CHAPTER 1: INTRODUCTION

Transcription

1 CHAPTER 1: INTRODUCTION 1.1 Introduction Inadequate performance of reinforced concrete bridges during the 1989 Loma Prieta and 1994 Northridge earthquakes focussed attention on the design of these structures. Researchers and bridge engineers identified aspects of the current design process that required additional research to achieve the desired level of structural performance and constructability. The design of bridge beam-column connections was identified as one such area, and in the ensuing years a number of research projects have addressed this topic. However, there is still uncertainty within the engineering community as to the most appropriate procedure for achieving the design goals for beam-column connections. This uncertainty likely will be resolved through additional experimental and analytical investigation of connection response. The current investigation focusses on development of a finite element model that is appropriate for investigating the behavior of reinforced concrete beam-column connections subjected to general loading and advances techniques for analysis of reinforced concrete structural elements. 1.2 Behavior of Reinforced Concrete Beam-Column Connections The intersection between a beam and column element defines a region of unique design, loading and behavior within a reinforced concrete frame. Considering the bridge interior beam-column T-connection as an example, Figure 1.1 shows actions at the perimeter of the connection under earthquake loading. For bridge systems, flexural yielding of the columns is the desired response mechanism. Thus, under severe loading and if the connection is adequately designed, the column could be expected to achieve significant postyield flexural strength while the beam flexural demands could be expected to approach 1

2 values associated with nominal flexural strength. These actions imply substantial shear loading of the connection, which could lead to connection damage or failure. Figure 1.1a: Section of a Reinforced Concrete Box-Girder Bridge Frame Subjected to Earthquake Loading (Note that Beam-Column Connection is Highlighted) Figure 1.1b: Loads on the Perimeter of an Interior Beam-Column Connection Figure 1.1: Earthquake Loading of an Interior Beam-Column Bridge Connection If connection design is inadequate for the shear load that develops under earthquake excitation, the connection may exhibit deteriorating stiffness and strength. This behavior 2

3 may result in inadequate structural performance. The beam-column connection provides continuity between the beam and column elements, establishing a continuous load path in the bridge frame. Thus, connection flexibility increases global structural flexibility. If the connection exhibits inelastic shear deformation or slip of reinforcement anchored in the connection, the increase in connection flexibility may be relatively large and may control structural response. Inelastic response mechanisms may result in deterioration of connection strength as well as stiffness. If connection strength is limited, the desired connection response mechanism, flexural yielding of the columns, will not develop, and damage will instead accumulate in the connection. Analysis of single-degree-of-freedom structures indicates that a strength-degrading response of critical structural component may result in premature structural collapse under earthquake loading as it promotes accumulation of inelastic deformation and strength loss in the established weak direction [Mahin and Boroschek, 1992; Rahnama and Krawinkler, 1995; Mahin, 1996]. Therefore, this behavior is of particular concern. Experimental investigation and observation of structural damage following recent earthquakes show that inadequately designed connections have the potential for producing inadequate structural response. Figure 1.2 shows the load-displacement history for two pairs of bridge beam-column connection sub-assemblies tested in the laboratory. Each pair consists of two similar connections, one in which joint deformation and slip of reinforcement is limited (Figure 1.2a and Figure 1.2c) and one in which joint shear deformation and slip of longitudinal reinforcement is more substantial (Figure 1.2b and Figure 1.2d). For the systems defined by data presented in Figure 1.2a and Figure 1.2c, increased column flexural strength (Figure 1.2c) results in increased load on the connection and ultimately increased inelastic deformation in the connection. For the more heavily loaded connection (Figure 1.2c), accumulation of connection damage is evident in the pinched hysteretic 3

