CRITICAL INVESTIGATION ABOUT BOND-SLIP IN BEAM-COLUMN JOINT MACRO-MODEL

Transcription

1 Istituto Universitario di Studi Superiori Università degli Studi di Pavia EUROPEAN SCHOOL FOR ADVANCED STUDIES IN REDUCTION OF SEISMIC RISK ROSE SCHOOL CRITICAL INVESTIGATION ABOUT BOND-SLIP IN BEAM-COLUMN JOINT MACRO-MODEL A Dissertation Submitted in Partial Fulfilment of the Requirements for the Master Degree in EARTHQUAKE ENGINEERING by SARA BROGLIO Supervisor: Dr. Rui Pinho Co-Supervisor: Prof. Haluk Sucuoglu May, 2009

2 The dissertation entitled Critical Investigation About Beam-Column Joint Macro-Model, by Sara Broglio, has been approved in partial fulfilment of the requirements for the Master Degree in Earthquake Engineering. Dr. Rui Pinho Prof.Haluk Sucuoglu

3 Abstract ABSTRACT Beam-column joint is considered a critical region in the structures under severe earthquake attacks. The joint region is subjected to horizontal and vertical actions: the magnitude of these forces is higher than in the adjacent beams and columns. Experimental researches indicate that elongation and slip of tensile reinforcements in a joint could result in significant rotation that increases total lateral displacement of the structure. The purpose of this work is to study the effect of bond slip and interface interaction in a T beam-column joint. In traditional analytical models this aspect is not considered and the intersection between the elements is supposed to be rigid. Starting from the joint model proposed [Mitra and Lowes, 2004], a critical approach is followed: some points of their theory are reviewed and some approximations are introduced. A flexible joint is developed and inserted in the structural model. The pseudo-static analyses are performed using a fibre-based Finite Element program. The results in terms of strains, internal actions, vertical and lateral displacements are presented and discussed. Keywords: beam-column joint; bond-slip; interface interaction; flexible joint; fibre-based Finite Element; i

4 Aknowledgements AKNOWLEDGEMENTS I would like to sincerely thank my supervisor Dr. Rui Pinho for being willing and available to help me. Thanks also to Prof. Haluk Sucuoglu for his effort to facilitate my research during his period in Italy. I would like to thank my family for its continuous support throughout this work. ii

5 Index TABLE OF CONTENTS Page ABSTRACT... i AKNOWLEDGEMENTS... ii TABLE OF CONTENTS... iii LIST OF FIGURES...v LIST OF TABLES... viii 1. INTRODUCTION Scope Objectives Outline SHEAR MECHANISM IN BEAM-COLUMN JOINTS Features of joint behaviour Equilibrium Criteria Shear Strength DESCRIPTION OF THE JOINT MODELS PROPOSED BY LOWES Lowes [1999] Lowes and Altoontash [2003] L.N.Lowes and Nilanjan Mitra [2004] EXPERIMENTAL TEST Design of As-Built Test Model Loading Material and Construction Concrete Properties...26 iii

6 Index Concrete Elastic Modulus Reinforcing Steel Properties Test Procedure Instrumentation Experimental Response of the As-Built Connection Load-Displacements Relationship Anchorage and Reinforcements ANALYSIS PROCEDURE AND RESULTS Description of Structural Model Traditional Model: Rigid Internal Joint Model with Flexible Joint:Bond Slip Springs Model with Flexible Joint: Slip Springs and Interface Springs INTRODUCTION OF A SIMPLIFIED RELATIONSHIP FOR BOND-SLIP SPRINGS CONCLUSIONS...67 iv

7 Index LIST OF FIGURES Page Figure 2.1. Features of column and joint behaviour [Paulay and Priestley,1992]...5 Figure 2.2. Mechanism of shear transfer at an interior joint [Paulay and Priestley, 1992]...6 Figure 2.3. External actions and internal stress resultants at an interior joint [Paulay and Priestley, 1992]...6 Figure 2.4. Compression strut model [Lowes and Mitra, 2004]...7 Figure 2.5. Bond stress and bar stress distributed for a bar anchored in a beam column joint [Lowes and Altoontash, 2003]...8 Figure 3.1. Finite Element mesh in the vicinity of a bond zone [Lowes, 1999]...10 Figure 3.2. Finite Element mesh in the vicinity of a bond zone with cover concrete element [Lowes, 1999]...10 Figure 3.3. Beam column connection core subjected to uniform shear loading for the case of uniform bond stress in anchorage zones [Lowes, 1999]...11 Figure 3.4. Beam column bridge connection core subjected to diagonal compression strut shear loading for the case of significant bond stress only in compression zone Figure 3.5. Finite element model of panels tested by Vecchio and Nieto [1991]...12 Figure 3.6. Discrete concrete cracking as computed using the model with flexible load frame and no initial concrete damage [Lowes, 1999]...14 Figure 3.7. Discrete concrete cracking as computed using model with initial damage[lowes, 1999]...14 v

