda, T., Sozen, M.A., Neilsen, N.N. Reinfored Conrete Response to Simulated Earthquakes. Journal of the Strutural Division, ASCE. 197; 96 (12), Vehio, F.J., Collins, M.P. The Modified Compression-Field Theory for Reinfored Conrete Elements Subjeted to Shear. ACI Journal 1986; 83 (2) V Zero-length slip rotation spring Zero-length shear spring Flexural spring L s Zero-length slip rotation spring (a) Lateral deformation Components V s f v (b) Spring representation of total response Figure 1. Lateral deformation of a reinfored onrete olumn F F onrete slip Reinforing bar s F omp. Maximum strength point ( v,n,v peak ) Beginning of shear degradation ( v,u,v peak ) u ' b l' d u b l d ub Response-2 d Axial load failure ( v,f, ) shear displaement (a) Proposed slip rotation model (b) Proposed shear model Figure 2. Proposed models for omponent deformations 1

11 Lateral fore (kip) Lateral fore (kip) Lateral fore (kip) Lateral fore (kip) Lateral fore (kip) 11 SC3 (Category I) W (Category II) Test data Model Drift ratio (a) Test data Model Drift ratio (b) 8 2CLD12 (Category III) W (Category IV) Test data Model Drift ratio () Test data Model No shear failure Drift ratio (d) 9 U6 (Category V) Test data Model Shear failure (not used) Drift ratio (e) Figure 3. Model preditions and test data for the lateral displaement (a) SC3, (b) 25.33W, () 2CLD12, (d) 4.48W, (e) U6 11

12 Fore or moment V p V y or M p or M y monotoni model or envelope Lateral fore V n ky k 1 ' k 1 monotoni model or envelope k 1 k 3 V r or M r k k 2 V r k 2 k' 2 Displaement or rotation axial load failure V r Shear displaement onset of shear failure (a) Lateral fore-flexural displaement (b) Lateral fore-shear displaement Figure 4: Hystereti rules for lateral fore-displaement relationship Speimen-I Speimen-II Speimen-III Speimen-IV Figure 5: Total predited and measured response of Columns tested by Sezen (22) 12