Journal of Engineering Mechanics. Submitted September 11, 2008; accepted July 7, 2009; posted ahead of print July 17, 2009. doi:10.1061/(ASCE)EM.1943-7889.0000071 CONCEPT AND FINITE ELEMENT MODELING OF NEW STEEL SHEAR CONNECTORS FOR SELF-CENTERING WALL SYSTEMS Richard S. Henry1, Sriram Aaleti2, Sri Sritharan, M.ASCE 3 and Jason M. Ingham, M.ASCE4 seismic resistance. ip t ABSTRACT: Self-centering precast concrete walls have been found to provide excellent Such systems typically exhibit low energy dissipation, requiring Ac N ce ot p C ted op M ye a di nu te s d cr supplementary dissipating components to improve their seismic performance. Mild steel shear connectors can provide an economical energy dissipating element. The design and analysis of steel shear connectors for a new precast wall system has been undertaken. A series of finite element analyses were conducted to investigate the behavior of different types of connectors. Emerged from these analyses is a oval shaped connector (O-Connector) that provided satisfactory force-displacement behavior and appeared well suited for the new wall system in high seismic regions. An extensive experimental test program was then conducted to verify the performance of the chosen O-Connector, which confirmed the expected response with sufficient energy dissipation. The experimental data demonstrated good correlation with the finite element model developed, providing satisfactory confidence in the finite element technique used for the development of the different connectors. 1 Ph.D Candidate, Dept. of Civil and Environmental Engineering, University of Auckland, Private Bag 92019, Auckland, New Zealand. Email: rhen048@ec.auckland.ac.nz 2 Ph.D Candidate, Dept. of Civil, Construction and Environmental Engineering, Iowa State University, Ames, IA 50011. Email: sriram@iastate.edu 3 Wilson Engineering Associate Professor and Assistant Chair, Dept. of Civil, Construction and Environmental Engineering, Iowa State University, Ames, IA 50011. Email: sri@iastate.edu 4 Associate Professor and Deputy Head, Dept. of Civil and Environmental Engineering, University of Auckland, Private Bag 92019, Auckland, New Zealand. Email: j.ingham@auckland.ac.nz Copyright 2009 by the American Society of Civil Engineers Journal of Engineering Mechanics. Submitted September 11, 2008; accepted July 7, 2009; posted ahead of print July 17, 2009. doi:10.1061/(ASCE)EM.1943-7889.0000071 Ac N ce ot p C ted op M ye a di nu te s d cr ip t CE Subject Headings: Connectors, Finite element method, Precast concrete, Shear walls. Copyright 2009 by the American Society of Civil Engineers Journal of Engineering Mechanics. Submitted September 11, 2008; accepted July 7, 2009; posted ahead of print July 17, 2009. doi:10.1061/(ASCE)EM.1943-7889.0000071 INTRODUCTION Structures utilizing self-centering characteristics have previously been found to demonstrate excellent seismic performance. Predominantly these structures use unbonded post-tensioning and are able to undergo large lateral deformations while minimizing damage to critical ip t structural members. The post-tensioning is designed to remain elastic during a design-level seismic event, thus providing the self-centering restoring force for the structure. However, Ac N ce ot p C ted op M ye a di nu te s d cr due to their elastically dominated response such structures generally exhibit low energy dissipation compared to traditional structures. Supplementary energy dissipating devices are typically needed to improve their seismic performance. The use of precast concrete walls as self-centering components was studied extensively during the PREcast Seismic Structural Systems (PRESSS) research program conducted during the 1990s (Priestley 1991). During the research program a jointed wall system using unbonded post-tensioning was developed and incorporated into the five storey test building (Nakaki et al. 1999; Priestley et al. 1999). The jointed wall system uses two of more precast concrete walls, post-tensioned to the foundation using unbonded tendons, and connected along the vertical joints with special shear connectors. These special shear connectors transfer forces between the precast panels and provide the primary source of energy dissipation by undergoing large inelastic deformations. As part of the PRESSS program, a study into the behavior of various shear connectors was conducted (Shultz and Magana 1996). The study included: notched shear plate (NSP), slotted flexural plate (SFP), inclined flat bar (IFB), X shaped axial plate (XAP), pinned tension struct (PTS), vertical joint friction (VJF) and U-shaped flexural plate (UFP). The experimental program examined the connectors’ behavior under a reverse cyclic vertical displacement Copyright 2009 by the American Society of Civil Engineers Journal of Engineering Mechanics. Submitted September 11, 2008; accepted July 7, 2009; posted ahead of print July 17, 2009. doi:10.1061/(ASCE)EM.1943-7889.0000071 history. The UFP, originally developed in the 1970’s (Kelly et al. 1972), was found by Shultz et al. to be one of the most suitable connectors, maintaining a stable force-displacement response up to large cyclic displacements while dissipating large amounts of energy. Following the study the UFP connector was included in the jointed wall system of the ip t PRESSS test building and it performed as expected (Priestley et al. 1999). Because it was constructed from stainless steel, the drawbacks of the UFP connectors are that it is expensive Ac N ce ot p C ted op M ye a di nu te s d cr and its behavior becomes dependent on strain history due to its isotropic hardening. PREWEC WALL SYSTEM While the PRESSS jointed wall system performed well during large scale testing, its implementation into real structures has been limited. This can be attributed to a reduction in moment resisting capacity when compared with a similar monolithic reinforced concrete wall, reducing its cost-effectiveness. To rectify this deficiency, a new system consisting of a Precast Wall with two steel or concrete End Columns (or PreWEC) has been developed (Aaleti and Sritharan 2007). All components are anchored to the foundation using unbonded post-tensioning and the special shear connectors are placed along the vertical joints to link the wall and column together horizontally. As with the previous jointed wall technology, under lateral loads the PreWEC system largely concentrates inelastic deformations at a single crack that opens up at the base of the wall and columns. The post-tensioning is unbonded to reduce the strain demand and is designed to remain elastic up to the design level drift, providing a restoring force to