COUPLING OF CONCRETE WALLS USING UNBONDED POST-TENSIONING. Yahya C. Kurama 1 and Qiang Shen 2 ABSTRACT. Introduction

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1 COUPLING OF CONCRETE WALLS USING UNBONDED POST-TENSIONING Yahya C. Kurama and Qiang Shen ABSTRACT This paper describes an analytical investigation of the expected seismic behavior of a new type of hybrid coupled wall system. Coupling of concrete walls is achieved by post-tensioning steel beams to the walls using unbonded post-tensioning tendons. Different from conventional hybrid coupled wall systems, the coupling beams of the new system are not embedded into the walls. One of the most important advantages of the new system is that it can be used to couple existing walls as a part of a strengthening and retrofit scheme. Introduction Previous earthquakes have shown that concrete coupled walls are one of the most effective lateral load systems for seismic regions. Conventional methods for coupling concrete walls include reinforced concrete beams cast monolithically with the walls and steel beams embedded into the walls (Harries, Harries et al. ) which may not be feasible or cost-effective for use in the seismic rehabilitation of existing construction. The research described in this paper focuses on hybrid systems with steel coupling beams that are not embedded into the walls. Instead, coupling of the walls is achieved by unbonded post-tensioning. As an example, Fig. a shows an eight-story coupled wall system and Fig. b shows an unbonded post-tensioned hybrid coupled wall subassemblage which includes a steel coupling beam and the adjacent concrete wall regions at a floor level. The wall regions extend to mid-story height above and below the floor level. The post-tensioning (PT) force is provided by multi-strand tendons on both sides of the beam web, not in contact with the beam (Figs.b-d). The tendons may be placed externally on either side of the walls (in the case of existing walls) or inside oversize ungrouted ducts in the walls (for new construction). Thus, the PT steel is anchored to the coupled wall system only at two locations at the outer ends of the walls. Steel plates are used at the outer ends of the walls to accommodate the PT anchorages and at the inner ends of the walls (i.e., adjacent to the beams) to accommodate bearing of the beams on the walls. In new construction, these plates may be embedded into the walls. Fig. c shows the expected Assistant Professor, Dept. of Civil Engineering and Geological Sci., Univ. of Notre Dame, Notre Dame, IN Doctoral Candidate, Dept. of Civil Engineering and Geological Sci., Univ. of Notre Dame, Notre Dame, IN 46556

2 l w l b (a) l w h w h s spiral PT tendon anchorage embedded plate l w C a C V b b d a reference line T a connection coupling region beam angle A cover plate coupling beam Fig.. Coupled wall system: (a) elevation view; (b) beam-to-wall subassemblage; (c) deformed shape; (d) coupling forces. l b A (b) beam/wall contact region gap opening (c) l b V b C bz + (T a + C a ) da V b = l b (d) z C b d b d b C a deformed shape of the subassemblage under lateral loads acting on the walls from left to right. The nonlinear deformations of the beam occur primarily as a result of gap opening along the beam-to-wall interfaces. Friction develops at the beam-to-wall interfaces due to the PT force, preventing sliding of the beam against the walls. Top and seat angles are bolted to the steel plates at the inner ends of the walls and to the beam flanges to provide: () additional vertical support to the beam; () additional moment resistance; and () energy dissipation during an earthquake. It is noted that it may be difficult to design and construct the angle-to-wall connections in existing walls. Under these conditions, the design forces for the angle-to-wall connections may be reduced by not connecting the angles to the beam (i.e., by using the angles only for vertical support to the beam). In a properly designed subassemblage, the desired behavior is yielding of the angles (if connected to the beam flanges) due to gap opening, with little yielding and damage in the beam and walls. The yielded angles can be replaced after the earthquake. As the subassemblage deforms, gap opening results in concentrated compressive stresses in the contact regions near the beam-to-wall interfaces (Fig. c). Flange cover plates are used at the beam ends to prevent or delay yielding of the beam flanges in compression and to prevent buckling of the flanges. The wall plates distribute the compressive stresses into the concrete. Moreover, in new construction, spiral reinforcement is used behind the embedded plates to transfer and distribute the total compression force without excessive deformations in the concrete. The lack of these spirals in existing walls may limit the amount of PT force used in the system. In comparison with conventional methods of coupling using cast-in-place concrete or embedded