On earthquake-resistant reinforced concrete frame

On earthquake-resistant reinforced concrete frame connections S.J. PANTAZOPOULOU AND J.F. BONACCI Department of Civil Engineering, University of Toronto, Toronto, ON M5S 1A4, Canada

Can. J. Civ. Eng. Downloaded from www.nrcresearchpress.com by University of Toronto on 11/15/12 For personal use only.

Received October 26, 1992 Revised manuscript accepted September 29, 1993 The behavior of earthquake-resistant reinforced concrete frame connections has been researched extensively over the past 30 years, but conflicting interpretations of the underlying physical problem and differences of opinion in defining acceptable performance criteria still pervade almost every aspect of connection behavior and design. This study explores the mechanics of reinforced concrete beam-column joints under lateral loads, with the aim to assess the parametric dependence of the behavior of these elements for the benefit of design. In the course of the study, published experimental information from around the world and results from a number of novel analytical studies are considered collectively in an attempt to broaden the scope and depth of the parametric description of joint mechanics. Apart from improved understanding of the physical problem, the most important outcome of this research is to formulate simple tools for design of earthquake-resisting beam-column connections using a consistent mechanics approach. Key words: beam-column connection, database, earthquake-resistant design, finite element analysis, reinforced concrete, shear strength, stirrups. Le comportement d'assemblages d'ossatures en bCton arm6 parasismiques a fait l'objet de recherches exhaustives au cours des trente dernikres annCes; toutefois, des interprktations contradictoires du problkme physique sous-jacent ainsi que des differences d'opinion dans la difinition de critkres de performance acceptables continuent de dominer presque tous les aspects du comportement et de la conception des assemblages. Cette Ctude examine la m6canique des assemblages poutre-poteau en bCton arm6 sournis a des charges latirales, afin d16valuer la dCpendance paramktrique du comportement de ces ClCments a des fins de conception. Au cours de cette Ctude, des donnCes expirimentales recueillies dans le monde entier et les rCsultats d'un certain nombre d'Ctudes analytiques ont CtC pris en considCration dans un effort en vue d'klargir la portCe et la pr6cision de la description paramktrique de la mCcanique des assemblages. Mis a part une meilleure comprChension du problkme physique, le plus important produit de cette recherche est la formulation d'outils simples pour la conception d'assemblages d'ossatures en bkton arme parasismiques b l'aide d'une approche mCcanique cohkrente. Mots clCs : assemblage poutre-poteau, base de donnCes, calcul parasismique, analyse des ClCments finis, biton armC, risistance au cisaillement, Ctriers. [Traduit par la rCdaction] Can. J . Civ. E n g . 21, 307-328 (1991)

1. Introduction Current requirements for design of earthquake-resistant, reinforced concrete beam-column connections have evolved through intense experimentation and debate that has taken up a significant fraction of the international research activity in the field of reinforced concrete over the last 30 years. Given the volume of readily accessible literature documenting this research, it would be expected that fundamental aspects of the mechanical behavior of these components would be well understood today. There are many reasons why such a desirable state of affairs has not been reached. Of all the various parts of a frame structure, the volume shared by an intersecting beam and column (commonly referred to as a beam-column joint) poses the greatest challenges to physical reasoning, and it attracts conflicting arguments regarding its mechanical function. Joints in frame structures resisting lateral loads are subjected t o a complex combination of actions, as illustrated in Fig. 1. A large portion of these forces are introduced by shear stresses developing at the boundaries of the joint and at the interfaces between the joint concrete and the beam or column reinforcement which is developed through the joint. Interface shear, or bond, is a poorly understood mechanical problem, and therefore contributes to the existing uncertainties. However, the main difficulty with joint mechanics is evident in the figure: steep NOTE:Written discussion of this paper is welcomed and will be received by the Editor until August 31, 1994 (address inside front cover). Prinlcd i n Can;,*;,

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force gradients occurring over a relatively small and geometrically complex region. The overall effect of these factors, which are further intensified by weakly understood material behavior, is that unification of concepts regarding the mechanics of joints has been very slow to develop. Because of its complexity, this physical problem does not lend itself to elegant idealizations. Instead, most researchers have used experimental observation as a basis to postulate conceptual models of the inner workings of joints. But most of these observations were obtained from tests done on isolated frame connections in which boundary conditions were highly idealized or simplified. Because performance and design standards differ worldwide, there is valid concern that the outcome of these tests could have been influenced by decisions made in designing or executing them, causing their results to reflect, to some extent, the views of the individual researchers. Another obstacle is that the literature is fragmented, consisting of numerous studies, all containing a small group of tests designed to study a limited number of variables, but providing no cross-relation between parallel groups of tests. The cumulative effect of these considerations is that enough data are available that conflicting views of the role of some variables can be defended, but it is not known whether the data are still too limited to prove decisively any particular assertion beyond doubt. However, the mass of information now available to us is such, that boundaries between individual experimental and analytical investigations can be crossed, and the existing differences in opinion that pervade experiment and analysis can be addressed.

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Beam Moments

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FIG.1. Actions in frame connection resisting lateral loads To obtain an authoritative description of the mechanical behavior of joints, and to establish the role of variables that have been shown to be significant in experimental reports, four mutually supplementary studies were undertaken in this paper. First, the points of conflict o r disagreement between prevailing mechanical models established over the past 30 years were identified. Then, a database of available tests (interior and exterior beam-column connection specimens without slabs, and loaded in one plane only) was used to study the influence of various parameters on the observed response; when possible, generalized conclusions about the role of these parameters were drawn from the experimental evidence. In the final two components of the study, the validity of the database conclusions was confirmed by two analytical models of differing degrees of computational complexity and extent of idealization (i.e., a nonlinear finite element model, and a simple conceptual construct of joint equilibrium and compatibility requirements). These analytical phases of the study also served to judge the ability of the models to reproduce the mechanical response of joints. The last two parts of the study explored the physical problem by an extensive computer analysis of interior and exterior beam-column joints, with the aim to provide simple tools for consistent design of these elements. Only conclusions that are supported by all independent phases of the study were considered general and beyond bias imposed by the assumptions or the limitations of any one particular component of the study. Those are summarized in the end of the paper. While many of these points have been asserted before in certain experimental studies, their presentation was based on narrowly focussed evidence, and they were usually counteracted by alternative conclusions obtained from other studies. A multi-approach investigation of the problem offers the unique opportunity to state conclusions with confidence and to settle the debate, provided that t h e results of t h e various analyses a r e in mutual agreement with each other.

2. Review of existing conceptual models The various frameworks for joint design have their origin in a small number of milestone experiments, but have been

subsequently shaped by further experimentation and continuous dialogue between several research groups. Although differences still exist between the models, today there is evidence of a slowly emerging consensus. In the following sections, the most important iterations that shaped code models are outlined, not only to establish the current state of the art on beam-column joints, but also to illustrate the manner in which differences in the philosophical outlooks of the design frameworks can influence interpretation of a purely mechanical problem. Dimensioning and detailing of joints according to the current design practice is directly linked to evaluating a measure of shear input to the joint, which is actually a normalized average shear stress. While references are made to joint shear stress levels in the following paragraphs, the details of transforming forces to normalized stresses differ in each approach so as to make them not directly comparable. 2.1. The ACl-ASCE Cornrnittee 352, 1976 recomrnerzclc~tions The problem of beam-column joints, as we know it today, was born with the era of capacity-design philosophies, which explicitly allow for the occurrence of controlled damage in frame structures subjected to strong ground motions. Prior to that era, joints were only considered in satisfying the requirements for development of beam reinforcement and were otherwise provided for as part of the column. In the 1976 recommendations, ACI-ASCE Committee 352 addressed the issue of joint shear strength under repeated large deformation reversals. Since joint deformation demand was not assessed quantitatively, the required strength was established comparatively by enforcing the strong-column weakgirder design concept and requiring that the joint is strong enough to sustain the forces associated with the development of the beam flexural strengths. For space frames, direction of bending was considered independently (i.e., biaxial stress interaction in the joint was neglected). In evaluating the force system loading the joint, yield stress of the beam reinforcement was enhanced by 25% to account for possible overstrength resulting from strain hardening. The design horizontal shear force input to the joint was determined from the equilibrium considerations shown in Fig. 2. Shear stresses were obtained by distributing the force over the effective cross sectional area of the joint, which was taken as the area of the core for regular joints; to recognize the confining influence of transverse beams when these were present on the lateral faces of the joint, the effective joint width for stress calculations was increased to that of the column. Dimensioning of the joint was controlled by limits on the a l l o w a b l e joint s h e a r stresses, equal to 1 . 6 7 d C M P ~ ( 2 0 f l p s i ) , established empirically to prevent excessive damage in the joint region. Whereas the old practice of treating the joint as part of the column was maintained, explicit instructions for detailing the joint as in column critical regions were introduced. These were intended to improve the anchorage capacity of bars anchored in the joint core and to maintain the integrity of the core should large forces produce spalling and loss of cover. A consequence of this practice is that increasing column axial compression would also increase the amount of required reinforcement in the joint. Additional reinforcement was determined from consideration of shear stresses. Based on the simple model of column flexure, it was argued that these shear forces are primarily resisted by the concrete core and the longitudinal column reinforcement. Thus, the


PANTAZOPOULOU AND BONACCI

Connection

Truss Mechanism ttt

-T+F column

FIG.2. Design models for beam-column joints: ( a ) the 1976 ACI model; (b) the strut and truss models of NZS (1982); (c) computation of horizontal joint shear according to current ACI-ASCE 352 recommendations.