self-center the structure. Through this innovative arrangement of components, the PreWEC system can be designed to obtain a moment capacity equal to that of a comparable monolithic reinforced concrete wall, while maintaining the benefits of the pervious jointed wall system. Copyright 2009 by the American Society of Civil Engineers Journal of Engineering Mechanics. Submitted September 11, 2008; accepted July 7, 2009; posted ahead of print July 17, 2009. doi:10.1061/(ASCE)EM.1943-7889.0000071 PreWEC Connector Requirements The shear connectors in the PreWEC system have two functions. Firstly, transferring forces between the wall and column elements they contribute to the system moment capacity. Secondly, they undergo large inelastic deformations and thus act as the primary source of relative vertical displacements at the wall to column interface. ip t energy dissipation in the system. Under cyclic loading, the connectors are subjected to The relative vertical Ac N ce ot p C ted op M ye a di nu te s d cr displacements are much larger in one direction due to differences in the levels of uplift that occur at the wall and column toes. This leads to the connectors experiencing an unsymmetrical cyclic displacement history. Considering the unique behavior of the PreWEC system, an investigation into suitable shear connectors has been conducted. A PreWEC wall specimen was analyzed for use in a four story prototype structure (Aaleti and Sritharan 2007) and subsequently used to determine the requirements for the shear connectors. Based on a simplified design procedure, a target forcedisplacement envelope was established for the connector. The connector was required to maintain a stable force-displacement response, maximize energy dissipation, and be able to sustain relative vertical displacements of up to 60 mm with the peak strains generated limited to less than 0.10. This value was chosen to reflect a dependable strain limit for mild steel to prevent fracture due to low cycle fatigue when subjected to repeated seismic cyclic deformations (Priestley et al. 1996). Grade 50 steel has an ultimate tensile strain of ~0.18 under monotonic loading. Priestley et al. recommend that for seismic loading the strain softening portion of the stress-strain response should be ignored, resulting in an effective ultimate strain limit of ~0.12 for Grade 50 steel. Additionally, when subjected to reverse cyclic loading the sum of the maximum tension and compression strains should not exceed the effective ultimate strain limit. As explained, for the PreWEC system loading in the Copyright 2009 by the American Society of Civil Engineers Journal of Engineering Mechanics. Submitted September 11, 2008; accepted July 7, 2009; posted ahead of print July 17, 2009. doi:10.1061/(ASCE)EM.1943-7889.0000071 negative direction is limited, thus the maximum strain was assumed to be ~0.02 in the negative direction. This results in a maximum allowable strain of 0.10 in the positive loading direction. Lastly, the initial stiffness of the connector was not included as a critical design parameter because the initial stiffness of the connector does not affect the initial stiffness of ip t the PreWEC system. The connectors rely on a vertical displacement resulting from uplift occurring at the base of the wall which initiates after the decompression point, or point at Ac N ce ot p C ted op M ye a di nu te s d cr which non-linear behavior occurs (Aaleti and Sritharan 2007). Types of connector Based on the requirements for the shear connectors and previous studies conducted, a list of possible suitable connectors was collated. Connectors were assigned to categories based on the mechanism of plastic deformation:      direct shear mechanism direct tension/compression mechanism flexural mechanism friction mechanism a combination of the above After studying the results from the experimental investigation by Shultz and Magana (1996), connectors using direct shear or tension/compression mechanisms were deemed less suitable. While these connectors can perform extremely well, they tend to generate large strain demands, resulting in displacement capacities much less than the 60 mm requirement selected for the PreWEC system. Copyright 2009 by the American Society of Civil Engineers Journal of Engineering Mechanics. Submitted September 11, 2008; accepted July 7, 2009; posted ahead of print July 17, 2009. doi:10.1061/(ASCE)EM.1943-7889.0000071 In consideration of the above finding, flexural yielding was identified as the most desirable mechanism for a PreWEC connector because more indirect load paths lower the strain demand, resulting in a larger displacement capacity. The U-shaped flexural plate (UFP) uses a rolling and flexural yielding mechanism to accommodate large vertical displacements with ip t stable force-displacement behavior. Due to reasons stated earlier, stainless steel UFP’s were avoided in this study and more economical connectors made from grade A50 mild steel were Ac N ce ot p C ted op M ye a di nu te s d cr investigated. It was decided that the most suitable and economic connectors would be plate type connectors using flexural dominated yielding mechanisms. Detailed investigation into the performance and design of such connectors is detailed here, concentrating on flexural plate connectors with various slot or hole configurations, as well as J and oval-shaped flexural connectors. FINITE ELEMENT MODELING In selecting flexural dominated plate connectors as the most suitable option for the PreWEC system, a series of finite element analyses were conducted to investigate their performance. Finite element models (FEM), developed using ABAQUS (2007), were used to evaluate different types of connector and different configurations. This allowed the optimal design to be determined prior to an experimental investigation of that connector. All finite element models were constructed using 3D deformable elements. A steel plate material model was defined to simulate grade A50 steel properties. An idealized bilinear stress-strain material model was used based on an elastic modulus of 200 GPa, a yield stress of 345 MPa, an ultimate stress of 450 MPa, and an ultimate strain of 0.18. No failure criteria were used in the steel material definition, so the stress-strain response showed no strength loss Copyright 2009 by the American Society of Civil Engineers Journal of Engineering Mechanics. Submitted September 11, 2008; accepted July 7, 2009; posted ahead of print July 17, 2009. doi:10.1061/(ASCE)EM.1943-7889.0000071 beyond the ultimate strain of 0.18. This did not affect the results of the analysis because a strain limit of 0.10 was used to determine