SHEAR RESISTANCE OF RC INTERIOR ECCENTRIC BEAM-COLUMN JOINTS

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1 13 th World Conferene on Earthquake Engineering Vanouver, B.C., Canada August 1-6, 2004 Paper No. 649 SHEAR RESISTANCE OF RC INTERIOR ECCENTRIC BEAM-COLUMN JOINTS Yasuaki GOTO 1, Osamu JOH 2 SUMMARY Experimental study was arried out to larify the influene of eentriity on the shear strength and failure mehanism of reinfored onrete interior beam-olumn joints. Four half-sale, ross-shaped speimens were tested to investigate the relationship of eentriity and strength redution. Test results show that the larger the eentri distane, the smaller the joint shear strength. Continuous analytial study by three-dimensional inelasti finite element analysis was arried out to examine preisely the shear failure mehanism of these joints. The analytial results show that the onentration of the shear stress of joint onrete is on the eentri side and in the region of onrete failure. INTRODUCTION The beam-olumn joints in many reinfored onrete (RC) buildings suffered damage during the disastrous Hyogoken-Nanbu earthquake in In 1999, design requirements for beam-olumn joints were enated in the AIJ (Arhitetural Institute of Japan) standard for RC strutures [1], whih is a well-known design guide in Japan. Researhers have investigated the ause of failure of these damaged buildings. They found that almost all damaged frames showed eentriity between the beam and olumn, and the joint shear strengths alulated aording to the AIJ RC standard were enough larger than the flexural strength of adjaent beams to ause flexural failure at the beam ends [2]. Therefore, they onluded the redution of joint shear strength might our in the atual buildings due to the eentriity between the beam and olumn. Beause there has not been muh researh on eentri beam-olumn joints, the influene of eentriity on joint shear strength and frame deformability has not been larified [3]. In some design odes that inlude the AIJ RC standard, the influene of eentriity on joint shear strength uses the effetive joint width [4][5]. For example, the effetive joint width aording to the AIJ RC standard is alulated as the beam width plus the minimum value of half the distane between the olumn fae and beam fae, or a quarter of the joint depth on both sides. The joint shear strength is alulated as the produt of the effetive joint area (defined by the effetive width and olumn depth) and the standard strength that depends on the joint onrete strength, onfiguration and onfinement ondition. In addition, joint reinforement does not effet joint shear strength, but it is does effet the onfinement of the joint ore onrete, whih results in dutile behavior of the frame. The failure mode of the beam-olumn sub-assemblage is defined as follows: when the joint shear 1 Assoiate Professor, Hokkaido University, Sapporo, Japan. gottsu@eng.hokudai.a.jp 2 Professor, Hokkaido University, Sapporo, Japan. joh@eng.hokudai.a.jp

2 strength is large enough, adjaent beams will yield and beam flexural failure will our (B-type). But in the ase that the joint shear strength is not large enough against the beam flexural strength, joint shear failure ours with a large displaement after beam yielding (BJ-type). If large amounts of beam bars are provided, the beam flexural strength beomes so large that joint shear failure will our before beam yielding (J-type). Besides these failure types, flexural and shear failure of both beam and olumn members is expeted, and also bond failure will be observed in suh ases as poor bond onditions, whih ours when using large-diameter bars as longitudinal reinforements [6]. The RC frame is designed aording to the weak-beam, strong-olumn onept, so that large energy dissipation is expeted, whih leads to the preferable behavior of strutures. It is neessary to establish the evaluation of not only joint shear strength but also the deformability of several types of frame onfigurations in strutural design. This study presents test results on the performane of eentri beam-olumn sub-assemblages subjeted to vertial gravity and lateral earthquake loading, and the analytial results of the shear failure mehanism of joints. EXPERIMENTAL PROGRAM Experimental work Speimens All speimens were ross-shaped in order to fous on the interior beam-olumn sub-assemblages. Speimens had neither transverse beams nor floor slabs (plane frames). The size of eah beam and olumn was the same for all speimens (beam setion 200 x 350 mm, length 3,000 mm; olumn setion 450 x 300 mm, height 1,750 mm). The differenes in eentri distane between the beam enter and olumn enter of the speimens was set as 0, 60 or 125 mm, whih gives eentriity ratios of 0, 0.12 and 0.25, respetively. In addition, the joint reinforement ratios were set as 0.25% (use letter "M") and 0.53% (use letter "U") volumetri ratios. For the speimen names, the seond letter and first number after the hyphen represent the joint reinforement ratio and eentri distane, respetively. Table 1 shows the properties of all speimens. The joint shear strength of all speimens was alulated aording to the AIJ Standard. All speimens were designed not to show shear failure of the beam or olumn prior to expeted failure. In order to larify the influene of eentriity on the joint shear strength, all speimens were designed to fail beause of joint shear failure. Therefore, a large number of beam bars were provided in order to generate large input to eah joint. Figure 1 illustrates in detail the reinforement of the speimens. In the speimens, a steel over plate was attahed to the beam onrete at the beam ends in order to prevent the onrete from being rushed due to ompressive fore. The first letter of the speimen names indiates the joint shear input at beam yielding, whih is defined by the produt of the beam bar area and its tensile strength. Speimen eentri distane Table 1. Speimen list Beam l=3000 a t σ y Column h=1750 Joint hoop Beam Bars (kn) Column Bars reinforement 0 60 pw=0.25% 3-D22 SD685 pt=1.66% D16 SD pg=1.98% 6φ SR295 UU pw=0.53%

