MINISTRY OF EDUCATION AND TRAINING NATIONAL UNIVERSITY OF CIVIL ENGINEERING Vo Manh Tung RESEARCH THE IMPACT OF THE BEAM-COLUMN JOINT DEFORMATION ON SEISMIC BEHAVIOR OF REINFORCED CONCRETE FRAME Major: Civil Engineering Code: 9580201 SUMMARY OF DOCTORAL DISSERTATION Ha Noi –2018 The work was completed at: NATIONAL UNIVERSITY OF CIVIL ENGINEERING Academic supervisor: Assoc Prof PhD Nguyen Le Ninh Reading Committee: Prof PhD Nguyen Tien Chuong Assoc Prof PhD Nguyen Ngoc Phuong PhD Nguyen Dai Minh The doctoral dissertation will be defended at the level of the State Council of Dissertation Assessment's meeting at the National University of Civil Engineering at hour .', day month year 2018 The dissertation is available for reference at the libraries as follows: - National Library of Vietnam; - Library of National University of Civil Engineering INTRODUCTION The necessity of the topic The beam-column joint (BC joint) is the intersection of beams and columns Underneath the earthquake effects, reinforced concrete BC joint have complex behavior and their destructive behavior often leads to the collapse of the frame Determination of shear strength and simulated behavior of BC joint has been proposed However, these models are not general and have a broad consensus In design, the BC joint is still considered to be the rigid zone At present, in the modern design of earthquake resistance, the BC joint must have sufficient strength to ensure that the beams and columns around it develop the desired plastic deformation In order to solve this problem, the design codes of earthquakeresistance have very strict requirements for the calculation and details, but avoid the problem of distortion, a very important factor affecting behavior of the frame when earthquake In Vietnam, there are currently no studies on the behavior of reinforced concrete BC joint The BC joint is considered an rigid zone Therefore, the "Research the impact of the BC joint deformation on seismic behavior of reinforced concrete frame" is very necessary Aims of the research a An overview of the models of durability and behavioral simulations of earthquake resistant reinforced concrete BC joint; b Experimental study of the types of reinforced concrete BC joint in Vietnam in order to clarify the problems: the possibility of deformation and force bearing, criteria for shear strength, suitable to the plastic responseof frame c Study of nonlinear calculation frames taking into consideration BC joint deformation designed in accordance with TCVN 9386: 2012 Object and methodology of the research Object: the reinforced concrete BC joint are available in actual construction in Vietnam Methodology: theory combined with experiments Significant contributions of the dissertation a The experiments showed that the types of reinforced concrete BC joint available in Vietnam are deformed when earthquake; The joint is designed in accordance with TCVN 9386:2012, which is inelastic failure, and the TCVN 5574:2012 and SP 14.13330.2011 (Russian Federation) are brittle failure, not suitable to create ductile mechanism for the frame structure Identification of the main factors affecting the behavior of the BC joint and the conditions to ensure the shear strength of the joint designed in Vietnam b The proposed three models simulate the shear deformation and bond slip of the BC joint The use of these models in static and dynamic analysis of reinforced concrete frames designed in accordance with TCVN 9386: 2012 shows that the deformation of the BC joint significantly changes the overall response of the structural frame Dissertation structure The dissertation includes Introduction, main chapters, Conclusion, list of published works by author, references and appendices CHAPTER BACKGROUND OF THE REINFORCED CONCRETE BEAM-COLUMN JOINT AND RESULTS ACHIEVED 1.1 THE FAILURE OF BC JOINT UNDER SEISMIC ACTIONS There are two types of failure that are commonly observed after earthquakes: (a) shear failure of the joint and (b) failure of the reinforcing anchor Cause due to lack of stirrups and anchor reinforcement is not enough in the joint area 1.2 CLASSIFICATION OF BC JOINTS The joints are classified according to: (a) the geometry and way of anchoring the reinforcement of beam (outer, inner), (b) the behavior of the joint (elastic, inelastic), (c) the detail of