8 Index Figure 3.8. Discrete concrete cracking as compute using model without initial damage [Lowes, 1999]...14 Figure 3.9. Computed and observed shear stress versus shear strain history for different panel models [Lowes. 1999]...15 Figure Reinforced concrete beam-column joint model [Lowes and Altoontash, 2003].16 Figure Definition of component deformation and generalized forces (a) Component deformation and forces, (b) Shear forces acting on shear panel component [Lowes and Altoontash, 2003]...16 Figure One-dimensional material model: (a) Material states, (b) Impact of hysteretic damage on load-deformation response [Lowes and Altoontash, 2003]...17 Figure Behaviour of reinforced concrete panel SE8 tested by Stevens et al.[1990] under cyclic shear loading: (a) Simulated response, (b) Observed response...18 Figure Bond stress and bar stress distribution for a bar anchored in a beam column joint...19 Figure Observed (a, b) and simulated response (c, d) of the Park and Ruitong [1988] building sub-assemblages Figure 4.1. Prototype multi-column frame [Lowes and Moehle, 1999]...22 Figure 4.2. Reinforced concrete bridge frame sub-assemblages tested by Lowes and Moehle [1999]...24 Figure 4.3 Loading scheme. Gravity and Earthquake loads [Lowes and Moehle, 1999]...25 Figure 4.4. Instrumentation used to measure global displacements and applied loads using in Lowes and Moehle test...26 Figure 4.5. Instrumentation used to measured joint deformation in Lowes and Moehle Test [1999]...29 Figure 4.6. Steel reinforcement strain gages. Lowes and Moehle Test [1999]...30 Figure 4.7. Instrumentation to measured column bar slip. Lowes and Moehle Test [1999]...30 Figure 4.8. Column longitudinal reinforcement strain [Lowes and Moehle, 1999]...31 Figure 4.9. Zone of disconnected concrete [Lowes and Moehle, 1999]...31 Figure Load versus beam longitudinal reinforcement [Lowes and Moehle, 1999]...32 Figure Beam longitudinal reinforcement strain history [Lowes and Moehle, 1999]...33 Figure Load versus reinforcement strain history [Lowes and Moehle, 1999]...34 Figure Load versus displacements [Lowes and Moehle, 1999]...35 vi

9 Index Figure Nominal joint shear strain measured with internal and external gages [Lowes and Moehle, 1999]...37 Figure Nominal joint shear stress versus shear strain measured with internal gages [Lowes and Moehle, 1999]...37 Figure Nominal joint shear stress versus shear strain measured with external gages [Lowes and Moehle, 1999]...37 Figure Nominal joint shear strain from external gages [Lowes and Moehle, 1999]...38 Figure Load versus column internal bar strain measured with gage sg4 [Lowes and Moehle, 1999]...39 Figure Load versus column internal bar strain measured with gage sg5 [Lowes and Moehle, 1999]...39 Figure Displacement versus slip of column longitudinal reinforcement (sl2) [Lowes and Moehle, 1999]...40 Figure Displacement versus slip of column longitudinal reinforcement (sl1) [Lowes and Moehle, 1999]...40 Figure 5.1. Discretization of RC cross-section in a fire based model [SeismoSoft]...41 Figure 5.2. Traditional model implemented with SeismoStruct [SeismoSoft]...42 Figure 5.3. Geometrical dimensions...42 Figure 5.4. Assumed displacement history applied at the column base for pseudo-static analysis...43 Figure 5.5. Beam section in which steel strain is reached for first...43 Figure 5.6. Column longitudinal reinforcements strains developed under experimental cyclic loading [Lowes and Moehle, 1999]...44 Figure 5.7. Strains in column: comparison between traditional model and experimental test 45 Figure 5.8. Shear at the column base in traditional model and in experimental test...45 Figure 5.9. Macro-model with slip springs...46 Figure Geometrical dimensions of the model with joint...47 Figure Force versus slip relationship for spring in the upper side of the beam...47 Figure Tensile stress versuss slip constitutive relationship [Lowes and Altoontash, 2003] and a possible approximation...48 Figure System stiffness definition: steel reinforcement as springs in parallel (beam section)...49 Figure Beam section in which steel strain is reached for first...49 vii

10 Index Figure Comparison of traditional model, model with slip springs and experimental test results in column...50 Figure Shear at the column base in traditional model, in model with slip springs and experimental test...50 Figure Traditional model and model with springs beam shear force comparison...51 Figure Subdivision of the beam...52 Figure Column lateral displacements...52 Figure Beam A, lateral displacement...52 Figure Beam A, vertical displacements...53 Figure Macro-model with slip and interface spring...53 Figure Idealized shear deformations behaviour...54 Figure Shear spring law for beams and column...56 Figure Beam Section in which steel strain is reached for first...56 Figure Strain comparison obtained with experimental test, analytical model with slip springs only and model with interface springs...57 Figure Shear at the column base in traditional model, in model with slip springs and experimental test...58 Figure Comparison of shear forces in the beam...59 Figure Displacement in x direction in BEAM element...59 Figure Displacements in x direction for COLUMN element...59 Figure Displacements in z direction for BEAM element...60 Figure 6.1. Bilinear approximation for bond-slip relationship...61 Figure 6.2. Beam section in which steel strain is reached for first...62 Figure 6.3. Strain results for asymmetrical tri-linear and bilinear approximated model Figure 6.4. Time history of shear at the column base. Comparison between values of shear obtained with asymmetrical tri-linear constitutive relationship and approximated bilinear model...64 Figure 6.5. Displacements in x direction for BEAM element...65 Figure 6.6. Displacement in x direction for COLUMN element...66 viii