steel beams, the coupling beams in the proposed system do not rely on the development of fixed-end forces at the beam-to-wall joints. Fig. d shows the coupling forces that develop from the formation of a diagonal compression strut in the beam upon lateral displacement of the walls, where V b is the coupling shear force. The amount of coupling between the walls and the energy dissipation of the subassemblage can be controlled by adjusting the total PT force P (which controls the total compression force in the beam, C b ), the tension and compression angle forces T a and C a (if the angles are connected to the beam flanges), the beam depth d b, and the beam length l b. As a result of post-tensioning, the initial lateral stiffness of an unbonded post-tensioned coupling beam before the initiation of gap opening is similar to the initial stiffness of a comparable T a wall region l w ap section at A A

3 coupling beam embedded into the walls. Thus, significant increases in the initial lateral stiffness of the walls can be achieved using this method. Gap opening results in a reduction in the lateral stiffness of the subassemblage, limiting the seismic forces and allowing the system to soften and undergo large nonlinear displacements, and thus period elongation without significant damage (except, possibly, the angles). The PT force controls the depth and width of the gaps. As the walls displace laterally, the tensile forces in the PT tendons increase, resisting gap opening. Upon unloading, the PT tendons provide a restoring force that tends to close the gaps, thus pulling the beam and the walls towards their undeformed position with little or no residual deformation (i.e., self-centering capability). Since the PT steel is not connected to the walls or the beams except at the ends, the strain distribution along the entire length of the steel is close to uniform, thus, delaying the nonlinear straining (i.e., yielding) of the steel. Furthermore, the PT force puts the walls and the beams into, primarily, a state of compression. As a result of the formation of gaps at the beam-towall interfaces (and the resulting diagonal compression strut in the beams), the tension stresses that are introduced into the walls from the beams are significantly reduced, thus reducing or preventing damage due to cracking. This makes the proposed method particularly suited for existing walls since no additional reinforcement may be required in the walls to accommodate coupling. Analytical Modeling The DRAIN-DX Program (Prakash et al. 99) is used for the analytical platform. As an example, a model which was developed for the beam-to-wall subassemblage in Fig. b is shown in Fig.. Analytical models of multi-story wall systems are constructed by joining the subassemblage models for the different floor and roof levels. Full details on the analytical modeling are provided in Shen and Kurama (). It is noted that the effect of the presence of slabs on the behavior of the walls and the coupling beams is beyond the scope of this research, and thus, slabs are not modeled. LEFT WALL REGION RIGHT WALL REGION wall angle element height beam elements wall contact elements elements kinem. constr. kinematic constraint truss element l l l w b w Fig.. Analytical model of a subassemblage. Each wall region is represented using two sets of fiber beam-column elements. The first set consists of elements in the vertical direction, referred to as the wall-height elements, to model the axial-flexural and shear behavior of the wall along its height. The second set of fiber elements is used to model the deformation of the concrete in the wall contact regions to the left and right of the coupling beam. These elements, called as the wall-contact elements, are in the horizontal direction. The fiber cross-section properties of the wall-contact elements are determined from the properties of an effective wall cross-section in the vertical plane as described in Shen and Kurama (). The stress-strain relationship of the concrete and steel fibers for the wall regions is a multi-linear idealization of the smooth uniaxial stress-strain relationship for the unconfined concrete, confined concrete, or steel used in the cross-section. Fiber beam-column elements are used to model the axial-flexural and shear behavior of the coupling beams, including the flange cover plates. The opening of gaps at the beam-to-wall interfaces is modeled by setting the tensile strength and stiffness of the fibers adjacent to the beamto-wall interfaces to zero. Thus, the displacements due to gap opening between points on either side