3 ,,,UU-125,UU e=0 150 joint setion steel over plate ( ) Stirrup UU D22 (SD685) beam setion ( ) lateral loading 1350 support 300 e=60 e=125 joint setion ( ) Hoop PL Fig. 1 Speimen detail 35 pw=0.25% pw=0.53% side view of joint axial loading UU-125 unit: mm Materials The design ompressive strength of the onrete was 24 MPa. The onrete onsisted of rushed stone having a maximum size of 13 mm. Table 2 summarizes the atual ompressive strengths of the onrete on test day. Table 3 shows the mehanial properties of the flexural reinforing bars and joint reinforement. The stress-strain relationship of eah bar was obtained by attahing a strain gage during the material testing, and the measured strain in this relationship was used to alulate the stress generated in the reinforement. Table 2. Conrete properties Speimen σ B ε max σ t E 1/3 (MPa) (µ) (MPa) (GPa) UU Table 3. Reinforement properties Classifiation σ y ε y σ max E s Elongation (MPa) (µ) (MPa) (GPa) (%) 6φ SR D6 SD D16 SD D22 SD Loading Figure 2 shows the loading setup. Speimens were tested in the upright position. The olumn was linked to a reation wall by hannel steel at the bottom and a hydrauli atuator at the top. The end of eah beam (refletion point) was linked to the reation floor by a pinned-end vertial support. Axial fore was generated by a hydrauli jak at the olumn bottom and an atuator at the olumn top. Speimens were also supported perpendiular to the loading plane (i.e., perpendiular to the paper). The torsion generated due to eentriity was restrained by H-shaped steel mounted at the olumn top and bottom. First, a onstant olumn axial fore was applied up to 1/6 of the onrete ompressive strength in stress, and then a lateral displaement was applied to the olumn top statially. Reversal displaements of 1/500, 1/200, 1/100 (2), 1/70 (2), 1/50 (2), 1/35 and 1/20 in the story drift angle were applied ylially. The numbers in parentheses indiate the number of repetitions of the same displaement.

4 500kN atuator for axial fore ross-shape steel for axial loading 1000kN load-ell pin restraint against torsion universal joint lateral loading atuator reation wall restraint against torsion pin speimen reation for beam universal joint olumn reation ounter weight 500kN hydrauli jak for axial fore 200kN load ell reation floor Fig. 2 Loading setup Disussion of test results Crak pattern Figure 3 shows the typial joint raking pattern that was observed after testing. Severe joint shear raking was observed on the flush side, but only a small rak appeared on the offset side. Beam bar yielding was not observed during testing. Speimen, in whih the eentri distane was equal to 0, (front) (bak) (flush side) (offset side) Fig. 3 Speimen appearane after test (blak piees in beam-end are steel overs)