shear strength of the joint was assumed to comprise two contributions: that of the concrete core, v,, and that of joint shear reinforcement, v,. For type-2 joints (those in earthquake-resisting frames), the concrete contribution to total shear strength was limited by the assumed occurrence of diagonal tension failure, to 0 . 2 9 q ~ (~3 . a5 f l p s i ) . This bound was increased to approximately 0.42vj-r M P a ( 5 f l p s i ) for joints confined by transverse beams, but was set to zero for joints subjected to a net tensile column axial force. Requirements for transverse reinforcement for shear in the form of closed hoops or stirrups were to be considered only to provide for the difference between nominal joint shear stress input and vc; however, as a lower bound, transverse reinforcement equivalent to one third of the joint shear was required to prevent gradual deterioration f; the core under repeated load reversals. An u p p e r bound of 1 . 2 5 c ~ ( ~1 5a c p s i ) was also specified for v,. The long-time practice of offsetting longitudinal column bars in the joint was discouraged. N O spkcific anchorage requirements for beam bars were given, but the designer was encouraged to use small diameter bars to reduce the amount of bond deterioration likely to occur under inelastic load reversals. 2.2. T h e rnodel of the New Zealand Standard ( 1 9 8 2 ) ; Criticism of the ACI model (Pnulay et al. 1978) The ACI-352 recommendations were critically examined in light of the performance criteria adopted at the time in New Zealand, where substantial advances towards the improvement of the capacity design philosophy for earth-

quake resistant structures were made (Paulay et al. 1978). In addition to the requirements posed by the strong-column weak girder design concept, it was required that special measures should be taken to ensure that the joint responds elastically during moderate seismic disturbances, whereas the capacity of coluinns should be preserved at all costs by eliminating any possibility of joint strength degradation. To account for all possible sources of overstrength, it was proposed that slab reinforcement adjacent to the beams be included, in addition to the 1.25 factor stated above, in estimating the beam flexural overstrength. The force system assumed to be acting at the joint boundaries upon formation of plastic hinges in the adjacent beams is illustrated in Fig. 2b. Using equilibrium considerations on the free body diagram of the joint, the probable maximum horizontal shear force, and the associated vertical shear force input to the joint were established, and it was proposed that both shears be considered in the joint design. For dimensioning of the joint, the limit on allowable shear stress was restricted to 1 . 5 e MPa. To resist the applied actions, it was postulated that an adequately detailed joint mobilizes two self-equilibrating mechanisms of shear transfer. The principal component of the first mechanism is a diagonal compression strut, transmitting actions at an angle P, determined from equilibrium requirements. This system of resistance was said to develop during the initial stages of the load, before yield penetration spreads from the adjacent beam plastic hinges into the joint core. It was claimed that, after a few significant cycles of flexural hinging, full-depth cracks develop in the beams at the column


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faces. Because of residual tensile strains in the reinforcement that build up in each inelastic cycle, it was argued that the normal stresses acting in the compression zones of the fraining members are eventually eliminated. Furthermore, the bond demand along the beam bars is increased, because under these circurnstances the total horizontal shear is introduced to the joint by bond stresses. Because yield penetration destroys bond, it was suggested that stress transfer migrates towards the central region of the joint, causing significant stress redistribution within the joint. In light of these phenomena, it was assumed that at that point, the diagonal strut mechanism can no longer be activated. The forces are then carried through a self-equilibrating truss mechanism, in which the core concrete supplies the necessary diagonal compression field, balanced by the boundary forces and horizontal and vertical tension in the reinforcement that passes through the joint core. Critical for the sustenance of the truss mechanism, but also very important for confinement of the core is the presence of distributed vertical reinforcement around the column perimeter. This was already adopted in New Zealand (NZS 1982), and was discussed for implementation in the ACI Code (ACI-3 18 1983). Application of this model, coupled with the stringent performance requirements of the New Zealand code, yields large amounts of horizontal and often vertical steel. T h e 1976 ACI recommendations only called for horizontal steel in the joint, and as such were found inadequate with regard to sustenance of the truss mechanism (Paulay et al. 1978). ACI's use of the column flexure analogy for the evaluation of joint shear reinforcement was also criticized, by stipulating that the mechanisms of resistance in beam-column joints are substantially different from those encountered in flexural members. By postulating a corner-to-corner diagonal failure plane across the joint core, the horizontal shear reinforcement was estimated to carry the entire probable horizontal shear stress input; similar considerations were applied in the vertical direction (Paulay et al. 1978). It was proposed that the column axial compression contributes to the compression strut by increasing its steepness; therefore its strength is increased when axial load is present. For conservatism, the contribution of the strut to the joint resistance is ignored unless significant column axial compression is transmitted through the joint. In addition, confinement reinforcement tied in directions normal to the plane of action, so as to limit the dilation of the joint due to cracking, was required. This confinement reinforcement was also computed, as in the ACI case, from column design requirements, and was reduced by 5 0 % in cases where beams framed on all faces of the joint to recognize the beneficial influence of transverse beams. To limit bond deterioration, particularly in interior joints where yield penetration was expected to develop on both faces, the size of beam bar diameters passing through the joint was limited to a small fraction, 5, of the column depth. This provision is intended to control the bond demand, particularly within the joint volume; 5 was set to 1/25 and 1/35 for Grade 40 and 60 reinforcements, respectively. 2.3. The revisecl ACI Cor,~nzittee352 tnodel (1985) The differences between the detailing requirements that the two alternative design models outlined in the preceding would produce triggered extensive experimental research designed to address the points of discrepancy. Some of the

results were embodied in the revised ACI Committee 352 recommendations (1985). First, the source of resistance in the joint was solely attributed to a diagonal compression strut forming across the compression zones of the framing members, and directly transmitting shear in the form of inclined compression. To address the question of vertical reinforcement in the joint, two steps were taken: (a) to prohibit offsetting of column bars in the joint region, and (b) to distribute the area of column reinforcement around the perimeter of the column cross section, for improved confinement of the joint core. The criticism regarding differences in circumstances between the critical region for column flexure and a joint prompted an attempt at establishing the function of the horizontal joint reinforcement on the basis of experimental observations. The committee concluded that the primary function of ties in a tied column was to preserve the integrity of the joint core by providing support against outward buckling of longitudinal bars and by providing confinement to the core concrete. Thus, the position that joints be detailed as in other critical regions of tied columns was retained along with all the implications this design choice has with respect to the influence of column axial compression on joint shear strength. The total horizontal reinforcement was reduced by 50% when beams framed into all faces of the joint, to recognize the confining action of these members o n the joint. In terms of design shear strength, several changes were implemented; specific guidelines were given for consistent evaluation of the design shear force on a horizontal plane at the midheight of the joint, as shown in Fig. 2c. Empirical limits for allowable shear stress were , established, expressed in multiples of C M P ~ depending upon the anticipated severity of the load history and the type of connection (multiples were 1.65, 1.25, and 1, for type-2 interior, exterior, and corner joints. Bond provisioils were also included in a similar manner as in the New Zealand model. However, the limits placed on bond demand were much less stringent, as the diameter of bars developed through the joint was only limited to 1/20 of the column dimension in the direction considered. To preclude other types of failure in the connection apart from beam flexural hinging, explicit design requirements were introduced regarding the ratio of column flexural strength to probable beam flexural strength. The design philosophy embodied in this proposal is that, during the anticipated deformation demands, the joint core is able to carry the specified shear forces provided the concrete within the joint is adequately confined. Because joint shear can cause dilation of the joint core, hoops play dual role of providing confinement to the core while, at the same time, participating in the joint shear resisting mechanism. Provided that column bars are uniformly distributed around the perimeter of the joint, the recommendations ignored the presence of vertical shear stress, which could be computed by establishing in that direction equilibrium requirements similar to those applied in Fig. 2c. The differences with the New Zealand code were addressed by attributing them to the excessive displacement demands imposed during tests of statically determinate connection assemblies, which reflected the appreciation of seismic risk in that country. It is stated that the ACI 352 provisions are intended for limited displacement and rotation levels, and that they also anticipate the beneficial effects of load redistribution in statically redundant frame structures.


PANTAZOPOULOU A N D BONACCI

2.4. The nzodel of the A r c h i t e c t ~ i r a lIrzstiture of Japarz (AIJ 1988; Kitayarrza et al. 1991; Otani et al. 1985; Otaizi 1991 ) At the time of this international activity, existing design methodologies in Japan were still retaining the allowable stress design, which is known to result in relatively wide columns. Under these conditions. beam-column ioints were generally not a problem. However, trends towards the use of high strength materials and the increasing popularity of ultimate strength design approaches prompted the need for design recommendations for critical areas such as joints (Otani et al. 1985; Kitayama et al. 1991; Otani 1991). A draft guideline was published in 1988 by the Architectural ~nstituteof Japan, which, although seemingly reconciliatory, has helped to carry the ongoing debate even further. For the first time, design criteria were introduced that were linked to an expected deformation demand level; stated design goals were to protect the joint against shear failure, and to prevent excessive bond-slip for storey displacements less than 1.5% of the storey height (some bond-slip was purposely tolerated in the guidelines, to the extent that the overall response of the frame was not expected to be significantly altered). With regard to joint shear resistance mechanisms, the combination of truss and strut action postulated in the New Zealand code (1982), and later in the CEB model code (1983), was also adopted here. However, contrary to the original postulate, it was argued that only the diagonal strut mechanism could survive throughout the deformation history of the joint; this, of course, presumes that adequate confinement is present to provide ductility to the core and prevent outward buckling of the column reinforcement. The truss mechanism was said to be sustainable only for as long as favourable bond conditions could be maintained along the beam and column reinforcement. To prevent dramatic loss of this mechanism, likely to be by beam yield, specific guidelines for controlling bond demand were included in the design approach. It was proposed that the magnitude of bond demand be kept low by increasing the column size or by reducing the beam bar diameters; once the bond resistance is lost, the truss mechanism is assumed to have diminished, followed by the development of large rotations in the beam plastic hinges. Then, the tensile forces in the reinforcement can only be resisted by concrete compression at the face of the joint, increasing the magnitude of compression stresses in the diagonal strut. Thus, in the Japanese model, the only reliable mechanism of resistance throughout the response is the main strut mechanism (Kitayama et al. 1991). Because the strut concrete is weakened by the reversed cyclic loading and by the increasing normal tensile strains, the compressive load carrying capacity of the strut decreases and eventually fails in compression. To prevent such shear failures, joint transverse reinforcement is needed primarily to provide confinement to the joint core concrete. Dimensioning of the joint is controlled by a limitation that bars a n c h o r e d there have d i a m e t e r s l e s s than f , / 3 . 2 f l ~ ~ a ,and by allowable joint shear stress limits of 0.25f: for interior joints and 66% of that amount for exterior joints. Thus, the concrete compressive strength is considered to be the most influential variable affecting joint shear resistance. This is in agreement with the ACI approach, but more drastic to a certain extent, since now the allowable stresses are proportional to the uniaxial compressive

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strength of concrete rather than to the square root of that variable. It was also argued that increasing the amount of joint lateral reinforcement does not effectively increase the shear strength of the joint, since the resistance is provided by the strut action; therefore it was proposed that minimal amounts are required for confinement (of the order of 0.4%, which is smaller than the ACI proposal), with an allowance for reduction if the shear stress input is lower than the allowable value. Column axial load was not considered effective in improving the strength of the joint and, unless it attains large magnitude, it was not expected to improve the bond conditions of the beam bars. To recognize the confining influence of the transverse beams, allowable stresses were increased to 0.33f: if beams frame on all faces of the connection.