4 of an interface are represented as distributed tensile deformation in the beam elements and the wallcontact elements. The reduction in the lateral stiffness of the subassemblage due to gap opening is represented by the zero stiffness of the fibers that go into tension near the interfaces. Each unbonded PT tendon is modeled using a truss element. The PT loads are simulated by initial tensile forces in the truss elements which are equilibrated by compression stresses in the fiber elements modeling the walls and the beam. Each truss element is connected to two nodes representing the anchorages between the PT tendons and the walls at the outer ends. The anchorage nodes are kinematically constrained to the node at the center of the corresponding wall region as shown in Fig.. The stress-strain relationship of the truss elements is a bilinear idealization of the smooth stress-strain relationship of the PT steel. The behavior of the top and seat angles (if connected to the beam flanges) is also modeled using fiber elements, referred to as angle elements. The angle elements represent the expected behavior of the angles under axial loading (parallel to the beam flanges) only. More details on the modeling of the angles, including the hysteretic axial-force-deformation relationship that was used for the angles, is given in Shen and Kurama (). The verification of the analytical model above and the nonlinear load-deformation behavior of prototype coupled wall subassemblages are also described in Shen and Kurama (). Behavior of Multi-Story Walls Under Static Loading This section discusses the expected behavior of prototype hybrid coupled wall systems under monotonic and cyclic lateral loading. Prototype coupled wall systems 8.5m 8.5m 8.5m (8ft) (8ft) (8ft) concrete wall steel beam (ft) (ft) (ft) (ft) (ft) (a) prototype system 6.m 6.m 6.m 6.m 6.m (#9@in.) 8.6mm@76mm t w =56mm (4in.) (#5@8in.) 5.9mm@457mm l =.5m (ft) w l =.5m (ft) w cover plate, t c =8.6mm (.5in.) 4-strand PT tendon a bp=95mm (.6in ) f bpi =.65 fbpu W 8 Fig.. Prototype structure: (a) plan view; (b) cross-section of cast-in-place wall near base; (c) cross-section of precast wall near base; (d) coupling beam. t w (b) ( -/8in. PT-bars) 6mm PT-bars, f wpi =.65 f wpu (c) (d) (#9@in.) 8.6mm@76mm D s = 5mm (6in.) d s =.7mm (.4in.) s =.8mm (.5in.) The investigation is based on a 8-story coupled wall system designed for the office building plan view shown in Fig. a for a region with high seismicity and a site with a stiff soil profile. The design of the prototype structure is described in full detail by Shen () with the structural design properties summarized below. Walls: The total wall height h w =.6m (with 4.88m for the first story and.96m for the other stories), wall length l w =.5m, and wall thickness t w =56mm (uniform). Two different types of systems are considered: () with monolithic cast-in-place reinforced concrete walls (referred to as

5 CIP-UPT system below); and () with precast concrete walls (referred to as PRE-UPT system below). The precast walls are similar to the walls described by Kurama et al. (999), constructed by joining precast wall panels along horizontal joints using unbonded post-tensioning bars running in the vertical direction. The cross-sections of both systems near the base of the walls are shown in Figs. b and c. It is assumed that a sufficient amount of concrete confinement is provided in the walls using spiral reinforcement near the corners at the base. The spiral diameter D s =5mm, spiral wire diameter d s =.7mm, and pitch s =.8mm. The unconfined concrete strength is assumed to be f c =4.4MPa and the yield strength of the mild steel reinforcement used in the cast-in-place walls is assumed to be f wsy =44MPa. The yield (i.e., linear-limit) strength and ultimate strength of the PT bars in the precast walls is f wpy =88MPa and f wpu =5MPa, respectively. Coupling beam subassemblages: The properties of the coupling beam subassemblages at each floor and roof level are the same. The beam length l b =.5m with a W 8 section as shown in Fig. d. The top and seat angles have a L8 8 -/8 section. It is noted that the paper focuses on I- sections for the beams, however, the findings can be easily applied to other types of steel beams, such as with hollow sections. Flange cover plates with thickness t c =8.6mm and length l c =46mm are used at the beam ends. The length of the cover plates was determined such that yielding of the beam flanges in compression does not occur where the plates are terminated. The width of the angles and the flange cover plates is equal to the beam flange width, b f =8mm. The thickness of the wall plates adjacent to the beams, t e =.8mm and the width of the plates is equal to the wall thickness, t w =56mm. Two spirals are used in each wall region, one spiral near each flange as shown in Fig. b and Fig. c. The spiral diameter D s =9mm, spiral wire diameter d s =.8mm, and pitch s =.8mm. The yield strength of the steel used in the beams, angles, cover plates, and wall plates is assumed to be f bsy =6MPa. Post-tensioning: Each coupling beam subassemblage at a floor or roof level is post-tensioned using four tendons, as shown in Fig. d. Each tendon consists of four.7mm seven-wire strands with a total area of a bp =95mm. The tendons are prestressed