POST-TENSIONED MOMENT CONNECTIONS WITH A BOTTOM FLANGE FRICTION DEVICE FOR SEISMIC RESISTANT SELF- CENTERING STEEL MRFS

Transcription

1 4th International Conerence on Earthquake Engineering Taipei, Taiwan October 12-13, 2006 Paper No. 108 POST-TENSIONED OENT CONNECTIONS WITH A BOTTO FLANGE FRICTION DEVICE FOR SEISIC RESISTANT SELF- CENTERING STEEL RFS J.. Ricles 1, R. Sause 2,. Wolski 3, C-Y. Seo 4, and J. Iyama 5 ABSTRACT New earthquake-resistant structural steel moment resisting rame (RF) systems are being developed by a research group led by Lehigh University in collaboration with Princeton and Purdue Universities under the NSF unded Network or Earthquake Engineering Simulation Research (NEESR) program. These innovative sel-centering (SC) structural systems are designed to be damage-ree under the design basis earthquake (DBE). This paper presents the results o experimental studies on a posttensioned riction connection or a sel-centering moment resisting rame (SC-RF). The connection consists o a riction device placed below the beam bottom lange, in order to avoid intererence with the composite slab, with post-tensioned high strength strands running parallel to the beam. Tests on the connection show it to possess excellent deormation capacity, minimize inelastic deormations in other elements o the connection, and return the structure to its pre-earthquake position. The results o the experimental studies are presented. Based on the experimental results, analytical models were developed in OpenSees. The ormulation or these and a comparison with the experimental behavior o the connection are presented. Keywords: Friction, Post-tensioning, Sel-Centering oment Resisting Frame, Steel oment Connection INTRODUCTION Damage to conventional steel moment resisting rames (RFs) in recent earthquakes has prompted innovative design and construction methods. As an alternative to welded construction, Ricles et al. (2001) developed a post-tensioned (PT) steel beam-to-column moment connection utilizing highstrength steel strands running parallel to the beam with bolted top and bottom seat angles. Under 1 Bruce G. Johnston Proessor o Structural Engineering, ATLSS Center, Dept. o Civil and Environmental Engineering, Lehigh University, PA, USA, jmr5@lehigh.edu 2 Joseph T. Stuart Proessor o Structural Engineering, ATLSS Center, Dept. o Civil and Environmental Engineering, Lehigh University, PA, USA, rs0c@lehigh.edu 3 Graduate Research Assistant, ATLSS Center, Dept. o Civil and Environmental Engineering, Lehigh University, PA, USA, mew8@lehigh.edu 4 Visiting Research Scientist, ATLSS Center, Dept. o Civil and Environmental Engineering, Lehigh University, PA, USA, cys4@lehigh.edu 5 Associate Research Fellow, ATLSS Center, Dept. o Civil and Environmental Engineering, Lehigh University, PA, USA, jui205@lehigh.edu

2 seismic loading, gap opening at the top and bottom beam langes will occur resulting in yielding o the angles. Angle yielding is the main energy dissipating mechanism or the connection, and the damaged angles will need to be replaced ater the earthquake. Prior research has shown that riction energy dissipation devices are eective in PT precast concrete RFs (orgen and Kurama 2004) and PT steel RFs (Rojas et al. 2005). This motivated the urther development o a riction energy dissipating device or steel sel centering RFs (SC-RFs) which would not be damaged and thereore not need to be replaced ater a design-level earthquake. This paper presents the experimental study o a PT riction connection or SC-RFs. In addition, analytical models implemented using OpenSees are presented that describe the hysteretic behavior o the connection. Connection Details PT CONNECTION OVERVIEW AND BEHAVIOR To exploit the energy dissipation characteristics o riction devices in a beam-to-column PT connection, but eliminate intererence with the composite slab, a bottom lange riction device (BFFD) was designed and implemented. A schematic o a PT connection with a BFFD is shown in Fig. 1. (a) (b) A Slotted keeper angle Reinorcing plate PT strands Anchorage BFFD Beam PT strands Column Reinorcing plate Shim Plates Friction bolts with Belleville washers Slotted plate welded to beam bottom lange Brass riction plate at A slotted plate/angle interace Section A-A Angles bolted to column Figure 1. Schematic elevation: (a) rame with PT connections and BFFDs, and (b) connection details. The BFFD consists o a vertically oriented slotted plate that is shop welded to the bottom beam lange and two outer built-up angles (column angles) that are ield bolted to the column. Sandwiched between the two outer angles are brass riction plates on both sides o the slotted plate. The riction plate material is AST B-19 UNS hal-hard cartridge brass. High strength bolts (reerred to as riction bolts) with Belleville disc spring washers provide the normal orce, compressing the entire assembly together. The disc-spring washers help to maintain the riction orce as shown by Petty (1999) and orgen and Kurama (2004). The BFFD is intended to be delivered to the site attached to the beam, and, ollowing the post-tensioning o the beams and columns, the column angles are bolted to the column. The connection also includes shim plates to maintain good contact between the beam lange and column lange, lange reinorcing plates, and a keeper angle at the beam top lange to prevent transverse and lateral movement o the beam at the column ace. Slotted holes in the keeper angle accommodate the gap opening at the beam top lange. oment-rotation Behavior The lexural behavior o a PT connection with a BFFD is characterized by gap opening and closing at the beam-column interace under cyclic loading. A conceptual moment-relative rotation relationship (-θ r ) or a one-sided connection is shown in Fig. 2, where θ r is the relative rotation upon gap opening at the interace between the beam and column.