the joint(brittle, ductile) 1.3 THE FORCE IMPACT ON BC JOINT Consider an interior joint, which is subjected to forces acting from the beams and columns (Figure 1.9a), resulting in internal forces as shown in Figure 1.9b Balancing these internal forces will be the shear force horizontally Vjh: Vjh = Cb1 +C sb1 +Tsb -Vc (1.1) or Vjh = Tsb1 +Tsb -Vc (1.2) So Vjh = (A s1 +A s )0 f y -Vc (1.3) in which Cb1- compression forced in concrete, Tsb1, Tsb2 or Csb1-tensile and compression in beam reinforcements , Vc- shear force of columns above and below the joint, As1 or As2– the areas of beam reinforcements, λ0and fy – overstrength factor and tensile strength of reinforcement Figure 1.9 The force acting on the interior joint Horizontal shear stress τjh and vertical shear stress τjv: V V  jh = jh = jv   jv (1.5), in which bj, hc and hb b j hc b j hb correspondingly, the effective width of the joint, column and beam height For exterior joint: Vjh = A s10 f y - Vc (1.7) 1.4 METHODS FOR DETERMINING SHEAR STRENGTH OF JOINT 1.4.1.The model determines the shear resistance of joint There are many computational models that have been proposed and classified in four ways The following are the two most commonly used computing models 1.4.2.Model of Paulay and Priestley According to Paulay and Priestley, the shear strength of the joint is a combination of strut mechanism and truss mechanism The first one contributes to Figure 1.12 Transmission shear horizontal shear force mechanisms: a) strut; b) truss; Vch and vertical al shear force Vcv from the diagonal compression force Dc (Fig 1.12a), while the second one contributes to the horizontal shear force Vsh and Vsv with the diagonal compression force Ds out through the bond of the reinforcement of the column and beams in the joint region (Fig 1.12b) With this model, Paulay and Priestley set up equations for calculating the horizontal strength Vjh and vertical shear strength Vjv 1.4.3 Model of A G Tsonos (1999, 2001) Tsonos' shear strengthmodel is also comprised of two mechanisms as proposed by Paulay and Priestley, but Tsonos argues that these mechanisms produce an evenly distributed stress field Tsonos then establishes the relationship between the vertical compression stress σ and the shear stress τ in the joint and consequently horizontal shear of joint: Vjh =  hc b j (1.45) (1.45) 1.5 THE SHEAR STRENGTH OF THE JOINTS S IN ACCORDANCE WITH THE DESIGN STANDARDS This section deals with the determination of shear strength in the design standards ACI 318M-2011, 2011, NZS 3101 (2016), TCVN 9386: 2012, EN 1998-1-1: 2004 and AIJ 1999 1.6 COMMENTS ON METHODS FOR DETERMINING THE SHEAR STRENGTH OF THE JOINTS The theoretical basis used to determine the shear strength Vjh are very different in the design of the earthquake resistance US standards focus on the dimensions of joint and the concrete strength fc The Vietnamese and European standards focus on the amount of stirrups in the joint and the axial force Nc of column 1.7 BC JOINT MODELS FOR NONLINEAR ANALYSIS There are many models for simulating the deformation of the BC joint that have been proposed for more than 60 years The following are the most prominent models of computation • The model is based on the experimental studies of Townsed and Hanson (1973), Anderson and Towsend (1977) • Models based on theoretical research combined with experiments:Plastic hinge models of Otani (1974), Banon et all (1981), Fillipou et al (1983, 1988), El-Metwally (1988), Alath Kunnath (1995), Pampanin (2002); Nonlinear springs models of Biddah Ghobarah (1999), Elmorsi et al (2000), Lowes et al (2003), Altoontash (2004), Shin LaFave (2004), Unal and Burak (2010) Model reviews: the models based on experiments are nontypical and objective, nonlinear springs models that reflect the actual behavior of the joints rather than the plastic hinge models, but need for specific software and large computing volume 1.8 COMMENT FROM THE STUDY OF OVERVIEW Under the impact of earthquakes, in the region of the BC joint appears large vertical and horizontal forces There is not yet a rational model of the shear bearing mechanism of BC joints that is unanimously accepted The criteria for evaluating shear strength in the standards differ considerably Paulay's and Priestley's models allow for the most rational interpretation of the shear