5 had severe joint shear raking on both sides. The joint over onrete spalled out when the story drift angle beame larger than 0.03 and severe raking was observed. Torsional raking was also observed at the olumn faes of the eentri speimens where the beams were onneted. Story shear vs. story drift angle Figure 4 shows the envelope urves of story shear vs. story drift angle for all speimens. The initial stiffness of eah speimen was similar, but the degradation beame obvious after onrete ompressive frature was observed in the joint. This figure also indiates that the maximum strength primarily depends on the eentri distane. V(kN) R(10 rad) Maximum strength Joint onrete frature UU Fig. 4 Story shear vs. story drift angle Ultimate strength Table 4 shows the test results for the olumn shear of all speimens and ompares the beam flexural strength and joint shear strength alulated by the proposed equations. The failure mode of all speimens was defined as joint shear failure (J-type), beause no yielding of the beam bar was observed, but severe joint onrete frature was observed. Figure 5 shows the relationship between maximum strength and eentriity ratio. This figure indiates that the tendeny for the shear strength beomes smaller as the eentriity ratio inreases. Therefore, the influene of eentriity on strength redution should be examined. The alulated beam flexural strength (al1 in Table 4) is larger than the experimental results for all speimens, beause beam yielding did not our. The two proposed equations shown in the footnote of Table 4 are used to alulate the joint shear strength. These two equations differ in their onsideration of eentriity. In Table 4, al2 is alulated by equation 2, using the effetive joint width defined in Figure 6, and al3 is alulated by equation 3, with diret onsideration of the torsional moment. The value of the joint shear strength alulated using either the al2 or al3 equation underestimates the test results, while the ratio of the alulated to observed strength dereases as the eentri distane inreases. This means that the estimation of the fator of safety for joint shear failure hanges aording to the eentri distane. The definition of effetive joint width was also examined in order to improve the estimation. For the ase in whih the beam is onneted at the enter of the olumn, the effetive joint width is smaller than the width of the joint ore onrete. If large eentriity exists between the beam and the olumn, the proposed effetive width inludes the joint over onrete, whih was no longer effetive at the ultimate stage of the test due to having been spalled out. Therefore, the effetive joint width should be modified to exlude the thikness of the over onrete. The alulated values using the modified width (al4) also underestimate the test results, but the ratio is almost onstant despite the hange in eentri distane.

6 Table 4. Test results Joint shear Beam flexural Speimen exp V Equation 2 Equation 3 Eq. 2 (modified width) (kn) al1v exp/al al2v exp/al al3v exp/al al4v exp/al J J J UU J al1: M u = 0.9 at σ y d (1) al2: b V ju = κ 2 φ Fj b ju D (2) al3: V ju =β jt al 2V ju (3) β jt = { 1+ ( e al 2V ju Tju ) }, T ju = ( 0.8 σ B pw σ wy ) b D where, unit: N, mm, MPa M u : beam flexural strength V ju : joint shear strength T ju : torsional strength a t : bar area σ : yield strength d y b : beam effetive depth κ : 1.0 (onfiguration fator) b 2 ju : effetive joint width 0. 7 φ : 0.85 (onfinement by transverse beams) F j : 0.8xσ (standard strength) D : olumn depth b : olumn width σ : onrete ompressive strength p B w : joint reinforement ratio σ : yield strength of joint reinforement wy exp V (kn) UU-125 e 1 =e/b Fig.5 Relation of observed strength and eentri distane B D/4 ANALYTICAL PROGRAM Failure mode Analytial method Referene speimens Three speimens of, and were seleted as referene speimens for the finite element method (FEM) analytial program to examine the influene of eentriity on the shear failure mehanism of an eentri beam-olumn joint. Analytial model A three-dimensional analysis program was needed for the onentri joint when the widths of the olumn and beam were not the same, and more needed for the eentri joint. This analysis was arried out using the DIANA (ver. 7.2) finite element program developed by TNO. The analytial model for eah speimen is shown in Figure 7. In the analysis, inremental displaements were given to both beam ends under onstant olumn axial fore, whereas the olumn displaement was given in the experimental work, beause no P-delta moment was generated with the axial loading system. Boundary onditions in the analysis were applied aording to the experiment. The torsion-restraining steel at the olumn end was also modeled using beam elements, beause pre-analysis showed that the presene of the fixed support greatly influened the result in the eentri joint. However, the fixed support was also applied in of the onentri joint. B b D/4 b 2 /2 b 1 /2 b 1 /2 1/2 D offset side flush side b ju Fig. 6 Joint effetive width (AIJ RC standard)