4 response and reduced connection stiffness is reflected in the fact that the connection must be subjected to a greatly increasing inter-story drift demand to develop the post-yield strength. For the systems defined by data presented in Figure 1.2b and Figure 1.2d, connection load demand in constant but the connection is retrofit to increase connection strength (Figure 1.2d). For the as-built connection (Figure 1.2b), once peak strength is developed, deterioration of connection strength and stiffness is reflected specifically in the relatively flat load-displacement response that is observed at diminishing load levels under increasing displacement demand. For this connection, in the post-peak regime of the presented experimental data, it is evident that the observed peak strength could not be achieved even if the system were subjected to large monotonically increasing displacement demands. However, until the column fails in flexure, the retrofit connection shows no reduction of connection strength and limited reduction in unloading stiffness under reversed cyclic loading. Observation of bridges in the Bay Area following the 1989 Loma Prieta earthquake show similar behavior. Damage to external beam-column connections in the Interstate 280 Viaduct in San Francisco during the Loam Prieta earthquake (Figure 1.3) severely limited the resistance of the viaduct to earthquake loading, forced demolition of the structure following the earthquake and likely would have resulted in collapse of the structure had earthquake ground motion been of greater intensity. To investigate the load-deformation response of a beam-column connection, it is necessary to consider connection behavior at a localized level. Local response mechanisms that determine connection behavior include those associated with flexure of the beams and column that frame into the connection, load transfer between concrete and reinforcing steel and shear transfer in the connection core. The flexural response of the beams and column defines the global load demand on the connection. Beyond load demand, flexural response of the framing element determines the stress distribution in the concrete and rein- 4

5 Lateral Load Versus Drift for a Laboratory Model of Two-Story Exterior Bridge Connection Designed in Accordance with Current Design Methods [Data from Mazzoni, 1998] Applied Lateral Load (kip) H Drift Ratio = /H Drift Ratio (%) Drift Ratio (%) Figure 1.2a: Specimen 1 (Design Joint Shear Stress is 15 f c psi), Minimal Joint Deformation and Minimal Slip of Anchored Figure 1.2b: Specimen 2 (Design Joint Shear Stress is 20 f c psi), Slip of Reinforcement Anchored in the Connection Lateral Load Versus Drift for a Laboratory Model of an Interior Bridge T-Connection Representative of California Construction in the 1950 s [Data from Lowes and Moehle, 1999] Load (kips) P, Displacement (inches) Figure 1.2c: As-Built Older Connections; Loss of Strength is Attributed to Failure of Column Reinforcement Anchorage Displacement (mm) Figure 1.2d: Retrofit Connections; Response Mechanism is Flexural Yielding of the Column Figure 1.2: Load-Displacement Response of Bridge Beam-Column Connections forcing steel at the perimeter of the connection and, as a result, affects the stress distribution in the connection core. With load defined at the perimeter of the connection, the bond 5

6 Figure 1.3a:Bridge Frame and External Beam-Column Connection Figure 1.3b: Damaged External Beam -Column Connections Figure 1.3: External Beam-Column Connections in the I-280 Viaduct in San Francisco, California Following the Loma Prieta Earthquake of 1989 [Photograph from the EQIIS Image Database, NISEE, University of California, Berkeley]. stress distribution defines the longitudinal steel stress distribution within the connection and thus the additional connection flexibility associated with extended yielding of the reinforcement. Bond response determines also the load distribution at the perimeter of the connection core. Inadequate bond strength may limit the capacity of the connection to transfer beam and column flexural loads resulting in a strength degrading response history under earthquake loading. Finally, connection response may be determined by behavior of the connection core. Under severe reversed cyclic shear loading, concrete in the connection core may crack under high principal tensile stress or crush under high principal compression stress. Also, accumulated damage in the connection core concrete may result in substantial inelastic deformation and strength loss. 6

7 The local response mechanisms that control connection behavior are defined by the behavior of plain concrete, reinforcing steel and bond-zone material under general reversed-cyclic loading. Consideration of material behavior associated with development of the local response mechanisms defines the required material modeling capabilities of the proposed model. Connection response is determined by the applied loading at the connection perimeter as controlled by flexural demand in the beams and column. Figure 1.4 shows an idealization of an interior beam-column bridge joint and the likely distribution of concrete and steel stress that develops at the perimeter of the connection under earthquake loading. The stress distribution presented in Figure 1.4 follows from the assumption that the column develops a flexural demand in excess of that corresponding to the nominal flexural strength and that the beams develop flexural demands approaching that corresponding to the flexural strength. Point A in Figure 1.4 locates the extreme fibers of the column flexural tension zone. In the vicinity of Point A, column steel carries tensile stress in excess of that corresponding to the yield stress. Column concrete in the flexural tension zone is cracked parallel to the column-connection interface and carries minimal tensile stress. Point B locates the column flexural compression zone. Here the column concrete carries compression stress parallel the column axis. The concrete furthest from the column neutral axis may experience severe compressive loading with compression strain parallel to the column axis in excess of that corresponding to peak uniaxial compressive strength. Compression loading in this range results in volumetric expansion of the concrete. If transverse reinforcing steel is present, volumetric expansion will be partially restrained and, as a result, concrete in the flexural compression zone carries some compression perpendicular to the column axis. Experimental data show increased uniaxial compressive strength for concrete under biaxial compression [Kupfer et al., 1969; Yin et al., 1989]. Also at Point B in the flexural compression zone, reinforcing steel carries compression 7