2.5. Criticisrn of the ACI 352 revisioizs (Palilny 1986) The new seismic provisions of the ACI were critically reviewed from the New Zealand research and design perspectives. Conceptual differences, responsible for the drastically different detailing and dimensioning requirements, were identified. A new minimum performance criterion was adopted, namely that beam plastic hinges maintain their post-yield strength for up to four displacement excursions in e a c h direction equal to four times that at the onset of yielding. Under these conditions, the shear input to the joint is expected to cause extensive diagonal cracking in the joint core; when this occurs, shear is transmitted across a diagonal compression field, represented by the truss mechanism discussed earlier. The claim that joint shear strength is not sensitive to joint shear reinforcement was considered untenable, and was attributed to design practices that produced some test specimens in North America that experienced anchorage failures rather than joint shear failures. Attributing a confining role to the horizontal joint reinforcement was criticized on grounds that the mechanisms of shear are drastically different from those of column flexure. It was stated that, whereas confining a column segment may increase its shear resistance, the amount of required reinforcement thus established is not in any way related to the shear demand, a practice liable to distract attention from the central problem of diagonal tension failure. Reducing the confining transverse reinforcement when transverse beams are present was also disputed. In real structures transverse beams may be simultaneously resisting loads of con~parablemagnitude in directions orthogonal to the main beam, rendering the conditions of joints at least as severe as in one-way situations. It was argued that in two-way situations, rather than reducing the joint shear reinforcement, special measures should be enforced to increase it. Furthermore, using equilibrium considerations, it was proposed that axial load improves the conditions in the joint, and therefore its presence should reduce the need for transverse reinforcement. The ACI recommendations, by linking the evaluation of transverse reinforcement to column design, not only ignore the beneficial influence of axial load, but rather penalize a joint subjected to high axial compression; therefore the two codes demonstrate opposing trends in the requirements for confinement, with the ACI requirements being on the unconservative side when small axial loads are acting on the columns. Anchoring the beam bars in the thoroughly cracked core was considered critical, since these bars are considered to be yielding in tension at one face and in compression at the

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other face of interior columns in the plastic hinge regions. Because the joint must provide enough bond resistance for this sign change to occur in bar stresses, development of reinforcement through an interior joint is one of the most difficult design criteria to fulfil, rendering the ACI recommendations unconservative on this issue as well.

2.6. Revisions in the New Zenlnnd outlook (Pnulny 1989; Cheung et al. 1993) Although it was never stated as such, the New Zealand code model was derived with reference to an implicit kinematic condition, namely that, upon formation of full-depth cracks in the plastic hinges of the adjacent beams, and from buildup of residual tensile strains, the concentrated beam rotations will be such that the zone of contact between the beams and the column will be minimized, the compression zones will diminish, and the entire compressive force will be carried by the compression reinforcement. Apart from the likelihood of such a scenario from purely mechanical considerations, reservations had been expressed in the ACI recommendations regarding the intensity of earthquake load that would be required to produce such circumstances. Thus, an alternative study was undertaken, postulating equilibrium of the overall members (beams, columns, and joints), to examine the problem of joints from yet another perspective (Paulay 1989). In this conceptualization of equilibrium, it was noted that at advanced stages of the response, where substantial cracking has occurred in the regions surrounding the joint including the joint itself, stresses in all reinforcement passing through these regions will be altered because of the phenomenon of tension shift. Based on this consideration, it was argued that all longitudinal reinforcement will be in tension throughout the region of the joint, including the plastic hinge locations adjacent to the joint. Therefore, no sign change would occur in rebar stresses as was postulated in previous models, in which case, the beam bars may not even be able to function as compression flexural reinforcement. These arguments led to the conclusion that, irrespective of bond deterioration, only a small fraction of the intended steel forces could be transmitted by means of bond to the concrete core of the joint, whereas the core itself was expected to undergo a significant amount of dilation. It was proposed that, to avoid these effects of tension shift, joint performance should be improved aiming to reduce the tensile stresses along the beam bars, and to provide anchorage within the joint core for the beam reinforcement to enable it to act as compression reinforcement when required by beam flexure. Despite the incompatibilities between the basic premises of the truss mechanism and the new model, the overal results of the new formulation were considered reassuring evidence of the existence and function of this particular system. With the truss mechanism as a reference, and in light of new evidence, the New Zealand design requirements were reviewed, and some revisions were proposed (Cheung et al. 1993). These were (a) to limit nominal shear stresses to 0.20-0.25 of fl, in order to avoid premature failure of the diagonal compression field, and (b) to tolerate some loss of quality of frame performance by relaxing anchorage requirements for interior beam-column joints (beam bar diameter can now be 1/25 of the column dimension). It is argued that, by allowing some bond deterioration of beam bars inside joint cores, the strut mechanism of shear resistance is enhanced, thus reducing the need for joint shear reinforcement. Apart

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from these alterations in philosophy, all other suggestions regarding the role of transverse beams, joint confinement, compressive axial load effects on the joint shear resistance, and the prevalence of the truss mechanism of resistance are maintained.

2.7. Discussion of the nzodels All models summarized in the preceding represent alternative admissible interpretations of the function of the main design parameters, since they all are derived by postulating possible internal stress paths in the joint. Because they reflect views of researchers from many parts of the world, the differences between models can be attributed to a number of circumstances, such as (a) local definitions of acceptable levels of performance, (b) local anticipated seismic risk, (c) local design and construction practices, and (d) subjective interpretation of the available experimental evidence. All three models use a number of empirical arguments to compensate for incomplete mechanical descriptions, either in the form of empirically derived design limits or in the form of equilibrium postulates. It is noteworthy that deformations are not considered as a factor in any of the design models, although the critical design state (earthquake action) is one associated with large lateral drifts. Consequently, it is difficult to know if the force levels considered in these design models are reasonable at all, or if they could possibly develop considering the response of the overall structure. Clearly, the most appropriate link to relate ideal demand on the connection to the overall structural response under lateral forces would be some measure of lateral displacement, such as proposed in the Japanese model. This, however, is mostly absent from the design considerations, or, if included, it is not used in design calculations but rather only in the formulation to relate ideal performance to a number of experimental observations. Two points regarding the methods of analysis are noteworthy. First, the separate calculation and provision for two measures of shear stress, horizontal and vertical, is surprising, as it is easily shown from first principles that these two quantities are identical; sustenance-of one by the mechanisms of resistance implies the automatic support of the other; and demise of one component implies simultaneous elimination of the other. Second, computation of the average joint shear stress from internal beam and column forces is somewhat complicated and leaves room for ambiguity; instead, considering beam or column equilibrium and evaluating the joint shear force from the moment gradient that occurs within the joint region is a simpler approach and sufficiently accurate for design purposes. In the remainder of this paper, this option for computing shear input to the joint will be adhered to.

3- Database study Of beam-co1umn connection tests The insights and experience about most aspects of beamcolumn joint behavior have been obtained mainly from experimental studies. Early tests conducted in the 1960s on simple connection models illustrated that joint reinforcement in the form of closed stirrups, in combination with column longitudinal reinforcement (so that joint reinforcement forms a closed cage), enhanced the shear resistance of joints and prolonged their survival through intense load reversals (Hanson and Conner 1967). Since then, a large amount of research has been conducted with the aim of establishing the relationship between the degree of deterio-



ration of joint resistance under cyclic loads and the amount of lateral reinforcement provided in the joint. The parameters considered in more than one of the studies were the amount of joint confinement, column axial load, input intensity of average joint shear stress, concrete compressive strength, bond demand along beam bars passing through the joint, and presence of transverse beams. Though the ensuing lessons have been numerous, the obscuring of evidence because of the limitations of the experimental studies has led to interpretations that are hampered by uncertainty. Uncertainty has led to debatable explanations of the workings of joints. It is ironic that what has fuelled debates, and what has been cited as proof for or against a particular postulate or a model, is experimental evidence that most often was obtained from a small set of tests designed to study the point under consideration. The existence of disparities among design models and the conflicting reports of observed experimental behavior have been attributed (Bonacci and Pantazopoulou 1993) to several factors: (a) limited size and breadth of the individual test series, (b) dissimilar performance standards applied in the design of the test specimens, (c) the fragmented, sequential nature of the evolution of experimental knowledge, and (d) interactions between experimental variables. To overcome these obstacles in obtaining unified interpretations of the experimental evidence, a database of all available studies was compiled by the authors, containing a total of 143 cyclic connection tests (these were statically determinate models without slabs, and loaded in a single plane, so that moment transfer occurred in the connection). Of those specimens, 86 were models of interior connections, whereas the remaining 57 simulated exterior beam-column joints. The results of the first part of the study, dealing with interior connections, along with parameter definitions and the general structure of the database has been presented extensively elsewhere (Bonacci and Pantazopoulou 1993). A similar analysis is presented in the Appendix for the exterior connection cases; note that, in general, exterior connections are more complicated than interior ones, and this is reflected by the greater scatter in the database plots. For this reason, interpretation of this set of data must be done in light of the results of the interior connections. For completeness, the Nomenclature section briefly defines the important variables. In the remainder of this section, the salient features of the study and sufficiently general conclusions related to parameters thought to influence connection mechanics are discussed. 3.1. Database results 3.1.1. Bias from local design practices and aizchorage requirenzents One of the most effective variables in organizing the data proved to be the country of origin of the tests. such a nontechnical factor might seem irrelevant with the mechanical problem studied, it actually suggests that different local design practices and performance criteria influenced the specimen designs and loading schemes. A measure of the differences in local definition of seismic risk and performance criteria could be inferred by the diversity in imposed load histories (a plot summarizjng for all exterior connections the amount of accumulated displacement ductility as a function of the load cycle number is given in Fig. A1 of Appendix 2). Because it is plausible that the observed sequence of failure in the connection may have been affected by the severity of the load, this parameter should be kept