bearing of joint and are included in many standards including Vietnam The recent nonlinear springs models are considered to be the most practical simulation of BC joint, but its application is limited due to the need for specific software and large computing volumes At present, there are no studies on the behavior of RC reinforced concrete under earthquake in Viet Nam CHAPTER DEFORMATIONS OF BC JOINTS 2.1 DEFORMATIONS OF BC JOINTS Under the impact of the earthquake, the BC joints is subject to very large shear forces will be deformed 2.2 THE COMPONENTS OF DEFORMATION Figure 2.2 Joint deformation a) Shear deformation, eformation, b) fixed fixed-end rotation The deformation of the BC joint consists of two components: the shear deformation of the joint panel γj and the θsl rotation of fixed-end (Figure 2.2) 2.3.THE FIXED-END ROTATIONS The longitudinal bars of the beam usually passes through or anchors to the joints They tend to be pulled out of the anchor anchorage zone when subjected to the force induced by the rotating θsl at the end of the beam (fixed-end rotation) Let s be the slip of the bars (Fig 2.4): s  sl = (2.1) in which:: ξ – is (1   ) the neutral axis depth, normalised to the effective depth, d The fixed-end end rotation at yielding  y db f y Figure 2.4 Fixed end is:  y , sl = f (2.5) in which: c rotation θsl ϕy, db, fy fc corresponding to the curvature of beam, the diameter of bar,, the tensile strength of the reinforcement and the compressive strength of the concrete at yielding.With the increase in the loads,, the deformation of the bar extends into the joint zone The length of yield deep deeper ly,p cause the additional slip (  s ly,p) as well as additional fixed end rotation at ultimate: Δθu,sl= ϕuly,p (2.6) with u - ultimate curvature at end of beam According to Fardis Δθu,sl= 5,5dbϕu (2.88) with cyclic load The bond of bars in the joint region is the decisive factor for Figure 2.8 M - θsl the magnitude of the rotation θsl The strength of bond in the joint depends on many factors: confined concrete, diameter of bar db, compressive strength of the concrete fc, surface of bar …bond slip models have been proposed by many authors, that's remarkable is the model of Biddah (Hình 2.8) Based on the results of the Morita and Kaku experiments, Biddah determined the slips of the bars as well as the slopes K1 and K2 of the model 2.4 THE SHEAR DEFORMATION OF JOINT The shear deformation γ of joint caused by shear stress τ determined by (1.5) mainly due to the bond along the longitudinal bars of the beams and the columns passing through the joints The shear stress is important factor affecting the durability and stiffness of the joint The standards ACI 318M-11, NZS 3101 (2006), TCVN 9386:2012 and EN 1998-1-1:2004 has evaluated shear resistance of joint as function of compression strength fc of concrete, not to take into account the stirrup ratios 2.5 COMMENTS ON DEFORMATIONS OF THE JOINTS The joint deformation consists of: rotation of the θsl at the end of the beams and shear deformation γj of the joint core The magnitude of θsl is the consequence of the loss of bond and the yield of the longitudinal bar of beam The bondstrength depends on many factors, in which the confinement of concrete core effect is the most important The magnitude of γj is determined indirectly through the shear stress τjh from the experiment In order to minimize the deformation joint, the design standards introduce different limit values τjh CHAPTER EXPERIMENTAL RESEARCH BC JOINT 3.1 THE OBJECTIVE OF EXPERIMENTAL RESEARCH Evaluation of the behaviors of the BC joint is designed in three ways: (1) according to TCVN 9386: 2012, (2) impact load according to TCVN 9386: 2012, calculated and detailed according to TCVN 5574: 2012 and (3) according to SP 14.13330.2011 Determine the deformation of the joint and the influencing factors Evaluate and analyze the factors affecting the behavior of the types of BC joint existing in Vietnam under earthquake; Establishment of the models of joints designed in accordance with TCVN 9386: 2012 for nonlinear analysis 3.2.DESIGN THE SPECIMENS Experimental specimens were interior BC joints in 1:1 scale, extracted from a 3-storey spaceframe constructed in Thanh Xuan district, Hanoi, designed in three scenarios Detailed of the specimens is given in Fig 3.3 (NK1 according to