7 restraining steel against torsion Z Y X UM - 0 UM - 60 UM Fig. 7 Analytial model Material models (a) Conrete Eight-node solid brik elements with four Gaussian points were assumed for the onrete. In the onstitutive model of the onrete, an asending ompressive stress-strain relationship was represented by the CEB Model Code (1990)[7], and the failure was evaluated by the failure riterion of Druker-Prager [8]. The post-peak behavior of the onrete at the beam end was modeled to not show stress relaxing beause of the existene of the restraint steel over, whereas the other onrete was modeled as the softening model shown in Figure 8, as defined by equation (4) based on the ompressive frature energy by Nakamura et al. [9]. The equivalent element length was defined as the diameter of the sphere with a volume equal to that of the onrete element. The smeared rak model was represented in the onrete element, where tension softening was onsidered aording to the equation proposed by Hordijk [10]. where, G = 8.8 f (4) f G f : onrete ompressive frature energy (N/mm) f : onrete ompressive strength (MPa) σ σb λ σ B (MPa) L:Element size λ:redution fator of ompressive strength E0 0 σt E0 ε0 ε Gf/ L ε εu Fig. 8 Equivalent uni-axial stress-strain urve of onrete

8 (b) Reinforement All reinforement was assumed to be from two-node truss elements. The stress-strain relationship of these reinforements was assumed to be bi-linear or tri-linear in aordane with the material test results. () Bond The bond between the beam longitudinal reinforement and onrete was expressed by line interfae elements. Bond properties, inluding the stiffness and strength of bond stress vs. the slip relationship, depend on the ondition around the reinforement. The stress ondition around the joint is onsidered to be that shown in Figure 9. The beam bars in the ompressive region were subjeted to lamping stress orthogonally by the ompressive stress of the olumn bending, whih auses larger stiffness and larger bond strength. The model for the bond stress vs. slip relationship, reommended by the CEB Model Code and shown in Figure 10, was adopted in this analysis; two types of onditions were applied for the onsideration mentioned above, i.e. good ondition or other ondition in the bond. The bond properties are shown in Table 5. The bond for the other reinforement of the olumn bar and shear reinforement was assumed to be perfet (no slip). τ max τ(mpa) Good τ f = 0.4 τ max τ' max All Other τ f τ' f 0 Kh(Kh) ' Slip(mm) Fig. 9 Stress ondition in joint Fig. 10 Bond stress-slip relationship Table 5. Bond speifiation Speimen Bond ondition Good Other Good Other Good Other K h (MPa/mm) τ max (MPa) Definition of the ompressive failure of onrete element The failure riterion of Druker-Prager was adopted as the failure judgment in this analysis. To detet a failed onrete element, the three prinipal stresses alulated at eah Gaussian point in the element were substituted into equation (5), then the element was identified as failed when the values of this equation for all Gaussian points within it were zero. where, ( ) f I, J = α I + J k = 0 (5) sinφ 6 sinφ α =, k = 3 3 sin 3 3 sin 1 ( φ ) ( φ ) I : first invariant of stresses