313

in mind when seeking to understand the combined influences of various factors on joint behavior. The most striking influence of local design practices on the results can be identified in the magnitude of the bond index (see Appendix 1). For example, specimens tested in New Zealand had large-sized columns, a design practice that invariably leads to low values for the bond index. The North American practice of small column sizes was underscored by the fact that two thirds of the specimens tested in North American laboratories experienced anchorage failure inside the joint. Some of the specimens tested in Japan also experienced bond failure, but the majority of the Japanese specimens had bond index less than 2 for interior specimens and less than 1.25 for exterior ones. By correlating the observed failure modes and the associated bond demands, it was found that limiting the design bond index to 1.65 and 0.85 (Grade 60 reinforcement) for interior and exterior connections, respectively, could be used as a design rule to minimize the likelihood of bond failures. Experimental responses supported earlier propositions that this mode should be avoided because it renders the connection a source of flexibility for the entire structure and reduces the energy dissipation capacity. In most cases, connections that were subjected to high bond demand experienced anchorage failures and, thus, were not able to develop their full strength, though they might have had substantial joint shear resistance. 3.1.2. Joint slzear stresses and crackii~g Because the magnitudes of the connection dpsign forces are associated with beam flexural hinging, the level of shear stress input to the joint upon yielding of the beams is one of the most important test variables, as it determines the extent to which the actual joint shear strength was actually tested and measured. By correlating the observed failure mechanism with the ratio of hoop potential, v,, to the shear input to the joint at the instant of beam flexural yielding, v,, it was found that interior joint shear failures were precluded by providing large amounts of hoops so that joint hoop potential exceeded that of the beams. 3.1.3. The effect o f coluinn axial load To explore the question of dependence of joint shear resistance on column axial load, the relationship between measured maximum joint shear stress factor, v,,,, and the nominal column axial stress (normalized by f i ) was sought. In this investigation, only beam hinging and joint shear failures were considered. Because the scatter was substantial, the data were further classified based on the magnitude of the shear potential of joint hoops. It was surprising to find no discernible correlation between the two variables. It was concluded that, more likely, deformability, rather than strength, would be affected by the column axial load. However, for lack of relevant experimental information, this point could not be pursued further in the database study. Only fragmented experimental evidence regarding deformations could be found in a limited number of recent tests, and they suggest that increasing column axial load tends to reduce the total lateral drift at yield (Kurose 1987). 3.1.4. The effect of concrete strength, f:. The influence of the concrete compressive strength on the maximum joint shear stress sustained before failure was inferred from plots of the available experimental data points for all joint shear failures. There was a linear increase in the sustainable joint shear stress with increasing concrete

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CAN. J . CIV. ENG. VOL. 21. 1991


compressive strength; a lower bound for allowable shear stress in the joint was found to be 10% of f i for interior connections, and 7.5% of fk for exterior connections. However, these constants were empirically obtained and are therefore sensitive to the definitions adopted for effective joint dimensions (Appendix 1). Similar attempts to establish a lower bound for joint shear strength have been reported by other investigators as well (Kitayama et al. 1991), though the empirical constants given were substantially different. 3.1.5. The influence of hoop reirzforcerrzent To study the role of hoops in the resisting mechanism of a joint, the relationship between the fraction of total shear that was resisted by the concrete core, normalized by the maximum measured joint shear stress, v,,, and the joint confinement index (Appendix I), was plotted for all specimens that had failed in joint shear. The data were organized in descending order with increasing confinement index, suggesting that the contribution of joint concrete to the joint strength decreases as the total available amount of hoops (i.e., confinement) is increased; therefore, the greater the demand on the hoops for confinement (likely to occur when the core is heavily stressed and has dilated by sufficient amount to stretch the hoops), the greater the demand on them as well for direct participation as shear reinforcement. That concrete participation decreased with increasing confinement simply indicates that the resulting excess shear capacity of the concrete core was not relied upon, evidently in contradiction with the anticipation of design. In the range of small confinement indices, the capacity of the core was minimal because the shear (i.e., diagonal tension) invariably induced dilation of the compressive struts, and therefore their strength was reduced. This clearly indicates that participation of the hoops in the shear-resisting mechanism of the joint is most significant when low amounts of confinement are provided for. Therefore, it can be said that the collective experimental evidence reaffirms previous suggestions that stirrups contribute to the shear resistance of the joints directly (by resisting part of the joint shear) and indirectly (by confining the concrete core, thereby enhancing its diagonal colnpressive strength). 3.1.6. The effect of transverse Oearns The influence of transverse beams on the failure mode was investigated for all failures. It was observed that no specimens were reported to have failed in joint shear when beams framed in all faces of the joint. Furthermore, these were the specimens that demonstrated the least amount of cyclic strength degradation. Some specimens with one transverse beam experienced joint shear failure, possibly because the mechanisms of resistance could not be supported at excessive deformations when some sides of the joint were free of lateral restraint. This result is significant because it suggests that interior joints that are confined in both directions by orthogonal beams are not critical in typical space frames, and therefore their consideration in design could be simplified. 3.2. S~linrnnry Only a few of the prevailing questions associated with the f u n c t i o n of variables in joint mechanics could be addressed coilclusively from the database study. Indeed, only indications or inconclusive evidence was obtained for many important issues, such as the influence of axial load on strength, the interaction between variables, and their effect

on joint deformability. Rather, the database study best illustrated the bounds of the available experimental information on beam column joints, and the restrictions imposed on the empirical interpretation of the mechanical behaviour of these elements. Limitations result from several factors: (a) The scope of the individual experimental studies comprising the database was restricted to studying the interaction of a few parameters at a time. Because the total number of parameters influencing the physical problem is typically larger than the number of specimens tested in any individual group, there are not enough tests to conclusively study the independent effect of any single parameter. (b) The objectives of the various experimental programs were often dissimilar to such an extent that the behaviors of specimens designed with different test philosophies are not directly comparable. Because specimen response is ultimately dominated by the weakest link of the connection, the actual shear resistance of the joint was only assessed experimentally when the weak link was the joint region itself. (c) Another problem is that almost all studies consider a surprisingly small range of values for many of the geometric variables so that very little can be generalized from each study. (d) Three additional circumstances are viewed as impairing factors in generalizing from database results. First, the differences in experimental technique around the world have helped diversify the database even further (i.e., the manner by which the specimen was loaded during testing, insufficient documentation of material properties, special attachments used on specimens, instrumentation, idealization of the prototype structure in deriving the assembly, scale effects). Second, the subordinate role of deformations in the design models, which is underscored by lack of pertinent experimental information (such as the breakdown of total connection deformation to the contributions of the various members), has eliminated a basis of comparison between tests, as it is not possible to compare joint performance between specimens at a given level of lateral drift identifying design earthquake intensity. Third, different perceived levels of risk around the world have led researchers until the 1980s to use a variety of displacement histories for testing of their specimens,-these histories being drastically different in terms of intensity level, waveform, and duration. Since it is not quite clear as of yet whether the severity of the load influences the sequence by which the internal active and passive mechanisms of resistance are mobilized, this additional dimension of the data contributes to a further reduction of the number of studies that are directly comparable to each other. 3.3. An(11ytical modeling of beam-col~lmnjoints T h e preceding review of experimental data has shown conclusively that the number of parameters affecting the behavior of beam-column joints exceeds the breadth of the available database. To compensate for the limitations of the experimental studies, analytical modeling was used to supplement the parametric study. A prerequisite for meaningful description of the mechanics of jornts i s considering the kinematic viriables of the problem in addition to requirements of stress equilibrium. Understanding the pattern and magnitude of deformations in such a coinplex nonlinear problem holds promise for reconciling the differences between, and for identifying the weaknesses of, the various admissible states of stress that are adopted in empirical models. It is also known from experimental obser-

3 15


tension


steel 3tress-3rraln Law

6, = ID,] Ec

I

Stress-Strain Law for Concrete

y)

I

w

'

x

(in principal directions)

FIG.3. Truss and plane-stress elements used to model reinforcement and concrete.

(a) plane-stress

f element

Action (MPa)

A

direction / of action

Y

favourable bond conditions 4

0

I

/

unfavourabie I

truss element

8

I

I

*

Slip (mm)

12

FIG.4. Contact element modeling reinforcement to concrete interface: ( a ) element; (b) action-deformation relationship.

vation that deformations can serve as indicators of performance for the connection. For example, it is safe to state that satisfactory joint behavior is associated with minimal contribution of joint distortion to the overall lateral drift of the structure. In a well designed joint, this contribution is expected to decrease as the adjacent plastic hinges in the beams develop inelastic action. In inadequate joints, the reverse has been reported in experiments, and in these cases the joint is primarily responsible for the inelasticity observed in the response. With special emphasis on deformation as an indicator of performance, two different analytical models are used to study the effect of several variables on the shear behavior of joints, including those that were examined in the database study. First, a nonlinear finite element analysis of complete beam-column connections is used to complement and to confirm the results of the experimental database investigation. Then, a simple mechanical construct of equilibrium and compatibility requirements for the joint panel is summarized, for use in design applications. In this mechanical derivation, the effects of axial load, tension softening of concrete compressive strength, and static redundancy were idealized. The success of the idealization and its pertinence for modeling beam-column joints is supported by the results of the finite element study. Mutual calibration of the two analytical alternatives is meant to establish their accuracy and to build confidence in their ability to model beam-column joints. Both models are used to carry out an analytical investigation

of the parametric dependence of joint mechanics, designed to complement and, if possible, to support the database study presented earlier.