8 stress. For moderate cyclic flexural demands, steel reinforcement typically carries compressive stress less than the yield stress. However, under severe reversed cyclic flexural loading, concrete cracks developed under tensile loading may not close immediately upon load reversal. In this case, at Point B concrete compressive stress is negligible, all compression load is carried by reinforcing steel and reinforcement likely yields in compression. Flexural action in the column is coupled with shear action, and consideration of shear transfer between the column and connection completes characterization of the column-connection interface. Experimental investigation suggests that both shear transfer across open concrete cracks [Paulay and Loeber, 1977; Laible et al. 1977; Hofbeck et al., 1969] and shear transfer through dowel action of reinforcing steel [Hofbeck et al., 1969] are limited. Thus, column shear is transferred into the connection predominately through concrete shear in the flexural compression zone. I C D F E concrete stress acting on connection B A G steel stress acting on connection H beam and column loads in the vicinity of the beam-column connection Figure 1.4: Idealization of the Stress Distribution at the Perimeter of the Connection Figure 1.4 shows also a representation of the concrete and steel stress distribution at the beam-connection interfaces. For bridge connections under moderate to severe earthquake loading, beam flexural demands could be expected to approach values associated with the nominal flexural strength. In this case, the distribution of concrete and steel stress at the beam-connection interface is similar to that of the column. Points A and C locate the 8

9 beam tension zones. Here the concrete cracking and associated reduction in concrete tensile strength is similar to that observed at the column-connection interface. Under flexural demand approaching nominal flexural strength, beam longitudinal reinforcement at Points A and C could be expected to carry tensile stress approaching or equal to the yield stress. Points B and D locate the beam flexural compression zones. In comparison with the column, reduced relative flexural demand for the beams results in reduced post-yield tensile strain in the beam longitudinal reinforcement and reduced concrete flexural crack widths. Also, because beam flexural demand is expected to be less than the nominal flexural strength, beam concrete could be expected to carry a maximum compression stress much less than the concrete compressive strength. As a result, volumetric expansion of the compression-zone concrete is limited, as is the induced passive confinement provided by transverse reinforcement. Unconfined beam compression-zone concrete would not be expected to spall. Further, beam longitudinal reinforcement at Points B and D could be expected to carry moderate compressive stress and likely will not yield in compression during the earthquake. As for the column, shear is assumed to be transferred predominately through the beam flexural compression zones. The beam and column concrete and steel stress distribution at the perimeter of the connection defines the load demand on the connection. Connection behavior is determined by the distribution of these loads within the connection. The concrete and steel stress distribution shown in Figure 1.4 indicates that column reinforcement carries tensile stress in excess of the yield stress at Point A and termination of the bar at Point E requires that the bar carries zero stress at that point. This variation in stress along the anchored length of the column reinforcing bar implies stress transfer between the reinforcing bar and the surrounding concrete. This stress transfer is referred to as bond. Bond is required also to transfer column reinforcement compressive stress at Point B into connection core con- 9