11 Index LIST OF TABLES Page Table 4.1. Concrete mix used for sub assemblages model...26 Table 4.2. Quantities used in concrete mix...27 Table 5.1. Steel strain limit. Numerical output for traditional model Table 5.2. Column strains comparison between traditional model results and experimental output...44 Table 5.3. Shear Forces at the column base: comparison between experimental outputs and traditional model outputs...45 Table 5.4. Average bond strength as a function of steel stress state [Lowes and Altoontash, 2003]...48 Table 5.5. Steel strain limit. Numerical output for model with slip springs only...49 Table 5.6. Beam shear results for traditional model and for model with springs...51 Table 5.7. Steel strain limit. Numerical output for model with slip springs only...56 Table 5.8. Column strains comparison between model with interface springs results and experimental output...57 Table 5.9. Shear Forces: comparison of results for all the models analyzed...57 Table Shear forces in the beam for the model with interface springs...58 Table 6.1. Steel strain limit. Numerical output for Model with slip springs only...62 Table 6.2. Comparison between results obtain with tri-linear model and approximated bilinear model...62 Table 6.3. Steel strains in the column. Comparison of results ix

12 Index Table 6.4. Shear forces in the beam for the model with approximated bilinear constitutive relationship...64 Table 6.5. Beam displacements in x direction. Numerical Values...65 Table 6.6. Column displacements in x direction. Numerical Values...66 x

13 Chapter 1. introduction 1. INTRODUCTION 1.1 Scope Beam-column joints are critical regions. In reinforced concrete structures, during severe earthquake attacks, brittle shear failure can occur in the joints, as well as cracking and frictional sliding under reverse cyclic loading. The ultimate resistance capacity depends directly on their different material behaviour (concrete damage, steel plasticity) but it must deal with crack opening and degradation of bonding between concrete and steel. The integration of all these items could make possible a realistic approach of global structures response. Bond behaviour is important from this point of view because its degradation increases the period of vibration (more flexible structures), decreases energy dissipation capacity and produces a global redistribution of internal actions. A traditional fibre-based Finite Element model, where the beam-column joint is supposed to remain elastic during the earthquake, cannot catch the real response of reinforced concrete structures. Laboratory testing of built sub-assemblages, with design details typical of pre constructions shows that joints with little or no transverse reinforcements and relatively high shear and bond stress demands exhibit severe stiffness and strength loss [Meinheit and Jirsa, 1977; Leon, 1990; Walker, 2001]. For this reason many models have been developed. One of these models [Lowes and Altoontash, 2003] represents the response of reinforced concrete beam-column joint under reverse cyclic loading. This model provides a representation of the primary inelastic mechanisms that determine joint behaviour: failure of joint core under shear loading and anchorage failure of beam-column longitudinal reinforcement embedded in the joint. Constitutive relationship are developed to define the load deformation response. Based on previous work, modifying it to improve the prediction of response and to extend the range of applicability, a new model formulation is proposed by Lowes and Altoontash [2003] to simulate the shear-strain response of joint core. This represents well stiffness and strength response parameters for joint with a wide range of design parameters. Both previous models show some limitations: the first, in terms of constitutive relationship, seems to be too much detailed to described the bond slip behaviour. In the second one, the main limit is represented by the location of springs that are placed at the centroid of the compressive and tensile zone respectively. 1

14 Chapter 1. introduction 1.2 Objectives Lowes and Altoontash [2004] model is mainly detailed in the definition of bond-slip relationship. The introduction of some approximations could improve its applicability without a great loss of efficiency. By making an extensive review of the previous models the main aims of this research are the following: the first one is to discuss the different theories about the joint modelling (models from 1999 to 2004 are considered [Lowes et al]) to understand which are the common points and the limits. The second purpose is to explore the possibility of using a simplified model, taking into account which could be the limitations of its own approximations. The checks on these simplified models are made using experimental data [Lowes and Moehle, 1999] when possible; Otherwise results are compared with the output of a traditional fibre-based Finite Element model. 1.3 Outline This study is organized into seven chapters. It covers several aspects ranging from the motivation behind the selection of the research topic, the literature review, the development of structural models with flexible joints. Chapter 1 is devoted to the presentation of the research topic and the identification of the general scope and specific objective. Theoretical aspects and description of the internal mechanism acting in the joint with particular attention for bond-slip mechanism, are described in Chapter 2, in order to understand some choices taken during the development of the flexible joint properties. The description of the evolution of the joint model is an important point in this research. Starting from the model proposed by Lowes [1999] to the last model implemented in 2004, common points and limitations are underlined to understand if such detailed models are useful and if some simplification are possible or not. This excursus is illustrated in Chapter 3. In Chapter 4, an experimental test is shown [Lowes and Moehle, 1999]. The goal of this test is to identify issues critical to the evaluation and retrofit of beam-column T-joint in older reinforced concrete bridge frame. The data of this work are used to define the material properties, the geometry of the structures and loading distribution useful for a correct computer model. Where possible, the analytical results are compared to the experimental output. Fibre-based Finite Element models are developed to check the behaviour of a structure with flexible beam-column joint. The output results are compared with the output of traditional model with elastic rigid joint. Dispersion diagrams are developed and discussed in Chapter 5. In Chapter 6 the effect on the global structural behaviour of a simplified model for bond slip springs is discussed. 2