to f bpi =.65f bpu, where f bpu =86MPa and f bpy =69MPa for the strands. The initial stress in the coupling beam (including the flange cover plates) due to post-tensioning is f bi =5MPa (equal to.97f bsy ). Behavior under monotonic loading 9 overturning/base moment (kn.m) CIP-UPT left wall concrete cracking st beam gap opening softening of left wall right wall concrete cracking st wall mild steel yielding st beam angle yielding st beam cover plate yielding st beam PT-tendon yielding two uncoupled walls right wall in coupled system left wall in coupled system PRE-UPT st beam gap opening left wall gap opening right wall gap opening softening of left wall st beam angle yielding st beam cover plate yielding st wall PT-bar yielding st beam flange yielding st beam PT-tendon yielding right wall concrete crushing two uncoupled walls right wall in coupled system left wall in coupled system Fig. 4. Monotonic loading: (a) CIP-UPT system; (b) PRE-UPT system. 9 overturning/base moment (kn.m) (a) (b) The thick solid lines in Figs. 4a and 4b show the overturningmoment-roof-drift behavior (where the roof-drift is equal to the roof lateral displacement divided by the wall height, h w ) of the CIP-UPT wall system and the PRE-UPT wall system, respectively under combined gravity and monotonic lateral loading. The gravity load is equal to % of the design dead load plus

6 5% of the design live load. For each coupled wall system, the lateral load applied at a floor or roof level is equally divided between the left and right walls as shown in Fig. a. A triangular distribution of lateral loads (applied from left to right) over the height of the walls is used with the maximum load at the roof. Figs. 4a and 4b show that the two systems are designed such that their overall overturningmoment-roof-drift relationships are similar to facilitate the comparisons described later. As the coupled wall systems displace laterally, they go through a number of states including: () softening of the left wall (defined as the state when the neutral axis at the base of the wall reaches half of the wall length); () softening of the right wall; () first wall steel (mild steel for the CIP walls and PT bars for the PRE walls) yielding; (4) first beam angle yielding; (5) first beam flange yielding; (6) first beam PT tendon yielding; and (7) wall base confined concrete crushing. It is noted that crushing of the confined concrete at the base of the CIP walls does not occur due to the large amount of spiral reinforcement used near the corners of the walls. For each prototype coupled wall system, the thin solid lines in Figs. 4a and 4b show the basemoment-roof-drift relationships of the tension (left) and compression (right) side walls. Similarly, the dashed lines in Fig. 4 show the overturning-moment-roof-drift relationship of the walls without any coupling (i.e., two walls with no beams in between). Coupling of the walls results in a significant increase in the lateral strength and initial lateral stiffness. For both systems, the initial lateral stiffness of the coupled walls is approximately 4.8 times the initial stiffness of the uncoupled walls (two walls). The degree of coupling between the walls (calculated as the difference in the overturning moment resistance of the coupled and uncoupled systems divided by the overturning moment resistance of the coupled system) at a roof drift of.5% is equal to, approximately, 68%. Parametric investigation The structural properties of the prototype coupled wall systems above are varied, then, a monotonic push-over lateral load analysis of each system is conducted. The results are used to determine how the behavior of the walls can be controlled by design. 4 softening of left wall 4 softening of left wall l w =.5 m ρ =.8% 4 ws softening of left wall d bw=5mm st wall mild steel yield Selected results from the l w=.9 m st wall mild steel yield ρ =.7% d =75mm ws st beam angle yield st beam angle yield st wall mild steel yield bw l w =.8 m st beam flange yield st beam flange yield ρ ws=.7% st beam angle yield d =69mm bw st beam tendon yield st beam tendon yield st beam flange yield parametric investigation st beam tendon yield of the CIP-UPT and (a) (b) (c) PRE-UPT wall systems are given in Figs. 5 and , respectively. Each figure shows the 4 softening of left wall 4 l b=.5 m softening of left wall 4 softening of left wall f bpi =.65fbpu a bp =95mm st wall mild steel yield l =.8 m overturning-momentroof-drift behavior of b st wall mild steel yield st beam angle yield a bp =98mm st wall mild steel yield f bpi =.55fbpu st beam flange yield l b=4.57 m st beam angle yield st beam angle yield st beam flange yield a bp =59mm f bpi =.75fbpu st beam tendon yield st beam flange yield st beam tendon yield st beam tendon yield three parametric (d) (e) (f) systems: Wall () is the same as the prototype Fig. 5. Parametric study of CIP-UPT system: (a) l w ; (b) ρ ws ; (c) d bw ; (d) l b ; (e) a bp ; (f) f bpi.