4. Finite element model The finite element model studied in this section is a twodimensional idealization of beam-column connections, with geometry similar to that of beam-column assemblies tested in experiments. Modeling relied on a variety of nonlinear finite elements, designed to represent the components of reinforced concrete. 4.1. Formulation Two-noded, nonlinear truss elements were used to model b e a m , c o l u m n , a n d joint r e i n f o r c e m e n t ; t h e typical action-deformation relationship of this element type follows the rule outlined in Fig. 3a. The secant element stiffness, D,, associated with the nodal displacements (degrees of freedom) is also given in Fig 30, with reference to the local element coordinates. Plain concrete was modeled using fournoded, plane-stress elements. Inelastic concrete behavior was defined internally along the principal axes, assuming that the directions of principal stress and principal strain are coincident. Relations between the two measures were based on the tension-softened stress-strain laws for concrete under two-dimensional states of stress, proposed by Vecchio and Collins (1986). Figure 3b depicts the form of the secant element stiffness model for concrete, D,, evaluated with


C A N . J. CIV. E N G . VOL. 21. 1994

A

support

FIG.5. Finite element idealization of specimen C1 (Otani et al. 1985). reference to the element natural coordinates. Detailed descriptions of truss and plane-stress nonlinear models of this type are available in the literature and will not be pursued further herein (e.g., Atrach 1992; Vecchio 1990). Bond conditions at concrete-reinforcement interfaces were modeled using a special element type, referred to in the remainder of this study as a contact element (Fig. 4). The element is a spring of zero initial length with two end nodes: one on the reinforcing bar and one on the concrete at the point of the interface (Atrach 1992). The direction of action of the spring is specified by means of additional (dummy) nodal points. The relative displacement between the end nodes of the spring represents the slip between steel and concrete, whereas the nodal spring force is the work-equivalent of bond stresses developed over the effective length of the reinforcement (truss) elements adjacent to the node under consideration. Formulation of the contact element is identical to that of truss elements, and can be obtained by simply replacing the effective truss stiffness coefficient ( E N L ) by the effective contact stiffness coefficient (KLvcl,), where the effective length L is half of the total length of the reinforcement (truss) elements separated by the node of the contact element; K, the material property in the above expression, is a nonlinear function of the total deformation experienced by the contact element (evaluated as the relative displacement between its end nodes); and d, is the diameter of the reinforcing bar.

4.2. Solutior1 strategy The solution strategy implemented for this study was an incremental secant stiffness approach with no iterations. Load was increased monotonically, and therefore the effects of unloading and of load reversals were not considered in the calculations. To achieve convergent and unique solutions, the load was applied in small increments; during the first load increment, a fraction of the total load was applied and a solution was obtained using the initial values of the material moduli to compute element stiffnesses for the various element types. At the end of the first load increment, element stresses and strains were computed and the material properties were updated. For subsequent load steps, the incremental load vector was increased in a manner following the load envelope

of typical connection tests. At every step, element stiffness matrices were computed using the updated material moduli. (These were evaluated from the relevant constitutive models based on the strain values computed in the previous step.) For plain concrete, in addition to the stress-strain constitutive relations described earlier, the program used the biaxial failure criterion of Kupfer and Gerstle to define tension failure. When, at a given Gauss point, the stress combination reached the failure surface while the octahedral stress was positive, tension failure was assumed to occur; beyond that stage, concrete was assumed cracked at the Gauss point under consideration. Upon cracking, Poisson's ratio was set to zero, and the concrete stiffness contribution was defined as in Fig. 3b. To avoid numerical difficulties, "zero" stiffness, whenever it appeared during calculations, was approximated by a very small positive value. To simulate displacement control in the finite element model, the loading apparatus used in the tests was idealized by means of very stiff springs. 4.3. Program verificatiorz The program was tested using as a reference the finite element model of a database specimen. This was specimen C1 tested at the University of Tokyo by Kitayama et al. (1991), which is one of the best-documented tests in the literature. It was selected as a case study because it was adequately detailed, and was designed to fail in accordance with the acceptable design philosophy for beam-column connections (i.e., plastic hinge formation in the beams, followed by shear failure of the joint panel). The finite element idealization of specimen C1 is illustrated in Fig. 5. Because stress transfer between truss elements representing reinforcement and the four-noded plane-stress elements representing concrete was achieved by means of contact elements, the mesh density (element size) was controlled by the requirement to produce a smooth bond stress variation in-between nodes. Previous studies have shown that for the types of bond-slip relations modeling the behavior of the contact elements (i.e., abrupt stiffness changes, post-peak softening), the length of the truss elements should be comparable to the diameter of the reinforcing bar in order to alleviate mesh sensitivity from the results (Ustuner 1992). For this reason, 100 concrete elements were placed within the joint panel.

PANTAZOPOULOUANDBONACCI


(b)

Interior Joint (Specimen C1)

experimental analytical

0

1

2 3 Storey Drift (%)

) Measured Deflection Components

4

Exterior ~ o i n t (otherwise identical to C1)

(C

Computed Deflection Components

beam joint FIG.6. Experimental and calculated responses for specimens C1: (a) storey shear response; (6) pattern of principal compressive stress; (c) contributions to storey drift (Otani et al. 1985).

Contact (bond) elements with the properties shown in Fig. 4b (denoted favourable) were provided along the beam main bars. Additional elements were also attached to joint hoops, but the stiffness of these elements was negligible (denoted unfavourable in Fig. 40), except for the end elements (at points where a bent hoop was turning), in which case a very stiff contact element was used at that node. Although in laboratory conditions specimen C I was loaded by displacing the column ends relative to each other, in the analysis beam ends were displaced instead, to minimize P-A effects. Reinforcing details and support conditions of the analytical model are illustrated in Fig. 5. Column axial load was applied in full magnitude froin the first load increment, while beam end loads were applied incrementally by means of stiff springs (simulating displacement c o n t r o l ) . Experimental and analytical responses are correlated in Figs. 6a-6c. Comparison of total forces, displacements,

member actions, and deformation estimates with the corresponding experimental values was deemed successful within the context of this research, which focusses on the study of connection mechanics rather than reproduction of experimental values. (Note that additional numerical tests designed to evaluate the mesh and load step sensitivity of the program were carried out as part of the program evaluation and are described extensively elsewhere (Atrach 1992). The final mesh and load discretization of typical connections were arrived at prior to the correlation study, based on requirements for unconditional convergence and mesh-independence of the analytical results.) With reference to the various equilibrium assumptions underlying the semi-empirical models outlined in the preceding, it is important to note that the pattern of principal compressive stresses shown in Fig. 60 was found to persist throughout the lateral displacement history (which ended

C A N . J . CIV.

ENG. VOL. 21,

1994

TABLEI . Parameters of finite element analysis

Case No.

VP (MPa) Bond c o n d i t i o n ' N n

1% drift

2% drift

3% drift


Interior cases C1'

C5 C6 C7 C8 C9 CIO CI I C 12 C13 C14 C15 C16 Exterior cases C17 C18 C 19 C20 C2 1 C22 'T: favourable; U: unfavourable. ?Specimen C1 from Otani et al. (1985).

at 4.5% story drift); this confirms the assertion by Kitayama et al. (1991) that the main diagonal compression strut is the most reliable mechanism of resistance in the joint core.

4.4. Parametric stiidy with finite eleineizts Data for the parameter study are drawn from a total of 22 runs of variations of the above model, obtained by altering the values of several geometric and material parameters. These were the bond condition along the beam bars within the joint, the shear potential of joint hoops, v,; the shear input to the joint upon yielding of beam bars, v,; and the column axial load (Appendix 1). Table 1 outlines the values of parameters tested in the study. When the properties of the contact elements attached to beam bars were as depicted in Fig. 4 a , bond conditions were considered favourable (Table 1). In order to simulate bond failure along the beam bars, the properties of the contact elements within the joint region and up to one beam depth away from the joint were reduced as in Fig. 40 (denoted unfavourable in Table 1). Column axial load is given in Table 1 as a percent of the nominal concentric failure load. The exterior connection models were derived from the typical interior mesh by eliminating one of the two segments of the main beam; in addition, anchorage of the bent portion of the beam bars was modeled using a very stiff contact element at the end of the horizontal embedded length. Because the aim in this study was to analyze joint mechanics in the post-cracked regime, only high levels of joint shear stress input, v,, were considered. A total of six models were analyzed, to study the effect of similar parameters as those considered for interior connections (models C17-C22 in Table 1).

4.5. Discussion of results The computed results are summarized in Table 1 and in Fig. 7. The magnitude of joint shear stress that could potentially be carried by joint hoops, v,, is given in Table I as a fraction of the shear input to the joint upon yielding of the beam reinforcement, v,. Also presented are the actual amounts of shear carried by joint hoops at four different levels of storey drift, v,, normalized by the same variable. Participation of hoops in joint shear resistance typically increased with the intensity of imposed lateral storey drift; however, joint hoops became fully engaged only in a limited number of cases. These cases, identified in Table 1 by having similar values of fractions v,/v, and v,,lv,, had favourable bond conditions and either a large joint shear input or, alternatively, very small amounts of joint hoops. It was observed that, even among specimens where all joint hoops yielded (i.e., the values v,/v, and lj,/vy were approximately equal), significant differences could be identified in the response by examining the sources of storey drift and the size of joint hoops contribution (Fig. 7). For models with favourable bond conditions and a low joint shear input ( C l , C3, and C5), contribution of joint distortions to the total storey lateral displacement was in the order of 17% at 0.5% storey drift, but it was reduced to 5% at 3% storey drift, regardless of the amount of joint hoops (cases C1 and C5). Column axial load acted against joint shear distortion and caused a reduction in the amount of distress in the joint (case C3). The analytical results indicate that column axial load is effective in reducing the deformability of the joint panel (resulting in stiffer response) and in increasing concrete core contribution to the joint shear resisting mechanism. The calculated stress fields within the joint suggested