15 Chapter 1. introduction In Chapter 7 the conclusion of this research are discussed. 3

16 Chapter 2. shear mechanism in beam-column joints 2. SHEAR MECHANISM IN BEAM-COLUMN JOINTS Beam-column joints are considered critical regions in the structures designed for inelastic response, under a severe earthquake attack. The joint regions are subjected to horizontal and vertical actions. The magnitude of these forces is typically higher than in the adjacent beams and columns. If not designed for, joint shear failure can result. The reversal moment across the joint means that the beam reinforcement is required to be in compression on one side of the joint. The bond stress needed to sustain this force gradient is high and this may cause bond failure and corresponding degradation of moment capacity accompanied by excessive drift. Detailed studies of joint for buildings in seismic regions have been undertaken only in the past 20 years. Between 1984 and 1989 significant effort, including coordinated experimental works, by researcher from United States, New Zealand, Japan and China were made. 2.1 Features of joint behaviour Under seismic action large shear forces could be generated into beam-column joints. These forces may cause failure in the joints core due to breakdown of shear or bond mechanism or both Equilibrium Criteria The joints are the elements generated by the connection between beams and columns. The forces acting on the joints are the actions carried by the framing elements: the joint regions are subjected to horizontal and vertical shear forces higher than in the adjacent beams and columns. It is possible to consider the joint as a free body on which forces generated by framing beams and columns are applied. Actions introduced by beam reinforcements (symmetrical ones in this case) to the joint are shown in Figure 2.1 to be internal tension T b and compression forces C b and vertical beam shear forces V b. 4

17 Chapter 2. shear mechanism in beam-column joints Figure 2.1. Features of column and joint behaviour [Paulay and Priestley, 1992] The joint as free body must be in equilibrium. Making the approximation: C b = (2.1) and considering that the beams shears on the opposite interfaces on the joint are equal, the equilibrium of the joint requires an horizontal column shear force of: (2.2) Writing the horizontal equilibrium equation, the large horizontal shear force across the joint region is given by: (2.3) Shear Strength Internal forces transmitted from adjacent members to the joints result in shear forces in horizontal and vertical direction. These shear forces lead to diagonally compression and tension stresses in the joint core and often diagonal cracks occur. The mechanism of shear resistance at this stage changes drastically: some of the internal forces, particularly those generated in the concrete, will combine to develop a diagonal strut. To prevent shear failure by diagonal tension, both horizontal and vertical shear reinforcements will be required. The amount of horizontal joint shear reinforcements may be significantly more than what would normally be provided in columns in the form of ties or hoops, in particular when the axial load in the column is small. 5

18 Chapter 2. shear mechanism in beam-column joints Figure 2.2. Mechanism of shear transfer at an interior joint [Paulay and Priestley, 1992] Figure 2.3. External actions and internal stress resultants at an interior joint [Paulay and Priestley, 1992] Typical moments, shear and axial forces introduced in the joint are represented in Figure 2.3. (2.4) As just defined in equation 2.4, in seismic design, V c is computed considering the beam flexural overstrength. Taking into account the equilibrium of vertical forces at the joint, it would lead to expression for vertical joint shear forces. Compression forces induced to the joint by the beam and the column at diagonal opposite corners of the joint are combined into a single diagonal compression force carried by a diagonal concrete truss, as shown in Figure 2.4. The shear forces developed in beams and 6

19 Chapter 2. shear mechanism in beam-column joints column are transmitted to the joint via the respective flexural compressive zones. Considering the position of neutral axis in each section, it is possible to define the width of the concrete truss. The total horizontal force is transmitted by the beam top flexural reinforcements to the joint by means of bond. A fraction of this force is transferred to the diagonal strut. When the axial load is not applied to the column, the inclination in the strut is similar to the potential linear plane, otherwise the inclination is steeper. Bond strength begins to deteriorate when the yield strain in steel is exceeded. In elastic joints higher average bond stress can be maintained. Bond deterioration due to plastic strain in a bar embedded in a joint core can contribute up to 50% of the overall deflection in beam-column sub-assemblages. Bond is not constant along the reinforcement bars; it is rapidly reduced outside the joint concrete core. Within the column joint core, high bond can be developed Figure 2.4 Figure 2.4. Compression strut model [Lowes and Mitra, 2004] because some confinement of concrete perpendicular to the beam longitudinal bars is always present. The bond slip relationship varies along the bar in function of the region of embedment considered. For this reason it is difficult to develop a simple model for the global reinforcement bond slip response. Bond slip behaviour is investigated by experimental test similar to traditional pull-out test. In such test the bond stresses are uniformly distributed around the periphery of the bar. Their effect is a uniform distribution of tangential and radial stresses in surrounding concrete. However, this is not the real situation because a bar at the top of a beam is in a more unfavourable condition respect to that within the joint. Because of the very large bond force, a splitting crack along the bar will usually form. The total bond force from a top beam bar needs to be transfer predominantly downward into the diagonal compression field of joint core. Therefore the distribution of bond stress is not uniform as in the standard case. Much larger bond stress will need to be generated in the side of the bar facing the joint core. Any bond in excess of about 15% of the total, which might be transferred toward the column, will have to enter the joint core: this involves shear transfer by shear friction across the horizontal splitting cracks. 7