7 system and the properties of Walls () and () are varied as shown. The following parameters are investigated: () wall length, l w ; () wall reinforcement ratio, ρ ws or ρ wp (defined as the total area of wall mild or PT steel divided by the gross wall area); () beam web depth, d bw ; (4) beam length, l b ; 8 6 f wpi =.65fwpu 6 6 f wpi =.55fwpu f wpi =.75fwpu 4 softening of left wall 4 softening of left wall 4 softening of left wall st beam angle yield l w =.5 m st beam angle yield ρ wp =.% st beam angle yield st wall PT-bar yield l w=.9 m st wall PT-bar yield ρ wp =.4% st wall PT-bar yield st beam flange yield l w =.8 m st beam flange yield ρ wp =.69% st beam flange yield st beam tendon yield st beam tendon yield st beam tendon yield (a) (b) (c) 8 6 softening of left wall 4 st beam angle yield l b=.5 m 4 softening of left wall 4 softening of left wall st beam angle yield st beam angle yield a =95mm f bpi =.65fbpu l b=.8 m bp st wall PT-bar yield l b=4.57 m a bp =98mm st beam flange yield st wall PT-bar yield st wall PT-bar yield f bpi =.55fbpu st beam tendon yield st beam flange yield st beam flange yield a bp =59mm f bpi =.75fbpu st beam tendon yield st beam tendon yield (d) (e) (f) Fig. 6. Parametric study of PRE-UPT system: (a) l w ; (b) ρ wp ; (c) f wpi ; (d) l b ; (e) a bp ; (f) f bpi. (5) beam PT tendon area, a bp ; (6) initial stress in beam PT tendon, f bpi ; and (7) initial stress in wall PT bar, f wpi (for PRE walls). The results in Figs. 5 and 6 show that the lateral strength and stiffness of the coupled wall system can be controlled by the beam PT tendon area a bp, in addition to the wall length l w, wall reinforcement ratio ρ ws or ρ wp, and beam web depth d bw. The yielding of the beam PT steel, which is significantly delayed due to unbonding, can be controlled by the initial stress in the PT steel, f bpi. The design parameters can also be adjusted to prevent or delay the yielding of the coupling beam flanges in compression. Behavior under cyclic loading 6 Figs. 7a and 7b show the behavior of the prototype CIP-UPT and PRE-UPT wall systems under combined gravity and cyclic lateral loading. The PRE-UPT system has limited inelastic energy dissipation and a large self-centering capability. The CIP-UPT system has relatively larger inelastic energy dissipation and a somewhat reduced but still high self-centering capability. For comparison, Fig. 7c shows the expected behavior of the CIP system with embedded steel coupling beams (referred to as CIP-EMB system below) representing conventional construction. The size of the coupling beams in the CIP-EMB system (W 9) is smaller than the beams in the CIP- UPT system (W 8) such that the overall 8 8 monotonic overturning-moment-roof-drift relationships of the two systems are similar to facilitate a comparative investigation. This is because, the strength of an unbonded post-tensioned steel coupling beam is smaller than the strength of an embedded steel beam of the same size since the unbonded CIP-UPT system CIP-EMB system (a) (c) 8 (b) (d) Fig. 7. Cyclic behavior: (a) CIP-UPT system; (b) PRE-UPT system; (c) CIP-EMB system; (d) CIP-UPT system without angles PRE-UPT system CIP-UPT system without angles

8 post-tensioned beam can not develop the full yield and plastic moment capacity of the beam section (Shen and Kurama ). Comparing the cyclic behavior of the CIP-UPT and CIP-EMB systems in Figs. 7a and 7c, it can be seen that the CIP-EMB system has significantly larger inelastic energy dissipation. However, the self-centering capability of the CIP-EMB system is considerably small indicating the possibility of significant residual (i.e., permanent) lateral displacements after a large earthquake. In contrast, the unbonded post-tensioned coupling beams provide a substantial restoring force to the CIP-UPT system (Fig. 7a) reducing residual drift. The results in Figs. 7a and 7b include top and seat angles used for inelastic energy dissipation at the beam-to-wall interfaces. To investigate the amount of energy dissipation provided by the angles, Fig. 7d shows the behavior of the CIP-UPT system without angles. In this case, the amount of PT force in the coupling beams is increased such that the overall monotonic overturning-momentroof-drift relationships of the systems with and without