TCVN 9386: 2012), Figure 3.4 (NK2 according to TCVN 9386: 2012 and TCVN 5574: 2012) and Figure 3.5 (NK3 according to SP 14.13330.2011) Figure 3.3 Model NK1 Figure 3.4 Model NK2 3.3.THE PROPERTIES OF MATERIAL The mechanical properties of concrete and reinforcement are given respectively in Tables 3.2 and 3.3 The specimens and mechanical properties of the Figure 3.5 Model NK3 materials were determined at the Laboratory and Building Inspection of the University of Civil Engineering 11 NK3 was crushed in cycle 14th similar to NK2 (Figure 3.23) Partial damage to the joint nt of the focus at the corners The column and beam ends are deformed by bending and shear 3.7 ANALYSIS RESULTS 3.7.1 Relationship between story shear - horizontal displacement The hysteresis show the relationship of V –story story shear horizontal displacement ement Δ of all three samples are symmetric and are pinching to different degrees due to slip and yield of the beam reinforcements,, especially in NK3 Figure 3.26: NK1 (Figure 3.26) 3.7.2 Story shear Experiment results show that the maximum story shear Vtb,max of NK1 appears at higher ductile levels, at later cycles and more ductile than the NK2 and NK3 (Table 3.7) Table 3.7 Parameters related to maximum story shear Parameters NK1 NK2 NK3 μΔ 3 Cycle 11 12 và Vtb,max (kN) +76,7; -64 +75,3; - 62,0 +69,0; 68,0 Δtb (mm) 69 54 81 Δtb/h (%) 2,3 1,8 2,7 3.7.3 The behavior of beams Reinforcing steel of NK1 does not lose bond,, does not slip, can develop full plastic deformation, as opposed to NK2 and NK3 This is due to the NK1 with the Figure 3.41 Relation θintermediate bar in column and the μΔ at the section of 50mm stirrup content 3.7 times greater from column (brach +) than that of NK2 and NK3 The 12 rotation angle θ of the beam end of the NK1 is also more stable and linear than that of the NK2 and NK3 (Figure 3.41) Deformation of beams of NK2 and NK3 is affected ed by shear distortion, low energy dissipation 3.7.4 The behavior of columns develop inelastic strain is better than NK2 and NK3 Thus, the rotation θ of the NK1 column end is linear in contrast to the NK2 Figure 3.52 Relation θ-μΔ and NK3 at the section at the 100 3.7.5 Behavior of the joint mm from surface of beam Hình 3.56 γ - Δ/h Hình 3.57.γ - μΔ Shear deformation of the joint The diagrams (3.56) and (3.57) show that the NK1 joint has the smallest shear deformation γ and increases linearly, in contrast to the NK2 and NK3 Deformation of the joint NK1 is ductile ductile, the remaining joints are brittle The stirrups in the joints has a decisive influence on the deformation characteristics of the joint Figure 3.59: Vt - γ Joint shear: joint shear Vt indicates the shear strength of concrete and reinforcement in the joints: Vt =Vjh = (As1 +As )f s - Vc (3.14) NK1 shear strengthis more than NK2 NK3 (Figure 3.59) 13 3.7.6 Analyzes the cause of failure of joints Differences in the design and detail in the joints, columns and beams led to various failures on the specimens (see Figures 3.17, 3.20 and 3.23) a) NK1 is capable of launching the truss mechanism (Chapter 1) while the NK2 and NK3 not have this capability b) As the load cycles increase in the non-elastic region, the NK1 joint zone is compressed and bended lesser by the beams and columns being flexed and the NK2 and NK3 joint zone compressed locally by the beams and columns Large rotational displacement when longitudinal reinforcement loses bond and weakened confined concrete is not capable of transmitting diagonal compression force deep into the core as in NK1 c) The cause of the large concrete splits along the column reinforcement on the two sides of the joint zone of the NK2 (Fig 3.20) is due to the expansion of the crack at the beam edge when the reinforcement is yielded and loses bond, due to the local edge of the panel joint is crushed and by the longitudinal reinforcements of column are buckling (lack of stirrup) NK3 is splitted less (Figure 3.23) due to the reinforcement of the column are bigger In NK1, the beams are yielded before the column and finally in the joint, following the principle of weak beam-strong column design In NK2 and NK3, the risk of damaging the beams, columns and joints is equal 3.7.7 Shear resistance of BC joint The calculation of limit stress τjh of the NK1 in accordance with TCVN 9386: 2012 gives a value (7.49 