9 J 2 : seond invariant of stresses φ : angle of internal angle : ohesion stress Redution fator of joint onrete Past experimental study has demonstrated that the onrete strut that is formed between shear raks an help the resistane mehanism of RC members subjeted to shear, but redution of the onrete ompressive strength ours aording to the inrement of the raking. Collins et al. [11] and Noguhi et al. [12] proposed an equation using the prinipal tensile strain of onrete to represent this harateristi. The researh work in this paper ould not onsider this influene, so the following proedure was adopted. First, an analysis was arried out using the normal strength obtained by material testing, and the maximum tensile strain of the onrete elements at ultimate strength was obtained in eah slie of blok shown in Figure 11. Then, the redution fator of eah slie of blok was alulated using Noguhi's equation (6), in whih the maximum tensile strain of the blok was substituted. Finally, the same analysis was arried out again using the redution fator for joint onrete, whih influened the stiffness of the joint onrete. The redution fator of eah speimen is shown in Table 6. where, 1 λ = ε 1u ε (6) λ : redution fator for onrete ompressive strength ε : prinipal tensile strain of onrete 1u ε 0 : strain at maximum ompressive strength 8 ~ 1 8(offset side) ~ 1(flush side) Table 6. Redution fator of onrete ompressive strength Y Z X Fig. 11 Loation of joint onrete elements Speimen Analytial results and disussion Story shear vs. story drift angle The analytial results of all speimens were ompared with the experimental results, as shown in Figure 12. The deterioration of stiffness in the analysis beame smaller than the experimental result, whih resulted in the larger ultimate strength. However, the strength redution aording to the inrement of eentri distane was obtained in the analytial results, and observed in the experimental results. showed greater post-peak redution of strength than did the eentri joints. This is beause the extension of the failure zone in the joint onrete was limited in the eentri joint of, whih will be detailed later. The failure mode of all speimens in the analysis was defined as joint shear (J-type), whih oinides with the experimental results.

10 V (kn) 200 (ana) : Analysis (exp) : Experiment (exp) (exp) (exp) (ana) (ana) (ana) R(10-3 rad) Fig. 12 Story shear vs. story drift angle Joint shear vs. joint shear distortion angle The analytial results on eah flush side and offset side are shown in Figure 13. Joint shear is alulated from equation (7) in the experimental results on the assumption that the beam moment arm is 7/8 of the effetive depth. On the other hand, the analytial value is obtained as the sum of the element shear loated in the layer at the middle height of the joint, whih is the integral of the shear stress obtained at the Gaussian points. The shear deformation of the analytial result is alulated from the displaement in the joint diagonal diretion, whih is the same proedure used in the experiment. The shear deformation angle on the flush side beame larger with the inrease of the eentri distane. On the ontrary, reverse joint deformation ourred on the offset side of, whih was similar to the experimental result, and was aused by the torsional fore that ated as a anel shear on this side. However, the joint deformation reversed at the large displaement due to the inrement of shear stress in the onrete element loated on the offset side. where, V j = C + C + T V = 2 T V (7) s s V j : joint shear C : ompressive fore ating at onrete C s : ompressive fore ating at beam bars T s : tensile fore at beam bars V : olumn shear V j (kn) solid: analysis broken: experiment flush side UM -0 UM -60 UM -125 γ s (10-3 rad) V j (kn) solid: analysis broken: experiment offset side UM -0 UM -60 UM -125 γ n (10-3 rad) Fig. 13 Joint shear vs. joint shear distortion angle

11 Torsional moment vs. torsional deformation angle The analytial results of the eentri joints are shown in Figure 14. The torsional moment was alulated as the produt of the joint shear and eentri distane, and the torsional displaement angle was alulated from the horizontal displaement of points that were loated on the top and bottom of the joint on both the flush side and offset side. The analysis shows good agreement with the experiment. M t (kn m) solid: analysis broken: experiment UM -60 UM -125 φ(10-3 rad) Fig. 14 Joint torsional moment vs. torsional deformation angle Compressive stress distribution of joint onrete Figure 15 shows the distribution of ompressive stress at the story drift angle of 1/100 radian and the maximum strength of two speimens, and, in order to examine the influene of eentriity on the stress distribution. Eah row in Figure 15 represents slies of the blok of elements. The region where the ompressive stress beame large is reognized approximately at the joint diagonal line, and so it is onsidered that a onrete ompressive strut was formed. The onrete strut was distributed eentrially to the beam-onneted portions. After the ultimate stage, the ompressive stress in the eentri joint () dereased due to failure on the flush side joint enter and the extended strut towers to the opposite side, while the strut extended uniformly on both sides in the onentri joint (). Shear stress distribution of joint onrete Figure 16 shows the shear stress distribution at the middle height of the joint in two speimens, and. Symmetri distribution was observed in the onentri joint and the stress dereased in all areas after the ultimate stage. Eentri distribution similar to the distribution of ompressive stress was also observed in the eentri joint, but the region where the shear stress inreased shifted to the offset side after the ultimate stage while the stress dereased on the flush side simultaneously. Failure of joint onrete In Figure 17, the hathed one indiates the failure of the joint onrete elements at the ultimate stage. Failure ourred in the elements olored in red, judging by the Druker-Prager riterion. In the onentri joint, the failure zone distributed symmetrially to the joint fae. However, failure was not observed on the offset side of the eentri joint.