3 Under applied loading, the connection has an initial stiness similar to that o a ully restrained welded moment connection when θ r equals zero (events 0 to 2). Once the applied moment overcomes the posttensioning orce, decompression o the beam lange rom the column ace occurs. This moment is reerred to as the decompression moment. As the applied moment continues to increase, the connection rotation is resisted by the BFFD. Rotation and gap opening are imminent (at event 2) once the applied moment is equal to the sum o the moments due to the post-tensioning and BFFD. As shown in Fig. 2, depending on whether there is gap opening at the beam top or bottom lange, event 2 occurs at a dierent moment level. This is due to a dierence in the distance rom the riction orce resultant in the BFFD and the center o rotation (COR) o the connection upon gap opening, which results in a dierent moment contribution rom the BFFD. The stiness o the connection ater gap opening depends on the elastic axial stiness o the PT strands. As loading increases, the elongation o the strands produces additional orce, thus increasing the moment capacity o the connection. Yielding o the post tensioning may occur at event 4. Upon unloading at event 3, θ r remains constant, where at event 5, the kinetic riction orce is zero. Between events 5 and 6, the moment contribution rom the BFFD changes direction due to a reversal o riction orce in the BFFD, where at event 6 the reversal o the rictional orce is complete. Between events 6 and 7, θ r reduces to zero as the beam lange comes back in contact with the shim plate but is not compressed. Between events 7 and 8, the moment decreases to zero. Imminent Gap Opening Decompression 2 1 Unloading Strands Yield Both Beam Flanges in Contact with Column θ r - θ r Μ θ r Μ Figure 2. Conceptual cyclic moment-relative rotation response or a one-sided PT connection with a BFFD. Except or the dierence in moment capacity and energy dissipation, a complete reversal in the applied moment will result in a similar connection behavior in the opposite direction o loading, as shown in Fig. 2. As long as the strands remain elastic and no signiicant beam yielding occurs, the PT orce is preserved and the connection will sel-center upon unloading. oment Capacity The moment capacity o a PT connection with a BFFD is equal to = Pd F r (1) 2 where P, d 2, F, and r are shown in Fig. 3 and equal to the beam axial orce acting through the centroid o the beam section with the lange reinorcing plates, distance rom the centroid o the beam section

4 to the beam lange orces C t and C b (see Fig. 3), riction orce resultant in the BFFD, and the distance rom the COR o the connection to the riction orce F, respectively. The second term in Eq. (1) is associated with the moment contribution ( F ) due to the riction developed in the BFFD. For a positive moment, r (see Fig. 3(a)) is used or r in the second term in Eq. (1) to determine, while capacity r (see Fig. 3(b)) is used in the second term in Eq. (1) to determine the negative moment F rom the BFFD. F (a) (b) Column COR C C COR t t v t y Strands not shown or clarity F d 2 Figure 3. Free body diagrams o a PT connection with a BFFD: (a) COR and (b) COR -. In the prototype PT rame, the beam axial orce P is equal to the sum o the post tensioning orce T and any additional axial orce F d produced by the interaction o the PT rame with the loor diaphragm (Garlock 2002). In the test setup no loor diaphragm existed. At imminent gap opening, the connection moment IGO overcomes the moment due to P as well as the riction orce F. Assuming that prior to gap opening P is equal to the initial post tensioning orce T o in the PT strands, IGO is determined using Eq. (1): where r and r is utilized to determine v t F Centroid o bolts x Beam c.g. (rein. beam section) r d 1 F F x F y V Column P = T d F r (2) IGO o 2 IGO and IGO, respectively. IGO and IGO are the imminent gap opening moments under positive and negative moment, respectively. The maximum riction orce in the BFFD, F, is equal to: F = 2µn T (3) b b F v b d 2 COR - v b C b C b COR - y Strands not shown or clarity Centroid o bolts x Beam c.g. d 1 (rein. beam section) r - F F F - y F - x V - P In Eq. (3) µ is the coeicient o riction, n b is the number o riction bolts, and T b is the bolt tension in the riction bolts. The actor o 2 accounts or the two riction suraces. Upon developing imminent gap opening in the connection, P increases due to the increase in the post tensioning orce as the PT strands elongate. The gap opening is related to θ r, whereby the posttensioning orce T can be written as a unction o θ r :