the ultimate displacement capacity for each connector. The steel material used a kinematic hardening model to simulate the steel cyclic behavior (Shen et al. 1995; Li et al. 2006). Meshing of the plates was completed using linear ip t 3D stress elements (i.e., C3D8R in ABAQUS) with 8 nodes and 1 integration point per element. The mesh size was approximately 5 mm. The plates were appropriately partitioned Ac N ce ot p C ted op M ye a di nu te s d cr to allow structured meshing to be used, resulting in rectangular dominated elements. Mesh widths were reduced around penetrations such as holes and slots to provide more realistic stress and strain predictions in the critical regions. The restraint conditions were idealized for the initial models to reduce computational time. The end face of the plate on the left side used a boundary condition to fix the displacement in all three degrees of freedom, while the end face on the right was coupled in all degrees of freedom to a reference point which was used to control the loading. The displacement controlled loading was applied by defining a displacement boundary condition on the reference point, restraining movement in all degrees of freedom except the vertical. The reversed cyclic loading history applied increasing vertical displacements on the reference point in steps of 10 mm up to a maximum 60 mm displacement. The FEM analyses produced force-displacement curves from the output at the reference point as well as the local stress and strain values for each element. Over thirty different FEM analyses were run to evaluate the performance of different flexural plate connectors. A selection of the most relevant and influential connectors that were modeled is included herein. These consist of slotted flexural plates (SFP), flexural plates with holes, J-shaped flexural plates and oval shaped flexural plates. Copyright 2009 by the American Society of Civil Engineers Journal of Engineering Mechanics. Submitted September 11, 2008; accepted July 7, 2009; posted ahead of print July 17, 2009. doi:10.1061/(ASCE)EM.1943-7889.0000071 Slotted Flexural Plate (SFP) Ac N ce ot p C ted op M ye a di nu te s d cr ip t The first connector modeled, SFP-1, consisted of a 127 mm by 177.8 mm, 6.35 mm thick plate with two 25.4 mm wide horizontal slots (Figure 1a). The FEM was constructed as previously described and the resulting deformed shape is shown in Figure 2a overlaid with the principal strain field when the connector was subjected to a 60 mm displacement. The flexural yielding occurring at the ends of the horizontal webs is clearly visible. As shown in Figure 3a, the predicted force-displacement response exhibited stable hysteretic loops with large amounts of energy dissipation from the flexural yielding mechanism. The predicted force-displacement response is plotted alongside the design envelope and it can be seen that SFP-1 falls about 10% below the required strength. The FEM does not include prediction of the failure mechanism and thus shows an idealized response with no strength degradation. Instead prediction of the displacement capacity was achieved by monitoring the peak strains generated at critical locations on the connector. FEM peak principal strains at 60 mm vertical displacement Figure 3a also includes predicted peak principal strains generated in the two most critical elements of the connector as a function of displacement. It is observed that the strain demand reached 0.35 (35%) at the required displacement of 60 mm, which is well beyond the ultimate strain limit of 0.10 chosen for the A50 steel. Using this strain limit, it is seen from Figure 3a that the displacement capacity of SFP-1 is 11 mm, which is well short of the target displacement of 60 mm. In an attempt to reduce the strain demand on the slotted flexural plate connector by allowing more flexural action, the aspect ratio was increased by lengthening the plate from 177.8 mm to 254 mm. SFP-2 (see Figure 1b) was modeled with this increased length, which, as expected, reduced the plastic rotations and corresponding strain demand. Figure 2b shows the FEM analysis output of SFP-2 at the peak 60 mm displacement with comparable behavior to SFP-1. The force-displacement response of this connector, shown in FEM peak principal strains at 60 mm vertical displacement Figure 3b, produced promising hysteretic loops; however the strength of the connector was 54% below the required strength. SFP-2 was successful in reducing the strain demand, with the predicted peak strain dropping to 0.2 and the displacement capacity at the 0.10 strain limit increased to 26 mm. While the connector strength could be increased by increasing the number of connectors or its thickness, increasing the displacement capacity was more critical. Copyright 2009 by the American Society of Civil Engineers Journal of Engineering Mechanics. Submitted September 11, 2008; accepted July 7, 2009; posted ahead of print July 17, 2009. doi:10.1061/(ASCE)EM.1943-7889.0000071 The strain demand could be reduced by further increasing the aspect ratio of the connector. However, a length greater than 254 mm would cause the connectors to be unsuitable given the dimensions of the prototype PreWEC system. Ac N ce ot p C ted op M ye a di nu te s d cr ip t Another option trialed was to change the orientation of the slots from horizontal to vertical. SFP-3 maintained the same plate dimensions as SFP-1, but the two horizontal slots were substituted with three vertical slots of the same width, see Figure 1c. The FEM was constructed in the same way and the resulting analysis output at 60 mm displacement is shown in Figure 2c. Flexural yielding is again apparent at the ends of the now vertical webs. The force-displacement prediction is plotted in FEM peak principal strains at 60 mm vertical displacement Figure 3c, the strength increased substantially from SFP-1 due to an increased number of locations for flexural yielding. SFP-3 produced a backbone curve that exceeded the required design envelope by 60%. However, due to the shortened length of the webs, the plastic rotation demands increased, leading to predicted peak strains higher than those observed for SFP-1. The vertical displacement capacity of the connector was reduced to just 8 mm. Flexural Plates with Holes One of the problems observed with the SFP is that the locations of plastic deformation are limited to small regions at the ends of the webs. To increase the potential locations for plastic deformation the slots were replaced with six 25.4 mm diameter holes for connector H-1, as shown in Figure 1d. The resulting FEM analysis is shown in Figure 2d with an increase in the locations