12 beam onneted (R= rad) R= rad R= rad R= rad R= rad (maximum strength) beam onneted R= rad R= rad R= rad R= rad Y Z X (MPa) Fig. 16 Distribution of shear stress in joint onrete beam onneted (R= rad) beam onneted 8 Z 7 (maximum strength) Y X (MPa) Fig. 15 Distribution of ompressive stress in joint onrete beam onneted Y Fig. 17 Distribution of failure elements (at maximum strength) Z X 1 CONCLUSIONS The seismi performane of eentri interior beam-olumn onnetions was investigated experimentally and analytially. The experimental work was arried out using four speimens that were given onstant vertial fore and yli horizontal loading. Then, an analytial study on the speimens was arried out using three-dimensional FEM. Experimental and analytial results revealed the following: 1) Comparison of the observed strength between speimens that failed in joint shear indiates that, as the eentri distane inreases, the joint shear strength dereases. This tendeny was observed in the experiment as well as the analysis. 2) The alulation of joint shear strength using the joint effetive width presribed in the AIJ standard underestimates the experimental results. The degree of underestimation depends on the eentri distane. 3) The joint shear strength alulated by the AIJ equation using the modified effetive joint width, whih is defined by taking the effetiveness of the joint onrete into onsideration, showed the good agreement with the experimental results.

13 4) The finite element analysis showed that the eentri distribution of the ompressive and shear stresses in the eentri joint onrete elements aused the loal failure of the onrete, whereas there was uniform distribution in the onentri joint. However, the strength dereased more gradually in the eentri joint than in the onentri joint, beause the onrete elements loated on the offset side beame effetive resistane after the ultimate stage. ACKNOWLEDGMENT This work was supported by a Grant-in-Aid for Sientifi Researh (C), No , from Japan Soiety for the Promotion of Siene (JSPS). REFERENCES 1. Arhitetural Institute of Japan "AIJ Standard for Strutural Calulation of Reinfored Conrete Strutures - Based on Allowable Stress Conept", (Japanese), Arhitetural Institute of Japan "Reommendation to RC Strutural Design after Hanshin-Awaji Earthquake Disaster - Cause of partiularly damaged and orresponding RC strutural design details", (Japanese), Joh O., Goto Y. and Shibata T. "Behavior of Reinfored Conrete Beam-Column Joints with Eentriity", Design of Beam-Column Joints for Seismi Resistane, SP-123, Amerian Conrete Institute, pp , ACI-ASCE Committee 352 "Reommendations for Design Beam-Column Connetions in Monolithi Reinfored Conrete Strutures (ACI 352R-02) ", Amerian Conrete Institute, Farmington Hills, Arhitetural Institute of Japan "Design Guidelines for Earthquake Resistant Reinfored Conrete Buildings Based on Inelasti Displaement Conept", (Japanese), Meinheit D. F. and Jirsa J. O. "Shear Strength of R/C Beam-Column Connetions", ASCE, Journal of the Strutural Division, Vol. 107, No.ST11, pp , CEB "CEB-FIP Model Code1990 Design Code", Thomas Telford Servie Ltd, W. F. Chen "Plastiity of Reinfored Conrete" MaGraw-Hill International Company, Nakamura H. and Higai T. "Compressive frature energy and frature zone length of onrete", Seminar on post-peak behavior of RC strutures subjeted to seismi loads,jci-c51e,vol.2, pp , TNO Building and Constrution Researh "DIANA User's Manual Non-linear Analysis, Release 7" 11. Vehio F. J. and Collins M. P. "The Modified Compression-Field Theory for Reinfored Conrete Elements Subjeted to Shear", ACI Strutural Journal, Vol.83, No.2, pp , Morita S. et al. "Basi Experiments and Development of Analytial Models to Improve Auray of FEM Analysis of RC Strutures", (Japanese) Grant-in-Aid for Sientifi Researh (A), Japan Ministry of Eduation, 1989