5 kskb T = To θrd2 (4) k k where T o is the initial post tensioning orce, and k s and k b are the axial stiness o the PT strands and beam, respectively. Connection Rotation s b CONNECTION DESIGN In order to design the PT connection with a BFFD, the maximum expected relative rotation, θ r,max, under the design earthquake is required. θ r,max is used to determine the moment capacity as well as the length o the slotted holes in the BFFD. Under the design earthquake the riction bolts should not bear against the slot at θ r,max. Connection rotation data or several Design Basis Earthquake (DBE) and aximum Considered Earthquake (CE) ground motions analyzed by Rojas et al. (2005) were examined. A log normal distribution was assumed to determine the probability o exceedance (POE) o θ r or the DBE and CE. A value o θ r,max equal to radians was selected or the design o the BFFD connection. During the DBE and CE, the POE or θ r o radians is less than 1% and 25%, respectively. A summary o the slot design is presented in Wolski (2006). Energy Dissipation Ratio For the SC-RF to have satisactory response under the design earthquake, the BFFD must provide suicient energy dissipation. For the connection, the energy dissipation characteristics are expressed by the eective energy dissipation ratio, β E, which is the ratio o the actual energy dissipation to the energy dissipation or an elastic-plastic connection o the same strength. As previously discussed, the hysteretic behavior o a one-sided PT connection with a BFFD is un-symmetric, as shown in the -θ r curve given in Fig. 2. For a two-sided connection, the overall -θ r behavior would be symmetric. As a result o this unsymmetrical behavior, an eective energy dissipation ratio must be deined or the positive ( β ) and negative ( β ) moment regions, where: E E F IGO β E = ; F β E = (5a,b) IGO The eective energy dissipation ratio, β E, is calculated as the average value o β and β E. Seo and Sause (2005) determined that a structure with a value o β E = 0.25 had good seismic perormance. On that basis, a value o β E = 0.25 was used in the connection design or most cases. In order to achieve this value, and were set equal to 0.65 and 0.45 o the nominal plastic moment capacity, IGO IGO pn, o the unreinorced beam section, and F and F selected to be equal to 0.25 pn and 0.05 pn, respectively. This would result in a positive moment connection capacity o about 0.82 pn to be achieved at a θ r o radians based on Eq. (1). Garlock (2002) designed several SC-RFs, where the required connection capacity o an exterior PT connection ranged rom 0.60 pn to 0.90 pn under the DBE. Based on previous work by Petty (1999) and Rojas et al. (2005), the coeicient o riction or a brass-steel interace is taken to be equal to 0.4 in determining the riction orce F in the BFFD using Eq. (3). Test atrix EXPERIENTAL PROGRA The ocus o the experimental program was to evaluate the perormance o the BFFD in a PT connection. Thereore, the beam specimen, reinorcing plates, and post tensioning strands were E