10 crete. Since reinforcement compression stress likely is less than the tensile stress, the zero stress state in the bar is assumed to occur at Point F. Finally, substantial bond strength is required also to achieve the stress variation along the beam longitudinal reinforcement implied by the predicted steel compression stress at Points B and D and the predicted tensile stress at Points A and C. For systems such as the beam-column connection where reinforcing steel is embedded in a large concrete volume and steel stress varies substantially along the embedment length, bond between concrete and reinforcing steel is identified as anchorage bond. In the vicinity of the beam-column connection, flexural bond also can determine structural response. Flexural bond refers to load transfer between concrete and flexural member longitudinal reinforcement; flexural bond is required for variation in the flexural demand along the length of a reinforced concrete beam or column. For the T-connection considered here. Flexural bond strength could be expected to affect significantly structural response where reinforcement carries stresses approaching or in excess of the yield strength such as at Points G, H and I in Figure 1.4. The load distribution with in the connection is determined in part by the bond response. If column reinforcement carries stress in excess of the yield stress at Point A, bond strength in the vicinity of Point A determines the length along which the column reinforcement carries stress in excess of the yield stress. This is length is referred to as the depth of yield penetration. Greater yield penetration implies increased inelastic deformation of the reinforcing steel and greater flexibility of the connection. Bond determines the manner in which steel stress at the perimeter of the connection is distributed within the connection core. Figure 1.5 shows two possible bond stress distributions within a typical bridge T-connection. If bond stress is essentially uniform, then steel stress is distributed to the connection core as shown in Figure 1.5a. However, if bond strength is significant only in the vicinity of beam and column flexural compression zones where concrete compres- 10

11 sion perpendicular to the axis of the reinforcing bar promotes load transfer between concrete and steel, then steel stress is distributed as shown in Figure 1.5b. The load distribution at the perimeter of the connection core in part determines the mechanism of load transfer within the connection core and thus the response of the connection core under reversed cyclic loading. concrete stress acting on connection steel stress acting on connection beam and column loads in the vicinity of the beam-column connection bond stress acting on connection core concrete I C D I C D E E F F B A G B A G H H Figure 1.5a: Approximately Uniform Bond Stress Distribution Figure 1.5b: Bond Strength Is Significant in the Vicinity of Flexural Compression Zones Figure 1.5: Bond Stress Distribution within the Connection The bond stress distribution that develops within the connection under earthquake loading is determined by a number of factors including the distribution of concrete and steel stress at the perimeter of the connection, the bond-zone concrete and reinforcing steel stress, strain and damage states and the distribution of transverse reinforcement in the bond zone. Experimental investigation indicates that bond strength is greatest if concrete does not have open cracks in the vicinity of the reinforcing bar, if the concrete carries compression perpendicular to the reinforcing bar and if steel reinforcement has not yielded in tension [Viawanthanatepa, 1979; Viawanthanatepa et al., 1979; Eligehausen et 11

12 al., 1983; Shima et al., 1987; Gambarova et al., 1989; Malvar, 1992]. For the beam-column connection there are anchorage bond zones with different bond conditions and different bond response histories. For example in the vicinity of Point A, concrete flexural cracks parallel the beam-connection interface and yielding of column reinforcing steel could be expected to limit bond strength. For column reinforcement in the vicinity of Point B, concrete in biaxial compression and unyielded steel loaded in compression could be expected to result in relatively high bond strength. These variations in the bond response follow from variations in the stresses at the perimeter of the connection. However, the concrete stress state in the anchorage zone is determined not only by the beams and column flexural demands but also by the distribution of transverse reinforcement within the connection. Experimental investigation suggests that load transfer between concrete and reinforcing steel results in some radial expansion of the reinforcement in the anchorage zone [Gambarova et al., 1989 and Tepfers et al., 1992]. This expansion can activate transverse reinforcement within the bond zone to confine anchorage zone concrete, provide compression of concrete in the direction perpendicular to the reinforcing bar and thereby increase bond strength. Typically, a significant volume of transverse reinforcement is required to develop a bond stress distribution as shown in Figure 1.5b. Finally, connection response is determined by the behavior of the concrete within the connection core. Loading of connection core concrete comes through transfer of the concrete stress developed in beam and column flexural compression zones and through transfer of reinforcing steel compression and tension stress as distributed to the connection core through bond. These external loads combine to define a global connection shear load. Evaluation of the concrete compression stress distribution at the perimeter of the connection suggests that this portion of the shear load activates the connection core concrete in compression as idealized in Figure 1.6. Two possible distributions exist for characterizing 12