PANTAZOPOULOU AND BONACCl


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C A N . J . CIV. ENG. VOL. 21, 1994

that the diagonal concrete compressive strut becomes wider and steeper as the magnitude of column axial load increases. Typically, a reduction in the contribution of joint deformations to the total storey drift was accompanied by a corresponding increase in the drift component that resulted from beam flexural deformations. Such a trend can be detected in the evolving patterns of Fig. 7. When, at increasing drift levels, beam contribution gains in magnitude over the joint participation, the major source of storey displacement is the inelastic rotation occurring in the beam plastic hinges, a situation that represents the ideal implementation of the earthquake design philosophy. It is noteworthy that increasing the amount of available joint hoops did not cause a proportional decrease in the amount of shear actually resisted by the hoops. Contrary to the obvious expectations of such a design decision, it was observed that at any given level of joint shear input, the more hoops that were provided in the joint, the greater was the portion of the total shear resisted by the hoops. For example, 20% of joint shear was resisted in model C1 by joint hoops, whereas this amount was increased to 40% in C5 (Table 1). Note that this result supports the earlier findings of the database study that participation of the joint concrete in the joint shear resisting mechanism decreases with increasing available amount of joint hoops. At higher levels of joint shear input, the parametric influences were substantially different. Models with favourable bond conditions developed large shear distortions regardless of the amount of available joint hoops (cases C7, C9, C11, C13, C14, C15, and C16). Joint contribution was responsible for approximately 20% of storey displacements at 0.5% drift, but reached 35% in some cases at 3% storey drift. Higher axial loads or larger amounts of joint hoops were effective in reducing these values; however, these measures were not able to reverse the pattern of failure which was characterized by significant joint deformations, unless a combination of large axial coinpression in the column (38% PC,) and a large amount of joint hoops (vplvy= 0.68) were used; this is evident by comparing models C9, C15, and C16 with C7, C13, and C14 in Fig. 7. As was seen in the cases with a low shear input, an increase in the available amount of joint hoops caused a corresponding (but not proportional) increase in the portion of joint shear that was actually resisted by the hoops. Yielding of joint hoops could only be avoided when large amount of hoops were provided. Again, computed results confirm the conclusion drawn from the experimental database study that yielding of joint hoops can be precluded if v, > v,; however, the analysis indicates that this would only be necessary if the anticipated input shear is severe. The behavior of exterior beam-column connections was examined only for large input of shear to the joint, set at 0 . 8 2 5 c ~ (models ~ a C17-C22). Model C17 with the smaller amount of hoops experienced considerable deformations within the joint, to the extent that all joint hoops yielded (vplvy= v,lv, = 0.17). The pattern of calculated field of principal compressive stresses for this specimen were plotted in Fig. 6b. Evidently, the main compressive strut mechanism that dominated the response of interior connections also forms here, however, it is no longer a redundant mechanism because the equilibrium of the upper node requires that large tensile forces be supported by bond along the column and beam main reinforcement. By comparison of

the calculated responses of cases C17, C l S , and C19, it appears that large amounts of joint hoops (v, > v,) can delay o r preclude yielding of joint hoops while controlling the magnitude of joint shear distortions. It is worth mentioning that computed hoop strains in model C l S were about 60% of the respective values in model C19, although the area of joint hoops in C18 was twice that of C19; thus the total shear resisted by the joint hoops in C18 was 25% greater than the respective amount in C19. Again, this is in confirmation of earlier findings from the experimental database study that contribution of joint core concrete to the joint shear resisting mechanism decreases with increasing amount of joint hoops. Although the influence of column axial load was not discernible in the experimental database study, the effects identified from the analytical results also carried over to exterior connections. Models C20 and C21 represent cases with high and low joint hoop potential. In both cases, column axial load was effective in confining the joint concrete and in delaying yielding of joint hoops; the fraction of shear resisted by joint hoops in these cases was reduced to 26% and 11% for large and small amounts of joint hoops, respectively.

4.6. The influence of bond conditions In terms of contribution to storey displacement, the bondslip mechanism competes with the joint distortion mechanism (they are springs in series), and thus the eventual increase in the contribution of one of these two sources of drift implies suppression of the other. For the sake of comparison, many o f t h e models with favourable bond conditions examined in the preceding had twin models in this study with poor bond conditions along the main beam bars (models C2, C4, C6, C8, C10, C12, and C22). Analytical results for these models indicated stiff joint panel behavior, with most of the story drift resulting from beam hinging and bond-slip deformations (the latter exceeding 40% of the total in some cases, as illustrated in Fig. 7). In all cases, yielding of beam bars was delayed, joint hoops developed small strains, whereas the joint shear input was mainly resisted by a diagonal concrete compressive strut in confirmation of the interpretation by Kitayama et al. (1991) outlined earlier. From the results, it appears that beam bars with favorable bond conditions induce more joint shear distortion to the joint panel, and require larger amount of joint hoops, whereas, in connections with poor bond conditions along the beam bars, joints rotate as rigid bodies to accommodate the excessive pullout of the reinforcement. The resulting increased connection flexibility could not be counteracted by larger axial loads (compare, for example, models C8 and C10) or by increased amounts of hoops (CS vs. C12); this is probably why tests done in North America, which were characterized bv excessive bond demand. had no benefit when axial loads were increased, whereas tests done in New Zealand, which were designed with favourable bond conditions, showed the reverse. Therefore, the computed results confirm the design philosophy that aims to preclude bond failures by providing adequate reinforcement anchorage. Model C22 was the only exterior connection assembly with poor bond conditions along the beam reinforcement anchorage (within the joint and one beam depth away from the joint face). Computed results indicated similar trends as in the case of interior connections, although the estimated total reinforcement slip was less, i.e., the amount of defor-


(b) Section B-B


Section A-A

u1 - ut = v tan B

'=

2(E1

= 2(c1 - 0 )tan 4

-

tan4

tan2 4 =

(Zb) 0 1

€ 2 - El € 1 - Et =€1

- El

€2

- Et

(2c)

02

-

01

=

= -v(tan B

v tan B

-

(64 (6b)

+I -) tan 0

FIG.8. ( a ) Kinematic and (b) equilibrium assumptions of the design model.

mation within the joint panel was reduced in comparison with results from a similar interior connection model having unfavourable bond conditions (for example, C8).

5. Design model and parameter study Despite the differences in the calculated responses of the connection assemblies analyzed in the preceding section, the estimated pattern of internal strain variation was strikingly similar in all joints. Specifically, all joint hoops were found to be in tension in the post-cracking regime, with the magnitude of lateral strain being slightly larger at the center of the joint, where dilation of the core has been reported to occur in experiments. Also, at drift levels exceeding the cracking limits, the joint concrete was found to be in a stress state that resembled a diagonal compressive strut forming along the diagonal of the joint, regardless of bond conditions along the beam reinforcement. The joint shear distortion, denoted here by y, was approximately uniform within the joint panel, but its magnitude (given as a measure of joint contribution to total story drift in Fig. 7) increased almost linearly with the corresponding average hoop tensile strains. Conforming with this information about joint kinematics, a model state of the joint panel (Pantazopoulou and Bonacci 1992) is summarized in this section that uses averaged stress and strain measures; therefore, equilibrium and compatibility requirements are not established pointwise, but in an average sense. An implicit requirement for averaging these variables is that the joint panel is properly detailed and that reinforcement is provided in amounts sufficient to control cracking. Contrary to previous empirical constructs that postulate the internal force paths, the fundamental assumptions of this formulation relate to the geometry of deformations (kinematics), which, as is illustrated from the results of the finite element study, can be visualized with greater confidence than the stresses.

A detailed description of the formulation has been presented elsewhere (Pantazopoulou and Bonacci 1992), and therefore only the key points of its derivation will be outlined. In an average sense, the geometry of deformation of the entire joint panel is fully described by three independent strain measures, i.e., the average longitudinal and transverse strains, E, and E,, and the average angle of distortion, y (Fig. 8). These deformation measures constitute a secondorder tensor, with the relevant properties of such measures (Fig. 8a). Stress measures associated with the above strains are the average vertical and horizontal stresses of the joint concrete, cr, and cr,, and the average boundary shear stress, v, resulting from direct member action, or from stress transfer, through bond, from the beam or column reinforcement to the joint core. Average stresses in the longitudinal and transverse joint reinforcement (including beam and column main reinforcement) are denoted by andA (Fig. 86). The stress variables satisfy the requirements of equilibrium, which, for the sake of simplicity, are written with reference to the longitudinal and transverse axes at the center of the joint (eqs. [3] and [4], in Fig. 86). Furthermore, the stress components cr,, cr,, and v also constitute a second-order tensor, following pertinent tensorial operations as outlined by eqs. [ 5 ] and [6] (Fig. 8). In the equations, p, and p, are the amounts of vertical and horizontal joint reinforcement (where p, = Pp, + p,, for which p, and p, are the percentages of horizontal beam reinforcement and horizontal stirrups in the joint, respectively; P reflects the degree of reduction of stresses occurring in the beam reinforcement in-between the face of the column and the center of the joint, and serves as an indicator of the quality of anchorage of beam reinforcement inside the joint. Thus, 0 < P < 1, with P = 0 for e x c e l l e n t a n c h o r a g e s a n d P = 1 f o r n o anchorage). Dimensions of the joint (depth, width, and height) are denoted by d,, 6, and h; N , is the column axial force; N,, represents

C A N . J. CIV. ENG. VOL. 21. 1994


Tokyo C1 case

0

I

0

I I

I

0.005

I

I

I

4

0.01 0.015 0.02 0.025 0.03 Joint hoop reinforcement ratio

I

0.035

0.04

FIG.9. Comparison between current ACI 352 design equation and the results of the design model for the case study. TABLE2. Parameter study

ditions a r e derived f r o m t h e general formulation (Pantazopoulou and Bonacci 1992): (i) Steel yield in two directions:

Result of increasing design variable quantity Design variable

Shear stress at hoop yield

Shear strain at hoop yield

( i i ( a ) )Steel yield in horizontal direction

+ crushing:

-

P\ h

.fy I 11,

Increase Increase Moderate increase Increase Increase Weak increase

Increase Increase Increase Moderate decrease Moderate decrease Decrease

the beam axial force, which results from partial restraint to beam expansion provided by adjacent columns in indeterminate frames. This approach allows for the use of any concrete constitutive model to relate principal compressive stress and strain, including those that can account for confinement and strain softening (Vecchio and Collins 1986). Concrete principal tensile stress is assumed to be zero. Stresses in horizontal and vertical reinforcement within the joint are related to corresponding strains by an elastoplastic steel model. The formulation can be used to describe the complete primary response of a joint as well as limiting joint shear strength (Pantazopoulou and Bonacci 1992). When it is used to trace the full response, the sequence of significant milestones in behavior (yielding in horizontal or vertical reinforcement, crushing of concrete along the principal diagonal) can be established along with the corresponding joint shear deformation for each. Possible response modes determining limiting joint shear resistance include (i) steel yield in one direction followed by yield in the orthogonal direction, or (ii) steel yield in one direction followed by crushing along the principal diagonal (crushing by itself also limits joint capacity, but this condition is rarely developed in joints with conventional reinforcement ratios and concrete strength). Expressions for limiting shear resistance for these two con-

(ii(b)) Steel yield in vertical direction

+ crushing:

where v,, is the limiting joint shear stress (minimum of eqs. [7], [8], and [91); p, and&, are the ratio and yield stress of horizontal reinforcement; p, and,f,, are the ratio and yield stress of vertical reinforcement; 11, is the horizontal (beam) axial stress; I[,, is the vertical (column) axial stress; f,'is the design compressive strength of concrete; and A is a coefficient dependent on concrete constitutive model that reflects influence of confinement and strain softening on usable fraction off,'. From the above expressions limiting joint shear resistance after joint reinforcement yielding, it is apparent that axial stresses in the column and beam play an active role, along with the quantity and strength of joint reinforcement, in determining the shear capacity of conriections, whereas the effectiveness of joint hoops in providing confinement is implicitly included in defining the maximum tolerable compressive stress in the concrete core, Af (Pantazopoulou and Bonacci 1992, Vecchio and Collins 1986).