6 designed so that no damage to these elements would occur during the test. The behavior o these elements is well understood rom prior experimental research by Garlock (2002). The test matrix or the study is given in Table 1, where θ r,max, β E,tar, T 0,exp, and F,exp are equal to the maximum θ r, target value or the eective energy dissipation ratio, measured initial post-tensioning orce, and riction orce based on the measured riction bolt orce and Eq. (3) in each test. The parameters in the experimental study included: riction orce level in the BFFD; loading protocol; bolt bearing in the BFFD; and the BFFD slotted plate weld detail. Two loading protocols were investigated in the tests: (1) a cyclically symmetric (CS see Fig. 6(a)); and an earthquake-based history (EQ see Fig. 6(b)). Both are discussed in more detail later. The same beam was used in all o the tests. In most cases, the riction bolts were retensioned beore each test. Table 1. Test atrix Test Experimental Parameter θ r,max Loading β E T 0,exp F,exp (rads) Protocol (%) (kn) (kn) 1 Reduced riction orce CS Design riction orce CS BFFD improved illet weld detail CS EQ Loading EQ Bolt bearing improved BFFD illet weld CS Assess column angle lexibility CS Bolt bearing BFFD CJP weld detail CS NEES actuator X X BFFD Reaction wall X Denotes lateral bracing PT strands Beam BFFD 3334 mm PT steel Beam Strong loor Column Column Figure 4. Test setup. Figure 5. Photo o PT connection with BFFD. Connection specimen and test setup A one-sided PT connection with a BFFD was investigated. The prototype beam section was a W36x300 which was scaled by a actor o 3/5 in the test specimen. The scaled beam was a Grade 50 W21x111 section (nominal yield stress o 345 Pa) with a length o 3334 mm. The scaled PT connection with a BFFD was tested in the setup shown in Fig. 4, in which the beam was rotated to the vertical position and the column rotated to the horizontal position. The area o interest o the connection is near the beam-column interace. The test setup boundary conditions included a nearly rigid bearing surace at the beam-column interace. Near the top o the beam an actuator with a cylindrical bearing imposed lateral displacements to the specimen, producing a moment at the beamcolumn interace. This orce boundary condition simulated a point o inlection in the beam in a RF subjected to lateral loading. Lateral bracing was provided at the top o the beam.

7 In an SC-RF, the elongation o each PT strand is the same due to the placement o the strands across multiple bays (see Fig. 1(a))To replicate this pattern o the PT strand elongation in the one-sided connection test specimen., it was necessary to concentrate the post tensioning strands at the centroid o the beam, as shown in Fig. 4. The post tensioning consisted o two 4-strand bundles and two 5-strand bundles, resulting in a total o 18 strands. The level o post tensioning orce ranged rom 2049 kn (Test 7) to 2227 kn (Test 1), see Table 1. The PT strands were not retensioned between tests. Dierences in the PT orce T o,exp between tests are due to a loss o post tensioned orce in prior tests. The BFFD had eight riction bolts ( mm diameter, A325 bolts). The riction orce in the tests ranged rom 242 kn (Test 1) to 541 kn (Test 7), see Table 1. The top and bottom lange reinorcing plates or the connection were designed in accordance with recommendations by Garlock (2002). As shown in Fig. 1(b), the bottom lange reinorcing plate was divided in hal and welded to the inside surace o the bottom lange in order to weld the slotted plate directly to the beam bottom lange. Shim plates were used to provide good contact between the beam langes and column lange. A photo o the test specimen connection region is given in Fig. 5. All tests had a illet weld detail attaching the BFFD slotted plate to the beam lange, except or Test 7, which used a CJP weld detail. Test 3 had an improved illet weld detail, consisting o larger illet welds. Instrumentation The instrumentation or the test specimen included: load cells to measure the applied lateral orce and the orce in each bundle o post tensioning strands; displacement transducers to measure the lateral displacement o the beam specimen, gap opening and closing at the beam-column interace; and strain gages to measure the strain in the column angles, slotted plate, and the beam langes. In addition, bolt strain gages were used in order to monitor the riction normal orce provided by the riction bolts o the BFFD. The beam in the connection region was white washed to provide visual evidence o yielding. Test Procedure The two loading protocols were included in the test program to evaluate the eect o the displacement history imposed by the actuator. In the cyclically symmetric (CS) loading protocol, an initial six cycles o pre-gap opening displacement were imposed, ollowed by displacements that produced the θ r history shown in Fig. 6(a), where the increment in θ r between cycles o dierent amplitude was radians. The irst six pre-gap opening displacement cycles were controlled using the actuator displacement as the control eedback. For the remaining cycles the control algorithm imposed actuator displacements such that the θ r target was provided (i.e., θ r was the control eedback). The displacement history or each test was imposed at a rate o 0.05 Hz, and was terminated when the θ r,max given in Table 1 was achieved. The θ r history or the earthquake-based (EQ) loading protocol is shown in Fig. 6(b), and has a θ r,max = radians. The specimen (Test 4) was loaded at a rate o one-eighth o real-time. The θ r history is based on the response computed by Rojas et al. (2005) o a PT connection in a 6-story SC- RF, where the structure was subjected to the west component o the ground motion recorded at the CHY036 station during the Chi-Chi earthquake record (scaled to the CE level). Rotation, θr (rads) (a) No. o Cycles Rotation, θr (rads) (b) Time (sec) Figure 6. θ r Loading protocols: (a) cyclically symmetric (CS), and (b) Chi-Chi earthquake (EQ).