of severe plastic deformation. As a result of this, it can be seen from the force-displacement prediction in FEM peak principal strains at 60 mm vertical displacement Figure 3d that the strength of the connector increased to three times the require design strength. Additionally, the hysteresis loops showed large amounts of energy dissipation. However, the strain demand was similar to SFP-1, peaking at around 0.35 during the 60 mm cycle. This resulted in a predicted displacement capacity of just 13 mm when the 0.10 strain Copyright 2009 by the American Society of Civil Engineers Journal of Engineering Mechanics. Submitted September 11, 2008; accepted July 7, 2009; posted ahead of print July 17, 2009. doi:10.1061/(ASCE)EM.1943-7889.0000071 limit was used. It was concluded that H-1 offered exceptional strength, but that the displacement capacity was still well below the requirements for the PreWEC system. Ac N ce ot p C ted op M ye a di nu te s d cr ip t Again, to reduce the strain demand the aspect ratio of the plate was increased by increasing its length. H-2, shown in Figure 1e had a length of 254 mm and contained eight holes of the same dimensions. The FEM at peak displacement, Figure 2e, showed evenly distributed plastic actions occurring over the entire plate. The forcedisplacement history plotted in FEM peak principal strains at 60 mm vertical displacement Figure 3e indicated that H-2 performed well, with stable hysteresis loops and strength about 2.5 times the required value. As expected the strain demand reduced, with peak strains limited to just 0.26 at the peak 60 mm displacement and an increased displacement capacity of 21 mm. Although H-2 produced promising results with greater than the required strength and energy dissipation, the displacement capacity was well short of the 60 mm required. Increasing the aspect ratio further to reduce the strain demand was again not considered a viable option for the PreWEC system. As mentioned before, the connector for PreWEC system experiences an unsymmetrical displacement loading. To take advantage of this, an innovative approach using inclined elliptical holes was trialed. The inclined elliptical holes were chosen as the strain demand would be much lower when the holes are stretched in the short axis providing an increased displacement capacity in the positive loading direction. Figure 1f shows the details of H-3, which consisted of the longer 254 mm length plate and included eight large elliptical holes orientated at 45 degrees. The FEM was constructed as previously described, but the loading protocol was modified. Instead of loading the connector symmetrically in both directions, it was decided to limit the negative displacement to 20 mm. This limit prevents loading to a large negative displacement that the unsymmetrical connector is not intended to be capable of withstanding. Figure 2f shows H-3 at the peak positive displacement of 60 mm and the opening of the elliptical holes is apparent. Looking at the force-displacement history in FEM peak principal strains at 60 mm vertical displacement Figure 3f the connector produced stable hysteresis loops and strength that exceeded the required envelope by over 40%. The strains were reduced with a predicted peak value being Copyright 2009 by the American Society of Civil Engineers Journal of Engineering Mechanics. Submitted September 11, 2008; accepted July 7, 2009; posted ahead of print July 17, 2009. doi:10.1061/(ASCE)EM.1943-7889.0000071 less than 0.3 at 60 mm and a displacement capacity of 25 mm using the 0.10 strain limit. Although successful in proving the viability of inclined elliptical holes, the displacement capacity was again well less than of the 60 mm design requirement. ip t J-Shaped Flexural Plate (J-Connector) After traditional flexural plate options failed to provide the required displacement capacity a Ac N ce ot p C ted op M ye a di nu te s d cr new style of connector was trialed. The J-shaped flexural plate (or J-Connector) can be cut from a steel plate, but the arrangement allows for a substantial reduction in strain demand as there is no direct tension path between the two ends resulting in flexurally dominant deformation. The modeled J-Connector shown in Figure 1g consisted of a 25.4 mm wide J shape cut from a 12.7 mm plate with square ends, each of which is welded on three sides. The unsymmetrical design of the J shape is aimed at minimizing the strain demand in the positive displacement direction. Again an unsymmetrical loading history was used with the negative displacement capped at 20 mm. The results from the FEM analysis that assumed no out-of-plane movement to the connector are displayed in Figure 2g at the 60 mm positive displacement. The flexural yielding mechanism is clearly visible in the two legs. Yielding was spread along almost the entire length of the J-Connector legs which significantly reduced the strain demand. The predicted strain demand at the critical elements, plotted in FEM peak principal strains at 60 mm vertical displacement Figure 3g, indicated that the connector can be subjected to the full 60 mm vertical displacement while only generating peak strains of 0.08. The side effect of this is that the plastic deformation is less effective and the resulting force-displacement showed a relatively small capacity. The hysteresis loops indicated extensive energy dissipation but the strength was well less than half the require design strength. Copyright 2009 by the American Society of Civil Engineers Journal of Engineering Mechanics. Submitted September 11, 2008; accepted July 7, 2009; posted ahead of print July 17, 2009. doi:10.1061/(ASCE)EM.1943-7889.0000071 Oval Shaped Flexural Plate (O-Connector) Ac N ce ot p C ted op M ye a di nu te s d cr ip t To increase the strength of the J-Connector while still maintaining the same flexural mechanism, an oval-shaped flexural plate O-Connector was considered. The first OConnector, shown in Figure 1h, was of similar dimensions to the J-Connector with a 25.4 mm width, 76.2 mm leg length and 12.7 mm thick plate. The connector is to be attached to a structural system by a 50.8 mm fillet weld on either side of each leg as shown in Figure 1h. The oval shape increased the potential location of plastic deformation from two to four legs resulting in twice the strength of the J-Connector. The FEM was constructed in the same way as the previous models. The welding conditions were again simulated by restraining the degrees of freedom along the welded faces of the O-Connector. The resulting strain field from the FEM analysis is shown in Figure 2h, indicating that plastic yielding occurred in the four legs of the