20 Chapter 2. shear mechanism in beam-column joints Figure 2.5. Bond stress and bar stress distributed for a bar anchored in a beam-column joint [Lowes and Altoontash, 2003] 8

21 Chapter 3. description of the joint models proposed by Lowes 3. DESCRIPTION OF THE JOINT MODELS PROPOSED BY LOWES Many models are developed to represent the real behaviour of beam-column joints. Early works to simulate the response of reinforced concrete frames, relied on the calibration of plastic hinges introduced at the end of beam-column line element to represent the inelastic behaviour of the joints. The next generation of models considers separately the inelastic response of beams, columns and joints, introducing zero length rotational spring elements [El- Metwally and Chen,1989; Alath and Kunnath, 1995]. Calibration of these models is based on experimental data characterizing the response of joint sub-assemblages. In this case the development of an objective, transparent model is difficult because the effects of multiple inelastic response mechanism are combined into a single moment rotation relationship. More recently, researchers have begun using continuum-type elements to represent the response of reinforced concrete joints in combination with transition elements, used to maintain compatibility with beam-column line elements. 3.1 Lowes [1999] The proposed Finite Element model incorporates non standard element formulations, solution algorithms and material models. Two aspects of the proposed model, requiring the most significant modification of the base Finite Element code, include meshing of the model to accommodate the bond element for appropriate representation of bond-zone behaviour and introduction of a solution algorithm appropriate for systems including material models with degrading strength and stiffness. Bond elements are introduced to represent the microscopic behaviour of the concrete and steel in the vicinity of the interface. A bond element has zero width, in order to represent radial forces developed in association with tangential bond forces; the model includes definition of radial bond response mode. Figure 3.1 shows how the bond element is idealized. 9

22 Chapter 3. description of the joint models proposed by Lowes Figure 3.1. Finite Element mesh in the vicinity of a bond zone [Lowes, 1999] Two nodes with identical coordinates and different element connectivity may not be possible within the structure of many codes and this requires the introduction of an independent meshing algorithm. The concept of cover concrete is introduced to represent the three-dimensional bond zone response. The concrete element in line with the bond elements presents the thickness of concrete equal to the thickness of the bond zone. If the radial forces associated with bond response are significant, the concrete cove could carry tension in direction perpendicular to the axis of reinforcing bars and develop splitting type crack. The deformation of the cover concrete element is modelled as not compatible with deformation of concrete element in plane with the bond and reinforcing steel element as shown in Figure 3.2. Figure 3.2. Finite Element mesh in the vicinity of a bond zone with cover concrete element [Lowes, 1999] 10

23 Chapter 3. description of the joint models proposed by Lowes The simplest representation of concrete-steel bond is achieved by introducing a one dimensional bond element: its introduction requires use of only one additional, repeated node while two additional elements are needed for the introduction of the two-dimensional bond elements. The response of reinforced concrete bond zone is defined by a number of parameters including the distribution of concrete damage, the embedded reinforcing steel stress-strain distribution, local bond slip response, average bond strength, global and local load displacement history. The analytical model results are compared with those given by laboratory tests. Correlation between flexural-bond behaviour computed by the Finite Element model and that observed in laboratory specimens is good. The Finite Element model represents well the fundamental characteristics of flexural bond zone in reinforced concrete elements. The model predicts crack-spacing and average bond strength typical of that observed in laboratory. It seems to evaluate well the orientation of localized cracks, while it is less accurate in representing localized crack orientation along discrete crack surface. The model predicts temporary losses in system strength, associated with initiation of significant discrete concrete cracks, typically not observed in laboratory. The next phase of model verification proposed by Lowes [1999] is focused on evaluating the response of reinforced concrete sub-system subjected to shear type loading. In these systems, anchorage zone defines the perimeter of the beam-column connection core. If the distribution of bond stress is quite uniform, the connection core is subjected to an approximately uniform shear loading, as illustrated in Figure 3.3. If the bond stress is significant only near the compression end of the bar, in the flexural compression zone, the connection core is subjected to shear in form of diagonal compression loading. Connection strength may be determined by the capacity of the core concrete connections to carry uniform shear and compression-strut shear. Figure 3.3. Beam-column connection core subjected to uniform shear loading for the case of uniform bond stress in anchorage zones [Lowes, 1999] 11

24 Chapter 3. description of the joint models proposed by Lowes Figure 3.4. Beam-column bridge connection core subjected to diagonal compression strut shear loading for the case of significant bond stress only in compression zone. While laboratory loading of these panels consists of applying uniform tension followed by unloading and reloading under uniform shear in combination with tension or compression, such loading is not possible in computer simulation. For the computer model, initial preloading and the resulting concrete damage is introduced by pre-damaging concrete element in the vicinity of the crack observed in the laboratory specimen. The goal of pre-cracking is simply to define the orientation of the fictitious concrete crack planes. It should be noted that if the concrete elements are initially cracked under tensile loading, the crack surfaces are established at 0 and 90 degree rotation from the horizontal. As a result, another crack surface cannot develop at a 45 degree angle from the horizontal, as observed in laboratory. Vecchio and Nieto[1991] tested two different frames, shown in Figure 3.5: Figure 3.5. Finite Element model of panels tested by Vecchio and Nieto [1991] 12