8 EXPERIENTAL RESULTS Cyclic Loading The moment-rotation (-θ r ) response or Test 2 is shown in Fig. 7. The moment at imminent gap opening under positive moment IGO,exp and under negative moment IGO,exp was reached at 0.53 pn and 0.40 pn, respectively, where pn o the W21x111 beam is 1576 kn-m. This value is less than the targeted value o 0.65 pn and 0.45 pn and is due to diiculties in achieving the target level o post tensioning orce in the specimen due to the bundling o the strands into our groups, each with a large number o strands (a value o about 80% o the targeted orce in the PT strands was achieved). The BFFD provided a moment capacity o = 0.21 pn and = 0.08 pn, which was close to F, exp the targeted value o pn and 0.05 pn, respectively. As the connection rotates, the elastic stiness o the strands provides an increase in moment capacity. Test 2 developed a maximum connection moment (at the beam-column interace) max,exp o 0.70 pn at 0.03 radians. Ater each cycle o loading, θ r returned to zero and energy dissipation occurred when the connection was unloaded, demonstrating the sel-centering capability and energy dissipation o the connection. Good agreement is seen between the connection predicted -θ r response by Eq. (1) and the measured experimental response, where the width o the hysteresis loops in the prediction by Eq. (1) is based on 2 F and 2 F in the irst and third quadrants, respectively, in Fig. 7. Some discrepancy exists between the prediction and experimental result at the unloading portions o the hysteresis loops. This is due to column angle lexibility that is not considered in the theoretical prediction. The lexibility in the column angle was measured in Test 6, and is documented in Wolski (2006). The sum o the measured tension in the riction bolts or Test 2 is shown plotted against θ r in Fig. 8. In general, the Belleville washers enabled the pretension orce to be maintained reasonably well in the riction bolts. F, exp 1.0 Normalized oment, / p,n imminent gap opening imminent gap opening -0.5 Experimental Theoretical - Eq. (1) Rotation, θ r (rads) Friction Bolt Tension Force, N (kn) Rotation, θ r (rads) Figure 7. oment-rotation response, Test 2. Figure 8. Total riction bolt orce, Test 2. The post tensioning orce-rotation response or Test 2 is shown in Fig. 9. The theoretical posttensioning orce or the specimen is calculated using Eq. (4). Good agreement between the experimental and theoretical values is seen in Fig. 9. The initial post tensioning orce is 2209 kn at θ r = 0 radians and increases linearly to 2972 kn at a magnitude o θ r = radians. At the end o a loading cycle, the post tensioning orce returns to the original value. The specimen was designed so that the post tensioning would not yield up to a magnitude o θ r = radians. No signiicant damage to the beam occurred during the Test 2. However, due to the seating o the beam, bearing yielding at the end o the beam langes occurred. Also, some minor web yielding occurred at the location o the slotted plate. Neither o these aected the global response o the connection. Test 2 achieved a measured eective energy dissipation ratio β E,exp o 17.9%, based on the

9 cycle o loading with an amplitude o θ r = radians. A summary o the test results or Test 2, along with all tests, are given in Table PT Force, T (kn) 2500 Eq. (4) Experiment T o Normalized oment, / p,n Test 1 Test Rotation, θ r (rads) Rotation, θ r (rads) Figure 9. Post-tensioning orce, Test 2. Figure 10. oment-rotation response, Tests 1 and 2. Test IGO,exp a p. n Table 2. Experimental Results IGO,exp a p. n F,exp a p. n F,exp a p. n max,exp a p. n c β E,exp (%) b b b b 34.7 a p,n = nominal plastic moment capacity o W21x111 section equal to 1576 kn-m b Indicates tests where slotted plate went into bearing against riction bolts c Based on cycle with θ r = radians, prior to riction bolt bearing Eect o Friction Force The eect o the level o riction orce in the BFFD was evaluated by comparing the response o Tests 1 and 2. In Test 1, the riction orce F,exp was 242 kn, which was 51% o that o Test 2. It is evident in Fig. 10, where the -θ r response o the two tests is compared, that the reduction in riction orce resulted in a reduced energy dissipation and a smaller moment at imminent gap opening under both negative and positive moment, leading to a smaller moment capacity o the connection upon gap opening. The reduced moment capacity is due to the reduction in and, which in Test 1 F,exp F,exp were 52% and 50% o the corresponding values in Test 2. As given in Table 2, IGO,exp IGO,exp and IGO,exp and in Test 1 was 0.43 pn and 0.36 pn,, representing a 19% and 10% reduction compared to the IGO,exp o Test 2. The eective energy dissipation ratio β E,exp achieved by Test 1 was 14.5%, which is 54% o the β E,exp o Test 2.