O-Connector. The force-displacement history for O-Connector (FEM peak principal strains at 60 mm vertical displacement Figure 3h) showed twice the strength of the J-Connector, and about 13% below the require design strength. The strain demand was similar to the J-Connector with the flexural yielding spread along a large length of each leg. A peak strain of just over 0.08 occurred during the maximum 60 mm vertical displacement. The O-Connector successfully maintained the displacement capacity of the J-Connector with strength close to the design envelope. Summary of FEM analyses The FEM analysis results are summarized in Table 1. The table compares the eight connectors previously described with regard to their strengths and displacement capacities. The results indicate that the flexural plates with slots or holes can provide useful connectors when the displacement requirements are small, but are not suitable for the PreWEC system designed for high seismic regions. The FEM study concluded that the most suitable connector was the oval shaped flexural plate (O-Connector), which provided adequate strength while maintaining a large displacement capacity. Copyright 2009 by the American Society of Civil Engineers Journal of Engineering Mechanics. Submitted September 11, 2008; accepted July 7, 2009; posted ahead of print July 17, 2009. doi:10.1061/(ASCE)EM.1943-7889.0000071 OPTIMIZATION OF O-CONNECTOR To optimize the O-Connector and better understand its behavior, a further series of FEM analyses were conducted. In these analyses, the effect of changes in various dimensions on the connector response was investigated, the resulting strengths and displacement capacities ip t were compared. Ten different O-Connector options were modeled with changes including: Ac N ce ot p C ted op M ye a di nu te s d cr connector length, width, loop radius, loop section width and plate thickness. The FEMs generated to analysis the O-Connectors were more sophisticated than previous models. The connector itself was modeled as before but the mesh was modified to increase the number of elements across the section width. Additionally, instead of assuming that the weld was providing a fully fixed restraint, the weld itself was introduced to the model. The 9.5 mm fillet welds were modeled with 3D stress elements with a global mesh size of approximately 4 mm. The weld material used a bilinear stress-strain definition with an elastic modulus of 200 GPa, yield stress of 500 MPa, ultimate stress of 600 MPa, and ultimate strain of 0.10. In addition to the introduction of the weld into the model, steel plates were added to simulate the actual loading conditions. In a PreWEC wall system, the connectors would be welded to steel plates cast into the wall and an end column. The plates were modeled with 3D stress elements and a 20 mm mesh. The weld bond between the connector, weld and plates was modeled using a tie constraint between the adjacent surfaces. The loading was applied as described in the previous section, although now through the steel plates. Loading was applied in 10 mm reverse cyclic increments up to a 60 mm peak vertical displacement. After running several trials a revised O-Connector design was obtained that optimized all the dimensional considerations. The optimized O-Connector, shown in Figure 4a, consists of an increased 31.75 mm loop width, overall connector width of 152.4 mm and leg length of Copyright 2009 by the American Society of Civil Engineers Journal of Engineering Mechanics. Submitted September 11, 2008; accepted July 7, 2009; posted ahead of print July 17, 2009. doi:10.1061/(ASCE)EM.1943-7889.0000071 88.9 mm. This resulted in a higher strength than required so the plate thickness was reduced to 9.5 mm, which was a more economical option. The FEM constructed for the optimized OConnector can been seen in Figure 4b with the strain field plotted at 60 mm displacement. The predicted force-displacement history in Figure 5 showed once again stable hysteresis envelope. ip t loops with large amounts of energy dissipation and strength just below the required design The low strain demand was maintained with the peak strain of 0.08 at the Ac N ce ot p C ted op M ye a di nu te s d cr maximum 60 mm vertical displacement, which is 20% below the limiting strain of 0.10. The optimized O-Connector appeared to be well suited for the PreWEC system with satisfactory force-displacement backbone curve, sufficient energy dissipation and greater than required displacement capacity. EXPERIMENTAL VALIDATION To validate the FEM predictions and to confirm the expected connector performance when subjected to cyclic loading, two tests were performed on the O-Connector, namely A and B. In each test, four individual connectors were tested to maintain symmetry of the test setup. The dimensions of each connector were the same as those of the optimized O-Connector in Figure 4, but with a reduced 44.45 mm weld length on each side. The connectors were cut from 9.53 mm thick grade A50 steel plate using a laser cutting technique to reduce the residual stresses induced during the fabrication process. Test setup A test setup, visible in Figure 6, was designed using steel tubes and steel plates to apply the desired vertical loading to the O-Connectors. The test setup consists of an outer U-frame and a central H-section that represented the end columns and the wall in the PreWEC system, respectively. In order to eliminate any eccentric loading, four O-Connectors were welded Copyright 2009 by the American Society of Civil Engineers Journal of Engineering Mechanics. Submitted September 11, 2008; accepted July 7, 2009; posted ahead of print July 17, 2009. doi:10.1061/(ASCE)EM.1943-7889.0000071 between the U-frame and H-section and tested simultaneously. This additionally provided a more accurate average of the connector’s response. Loading was applied in a displacement control mode, with a relative vertical displacement applied to the O-Connectors. As well as the displacement and force output from the test machine, external LVDTs and strain gauges Ac N ce ot p C ted op M ye a di nu te s d cr FEM predicted maximum strains to occur in the O-Connector. ip t were used for data acquisition. Strain gauges were mounted at the locations at which the The loading protocol used for Test-A was developed to simulate the expected displacement history to which the connectors will be subjected during a reverse cyclic load test of the PreWEC-1 prototype specimen (Aaleti and Sritharan 2007). The displacement history consisted of an unsymmetrical reverse cyclic loading up to a maximum peak displacement of 50.8 mm in the positive direction. The displacements