25 Chapter 3. description of the joint models proposed by Lowes In these analytical model the concrete mesh is 18 by 18 elements. In the most heavily reinforced areas, reinforcement is 2-6 mm diameter bars spaced at 50 mm. All reinforcing bars are connected to concrete element via bond element and the grey elements shown in Figure 3.5 are damaged prior to application of shear load. Vecchio and Nieto [1991] indicate that the loading is achieved through the application of approximately uniform loads to the five shear keys embedded along each of panel edges. Load control is not possible in computer simulation nor is the application of shear load in combination with level of tension or compression loading. In the computer simulation, only the case of pure shear load is considered and this loading is applied under displacement control. As declared before, two different load frames are used. Load Frame A is a stiff frame composed by truss elements, connected to every node of the panel edge and subjected to point loading through displacement control at the two extreme nodes. The stiff frame provides the redistribution along the edges of the panel as a function of the panel damage. Given the stiffness of the exterior frame and the concrete damage pattern significant redistribution is observed and an absolutely uniform loading is not achieved. Load Frame B consists of a relatively flexible frame composed of axial elements and connected to the panel in five points along each edge. The exterior frame is flexible; only a little redistribution is possible and an approximately constant shear is applied to each edge of the panel. For Finite Element models, average and shear strain are defined in different way for the two different load frames. For Load Frame A, shear stress is defined as the total load applied to the extreme nodes of the load frame divided by the shear surface of the panel. For the flexible frame, shear stress is defined on the basis of the load transferred from the flexible frame to the concrete panel at each node on the panel edge. For both model shear deformation is the relative deformation of the model nodes at the measurement point used in laboratory experiments. The computed and observed behaviours of the panel are compared on the basis of concrete damage pattern. The Figures 3.6, 3.7 and 3.8 describe the computed concrete pattern under moderate levels of shear loading for three different models. These data show the orientation of discrete cracking in the concrete panel prior to the development of highly localized failure mechanism. In general, data present discrete cracking oriented perpendicular to the direction of maximum principal tensile stress at an angle of 45 degrees, as observed in laboratory. 13

26 Chapter 3. description of the joint models proposed by Lowes Figure 3.6. Discrete concrete cracking as computed using model with initial damage[lowes, 1999] Figure 3.7. Figure 3.7. Discrete concrete cracking as compute using model without initial damage [Lowes, 1999] Figure 3.8. Discrete concrete cracking as computed using the initial concretee damage [Lowes, 1999] model with flexible load frame and no 14

27 Chapter 3. description of the joint models proposed by Lowes Within the most heavily damage region of the panel, the concrete elements, that are initially damaged, accumulate less damage respect to adjacent elements. In laboratory test, the initial concrete cracking does not appear to affect the orientation of concrete cracking developed under shear loading. The computed and observed panel behaviour is compared also in terms of shear stress versus shear strain histories. The different behaviours are shown and compared in Figure 3.9. Figure 3.9. Computed and observed shear stress versus shear strain history for different panel models [Lowes, 1999] The computed response is initially linear elastic. Once cracking has occurred, shear strength decreases with increasing shear strain as damage distributes throughout the panel. One or more discrete crack zones dominate the response and shear strength begins to increase with increasing shear strain. Failure of the system is reached when all the reinforcing steel, crossing the centre of the panel, yields and the model becomes instable. Since the laboratory testing is conducted under load control, it is not possible to observe a region in which shear strength deteriorates. The definition of an initial shear-friction strength equal to the concrete compressive strength appears to produce quite accurate computed response. The introduction of two orthogonal cracks is not sufficient to represent the behaviour defined by damage on a single crack surface direction between the two cracks. Finally, data from this study underline the importance of accurate representation of system boundary conditions. While the investigators suggest that the applied loading of the panel is uniform, evaluation of reinforcement and shear keys detailing in the panel, as well as the computed response, indicate that either is not the case or that uniform loading from the actuators is distributed along the panel edge by reinforcing steel, shear keys and shear keys anchorage dowel. 15

28 Chapter 3. description of the joint models proposed by Lowes 3.2 Lowes and Altoontash [2003] Figure 3.10 shows the joint model proposed by Lowes and Altoontash [2003]. At the perimeter of the joint the element displacement field is defined by two translation and one rotation at each of four external nodes. The element formulation is compatible with line elements used in two dimensional structural analysis. The joint element is a classical superelement, composed of four internal nodal translations and 13 one-dimensional components. Determination of the element material state requires the solution of a non linear system to determine the internal translations that satisfy equilibrium. Figure Reinforced concrete beam-column joint model [Lowes and Altoontash, 2003] Figure Definition of component deformation and generalized forces (a) Component deformation and forces, (b) Shear forces acting on shear panel component [Lowes and Altoontash, 2003] The generalized displacement history of four external and four internal element nodes defines the material state of the joint element and the deformation history of the eight bar-slip springs, four interface shear springs and one shear panel component that form the joint model. One-dimensional material constitutive relationship defines component forces presented in Figure 3.11 as f i, function of the component deformation histories. For the shear panel, the complementary component force f 13 is the nominal shear stress developed in the joint core multiplied by the volume of joint core. Complementary to the 16 internal and external nodal displacements, there is a set of 16 internal and external nodal resultants. Nodal resultants can be computed from component forces imposing equilibrium at both internal and external degrees of freedom. 16