10 Eect o Loading History The -θ r response or Test 4, with the EQ loading protocol is shown in Fig. 11, where it is compared to the response o Test 2. As stated earlier, the EQ θ r history is rom an analysis o a 6-story RF under the Chi-Chi earthquake record (scaled to the CE level). This history was chosen, since as shown in Fig. 6(b), there are several non-symmetrical cycles o θ r which occur throughout the record. The history is 80 seconds in length, and as noted previously the test was run eight times slower than real-time which resulted in a requency o loading o about 0.5 Hz. Test 2 had a loading requency o 0.05 Hz. In Fig. 11 the connection in Tests 2 and 4 appear to have perormed in a similar ashion to previous tests, and as beore, the sel-centering capability was demonstrated ater each cycle o loading. The rounding o the hysteresis loop upon unloading was observed again due to the lexibility o the BFFD column angles. Table 2 shows that the moments at imminent gap opening, IGO, exp, moment contribution rom the BFFD, F, exp, and the eective energy dissipation ratio β E,exp are nearly the same or the two tests. The connection in Test 4 developed a smaller maximum moment o 0.65 pn than Test 2 (where max,exp max,exp = 0.70 pn ) because Test 4 was subjected to a smaller value o θ r,max o radians. In general, the connection in Test 4 did not appear to be eected by the dierence in load history and loading rate, and perormed well under the applied earthquake loading. Normalized oment, / p,n Test 2 Test Rotation, θ r (rads) Normalized oment, / p,n Friction bolts go into bearing Friction bolts go into bearing Friction bolts ail in shear Test 2 Test Rotation, θ r (rads) Figure 11. oment-rotation response, Tests 2 and 4. Figure 12. oment-rotation response, Tests 2 and 7. Eect o Bolt Bearing The eect o bearing o the riction bolts on the edge o the slotted holes in the BFFD was evaluated by comparing the response o Tests 2 and 7. Shown in Fig. 12 is the -θ r response or Tests 2 and 7. The initial orce T o,exp in the PT strands was slightly smaller in Test 7 (2049 kn), while the riction orce F,exp due to the riction bolts was slightly higher (541 kn) in Test 2, see Table 2. As a result the moment contribution rom the BFFD, F,exp and F,exp, and at imminent gap opening, IGO,exp and IGO,exp, were slightly larger in Test 7 than in Test 2 (see Table 2 and Fig. 12). Fig. 12 shows that when the bolts went into bearing, which initially occurred at a magnitude o θ r o about radians, the moment capacity o the connection would initially increase due to the bolt bearing orce developed in the BFFD. The result o bolt bearing led to deorming the riction bolts, where upon unloading the connection the bolts were elongated and bent, and thereore suered a loss in their pretension orce. The bent bolts did not go into bearing until the maximum amplitude o θ r rom the previous cycles was surpassed. Consequently, in subsequent cycles o the same amplitude o θ r, the riction orce in the BFFD would be reduced due to the loss o tension orce in the riction bolts, leading to a loss in moment capacity o the connection. In subsequent cycles with a greater magnitude o θ r, the riction

11 bolts would go into bearing and increase the moment developed in the BFFD. The loss in tension in the riction bolts led to a pinching in the hysteretic response and a reduction in the energy dissipation capacity o the BFFD. In Test 7, the CJP weld detail or the BFFD attachment to the beam lange resulted in the bolt shear capacity being achieved without ailure o the BFFD weld detail. Upon shearing the bolts in Test 7, which occurred at θ r = radians, the connection did not dissipate energy but continued to sel center due to the post tensioning orce in the PT strands remaining intact. In Test 5, which used a illet weld detail to attach the slotted plate o the BFFD to the beam, the illet weld developed a low cycle atigue ailure when the riction bolts went into bearing. ANALYTICAL ODELING OF PT CONNECTIONS WITH A BFFD Analytical models o a PT connection with a BFFD were developed using the OpenSees computer program (azzoni et al., 2006). Since the riction orce in the BFFD changes direction due to the kinematics under the cyclic loading, it was necessary to consider a two-dimensional ormulation to model the riction orce in the BFFD in order to obtain the correct direction o the riction orce resultant. The analytical model or the rictional orce resultant included a bidirectional plasticitybased model, and a directional velocity-based model. The experimental data was used to evaluate the accuracy o each o these models. The ormulations or each are described below. Bidirectional Plasticity-Based odel The two components o the riction orce in the BFFD (see Fig. 3) deine the riction orce vector F, where F = {F x, F y } T. The direction o the riction orce resultant is equal to that o the instantaneous velocity vector,, where: F = F (6) The orce-deormation behavior or the riction orce is modeled using an elasto-perectly plastic model with a large elastic stiness, k i. The maximum riction orce that can develop, F, was given previously by Eq. (3), and is equated to the yield orce F y to deine the diameter o the yield surace. The yield unction Φ(F ) or the bi-directional plasticity model is: ( F ) = F Fy Φ (7) where F is determined rom Eq. (8): F ( v ) k (8) = i v p In Eq. (8) v and v p are the total and the plastic deormation vectors, respectively. The circular yield surace provides the magnitude o F during plastic low, where according to the associated plastic low rule, the incremental plastic deormation vector dv p is normal to the yield surace during plastic low: ( F ) ( F ) Φ F d v p = λ = λ = λ n (9) F In Eq. (9) n is the outward normal vector o the yield surace deined by Φ(F ), and λ is the magnitude o plastic deormation, where λ 0. Eq. (9) indicates that the direction o the incremental plastic deormation vector is in the same direction as F during plastic low. Hence, rom Eq. (6), the ollowing can be written:

12 F = F F dv dv p p (10) Eq. (10) is an approximation since the bidirectional plasticity model ormulation does not result in truly rigid plastic behavior, which Eq. (6) assumes. A more detail discussion about the bidirectional plasticity model can be ound in Huang (2002). Directional Incremental Velocity-Based odel From Eq. (6), the dierence F in the riction orce vector F at time t and t t can be expressed as: ( t t) ( t t) F = F ( t t) F ( t) = F (11) () t Perorming a Taylor series expansion o Eq. (11) at =0, and truncating the higher order terms yields the ollowing relationship between F and the change in the instantaneous velocity : () t 2 F y x F 2 3 x y v & x y = C (12) where is { v & x, y } T, and t t t. C In Eq. (12) can be treated as a damping matrix in the analysis. An analysis using the directional velocity-based model involves determining the increment value F and summing the result with the riction orce vector rom the beginning o the time step to obtain the riction orce at the end o the time step. Description o Analytical odels equals ( ) - ( ) An analytical model or the post tensioned subassembly test specimen was developed using the OpenSees computer program. This model was used to conduct cyclic nonlinear pushover analyses o the test specimen. In this model, the nonlinear beam column element in OpenSees (nonlinearbeamcolumn) was used to model the beam and the column. The eect o axial, lexural and shear deormations are included in this element. The elastic beam column element (elasticbeamcolumn) with released end moments was used to model the post tensioning strands. Gap opening between the beam langes and the column ace was modeled using two zero length elements (zerolength) located at the beam langes at the beam-to-column interace. The elements were assigned rigid elastic compressive stress and zero tensile stress properties to act as gap elements. The panel zone was modeled using an inelastic rotational spring zero length element and multi-point constraints (Ricardo, 2006). The column angles in the BFFD were modeled with a zero length section element (zerolengthsection). The zero length surace element (surace) was used to model the bidirectional riction orce in the BFFD, where the bidirectional riction orce is based on the bidirectional plasticity model described above. Alternatively, the zero length element was used to model the bidirectional riction orce in accordance with the directional incremental velocity-based model described above. A modulus o elasticity E o 200 GPa was used or the beam and column elements o the analytical model with a large yield stress, thereby assuming elastic behavior o the members during the analysis. For the post tensioning strand element, an E o GPa was used. For the column angle element, the stiness observed rom the result o Test 6 was used to deine the property in the y-direction o the BFFD (see Fig. 3). The stiness in the x-direction o the BFFD model was determined to be twice that in the y-direction, by matching the -θ r relationship o the analytical prediction with that o the test