in the negative direction were capped at 12.7 mm. As explained previously the loading of the connectors in the PreWEC system is unsymmetrical and this value represents a conservative negative displacement limit. At each displacement level, the connectors were cycled three times to observe the stability of the force-displacement response. During Test-B, the loading protocol was modified and the connectors were subjected to a true displacement history measured during the large scale testing of the PreWEC-1 specimen (Sritharan et al. 2008). The recorded displacement history ended at a peak positive displacement of 53 mm, so the record was extrapolated to a peak of 71 mm until failure occurred to the connectors. To determine the true properties of the steel used for the connector’s three tensile test coupons were machined from the same 9.53 mm thick A50 steel plate used for the O-Connectors. The tensile tests was carried out according to ASTM standards for tension testing of metallic Copyright 2009 by the American Society of Civil Engineers Journal of Engineering Mechanics. Submitted September 11, 2008; accepted July 7, 2009; posted ahead of print July 17, 2009. doi:10.1061/(ASCE)EM.1943-7889.0000071 materials (ASTM Committee E-28 1991). Measured stress-strain results for two of the tensile coupons are plotted in Figure 7 with an enlargement of the 0-0.05 strain region. Detailed FEM of Test Configuration ip t To improve the accuracy of the analyses, improvements were made to the existing FEM by incorporating a model for the entire test rig as shown in Figure 8. The model of the actual O- Ac N ce ot p C ted op M ye a di nu te s d cr Connector remained the same but the grade A50 steel definition was changed from the assumed values to a true stress-strain curve based directly on the monotonic tensile tests. A combined kinematic/isotropic hardening model was used with a half cycle stress-strain input. The FEM of the test rig was created using 3D linear stress elements based approximately on a 20 mm quadrilateral mesh. The individual parts of the rig used tie constraints at the adjoining faces to simulate effects of welds. The bottom loading plate used a boundary condition restraint to simulate the grip, preventing movement to the surfaces of the plate in all directions. The top loading plate was constrained in all degrees of freedom to a reference point. The vertical displacements were applied via a series of displacement boundary conditions to the reference point. The analysis of this test setup was run and is reported with the experimental test results below. Experimental and Analytical Results The results from Test-A indicated that the O-connectors behaved as expected for the most part. It can be seen in the force-displacement response in Figure 9 that the connectors provide strong stable hysteresis loops with sufficient energy dissipation. The O-Connectors began to experience out-of-plane buckling during the 31.75 mm displacement cycle. As the out-ofplane bucking became more pronounced during large displacement cycles, see Figure 10, Copyright 2009 by the American Society of Civil Engineers Journal of Engineering Mechanics. Submitted September 11, 2008; accepted July 7, 2009; posted ahead of print July 17, 2009. doi:10.1061/(ASCE)EM.1943-7889.0000071 significant strength degradation occurred. To prevent this out of plane movement occurring in future tests, a retrofit to the connector was provided with a pair of steel restraining plates and a close of view of a plate in Test-B is shown in Figure 11. ip t The results from Test-B showed improved performance with no out-of-plane buckling occurring. The force-displacement loops, shown in Figure 12, were stable up to positive Ac N ce ot p C ted op M ye a di nu te s d cr displacements of 57 mm, with some strength degradation occurred during the cycle to 71 mm when the connectors started to fracture. The restraining plates were successful in preventing any out-of-plane buckling and allowed the full displacement capacity of the O-connector to be reached without any significant loss in strength. Ultimately, if the design predicted displacements in excess of 25 mm, the restraining plates would be required. The FEM analysis was run for the test specimens as described earlier, using the measured steel stress-stain properties from the material tests. A comparison of the predicted forcedisplacement response of a single connector in Test-B is plotted alongside the test results in Figure 12. It is observed that the FEM provides accurate prediction of the connector’s response. The FEM accurately predicts the loading and unloading stiffness and only marginally underestimates the connector’s strength. At a more local level, the predicted strain from an FEM element at the same location and direction as a mounted strain gauge is plotted for comparison in Figure 13. Only the values at the cycle peaks are shown to allow for a clear comparison. The experimental readings are terminated at strain of approximately 0.04 when the gauges reached their measuring limit. The prediction of the tensile strains is good with the FEM overestimating the strains by only 10% at a displacement of 45 mm. The FEM predicted a displacements capacity of 62.5 mm for this O-Connector at the 0.10 strain limit. Finally, the FEM predicted touching of the connectors in the test setup to occur at a Copyright 2009 by the American Society of Civil Engineers Journal of Engineering Mechanics. Submitted September 11, 2008; accepted July 7, 2009; posted ahead of print July 17, 2009. doi:10.1061/(ASCE)EM.1943-7889.0000071 displacement of ~60 mm (as seen in Figure 8b). Although the displacement exceeded 60 mm during the Test-B, touching was not observed because the connectors began to fracture during this load cycle, altering their displaced shape. ip t CONCLUSIONS The design and analyses of steel shear connectors for use in self-centering precast concrete Ac N ce ot p C ted op M ye a di nu te s d cr walls has been presented. The aim was specifically to determine a suitable connector for use in the recently developed PreWEC wall system. A review of previous studies indicated that the use of a flexural deformation mechanism would be the most suitable, providing stable hysteresis loops with large amounts of energy dissipation and increased displacement capacity. A series of finite element analyses were conducted to investigate the behavior of the following connector types: slotted flexural plates (SFP), flexural plates with holes, J-shaped flexural plates (J-Connector), and oval shaped flexural plates (O-Connector). After comparing the predicted force-displacement response and