13 transfer of reinforcing steel stresses through the connection. Activation of a particular mechanism depends on the bond stress distribution at the perimeter of the connection core as well as the distribution of damage within the connection. If the bond stress distribution and the distribution of concrete damage at the perimeter of the connection are approximately uniform, then a shear-panel mechanism may develop as idealized in Figure 1.7a. If bond strength is significant only in the vicinity of beam and column flexural compression zones and damage to connection core concrete promotes loading of the concrete in these areas, then a compression strut mechanism will develop as idealized in Figure 1.7b. The mechanism of shear transfer in the connection core determines the distribution of connection damage and establishes a basis for design of connection transverse reinforcement. Experimental and analytical investigation of reinforced concrete panels indicates that under uniform shear loading, panel response is characterized by cracking of plain concrete when concrete principal tensile stress exceeds concrete strength [Vecchio and Nieto, 1988 and Stevens et al., 1988]. This cracking is perpendicular to the direction of principal tensile stress. Under reversed-cyclic loading, orthogonal cracking is observed [Stevens et al., 1988]. Investigation indicates also that behavior is determined by the level of tensile and shear traction transferred across crack surfaces [Vecchio and Collins, 1986; Belarbi and Hsu, 1994, and Rose et al., 1999]. If connection shear is transferred through development of a compression strut, then transverse reinforcement in the connection will act to confine connection core concrete. Failure of the connection is defined by yielding of this reinforcement. If shear is transferred through both a compression strut mechanism and a distributed shear panel mechanism, then connection transverse reinforcement also acts to carry shear through development of distributed strut-and-tie mechanisms. These mechanisms of connection load transfer were presented first by Paulay et al. [1987]. 13

14 concrete stress acting on connection steel stress acting on connection core beam and column loads in the vicinity of the beam-column connection concrete compression zone and orientation of principal stress Figure 1.6: Idealization of Transfer of Framing Member Concrete Stress Through the Connection Core concrete stress acting on connection steel stress acting on connection bond stress acting on connection core concrete connection core concrete active in shear transfer beam and column flexural, axial and shear loads in the vicinity of the connection Figure 1.7a: Approximately Uniform Bond Figure 1.7b: Bond Strength Is Stress Distribution Significant in the Vicinity of Flexural Compression Figure 1.7: Transfer of Framing Member Steel Stress Through the Connection Core Evaluation of the localized mechanisms that control connection response as well as the concrete, steel and bond-zone material behavior that defines these local mechanisms defines the characteristics that must be incorporated into a model proposed for use in 14

15 investigation connection response. In particular the previous evaluation suggests the need to represent flexural response of reinforce concrete beams and columns under reversed cyclic loading including the distribution of concrete normal and shear stress and activation of passive confinement provided by transverse reinforcement under reversed cyclic loading. Also, prediction of connection behavior requires representation of bond-zone response including variation in bond strength due to concrete and steel stress state; radial expansion of bond zone to activate transverse reinforcement. Finally, evaluation of connection behavior indicates the need to accurate represent the response of the connection core to reversed cyclic shear both in the form of a uniform shear loading and a compression-strut loading. Ultimately, a proposed connection model must provide the framework for objectively representing these fundamental characteristics of response on the basis of the connection design parameters rather than the analysts assumptions. 1.3 Analysis of Reinforced Concrete Beam-Column Connections In order to predict the response of reinforced concrete beam-column bridge connections, it is necessary to develop an analytical model that has the capacity to account for the localized response mechanisms that determine global behavior. Since engineers became interested in rational connection design, a number of models have been proposed to predict the behavior of reinforced concrete beam-column connections under earthquake loading. These models range in sophistication from simplified models that are appropriate for connection design to multi-dimensional finite element models. All of these models are develop on the basis of some initial assumptions regarding connection behavior. Given the complexity of connection response, simple models require the introduction of broad assumptions defining global load-transfer mechanisms within the connection. Here a plausible model identifies a load distribution that satisfies equilibrium but not necessarily compatibility. Such models do not provide a framework for explicitly considering local- 15