5.1. Pnr-a~rzeterst~lc1.yo f joirzt belzaviolThe model just summarized was used to illustrate the influence of various design parameters on joint shear stress and shear strain that can be tolerated up to the onset of hoop yield (Bonacci and Pantazopoulou 1993). This parametric study illustrated how the model can be used to consider the consequences of potential design decisions on the load-carrying capacity and deformability of joints. Design variables conal strength, f,'; sidered were the concrete ~ ~ n i a x i compressive


PANTAZOPOULOU AND BONACCI

yield stress of joint hoops, f,,;amounts of horizontal and vertical joint reinforcement, p, and p,, volumetric ratio of joint hoops, p,; and horizontal and vertical axial stresses, N,,lf,'Dh and N,lffbd, ( b , h, d , the dimensions of the joint, according with earlier definitions used in assembling the database). Once again, nominal values for these variables were taken to represent the characteristics of specimen C1 tested at the University of Tokyo (Kitayama et al. 1991). The influence that each parameter had on tolerable shear and on the amount of associated joint distortion is classified in Table 2 depending on whether an increase in the design parameter caused a col~espondingincrease or a decrease in the response variable considered. The trend is assessed by the deviation of the response variables from the nominal values of the reference specimen. Only cases for which hoop yield was not preceded by concrete crushing or by yield of the column longitudinal reinforcement were included in the results. Of four possible outcomes (in terms of joint shear stress and strain tolerated at hoop yield), parameter changes that caused simultaneous increase on tolerable joint shear stress and on the associated deformability at hoop yield represent the optimum design choice. (Note that deformability prior to hoop yield is a significant indicator of the success of a given design, since it is an approximate measure of the lateral story drift it would take to yield the joint.) While other combinations may also represent acceptable design paths, they are less desirable, as they increase either shear stress or strain at hoop yield at the expense of the other. It can be observed, then, that increasing ps, N,,lDh, or f,, is most beneficial to the overall response. For structures with appreciable lateral stiffness (so that demand for joint deformation is relatively low), increasing p, or N , l b d , is an effective way to increase the joint shear stress that can be carried before hoops yield. Conversely, for structures with weak beams (so that demand for joint shear stress is relatively small), decreasing p, or N,lDrl, would delay hoop yield to higher story drifts. Table 2 also suggests that increasing ffis not a particularly effective design option for joints. Shear capacities associated with connection failure by yield of vertical reinforcement (dashed line) or by crushing of concrete along the principal diagonal (solid line) after hoop yield are plotted against the ratio of hoop reinforcement in Fig. 9 (all other parameters are those of specimen C1 again). For this particular example, it can be observed that capacity will be limited by steel yielding and that, for any ratio of hoops, it is about equal to the value recommended by ACI-ASCE Committee 352 (1985, 1991).

6. Summary and closing remarks The research described in this paper was an effort to explore the mechanics of beam-column joints in reinforced concrete structures, with the objective of illustrating the influence of various design parameters and of assessing supply and demand under the action of severe lateral loads. First, the existing interpretations were reviewed and the points of disagreement between the design approaches of the North American, Japanese, and CEB - New Zealand codes were compiled. 1t-was concluded that different postulated internal stress paths, invoked by these codes to describe equilibrium of forces in the joint, led to substantially different theses about the role of some important variables, such as joint reinforcement, joint core concrete, column axial load, transverse beams, and bond resistance. These

323

differences were also reflected in practical issues, such as design criteria for dimensioning and detailing of joints. The need for unification of concepts was pursued in this study through consistent re-evaluation of the available experimental evidence, and through extensive analytical modeling. From the experimental database, the most striking result was the identification of bias in the design and testing of specimens, reflecting the code practice of the country of origin of each experimental study. Because of the large number of parameters influencing the behavior, it was found that whereas experimental trends could be observed, very few points could be supported conclusively. For this reason, a parallel analytical parameter study was carried out using (i) a refined nonlinear finite element model of beam-column assemblies and (ii) a simple mechanical construct that satisfies requirements of equilibrium and compatibility in the joint panel. A number of conclusions were d r a w n from the analysis, for the most part, confirming the experimental evidence. Conclusions most useful for design applications were the following: (a) Joint hoops serve to confine the joint core, while at the same time they participate to the shear resisting mechanism of the joint panel. (b) Participation of the joint core concrete to the mechanism of shear resistance decreases as the amount of joint hoops is increased. (c) Joint performance deteriorates rapidly after yielding of joint hoops. To preclude hoop yielding, the shear resisting capacity of the hoops should exceed the shear input to the joint upon yielding of the adjacent beams. (d) Transverse beams are effective in precluding joint shear failures by confining the joint core concrete, particularly in interior connections. (e) To minimize the amount of connection flexibility, the column must be dimensioned so that the bond index is kept at low levels (less than 1.65 for interior and less than 0.85 for exterior connections). (f) The simple analytical model described herein was capable of reproducing the behavior of joints in agreement with evidence from experimental and finite element studies. The resulting design equations are sensitive to the important design variables, a feature that renders them advantageous over the existing design approaches which set allowable stress limits that are only influenced by the cylinder strength of concrete. Because of its simplicity, the model lends itself to design applications, without compromise in the consistent description of mechanics. It is therefore proposed as a viable alternative for the development of unified design criteria. While several of the conclusions outlined might appear familiar or may even be adopted by some design standards, it is noteworthy that these points have never before been proven on the basis of a rigorous investigation of the complete evidence. The insights gained from the multiple dimensions of the study presented (i.e., analysis of database, nonlinear finite element parametric study, and conceptual idealization of the mechanical problem) is the removal of the elements of uncertainty associated with the individual components of the investigation, when these are considered separately.

Acknowledgments The work presented in this paper was carried out jointly by the authors, at the University of Toronto, Canada. Financial

324

CAN. J. CIV. ENG. VOL. 21, 1993


support for the study was provided by the Natural Sciences and Engineering Research Council of Canada (NSERC grants No. O G P 0 0 4 2 0 3 3 and OGP0042154). T h e authors extend their appreciation to Mr. O m a r A t r a c h , f o r m e r g r a d u a t e s t u d e n t a t t h e University o f Toronto w h o d e v e l o p e d t h e finite element program and carried out t h e finite element parameter study under their supervision. ACI Committee 318. 1983. Building code requirements for reinforced concrete. ACI 318-83, American Concrete Institute, Detroit, Mich. ACI-ASCE Committee 352. 1976. Recommendations for design of beam-column joints in monolithic reinforced concrete structures. ACI Journal, 73(7): 375-393. ACI-ASCE Committee 352. 1985. Recommendations for design of beam column joints in monolithic reinforced concrete structures. ACI Journal, 82(3): 266-283. AIJ. 1988. Design guidelines for earthquake resistant reinforced concrete buildings based on ultimate strength concept. Architectural Institute of Japan, Tokyo, Japan. October. (in Japanese; see Otani et al. 1985). Atrach, 0 . M. 1992. Behaviour of interior and exterior beamcolumn joints under earthquake conditions. M.Sc. thesis, Department of Civil Engineering, University of Toronto, Toronto, Ont. Bonacci, J., and Pantazopoulou, S. 1993. Parametric investigation of joint mechanics. Proceedings, ACI Structural Journal, 90(1): 61-71. CEB-FIP. 1983. Model code for seismic design of concrete structures. Bulletin d'hformation, No. 160, Paris, France. Cheung, P.C., Paulay, T., and Park, R. 1993. Behaviour of beamcolumn joints in seismically loaded R.C. frames. The Structural Engineer, 71(8): 129-1 38. Ehsani, M.R., and Wright, J. 1985. Exterior reinforced concrete beam-to-column connections subjected to earthquake-type loading. Proceedings, ACI Journal, 82(4): 188-195. Fujii, S., and Morita, S. 1992. Comparison between interior and exterior RC beam-column joint behavior (1991). III Design of beam-column joints for seismic resistance. ACI Special Publication SP-123, American Concrete Institute, Detroit, Mich., pp. 145-165. Hanson, N.W. 197 1. Seismic resistance of concrete frames with grade 6 0 reinforcement. ASCE Journal of the Structural Division, 97(6): 1685-1700. Hanson, N.W., and Conner, H.W. 1967. Seismic resistance of reinforced concrete beam-column joints. ASCE Journal of the Structural Division, 93(5): 533-560. Kaku, T., and Asakusa, H. 1991. Bond and anchorage of bars in reinforced concrete beam-column joints. In Design of beamcolumn joints for seismic resistance. ACI Special Publication No. SP-123, American Concrete Institute, Detroit, Mich., pp. 401-424. Kitayama, K., Otani, S., and Aoyama, H. 1991. Development of design criteria for RC interior beam-column joints. In Design of beam-column joints for seismic resistance. ACI Special Publication SP-123, American Concrete Institute, Detroit, Mich., pp. 97-123. Kurose, Y. 1987. Recent studies on reinforced concrete beam column joints in Japan. PMFSEL Report No. 87-8, Phil M. Ferguson Structural Engineering Laboratory, Department of Civil Engineering, The University of Texas at Austin, Austin, Tex., December. Lee, D., Wight, J.K., and Hanson, R.D. 1977. RC beam-column joints under large load reversals. ASCE Journal of the Structural Division, 103(12): 233772350, Milburn, J.R. 1982. Behavior of beam-column joints designed to NZS3101. Research Report 82-7, Department of Civil Engineering, University of Canterbury, Christchurch, New Zealand.