displacement capacity the OConnector was selected as the most suitable connector type for PreWEC systems in high seismic regions. However, other connectors may be used for PreWEC systems in low or moderate seismic regions or for connecting other precast elements demanding less displacement capacities (e.g., panel-to-panel connection in a precast flooring system and floor-to-wall-connection). Further FEM analyses were conducted to determine the optimum dimensions of the O-Connector. An experimental test program was conducted with two test specimens each containing four OConnectors. The experimental results validated the connector’s performance demonstrating Copyright 2009 by the American Society of Civil Engineers Journal of Engineering Mechanics. Submitted September 11, 2008; accepted July 7, 2009; posted ahead of print July 17, 2009. doi:10.1061/(ASCE)EM.1943-7889.0000071 excellent force-displacement characteristics with stable hysteresis loops and sufficient energy dissipation. The first test demonstrated the expected out-of-plane buckling of the connector and its influence on the force-displacement response of the connector. This problem was overcome by adding a simple restraining plate in the second test. The experimental results prediction for both the connector strength and critical strains. ip t also provided validation to the analysis of the FEM. The FEM was found to provide accurate The strain limit of 0.10 Ac N ce ot p C ted op M ye a di nu te s d cr imposed to predict the displacement capacity proved to satisfactorily predict the failure of the O-Connector. ACKNOWLEDGEMENTS The authors would like to acknowledge financial support provided by a) the New Zealand Tertiary Education Commission, b) the Research and Education Advanced Network New Zealand Ltd., and c) the U.S. National Science Foundation (NSF) through the International Research and Education in Engineering (IREE) program as a supplement to Grant No. CMS 0324559. The program directors administered the IREE funding at NSF were Drs. Win Aung and Douglas Foutch. Any opinions, findings, and conclusions expressed in this paper are those of the authors, and do not necessarily represent those of the sponsors. Copyright 2009 by the American Society of Civil Engineers Journal of Engineering Mechanics. Submitted September 11, 2008; accepted July 7, 2009; posted ahead of print July 17, 2009. doi:10.1061/(ASCE)EM.1943-7889.0000071 REFERENCES Aaleti, S., and Sritharan, S. (2007). "A precast wall with end columns (PreWEC) for seismic applications." Proc., 8th Pacific Conference on Earthquake Engineering, Singapore, Paper ip t 157. Ac N ce ot p C ted op M ye a di nu te s d cr ABAQUS user's manual version 6.7. (2007). Dassault Systèmes Simulia Corp. ASTM Committee E-28. (1991). "Standard test methods for tension testing of metallic materials." American Society for Testing and Materials, Annual book of ASTM standards. Kelly, J. M., Skinner, R. I., and Heine, A. J. (1972). "Mechanisms of energy absorption in special devices for use in earthquake resistant structures." Bulletin of the New Zealand Society for Earthquake Engineering, 5(3). Li, B., Reis, L., and de Freitas, M. (2006). "Simulation of cyclic stress/strain evolutions for multiaxial fatigue life prediction." International Journal of Fatigue, 28(5-6), 451-458. Nakaki, S. D., Stanton, J. F., and Sritharan, S. (1999). "An overview of the PRESSS five-story precast test building." PCI Journal, 44(2), 26-39. Priestley, M. J. N. (1991). "Overview of PRESSS research program." PCI Journal, 36(4), 5057. Priestley, M. J. N., Seible, F., and Calvi, G. M. (1996). Seismic design and retrofit of bridges, John Wiley and Sons, New York. Copyright 2009 by the American Society of Civil Engineers Journal of Engineering Mechanics. Submitted September 11, 2008; accepted July 7, 2009; posted ahead of print July 17, 2009. doi:10.1061/(ASCE)EM.1943-7889.0000071 Priestley, M. J. N., Sritharan, S., Conley, J. R., and Pampanin, S. (1999). "Preliminary results and conclusions from the PRESSS five-story precast concrete test building." PCI Journal, 44(6), 42-67. ip t Shen, C., Mamaghani, I. H. P., Mizuno, E., and Usami, T. (1995). "Cyclic behavior of structural steels. II: theory." Journal of Engineering Mechanics, 121(11), 1165-1172. Ac N ce ot p C ted op M ye a di nu te s d cr Shultz, A. E., and Magana, R. A. (1996). "Seismic behavior of connections in precast concrete walls." Proc., Mete A. Sozen Symposium, ACI SP 162, American Concrete Institute, Farmington Hills, MI. Sritharan, S., Aaleti, S., Henry, R. S., Liu, K. C., and Tsai, K. C. (2008). "Introduction to PreWEC and key results of a proof of concept test." Proc., Nigel Priestley Symposium, Kings Beach, CA. Copyright 2009 by the American Society of Civil Engineers Journal of Engineering Mechanics. Submitted September 11, 2008; accepted July 7, 2009; posted ahead of print July 17, 2009. doi:10.1061/(ASCE)EM.1943-7889.0000071 List of tables Table 1 – Summary of connector dimensions and capacities obtained from FEMs Figure 1 – Sketches of connectors modeled Ac N ce ot p C ted op M ye a di nu te s d cr Figure 2 – FEM peak principal strains at 60 mm vertical displacement ip t List of figures Figure 3 – Force-displacement and peak strain predictions for connector FEMs Figure 4 – Optimized O-Connector Figure 5 – Force-displacement and peak strain prediction for optimized O-connector Figure 6 – Experimental test setup used for O-Connector tests Figure 7 – Measured stress-strain results for tensile coupons Figure 8 – FEM of the test rig and O-Connectors Figure 9 – Measured force-displacement response of Test-A Figure 10 – Out-of-plane buckling of the connectors in Test-A at 50 mm displacement Figure 11 – Restrainer plate used to prevent out-of-plane buckling of the connector in Test-B Figure 12 – Comparison of measured and calculated force-displacement response of Test-B Figure 13 – Comparison of measured and calculated strain in a critical location of a connector Copyright 2009 by the American Society of Civil Engineers Journal of Engineering Mechanics. Submitted September 11, 2008; accepted July 7, 2009; posted ahead of print July 17, 2009. doi:10.1061/(ASCE)EM.1943-7889.0000071 Tables Table 1 – Summary of connector dimensions and capacities obtained from FEMs Figures ip t Figure 1 – Sketches of connectors modeled Figure 2 – FEM peak principal strains at 60 mm vertical displacement Ac N ce ot p C ted op M ye a di nu te s d cr Figure 3 – Force-displacement and peak strain predictions for connector FEMs Figure 4 – Optimized O-Connector Figure 5 – Force-displacement and peak strain prediction for optimized O-connector Figure 6 – Experimental test