MPa) greater than the value in ACI 318M-2011 (6.73 MPa) and NZS 3101 (2006) (6.3 MPa) The stirrup ratio in NK1 joint zone is 2.5 times greater than the ACI 318M-2011 minimum value, while NK2 and NK3 are 1.5 times smaller While the maximum shear stress τjh of all three samples (3.1 MPa, 2.93 MPa and 3.01 MPa) was less than half the limit value τjh defined by the three criteria above, but the behavior of NK2 and NK3 is completely 14 unacceptable As a result, for joints in Vietnam, the content of stirrup in the joint zone is more important than the shear stress limit It is therefore necessary to consider additional conditions to ensure the rigidity and durability of TCVN 9396: 2012 3.7.8 Secant stiffness of the specimens The stiffness of all the specimens is degraded during loading The degradation of NK1 is the lowest, NK2 is the fastest, while NK3 has smallest stiffness 3.7.9 Energy dissipated of the specimens The energy dissipated is represented by the area of the forcedisplacement hysteresis at each cycle NK1 and NK2 have the same amount of accumulated energy dissipated at the first 14 load cycles, while the NK3 was the largest 3.7.10 Equivalent viscous damping factor The equivalent viscous damping factor ξ is defined by the dissipated energy balance in each cycle in the nonlinear system with the equivalent linear system After yielding, the ξ factor of NK1 is much larger than that of NK2 and NK3 At the same time, the energy dissipation of the NK1 was more stable than the other specimens The relationship ξ - μΔ of the NK2 and NK3 shows that ξ is strongly reduced at the high ductile level 3.8 COMMENTS ON EXPERIMENTAL RESULTS Under earthquakes, NK1 designed according to TCVN 9386: 2012 is inelastic failure, while NK2 and NK3 are brittle failure The reinforced concrete frame systems are designed according to SP 14.13330.2011 and according to TCVN 5574: 2012 are not suitable to develop inelatic failure mechanism For ductile class medium frames (DCM), the stirrup in the joint zone is very important to ensure confined effect rather than the shear stress limit as specified in the modern design standards Under earthquakes, the joints will be deformed, even when designed in accordance with the modern standards Therefore, it is necessary to consider the shear deformation of joints 15 CHAPTER MODELING OF BC JOINTS UNDER EARTHQUAKES 4.1 DEFORMATION OF JOINTS AND ITS EFFECTS TO THE OVERALL BEHAVIOR OF FRAMES Deformation of joint affects the behavior of the frame Therefore, it is necessary to model the shear deformation and bond slip of reinforcement under earthquakes for nonlinear analysis 4.2 MODELLING OF BC JOINT 4.2.1.The contribution of deformation of joint to the lateral displacement of the frame Figure 4.2 shows the effect of the shear deformationj the horizontal Figure 4.2 The contribution (γj)on displacement of the istory (Δi) of the shear deformation at the exterior and interior joints The shear deformation γj is for the column with the relative shear displacement Δci= γjhb and the displacement of beam end: Δbj= γjLb 4.2.2 Modeling of shear deformation In view of the effect of the shear deformation on the behavior of the frame, using the Figure 4.3 Modeling of model in which the shear springs shear deformation in the column ends and the bending springs in the beam ends In the physical view, for the Hình 4.5 spring of shear, the relation of the shear force Vjh and the displacement of the column end Δcj = γjhb, for the rotate spring is the relation of the bending moment Mb and the shear deformationγj 16 4.2.3 Determine the characteristics of the springs According to the results of theoretical studies in Chapter 1, according to (1.1) the column shear force at the interiorjoint: Vc=(Csb1+Cb1+Tsb2) – Vjh = A - Vjh (4.2a) , also in the exteriorjoint: Vc=Tsb2-Vjh (4.2b) From (1.5), determine the horizontal shear force Vjh from the values τjh Thus, to determine the Vc and corresponding to it, Vjh must perform a computational process according to the diagram in Figure 4.5 The calculated result will be relations Vc - Δcj and Mb - γj if know the relation τjh - γj of the joint 4.2.4 Establishing the ideal relationship τjh–γ a) Interior joint: From the results of experiments in Figure Figure 4.6 Relationship: shear 3.59, establish the deformation γj and a) Vjh; b) τjh relationship τjh-γj (Figure form NK1 4.6b) and idealized in the form of a four-segment line (Figure 4.7) Point B has coordinates τjh,y=2,8MPa and γj,y=0,0004rad at beam reinforcement yielded, the point Figure 4.7.