Mogami, T. et al. 1983. Structural tests for developing high-rise reinforced concrete layered construction system. Taisei Technical Research Report, No. 16, December. Morita, S., and Fujii, S. 1984. Interactive decay of bent-bar anchorage and joint shear capacity at exterior beam-column joints under reversed cyclic loading. Proceedings of the 1st Uaited States - New Zealand - Japan Seminar, Monterey, Calif. NZS 3 101. 1982. Code of practice for the design of concrete structures. Parts 1 and 2. Standard Association of New Zealand, Wellington, New Zealand. Otani, S. 1991. The Architectural Institute of Japan (AIJ) proposal of ultimate strength design requirements for RC buildings with emphasis on beam column joints. III Design of beamcolumn joints for seismic resistance. ACI Special Publication SP-123, American Concrete Institute, Detroit, Mich., pp. 125-144. Otani, S., Kitayama, K., and Aoyama, H. 1985. Beam bar bond stress and behaviour of reinforced concrete interior beamcolumn connections. Proceedings, 2nd U.S.-N.Z.-Japan Seminar on Design of Reinforced Concrete Beam-Column Joints, Department of Architecture, University of Tokyo, Tokyo, Japan, May 29-30, pp. 1-40. Pantazopoulou, S., and Bonacci, J. 1992. Consideration of questions about beam-column joints. Proceedings, ACI Structural Journal, 89(1): 27-36. Park, R., and Milburn, J.R. 1983. Comparison of recent New Zealand and United States seismic design provisions for reinforced concrete beam-column joints and test results from four units designed according to the New Zealand Code. Bulletin of the New Zealand National Society for Earthquake Engineering, 16(1): 3-25. Paulay, T. 1986. A critique of the special provisions for seismic design of the building code requirements for reinforced concrete (ACI 31 8-83). ACI Journal, 83(2): 274-283. Paulay, T. 1989. Equilibrium criteria for reinforced concrete beam-column joints. ACI Structural Journal, 86(6): 635-643. Paulay, T., and Park, R. 1984. Joints in reinforced concrete frames designed for earthquake resistance. Research Report No. 84-9, Department of Civil Engineering, University of Canterbury, Christchurch, New Zealand, June. Paulay, T., Park, R., and Priestley, M.J.N. 1978. Reinforced concrete beam-column joints under seismic actions. ACI Journal, Proceedings, 75(11): 585-593. Seckin, M., and Uzumeri, S.M. 1978. Examination of design criteria for beam-column joints. Proceedings, 6th European Conference on Earthquake Engineering, Dubrovnik, Yugoslavia, September. Ustuner, T. 1992. An analytical study of bond deterioration caused by yield penetration. M.Sc. thesis, Department of Civil Engineering, University of Toronto, Toronto, Ont. Uzumeri, S.M. 1977. Strength and ductility of cast-in-place beam-column joints. In Reinforced concrete structures in seismic zones. ACI Special Publication SP-53, American Concrete Institute, Detroit, Mich., pp. 293-350. Vecchio, F.J. 1990. Reinforced concrete membrane element formulations. ASCE Journal of Structural Engineering, 116(3): 730-750. Vecchio, F.J., and Collins, M.P. 1986. The modified compressionfiled theory for reinforced concrete elements subjected to shear. ACI Journal, 183(2): 219-231.

Appendix 1. Nomenclature Joint dimensions: Effective dimensions were taken to be t h e height o f t h e b e a m , a n d t h e d e p t h a n d width o f t h e column containing the joint.

( a ) Classification of failvre modes (Tcible A I ) 1. Formation of plastic hinges in the beams.

325



-x

70,

2

0

Bond Index (MPa)

Joint Shear Failures I

2

4

6

8

10

12

14

16

18

Cycle No.

Bond Index (MPa) I

I

1

2

I

20

F I G . A l . Range of testing rates for exterior connection experiments.

160

I

1120

1

I

Bond Index (psi)

- Bond Failure I

Joint Shear Failure Beam Hinging

Column Hinging

FIG.A3. Influence of design philosophy regarding bond demand on failure pattern. (N.A. denotes North America; N.Z. denotes New Zealand.)

No Bond Failures

2. Bond Index (psi)

I

N.Z. Bond Failure Column Hinging

Joint Shear Failure Beam Hinging

FIG.A2. Influence of bond demand on failure mode 2. 3. 4. 5.

Joint shear failure detected by hoop yielding. Special cases of unreinforced joints failing in shear. Bond failure inside the joint. Column hinging.

( b ) Dernand atzcl perfbt.tnntzce tnensures Bond index (Otani et al. 1985; Kitayntna et al. 1991): Average bond stress, normalized by c ( M P a ) , that develops over the column depth when ( i ) beam bars yield in tension and compression at both column faces of an interior beamcolumn joint and ( i i ) beam bars yield in tension at the column face, but bar stresses reduce to zero at the tip of the available bar anchorage length for exterior connections. The phenomenon of bond deterioration is associated with larger values of the bond index. Average horizotzml shear stress, v,,,: Computed from specimen reactions according to Fig. 1, and normalized by c ( M P a ) . Shear potetztial of hoops, v,, (expressed in multiples of c ( M P a ) ) : Average joint shear that can be resisted by joint hoops yielding in the direction of the applied load. Potetztial of bea~nreinforcement, v,, (expressed in multiples of f l ( M P a ) ) : Average joint shear stress input upon flexural yielding of the adjacent beams (this is the design load).

Japan

N.A.

Country of Origin Joint Shear Failures

c

Beam Hinging

FIG.A4. Population of tests viewed according to experimental objectives. Shear fraction resisted by the joint core: When connection is limited by joint shear failure, which requires yielding of joint hoops, then the component of maximum measured joint shear stress, v,,,, which is in excess of the joint hoop potential represents the shear resisted by the concrete core by means of the diagonal compressive strut mechanism. Joint confinemetzt index: psvfyS/f~ where p,, is the volumetric ratio of joint reinforcement and f,,, is the yield stress of that reinforcement.

Appendix 2. Database of exterior beam-column joints Table A1 summarizes the experimental results of 57 exterior connections tested under static load reversals simulating earthquake loads. The experiments were done over the past 3 0 years in Canada (9), Japan (27), U.S. (19), and New Zealand (2). Failure modes, as identified from the experimental reports, and calculations of various demand measures and performance indicators according to the nomenclature (Appendix 1) are included in the table. When applied on the column of the exterior connection, static axial compression is given as average column axial stress (computed


TABLEA l . Summary of experimental database

Reference Uzumeri (1977)

Morita and Fujii (1984)

Lee et al. (1977)

Ehsani and Wight (1985)

ID

SP 1 SP2 SP3 S P4 SP5 SP6 SP7 SP8 SP9 U41L S41L R41L 2 5 6 1B 2B 3B 4B 5B 6B

Paulay and Park (1984)

3 4

Hanson (1971)

3 4 5

Hanson and Conner (1967)

I I- A I1 I11 IV

v

V-A

No. of transverse beams

Hinge relocation (mm)

Beam f:

(MPa)

(&a)

-

exterior connection specimens

Hoop .f~.

(ksi)

Hoop volumetric ratio (%)

Column Bond index

izlf;

(%)

Failure mode

v,,,

v,,

v,

327



Column Axial Load, PC, (%)

----

ee mmmooommmooomoommm e e m m m m eee0000weee000000e0000eee

-mm

NNPIN N N N N N P I N N N N N N ~ I N N N N N

Column Axial Load, PC, (%)

med v, t-t-

t-t-t-t-

t-t-t-t-t-t-t-t-t-t-t-t-t-t-t-t-t-t-

e e eeee eeeeeeeeeeeeeeeeee mm mmmm mmmmmmmmmmmmmmmmmm

22

=!=J!=!=J!

mm

N N N N

+--eaoN-oe-maomt-mo meeememeeeemeemmme

I I

I I I I

I I I I I I I I I I I I I I I I I I

I I

I I I I

I I I I I I I I I I I I I I I I I I

mmmm

9????r?1l'?r?Dq9r?=J!?C???

+

low v,

FIG.AS. Influence of column axial stress on joint strength: (a) joint shear failures; (b) beam hinging. ( I psi = 6.89 kPa.)

Joint Shear Failures

FIG.A6. Effect of hoops on concrete contribution to joint shear strength. over the column gross area), and normalized by j'i. Volumetric hoop reinforcement, expressed as a fraction of the total volume of the joint, ranged between 0% and 1.45%. The design bond-index ranged between 0.55 and 2.4, the first number representing favourable bond conditions and the second representing cases of excessive bond demand (the upper limit corresponds to 13 MPa average bond stress along the beam bars). Maximum values of the measured average joint shear

C A N . J . CIV. ENG. VOL. 21, 1994

Joint Shear Failures


2.0

I

r

fi (ksi) FIG.A7. Relationship of joint shear strength to concrete cylinder strength. stresses input to the joint, v,, ranged from 0.45 to 0.95 C ( M P ~ for ) specimens failing in mode 2 (joint shear failure). Figures A1-A8 summarize the results of the database study. In general, the distributions of the data show much greater scatter than the results of similar analyses done on interior beam-column joints (Bonacci and Pantazopoulou 1992); this is attributed to the large number of parameters affecting the response of exterior joints. For example, the anchorage of beam bars in exterior connections occurs entirely within the joint core (along the bent segment of the bar as well), and therefore the geometry of the anchorage and the extent of cracking of the core concrete affects the

No. of Transverse Beams

Beam Hinging Joint Shear Failure FIG.A8. Influence of transverse beams on joint performance. slippage of the reinforcement, a parameter that is in no way represented in the experimental reports apart from the occasional mention of bond failure. Because of the different anchorage circumstances of the top and bottom beam reinforcement, the direction of bending constitutes an additional dimension in the database of exterior connections, particularly regarding the mechanism or resistance and the mode of failure; with reference to Fig. 6, it is evident that anchorage conditions of the lower beam reinforcement become critical when the beam is bent counterclockwise, since that reinforcement is essential for equilibrating the horizontal component of the diagonal compression strut.


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22. Mostafa Elmorsi, M Reza Kianoush, and W K Tso. 2000. Modeling bond-slip deformations in reinforced concrete beamcolumn joints. Canadian Journal of Civil Engineering 27:3, 490-505. [Abstract] [PDF] [PDF Plus]