angles are similar to facilitate a comparative investigation. As expected, there is a significant reduction in the inelastic energy dissipation of the system without the angles. Since unbonded post-tensioned coupling beams without angles do not dissipate much energy (Shen and Kurama ), the amount of energy dissipated in Fig. 7d is provided primarily by the cast-in-place reinforced concrete walls. It is expected that the angles play an even more important role in the inelastic energy dissipation of the PRE-UPT system in Fig. 7b. Behavior of Multi-Story Walls Under Earthquake Loading This section investigates the expected behavior of hybrid coupled wall systems based on nonlinear dynamic time-history analyses under earthquake loading. For this purpose, Figs. 8a-d show roof-drift (percent) roof-drift (percent) LA7 (PGA=.46g) 5 5 time (seconds) (a) CIP-UPT uncoupled walls coupled walls CIP-EMB LA7 (PGA=.46g) 5 5 time (seconds) (c) roof-drift (percent) roof-drift (percent) LA7 (PGA=.46g) 5 5 time (seconds) (b) Fig. 8. Roof-drift time-history: (a) CIP-UPT system; (b) PRE-UPT system; (c) CIP-EMB system; (d) CIP-UPT system without angles. PRE-UPT uncoupled walls coupled walls CIP-UPT without angles LA7 (PGA=.46g) 5 5 time (seconds) (d) the roof-drift time-history of the wall systems described above under the LA7 ground motion as follows: Fig. 8a CIP-UPT system with and without coupling; Fig. 8b PRE-UPT system with and without coupling; Fig. 8c CIP-EMB system; and Fig. 8d CIP-UPT system with the top and seat angles removed. The LA7 ground motion record is a %-in-5-year record from the SAC Steel Project (Somerville et al. 997) for a site with a stiff soil profile in Los Angeles. In order to represent the seismicity of the region for which the prototype walls were designed, the LA7 record from Somerville et al. (997) was scaled down to a peak acceleration of.46g (using a scale factor of.64). The dynamic analyses were conducted using a viscous damping ratio of ζ=% in the first and third modes of the structures (using Rayleigh damping). As a result of the significant increase in the lateral stiffness and strength of the walls, Figs. 8a and 8b show that the maximum roof-drifts of the coupled systems are smaller than the maximum

9 roof-drifts of the uncoupled systems. The ratio between the maximum roof-drift demand of the coupled and uncoupled walls is equal to.5 and.6 for the CIP-UPT and PRE-UPT systems, respectively. Furthermore, the uncoupled cast-in-place walls seem to accumulate some residual drift (residual drift.6% in Fig. 8a), whereas the coupled system does not accumulate any significant residual drift. This is even more pronounced in Fig. 8c for the cast-in-place walls coupled with embedded steel beams (residual drift.7%). The significant restoring force provided by the unbonded post-tensioned coupling beams is quite clear from these figures. The effect of the inelastic energy dissipation on the maximum roof-drift of the coupled walls can also be seen from Fig. 8. As compared to the CIP-EMB system, the maximum roof-drifts of the CIP-UPT system, the PRE-UPT system, and the CIP-UPT system without top and seat angles are increased by 8.8%,.%, and 5.%, respectively. Conclusions This paper presents a new type of hybrid coupled wall system for seismic regions using unbonded post-tensioning. An analytical model based on fiber elements is developed to represent the nonlinear hysteretic lateral load behavior of the system. Nonlinear static and nonlinear dynamic timehistory analyses of prototype walls are conducted. The effect of structural design parameters such as the amount of post-tensioning, beam properties, and wall properties on the behavior, including the amount of coupling, energy dissipation, and deformation capacity is investigated. Systems with precast concrete walls as well as cast-in-place reinforced concrete walls are considered. The expected seismic behavior is compared with the behavior of systems with embedded steel coupling beams and systems without coupling. The following conclusions are made based on the paper.. Unbonded post-tensioned steel beams can provide stable levels of coupling, similar to the levels of coupling that can be developed using embedded steel beams, between concrete walls over large nonlinear cyclic