τjh-γj C has coordinates τjh,u=3,1MPa γj,u=0,0025rad According to ASCE 41-13, assuming residual durability τjh,D=0,2τjh,y, The shear deformations at points D and E are: γj,D=0,02rad γj,E=0,025 rad (Figure 4.7) b) Exterior joint Based on Biddah's experiments on the exterior Figure 4.8 J2 of Biddah joint (Figure 4.8), establishing the ideal τjh - γj relationship is also done in the same way as the 17 interiorjoint As shown in Figure 4.9b, point B has coordinates τjh,y=1,8MPa; γj,y=0,0008rad, the he point C has coordinates τjh,u=2,0MPa γj,u=0,003rad Points D and E are similar Figure 4.7 4.2.5 Establish the relation Vc - Δc Mb- γj of joint 4.2.5.1 RelationshipMb - A and Mb - Tsb To establish relations VcΔc and Mb-γj follow ollow the diagrams in Figure 4.5 4.5, need to determine the relations relationship Mb–A and Mb-Tsb, in which A=Cbs1+Cb1+Tsb2 With the Figure 4.9 Relation γj and assumptions used, relation a)Vjh; b) τjh of J2 Mb-A of NK1 Mb-Tsb of J2 are given in Figures 4.10 and 4.11 Figure 4.10 Figure 4.11 Figure 4.12 Vc – Δc and Mb - γj 4.2.5.2 Relation Vc – Δc and Mb - γj On the basis of the results made, relation Vc–Δc Mb γj for shear and nd bending springs used in nonlinear analysis, see Figure 4.12 4.3 MODELLING OF BOND SLIP Figure 4.13:Mb–θsl Based on theoretical and empirical studies in Chapter 2, the bond slip model of the reinforcement in the joint indicates the rotational displacement due to bond slipθsl and the bending moment Mb as shown in Figure 4.13 18 The values θy,sl and θu,sl are defined respectively in expressions (2.5) and (2.8) in Chapter 4.4CALIBRATION, MODEL EVALUATION OF JOINTS 4.4.1 Interior joint NK1 Calibration is performed for the rigid joint case and flexible joint (in terms of sheardeformation and slip) (Figure 4.14) Figure 4.14 Diagram of plastic hinge for the case: a) Rigid; b) flexible joint With the results of the experiment,, the relationshipsVc-Δcj, Mb-γjandMb-θslare shown in Figures 4.15 and 4.16.Nonlinear analysis of specimenNK1 by push-over method with SAP2000 Figure 4.15 Figure 4.16 for the capability curves as shown in Figure 4.18 In the case of flexible join joints, the results of the experiment are perfectly consistent with the results of the analysis The Figure 4.18.V-Δ of NK1 proposed computational models accurately reflect the actual behavior of the joints 4.4.2 Exterior joint J2 The calibration of the proposed models is simi similar to that of the NK1 Figure 4.22 shows the curves obtained from the analysis Compared Figure 4.22 V-Δ of J2 with the experimental results, 19 the proposed models accurately reflect the actual behavior of the subassemblage 4.5 COMMENTS ON THE PROPOSED MODELS • The proposed models are simple and easy to apply to common structural analysis software compared to the previously proposed computational models • The results of the analysis using the proposed calculation models are quite consistent with the results of empirical research • Consideration of the deformation of the BC joints when analyzing the reinforced concrete structure is absolutely necessary CHAPTER - NONLINEAR ANALYSIS FRAMESTRUCTURE UNDER EARTHQUAKE 5.1 INTRODUCTION Currently in the actual design, the BC joints is still considered rigid In order to evaluate the practical response of the reinforced concrete frames designed in accordance with TCVN 9386: 2012 when considering the joint deformation, the proposed models were used for nonlinear static and nonlinear dynamic analysis 5.2 DATA FOR STRUCTURAL ANALYSIS The analysis is performed on the K4 planarframe given in Figure 5.1 Frame with DCM (ductility class medium), agR = 0.1097g is designed and fully detailed according to TCVN 9386: 2012 5.3 DETERMINATION OF THE CHARACTERISTICS OF THE JOINT MODEL In order to establish the models of frame taking into accountjointdeformation for nonlinear analysis, the parameters of the K4 frame such as geometry, reinforcement detail, mechanical properties of materials, … were used to establish the ideal relations τjh-γj, Vc-Δcj, Mb-γj, and Mb-θslj for interior and exteriorjoints Figures 5.4, 5.5, and 5.6 respectively represent curves representing relations Vc-Δcj, Mb-γj, and