29 Chapter 3. description of the joint models proposed by Lowes Given a set of imposed external and internal nodal displacements, determination of the element material state requires a solution for four unknown internal displacements in order to satisfy the internal equilibrium of the element. The proposed joint model formulation enables the simulation of inelastic behaviour, due to any kind of possible failure that can occur in the joint (anchorage failure, failure of joint core under shear loading and failure of interface-transfer mechanism). Constitutive relationships are developed to define the load deformation behaviour of shear panel component and shear component as a function of material properties, joint geometry and joint reinforcement layout. To define the constitutive laws, fundamental material behaviours and experimental data are used. The joint element and constitutive material relationships are compared with the response of some laboratory tests. Few data are available for use in evaluating a constitutive relationship for the interface-shear component of the model. A general one-dimensional hysteretic model is used to represent the response of each of the components of the element. A response envelope, an unloading-reloading path and three damage rules, that control evolution of this path, define the one-dimensional material model. Hysteretic damage is simulated through deterioration in unloading stiffness (unloading stiffness degradation), deterioration in strength achieved at previously unachieved deformation demands (strength degradation) and determination in the strength development in the vicinity of the maximum and minimum deformation demands (reloading strength degradation). Figure One-dimensional material model: (a) Material states, (b) Impact of hysteretic damage on load-deformation response [Lowes and Altoontash, 2003] 17

30 Chapter 3. description of the joint models proposed by Lowes Figure 3.13 Behaviour of reinforced concrete panel SE8 tested by Stevens et al.[1990] under cyclic shear loading: (a) Simulated response, (b) Observed response As previously discussed, an earthquake attack results in shear loading at the joint core. The inelastic response is simulated by the shear panel (simulation of inelastic core behaviour). On the basis of previous research a constitutive relationship is developed to define deformation of shear panel on the basis of material properties and joint geometry. This constitutive model is developed employing Modified Compression Field Theory (MCFT) [Vecchio and Collins, 1986] to define the envelope of shear stress strain history of the joint core; experimental data provided by Stevens et al [1991] are used to described response under cyclic loading. This procedure allows the user to define behaviour using material properties, joint geometry, and joint reinforcing steel ratio. Only few experimental investigations consider the response of reinforced concrete element under pure shear. Figure 3.13 shows the linear interpolation of the monotonic envelope, as a result of the MCFT model, and the simulated response of reversed-cyclic loading. Discrepancies in the results are due to the relative simplicity of the model applied. Earthquake loading results in substantial bond demand for longitudinal reinforcements. A constitutive model is developed for the load-deformation history of bond slip springs that simulate the inelastic anchorage-zone response. This model is developed using data from experimental testing of anchorage-zone specimens and assumption about the bond-stress distribution within the joint. The envelope of the bar-stress versus slip relationship is based on several approximations and simplified assumptions: constant bond stress for reinforcements in elastic range and slip defined as the relative movement of reinforcing bar with respect to the perimeter of the joint and function of strain distribution along the bar. The bar is assumed to exhibit zero slip for zero stress. 18

31 Chapter 3. description of the joint models proposed by Lowes Figure 3.14 Figure Bond stress and bar stress distribution for a bar anchored in a beam column joint Average bond strength is based on experimental data and previous investigations. The cyclic response is calibrated on data provided by Eligehausen et al.[1983] and Hawkins et al.[1982], used for defining these model parameters. (a) Comparison of Simulated and Observed Response. The model is evaluated through the comparison of simulated and observed response for a series of building frame subassemblages tested in laboratory under pseudo-static reversed cyclic loading by Park and Ruiton [1988]. Numerical models were developed to simulate Park and Ruitong [1988] experiment using MATLAB; these models comprised lumped plasticity beam-column Figure Observed (a, b) and simulated response (c, d) of the Park and Ruitong [1988] building sub-assemblages. 19