13 result. A large initial stiness was assumed in the BFFD element ( 150 times the column angle element in the y-direction), with the yield orce (i.e., maximum riction orce) set equal to F,exp. The construction sequence o the test specimen had the post tension orce applied beore the BFFD is installed. Consequently, the BFFD element was activated in the OpenSees model ater the initial post tensioning orce was applied to the model. Cyclic loading analyses were subsequently perormed using the displacement history that was applied to the test specimen. In the model with the bidirectional plasticity ormulation, the cyclic loading analysis was perormed using a static analysis procedure. However, the model with the directional incremental velocity-based ormulation required a transient dynamic analysis in order to compute the velocity. In this model, a mass was placed at the node corresponding to the loading point in the test specimen (i.e., at the end o the beam), and a ground acceleration history was applied to the base o the test specimen to achieve the target displacement amplitudes at the end o the beam. A small mass was added to the nodes o the BFFD element and mass proportional damping was used in order to avoid high requency errors in the velocity at these nodes. Validation o odels The analytical models with the BFFD based on the bidirectional plasticity and the directional velocity were veriied by conducting analyses o the test specimens, and comparing the computed response with the experimental behavior. The -θ r results rom the analysis o Test 2 are given below in Fig. 13, where they are compared to the experimental results o Test 2. These igures show that the analytical models adequately capture the -θ r behavior o the connection in Test 2. The reduction in stiness in the -θ r response due to column angle lexibility during unloading is well captured by both analytical models and so is the energy dissipation capacity. One characteristic that both models have in common is that they do not accurately capture the additional increase in moment capacity with increasing cyclic amplitude o θ r. This is due to using a ixed location or the contact point where the gap elements were deined in the model. In the experiment it was observed that the COR moves slightly toward the extreme iber o the reinorced beam lange during the tests as the beam rotates, causing the distance between the COR and the riction orce resultant in the BFFD, and thereore connection moment to increase as the connection rotates with increasing θ r. Normalized oment /p,n Experimental Analytical Normalized oment /p,n Rotation θ r (rad) Rotation θ r (rad) (a) Bidirectional plasticity model (b) Directional incremental velocity model Experimental Analytical Figure 13. Comparison o -θ r relationships o analytical models and experimental response rom Test 2. SUARY AND CONCLUSIONS A post-tensioned moment connection with a bottom lange riction device (BFFD) or use in a selcentering moment resisting rame (SC-RF) was developed and experimentally investigated. The test

14 results demonstrate that the BFFD provides excellent energy dissipation while the PT connection provides stiness, strength, and deormation capacity under cyclic and earthquake loading. In addition, the connection sel-centers without residual drit as long as the PT strands remain elastic. During the tests, the magnitude o maximum riction orce remained relatively constant and the brass riction plates provided a good riction surace. It was also observed that the simple design model presented needs to be improved in order to include the lexibility o the column angles in the BFFD. The models implemented using OpenSees enabled the column angle lexibility to be accounted or, and consequently improved predictions or the connection moment-relative rotation. The OpenSees connection models are currently being used to analyze SC-RF systems with PT connections with a BFFD under seismic loading conditions. These analyses will be used to assess the behavior o the models in a SC-RF and to study the seismic perormance o these rames. ACKNOWLEDGEENTS This paper is based upon work supported by the National Science Foundation under Grant No. CS , within the George E. Brown, Jr. Network or Earthquake Engineering Simulation Research (NEESR) program and through Grant No. CS (NEES Consortium Operation). Any opinions, indings, conclusions, and recommendations expressed in this material are those o the authors and do not necessarily relect the views o the National Science Foundation. REFERENCES Garlock, Full-Scale Testing, Seismic Analysis, and Design o Post-Tensioned Seismic Resistant Connections or Steel Frames. Ph.D. Dissertation, Department o Civil and Environmental Engineering. Lehigh University, Bethlehem, PA. Huang, W-H Bi-directional Testing, odeling, and System Response o Seismically Isolated Bridges. Ph.D. Dissertation, Department o Civil and Environmental Engineering. University o Caliornia, Berkeley, CA. Herrera, R Seismic Behavior o Concrete Filled Tube Column-Wide Flange Beam Frames. Ph.D. Dissertation, Dept. o Civil and Environmental Engineering. Lehigh Univ., Bethlehem, PA. azzoni, S., ackenna, F., and Fenves, G. L., OpenSees Command Language anual, PEER, University o Caliornia, Berkeley, CA. orgen, B. and Kurama, Y.C A Friction Damper or Post-Tensioned Precast Concrete oment Frames, PCI Journal, 49(4), Petty, G Evaluation o a Friction Component or a Post-Tensioned Steel Connection..S. Thesis, Department o Civil and Environmental Engineering. Lehigh University, Bethlehem, PA. Ricles, J., Sause, R., Garlock,., and Zhao, C Post-Tensioned Seismic-Resistant Connections or Steel Frames, Journal o Structural Engineering, 127(2), Rojas, P., Ricles, J.. and Sause, R Seismic Perormance o Post-Tensioned Steel RFs with Friction Devices, Journal o Structural Engineering, 131(4), Seo, C.-Y. and Sause, R Ductility Demands on Sel-Centering Systems under Earthquake Loading, ACI Structural Journal, 102(2), Wolski, Experimental Evaluation o a Bottom Flange Friction Device or a Sel Centering Seismic oment Resistant Frame with Post-Tensioned Steel oment Connections.S. Thesis, Department o Civil and Environmental Engineering. Lehigh University, Bethlehem, PA.