Mb-θslj of interior and exteriorjointsfrom the 1st to 5thstory of frame K4 The computational models for the joints of the 6th - 9th story are also defined 20 Figure 5.1 Structural layout and planar frame Figure 5.4 Vc - Δcj of interior and exteriorjointof 1–5 stories Figure 5.5 Mb –γj of interior and exterior joint of 1–5 stories 5.4 ANALYSIS OF REINFORCED CONCRETE FRAME STRUCTURES 5.4.1 Analysis cases : (i) rigid joint (noconsidering joint deformation; (ii) flexible joint (considering joint deformation) When analyzing the structure, in Figure 5.6 Model of addition to the joint deformation bond slip of K4 models established above, the analysis model is with plastic hinges at the ends of columns and beams that are characteristic for ASCE 41-13 21 5.4.2 Push-over analysis Analysis results according to SAP2000 for capability curves and horizontal displacements (Figure 5.7) The analysis showed that in both cases, the plastic hinges appeared in beamsbefore in columns In case of flexible joint, deformation of joint appears early and severely weakens the stiffness of the beams, the shear capacity of the frame is degraded prematurely, the plastic hinges at the lower end of the first level columns appear earlier than in the case of rigid joint, the difference in horizontal displacement at the roof level has a significant increase Figure 5.7 (a) Capability curves; (b) Deformed shape corresponding to base shearof 750 kN 5.4.3 Nonlinear time histories analysis K4 frame is affected by earthquakes as a accelerogram records with peak ground acceleration (PGA) appropriate to the magnitude of earthquakes that may occur in Vietnam The accelerogram record was selected at El Centro station during the 1979 Imperial Valley earthquake, in the direction of 1400 in the California region of the United States (Figure 5.10) with ag, max = 0.08g; 0.15g and 0.25g corresponding to minor, moderate and severe earthquakes Figure 5.10 Accelerogram records The analysis was performed using the SAP2000 software for 22 two cases without consideration of joint deformation and with consideration of joint deformation established above, while the behavior patterns of the plastic hinges were concentrated centrated at the ends column and beam in accordance with ASCE 41-13 13 as push pushover analysis Figure 5.14 shows horizontal displacement diagrams at the K4 roof level for the two cases considered Analysis results show that base shear in case of rigid joint is higher than flexible joint case (difference 8.3%, 7.3% and 15%) and decreased more slowly over time Horizontal displacement at the roof level in the case of flexible joint is greater in the case of rigid joint (4%, 4.1% and 5%) and degraded more rapidly over time In case of minor earthquakes, the plastic hinges are not present in both cases Considering the joint deformation, in the case of moderate earthquakes, the columns of 1st story are hinged ed when the plastic hinges of beams propagate to the 6th level,, the case of ssevere earthquake column is failure when the plastic hinges spread to the 7th and 8th levels ag,max=0.08g ag,max=0 =0.15g ag,max =0,25g Figure 5.14 Horizontal displacement at the of the roof level 5.5 COMMENTS Models of deformation joint are set up simple and easy to install into commercial software 23 The results of the analysis are quite consistent with the conclusions from the experimental results and theoretical studies suggesting that the proposed models are reliable Joint deformations significantly increases the horizontal displacement of the frame, reducing the shear strength of frame, degrading the beam stiffness , making the columns on the 1st story failure early These are problems to consider when designing to make the structure more secure and reliable under strong earthquakes CONCLUSION CONCLUSION All types of reinforced concrete beam-column joint in Vietnam are deformed under earthquake, including the joint type designed from the point of view of modern earthquake resistance (TCVN 9386: 2012) The joint is designed in accordance with TCVN 9386: 2012, which is ductile failure, while the joint is designed according to TCVN 5574: 2012 and SP 14.13330.2011 are brittle failure, not suitable to create plastic hinge mechanism in frame structure when earthquake The behavior and failure behavior of the joints is influenced by the