32 Chapter 3. description of the joint models proposed by Lowes elements and the proposed joint element. Compared results are in Figure The comparison of simulated and observed response for a series of beam-column joints indicates that the proposed model represents well the fundamental characteristics of response for joints subjected to moderate shear demands. 3.3 Lowes and Mitra [2004] A study by Mitra and Lowes [2004] suggests a way to modify the joint model proposed by Altoontash and Lowes [2003]. The main modifications are: Bar-slip springs are located at the centroid of the beam and column flexural tension and compression zones rather than at the perimeter of the joint. A new model is used to calibrate joint-panel component, assuming a diagonal compression strut mechanism for load transfer within the joint [Paulay et a, 1978] rather than an uniform field. The new model simulates deterioration of strength. A new bond slip model is proposed, in order not to exhibit negative stiffness prior to reinforcing steel reaching ultimate strength to avoid numerical instability. The shear panel component of the joint element is used to simulate strength and stiffness degradation due to joint core damage under severe demands. This new model assumes that the shear is carried by a concrete compression strut and the transverse reinforcement acts to increase the strength and deformation capacity of this strut. The new shear model is calibrated using simulated and observed data. Assuming that joint shear load is transferred via concrete compression strut, it is possible to predict shear response of confined concrete. The strut orientation is supposed to be constant and defined by the geometry of the beams and columns flexural compression zone. Depth of the strut is defined as the maximum of out of plane depth of the beam and the column. The confined concrete model is the Mander [1988] one and it defines the stress and strain response of the strut. Column longitudinal and joint horizontal reinforcing steel confines the joint core concrete. Only the components of confining forces acting perpendicular to the strut direction are considered. Concrete compressive strength is reduced to take into account cracking parallel to the axis of the strut [Vecchio and Collins, 1986; Belarbi and Hsu, 1995]. The result of previous research indicates that concrete compressive strength is reduced by tensile cracking due to cyclic loading [Stevenson et al, 1991]. The joint carries shear only through compression strut. The bar-slip used for the joint model simulates stiffness and strength loss associated to the deterioration of beam and column reinforcement anchorage in the joint. A review of experimental data by Mitra and Lowes [2004] indicates that the 3.00 mm of slip proposed by Lowes and Altoontash [2003] was too conservative. (a) Comparison of Simulated and Observed Response. Failure Mechanism. The inelastic failure mechanism is correctly simulated. Initial and Unloading Stiffness. The proposed model represents well the observed initial stiffness and the unloading stiffness at the maximum load. 20

33 Chapter 3. description of the joint models proposed by Lowes Post-yield Tangent Stiffness. The post-yield stiffness is well predicted. The coefficient of variation between observed and simulated result is about 22%, but considering the high number of parameters influencing the results (post peak response of shear panel, the hardening response, flexural stiffness of beams and columns), it is possible to consider this value sufficiently low. Maximum Strength. The model represents well the observed maximum strength of the sub-assemblage, with the average ratio of simulated to observed response equal to Drift at Maximum Strength. Drift at maximum strength is simulated with less accuracy than strength. Strength Loss at Final Drift Level. On average the model predicts well the observed strength during the final load cycle. These results validate the proposed shear panel calibration model and the proposed strength reduction model for joints that exhibit yielding of beam longitudinal reinforcement steel prior to the joint failure. Pinching Ratio. On average the model predicts the observed pinching ratio closely. 21

34 Chapter 4. experimental test 4. EXPERIMENTAL TEST The experimental test considered in this study was performed by Mohele and Lowes [1999]. The goal of this research was to identify issues critical to the evaluation and retrofit of beam column T-joints in older reinforced concrete bridge frame. The whole experimental test considered three models: As-built model (Model One) Two retrofit models sub-assemblies from a single prototype frame (Model Two and Model Three) In this study the results given by the test on the as-built model (Model One) are considered. In order to assess the design details controlling the response of as-built connections to earthquake loading, a prototype multi-column frame was designed. Figure 4.1. Prototype multi-column frame [Lowes and Moehle,1999] This Model was tested in laboratory. The Model One displayed essentially no ductility under simulated earthquake loading. Cracking of concrete cover in the joint area was observed during the initial cycles of loading and, during the test, the damage accumulated in the joint. 22

35 Chapter 4. experimental test Throughout the test, instrumentation measured progressive slip of column reinforcement; measurement of beam longitudinal reinforcement strains appears to indicate that this reinforcement was also slipping through the joint. The relatively poor response of Model One was attributed to loss of anchorage of column longitudinal reinforcements terminating in the joint, degradation of joint concrete due to high joint stresses and reduced bond slip capacity along the length of the beam longitudinal reinforcement passing through the joint. 4.1 As-Built Model The as-build prototype was designed considering a review of engineering drawings of RC bridges designed and constructed between 1950s and 1960s. This frame included details considered as critical for the beam-column joint behaviour. The bridge review focused on the older RC bridges in California, characterized by a single level and multi-column frame perpendicular to the roadway. Details of interest for this study are the following: Gross member dimension Reinforcement details in the interior beam-column joint Flexural reinforcement ratio for beams and columns Location of cut-off for flexural reinforcements in beams Anchorage lengths for column flexural reinforcements terminating in the interior beam column joint Column axial load Foundation conditions During the 1950s and 1960s, common practice did not dictate any consideration about the relative flexural capacity of the beams and columns framing into a joint, about force transfer through the joint capacity or concerning member shear capacity as function of member flexural capacity. For this reason it is common to find existing bridges of this period in which undesiderable failure mechanism could occur during an earthquake. For the Model One the following target design concepts are considered: The sum of the cap beam nominal flexural strength exceeds the column nominal flexural strength. Yield of the beam is expected prior to flexural yielding of the column. Considering the method recommended by the ACI-ASCE Committee 352 [A1], the nominal horizontal joint shear developed when the column reaches its nominal flexural strength, is expected as follows: Where: A ACI is the effective joint area in in2 V j =6.2 A ACI f c, lbs 23