16 ized response, and the application of these models to investigation of connection behavior is limited. However, these models do contribute to identification of the required modeling capabilities. More sophisticated models provide a link between deformation and compatibility by introducing explicit representation of concrete, steel and/or bond-zone material response. If material models are sufficiently simple and connection behavior is grossly represented, a closed-form solution can be developed defining connection deformation as a function of applied load and connection design. Material models or assumed connection response mechanisms may be too simple for effective use in investigating connection response, but these models do suggest trends in behavior that must be represented by a more sophisticated and detailed model. As material models are further refined and extended to represent response under general loading, the finite element method provides the most appropriate framework for predicting connection response. The finite element method provides a means of introducing sophisticated material constitutive relationships to predict connection response at the local level on the basis of connection design. In developing a model to predict connection response, simplified models that support current design recommendations contribute to establishing required modeling capabilities. The models that have been developed on the basis of experimental data to indirectly or directly support current design recommendations include the compression-strut model [Paulay et al., 1978], the shear-panel model [Paulay et al., 1978], and the generalized strut-and-tie model [Priestley, 1993]. These models provide a representation of connection load-transfer under the design level earthquake loading. These models provide no explicit information about connection performance with the exception that they imply maintenance of a stable load-transfer mechanism under severe earthquake loading. These models all require introduction of comprehensive initial assumptions including the stress-strain distribution at the boundary of the connection, bond strength at particular points within the 16

17 connection, the bond stress distribution within the connection, the mechanism of shear transfer within the connection core and the assumption that accumulated damage will not result in premature failure of the connection. The compression-strut model is one such design model. In this representation of connection response, it is assumed that bond strength is significant only in the vicinity of beam and column flexural compression zone. Thus, transfer of concrete and steel loads at the perimeter of the connection follows the representations shown in Figure 1.6 and Figure 1.7b. If connection response is characterized by this model, transverse reinforcement is designed to confine connection core concrete that is loaded in compression to stresses approaching compression strength. The shear-panel model is another design model. In this representation, it is assumed that bond stress is more uniformly distributed through the connection. Thus, the beam and column steel stress is distributed through the connection as idealized in Figure 1.7a. If it is assumed that yielding of longitudinal reinforcement in the beams and column results in concrete flexural cracks remaining open upon load reversal, it follows that all flexural compression load in these elements is transferred into the connection through longitudinal reinforcement. In this case, connection loading is idealized solely by Figure 1.7a; otherwise beam and column flexural compression stress may be assumed to be transferred through the connection as idealized in Figure 1.6. If the shear-panel mechanism characterizes connection response under severe earthquake loading, the connection core carries uniform shear and transverse reinforcement in the connection is designed to carry the applied shear load. A third design model is the generalized strut-and-tie model. Here it is assumed that transfer of concrete and steel stresses developed outside the perimeter of the connection may be idealized as occurring through a series of concrete compression struts and rein- 17

18 forcing steel tension ties. A plausible strut-and-tie model satisfies the previously identified assumptions as well as the assumption that the bond stress demand implied at nodes connecting struts and ties can be achieved and the orientation of concrete compression struts follows the orientation of concrete principal stresses. If the strut-and-tie model defines connection response, steel reinforcement is designed to carry the tie forces required for equilibrium. Assuming that these simplified models represent the global response of connections with variable design parameters under variable design level loading, this defines the requirements for newly developed connection models. A new model should have the capacity to predict connection behavior of a compression-strut, a shear-panel and a generalized strut-and-tie type mechanism. Specifically, the model should represent volumetric dilation of plain concrete under compression type loading, uniform shear loading of reinforced concrete panels and bond failure of concrete-steel nodes. Further, the model should predict development of a particular global response mechanism as a function of the initial design or load history. In particular, a newly developed model should represent the distribution of concrete-to-steel bond in order to predict development of a compression-strut versus a shear-panel mechanism of load transfer. Simplified models have provided also the foundation for development of analytical tools that more accurately predict connection response at the global and local level. Like the simplified design models, these advanced models typically define response on the basis of equilibrium of connection loads. However, here connection deformation is introduced as a means of limiting the possible equilibrium distributions. One such model is that proposed by Paulay [1989]. Here connection response is defined by the magnitude, orientation and assumed distribution of forces on the perimeter of the connection. By introducing a number of assumptions about material response and the distribution of forces at the 18