setup used for O-Connector tests Figure 7 – Measured stress-strain results for tensile coupons Figure 8 – FEM of the test rig and O-Connectors Figure 9 – Measured force-displacement response of Test-A Figure 10 – Out-of-plane buckling of the connectors in Test-A at 50 mm displacement Figure 11 – Restrainer plate used to prevent out-of-plane buckling of the connector in Test-B Figure 12 – Comparison of measured and calculated force-displacement response of Test-B Figure 13 – Comparison of measured and calculated strain in a critical location of a connector in Test-B Copyright 2009 by the American Society of Civil Engineers Figure 1 Journal of Engineering Mechanics. Submitted September 11, 2008; accepted July 7, 2009; posted ahead of print July 17, 2009. doi:10.1061/(ASCE)EM.1943-7889.0000071 177.8 254 25.4 38.1 25.4 25.4 25.4 25.4 127 25.4 127 R12.7 R12.7 Plate thickness = 6.35 mm Plate thickness = 6.35 mm (a) SFP-1 (b) SFP-2 178.8 177.8 R12.7 25.4 25.4 127 25.4 38.1 38.1 38.1 R12.7 Plate thickness =6.35 mm Plate thickness = 6.35 mm (c) SFP-3 (d) H-1 254 254 50.8 R12.7 50.8 127 50.8 50.8 127 50.8 60 45° 38.1 38.1 Plate thickness = 6.35 mm Plate thickness = 6.35 mm (e) H-2 63.5 57.2 (f) H-3 B 76.2 A 50.8 25.4 127 76.2 76.2 25.4 76.2 R38.1 R38.1 R63.5 Plate thickness = 12.7 mm (g) J-Connector 30 R63.5 Plate thickness = 12.7 mm (h) O-Connector Figure 1 – Sketches of connectors modeled Copyright 2009 by the American Society of Civil Engineers 127 Accepted Manuscript Not Copyedited 38.1 Figure 2 Journal of Engineering Mechanics. Submitted September 11, 2008; accepted July 7, 2009; posted ahead of print July 17, 2009. doi:10.1061/(ASCE)EM.1943-7889.0000071 (a) SFP-1 (b) SFP-2 (c) SFP-3 (e) H-1 (d) H-2 (f) H-3 Strains (a) to (f) (g) J-Connector (h) O-Connector Strains (g) & (h) Figure 2 – FEM peak principal strains at 60 mm vertical displacement Accepted Manuscript Not Copyedited Copyright 2009 by the American Society of Civil Engineers Figure 3 Journal of Engineering Mechanics. Submitted September 11, 2008; accepted July 7, 2009; posted ahead of print July 17, 2009. doi:10.1061/(ASCE)EM.1943-7889.0000071 (a) SFP-1 (b) SFP-2 (c) SFP-3 (d) H-1 (e) H-2 (f) H-3 (g) J-Connector (h) O-Connector Figure 3 – Force-displacement and peak strain predictions for connector FEMs Accepted Manuscript Not Copyedited Copyright 2009 by the American Society of Civil Engineers Figure 4 Journal of Engineering Mechanics. Submitted September 11, 2008; accepted July 7, 2009; posted ahead of print July 17, 2009. doi:10.1061/(ASCE)EM.1943-7889.0000071 88.9 50.8 88.9 31.8 88.9 R44.5 R76.2 Plate thickness = 9.35 mm (a) Dimensions (b) FEM at 60 mm disp. Figure 4 – Optimized O-Connector Accepted Manuscript Not Copyedited Copyright 2009 by the American Society of Civil Engineers Figure 5 Journal of Engineering Mechanics. Submitted September 11, 2008; accepted July 7, 2009; posted ahead of print July 17, 2009. doi:10.1061/(ASCE)EM.1943-7889.0000071 Figure 5 – Force-displacement and peak strain prediction for optimized O-connector Accepted Manuscript Not Copyedited Copyright 2009 by the American Society of Civil Engineers Figure 6 Journal of Engineering Mechanics. Submitted September 11, 2008; accepted July 7, 2009; posted ahead of print July 17, 2009. doi:10.1061/(ASCE)EM.1943-7889.0000071 H-section Connectors U-frame 50 mm Loading point Figure 6 –Experimental test setup used for O-Connector tests Accepted Manuscript Not Copyedited Copyright 2009 by the American Society of Civil Engineers Figure 7 Journal of Engineering Mechanics. Submitted September 11, 2008; accepted July 7, 2009; posted ahead of print July 17, 2009. doi:10.1061/(ASCE)EM.1943-7889.0000071 Figure 7 – Measured stress-strain results for tensile coupons Accepted Manuscript Not Copyedited Copyright 2009 by the American Society of Civil Engineers Figure 8 Journal of Engineering Mechanics. Submitted September 11, 2008; accepted July 7, 2009; posted ahead of print July 17, 2009. doi:10.1061/(ASCE)EM.1943-7889.0000071 (a) FEM assembly (b) FEM at 60 mm disp. Figure 8 – FEM of the test rig and O-Connectors Accepted Manuscript Not Copyedited Copyright 2009 by the American Society of Civil Engineers Figure 9 Journal of Engineering Mechanics. Submitted September 11, 2008; accepted July 7, 2009; posted ahead of print July 17, 2009. doi:10.1061/(ASCE)EM.1943-7889.0000071 Figure 9 –Measured force-displacement response of Test-A Accepted Manuscript Not Copyedited Copyright 2009 by the American Society of Civil Engineers Figure 10 Journal of Engineering Mechanics. Submitted September 11, 2008; accepted July 7, 2009; posted ahead of print July 17, 2009. doi:10.1061/(ASCE)EM.1943-7889.0000071 Figure 10 – Out-of-plane buckling of the connectors in Test-A at 50 mm displacement. Accepted Manuscript Not Copyedited Copyright 2009 by the American Society of Civil Engineers Figure 11 Journal of Engineering Mechanics. Submitted September 11, 2008; accepted July 7, 2009; posted ahead of print July 17, 2009. doi:10.1061/(ASCE)EM.1943-7889.0000071 Connector Restrainer Figure 11 – Restrainer plate used to prevent out-of-plane buckling of the connector in Test-B Accepted Manuscript Not Copyedited Copyright 2009 by the American Society of Civil Engineers Figure 12 Journal of Engineering Mechanics. Submitted September 11, 2008; accepted July 7, 2009; posted ahead of print July 17, 2009. doi:10.1061/(ASCE)EM.1943-7889.0000071 Figure 12 – Comparison of measured and calculated force-displacement response of Test-B Accepted Manuscript Not Copyedited Copyright 2009 by the American Society of Civil Engineers Figure 13 Journal of Engineering Mechanics. Submitted September 11, 2008; accepted July 7, 2009; posted ahead of print July 17, 2009. doi:10.1061/(ASCE)EM.1943-7889.0000071 Figure 13 – Comparison of measured and calculated strain in a critical location of a connector in Test-B Accepted Manuscript Not Copyedited Copyright 2009 by the American Society of Civil Engineers Table 1 Journal of Engineering Mechanics. Submitted September 11, 2008; accepted July 7, 2009; posted ahead of print July 17, 2009. doi:10.1061/(ASCE)EM.1943-7889.0000071 Connector Length (mm) Openings SFP-1 177.8 SFP-2 Strength Displacement capacity kN % Required Capacity mm % Required Capacity Horizontal slots 32 91 11 18 254 Horizontal slots 16 46 26 43 SFP-3 177.8 Vertical slots 56 160 8 13 H-1 177.8 Holes 108 309 13 22 H-2 254 Holes 86 246 21 35 H-3 254 Elliptical holes 50 143 25 42 J-Connector N/A N/A 15 43 60+ 100 O-Connector N/A N/A 31 87 60+ 100 Table 1 – Summary of connector dimensions and capacities obtained from FEM Accepted Manuscript Not Copyedited Copyright 2009 by the American Society of Civil Engineers