amount of stirrup and intermediate reinforcement in the joints Therefore, the condition to ensure the shear strength of joints designed in Vietnam is that the stirrup in the joint area is more important than the limit shear stress Therefore, it is necessary to study the adjustment and supplementation of the prescribed conditions for the limit shear stress in TCVN 9386: 2012 The models of shear deformation and bond slip of the joint proposed by the author are based on the joint shear stress relationship - joint shear deformation obtained from experiments and theoretical studies to take into account joint deformation to the overall response of the frame structure is designed according to the modern resistance concept shows: 24 a) The ability curves obtained from the push-over analysis in terms of joint deformation by the proposed models are quite consistent with experimental results b) Static and nonlinear analysis results of a story reinforced concrete frame system are designed in accordance with TCVN 9386: 2012 with proposed models that are quite consistent with findings and evaluations drawn from the results experiments and theoretical study by the author The deformation of the joints changes the overall reaction of the frame structure, which significantly increases the horizontal displacement of the frame, reducing the shear strength of frame, degrading the beam stiffness , making the columns on the 1st story failure early c) The setup of the joint deformation by the method of author is quite easy and simple to install into the existing commercial software such as SAP2000, Etabs This is the superiority of the model of the author compared to the previous proposed models SUGGESTIONS For highly trustful joint deformation models, further empirical studies on interior and exterior joints should be made The results from the author's study may be considered as valuable experiences for experiments that will be performed in the future and the proposed joint models are a good way forward BC joints designed in accordance without TCVN 9386: 2012 are not suitable for earthquake ressistance and not make frame structures (beams and columns) develop their maximum deformation and bearing capacity It is therefore imperative to avoid this type joint in the design and construction of structures in the strong seismic zone in Vietnam In order to ensure the safety of the frame struture in Vietnam, it is necessary to consider the design of the joints and the need for more detail rules, specially minimum amount of stirrup in the joint area LIST OF PAPERS PUBLISHED RELATED TO DISSERTATION Nguyen Le Ninh; Vo Manh Tung " Một số vấn đề việc thiết kế nút khung bê tơng cốt thép tồn khối chịu động đất ", Journal of Building Science and Technology No 25, 9/2015, University of Civil Engineering Nguyen Le Ninh; Vo Manh Tung " Ảnh hưởng khe nứt đến phản ứng khung bê tông cốt thép chịu động đất" Journal of Building Science and Technology No 2/2016, Institute of Building Science and Technology Nguyen Le Ninh; Vo Manh Tung " Nghiên cứu thực nghiệm phá hoại biến dạng nút khung bê tông cốt thép chịu động đất", Journal of Architecture and Building Science 28, 10/2017 Nguyen Le Ninh; Vo Manh Tung, "Experimental study on the failure and deformation of beam-column joints under seismic loads", Journal of Building Science and Technology No 6, 11/2017, University of Civil Engineering Nguyen Le Ninh; Vo Manh Tung " Biến dạng nút khung bê tông cốt thép chịu động đất ", Journal of Building Science and Technology No 4/2017, Institute of Building Science and Technology Nguyen Le Ninh; Vo Manh Tung "Modeling of nonlinear behavior of reinforced concrete beam-column joint under seismic load", Journal of Structural and Building Technology 1/2018 ... Ninh; Vo Manh Tung " Nghiên cứu thực nghiệm phá hoại biến dạng nút khung bê tông cốt thép chịu động đất" , Journal of Architecture and Building Science 28, 10/2017 Nguyen Le Ninh; Vo Manh Tung,... 9/2015, University of Civil Engineering Nguyen Le Ninh; Vo Manh Tung " Ảnh hưởng khe nứt đến phản ứng khung bê tông cốt thép chịu động đất" Journal of Building Science and Technology No 2/2016,... Vo Manh Tung " Biến dạng nút khung bê tông cốt thép chịu động đất ", Journal of Building Science and Technology No 4/2017, Institute of Building Science and Technology Nguyen Le Ninh; Vo Manh