19 perimeter of the connection, Paulay draws conclusions about the level of performance associated with the panel and compression-strut mechanisms previously discussed as well as suggests the effect on performance of transverse reinforcement in the connection core. While the model may be applied to investigating global connection response, it does not provide an objective model for investigating connection response. In particular, Paulay notes that predicting connection performance on the basis of the design parameters requires accurate representation of the concrete-to-steel bond stress distribution as well as the orthotropic response of damaged concrete. Another model that extends the simplified design models is that proposed by Pantazopoulou and Bonacci [1992, 1993]. This model provides a means of explicitly introducing connection deformation and bond response into the analysis. This model is developed to represent the response of the confined concrete with the core of a building beam-column connection. Here the entire concrete core is assumed to have a uniform stress-strain field. Loading of the connection core is defined on the basis of simplified representations of the stress fields in the framing members. A material model is introduced to represent the behavior of well-confined and unconfined concrete, and concrete principal stresses are evaluated to determine connection response. The model is used to evaluate the effect on connection strength and deformation of various design parameters including the volume of transverse steel, column axial load and beam and column behavior. The model predicts well trends in experimental data defining connection response and provides reasonable prediction for configurations and load cases not yet tested in the laboratory. However, like the previously discussed models, the representation of a uniform stress-strain history within the connection core idealizes connection response at too coarse a level to be appropriate for use in predicting connection response as determined by local failure mechanisms. 19

20 These limitations as well as several associated with the previous models are eliminated by application of the finite element method to analysis of beam-column connections. One of the few models developed to investigate connection response is that presented by Pantazopoulou and Bonacci [1993]. Here the behavior of an interior building connection is investigated using a two-dimensional finite element model. This model includes a plane stress representation of concrete material response that predicts softening of concrete under severe compressive and tensile loading, explicit representation of reinforcing steel elements and a one-dimensional representation of bond force transfer between concrete and reinforcing steel in which high bond strength is assumed for favorable bond conditions and low bond strength is assumed for unfavorable conditions. Pantazopoulou and Bonacci achieve reasonably good correlation between predicted and observed response for a specimen tested in the laboratory. The model is then used in a parametric study to evaluate the effect of design parameters on connection behavior. The results of this investigation emphasize the need to include many aspects of material and system response within the finite element model as well as the potential of the finite element method for predicting the localized and global response mechanisms that determine connection behavior. The investigation presented by Pantazopoulou and Bonacci [1993] suggests that the finite element method provides the necessary framework for predicting global connection response on the basis of localized response mechanisms. Such a model predicts connection behavior on the basis of an assumed material response model. Unlike the required initial assumptions for more simplified connection model, material models defining the response of concrete, steel and the bond-zone are fully defined on the basis of experimental data. Thus, the finite element model has the potential to provide a relatively objective prediction of connection response for general connection design and loading. 20

21 1.4 Finite Element Modeling of Reinforced Concrete Beam-Column Connections The current research project focusses on development of a finite element model that is appropriate for investigating reinforced concrete beam-column bridge connection behavior under earthquake loading. The research comprises development of constitutive models to represent behavior of the materials that compose a connection on the basis of experimental data, development of techniques that are appropriate for analysis of reinforced concrete systems, verification, and calibration of the global model for reinforced concrete systems of increasing complexity. Chapters 2, 3 and 4 respectively discuss development of the plain concrete, reinforcing steel and bond-zone constitutive models and finite element implementation. Each of these chapters follows a similar format. First material behavior is defined on the basis of experimental data. Previously proposed constitutive models are evaluated both to identify modeling techniques and formulations that may be of use to the current investigation as well as to further clarify material response. Next, the qualitative evaluation of connection response as well as laboratory data are used as a basis for identifying the material characteristics that appropriately are included in the current model. Drawing on previously proposed material models, a constitutive model and, as appropriate, finite element implementation are proposed for to meet the goals of the current investigation. Finally, the proposed model is verified through comparison of computed and observed response. Chapter 5 presents calibration, verification and application of the global model. This chapter begins with a discussion of the non-standard modeling and analysis techniques required in the current investigation to enable analysis of a global model comprising plain concrete, reinforcing steel and bond-zone material. The remainder of the chapter considers the application of the model to predict the response of increasingly complex reinforced concrete systems, beginning with a plain concrete beam and culminating with a series of 21

22 reinforced concrete beam-column bridge connections. Computed response is compared with experimental data. For each reinforced concrete system a number of finite element models with different model parameters are used and variations in these model parameters are suggested to improved efficiency, stability and accuracy of the model. Chapter 6 completes the current presentation. A brief discussion of the merits and failings of the currently proposed model is provided. Results of the current investigation suggest that additional fundamental research is required if computer simulation is to be a viable tool for future research and design of reinforced concrete structures, a discussion of additional research needs in the area of characterization of material response through experimental investigation, material modeling and non-linear analysis is presented. 22