deformations. As a result of unbonding of the post-tensioning steel and gap opening along the beam-to-wall interfaces, little damage is expected to occur in the coupling beams and in regions of the walls near the beams. The coupled wall systems have a large self-centering capability and significant lateral stiffness, strength, and ductility.. The lateral strength and degree of coupling, as well as the lateral stiffness of the walls can be controlled by the amount of post-tensioning steel in the beams. The yielding of the beam posttensioning steel, which is significantly delayed due to unbonding, can be controlled by the initial stress in the post-tensioning steel. The design parameters can also be adjusted to prevent or delay the yielding of the coupling beam flanges in compression.. As a result of the significant increase in the lateral stiffness and strength of the walls, the maximum lateral displacements of unbonded post-tensioned coupled walls during an earthquake are expected to be smaller than the maximum displacements of comparable walls without coupling. 4. Unbonded post-tensioning provides a significant restoring force to the walls reducing the residual (i.e., permanent) lateral displacements after a large earthquake as compared to cast-in-place walls with embedded steel coupling beams and cast-in-place walls without coupling. 5. Unbonded post-tensioned hybrid coupled walls dissipate less energy than walls with embedded steel coupling beams resulting in larger maximum lateral displacements during an earthquake. Most of the energy dissipation in unbonded post-tensioned coupling beams is provided by the top and seat angles used at the beam-to-wall interfaces.

10 6. One of the most significant advantages of unbonded post-tensioned construction is that it can be used to couple existing walls as a part of a seismic retrofit and strengthening scheme. The post-tensioning tendons can be placed outside the walls for this purpose. Moreover, since the coupling beams are not embedded into the walls, the selection of the beam shape and size is not affected by the reinforcing details in the walls. This also leads to a simpler construction. Acknowledgements The investigation is funded by the National Science Foundation (NSF) under Grant No. CMS as a part of the U.S.-Japan Cooperative Earthquake Research Program on Composite and Hybrid Structures. The support of the NSF Program Director Dr. S. C. Liu and Program Coordinator Dr. S. Goel is gratefully acknowledged. The authors also thank the ACI Committee 5 on Composite and Hybrid Structures and Dr. K. Harries of the University of South Carolina for their comments and suggestions in the conduct of the work. The opinions, findings, and conclusions expressed in the paper are those of the authors and do not necessarily reflect the views of the NSF or the individuals and organizations acknowledged above. References Harries, K., Gong, B., and Shahrooz, B. (). Behavior and design of reinforced concrete, steel, and steel-concrete coupling beams. Earthquake Spectra, EERI, 6(4), Harries, K. (). Ductility and deformability of coupling beams in reinforced concrete coupled walls. Earthquake Spectra, EERI, 7(), Hibbitt, Karlsson, and Sorensen. (998). ABAQUS user s manual. Hibbitt, Karlsson, & Sorensen, Inc., Version 5.8. Kurama, Y., Sause, R., Pessiki, S., and Lu, L.W. (999). Lateral load behavior and seismic design of unbonded post-tensioned precast concrete walls. ACI Structural Journal, 96(4), 6-6. Prakash, V., Powell, G., and Campbell, S. (99). DRAIN-DX base program description and user guide; Version.. Rep. No. UCB/SEMM-9/7, Department of Civil Engineering, University of California, Berkeley, CA. Shen, Q. (expected ). Seismic analysis, behavior, and design of unbonded post-tensioned hybrid coupled walls. Ph.D. Dissertation in preparation, Department of Civil Engineering and Geological Sciences, University of Notre Dame, Notre Dame, IN. Shen, Q. and Kurama, Y. (expected ). Nonlinear behavior of post-tensioned hybrid coupled wall subassemblages. Accepted for the ASCE Journal of Structural Engineering. Somerville, P., Smith, N., Punyamurthula, S., and Sun, J. (997). Development of ground motion timehistories for phase of the FEMA/SAC steel project. Report SAC/BD-97/4, SAC Joint Venture, Sacramento, CA.