4th International Conference on Earthquake Engineering Taipei, Taiwan

October 12-13, 2006

Paper No. 108

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

CENTERING STEEL MRFS

J. M. Ricles1, R. Sause2, M. Wolski3, C-Y. Seo4, and J. Iyama5

ABSTRACT

New earthquake-resistant structural steel moment resisting frame (MRF) systems are being developed by a research group led by Lehigh University in collaboration with Princeton and Purdue Universities under the NSF funded Network for Earthquake Engineering Simulation Research (NEESR) program. These innovative self-centering (SC) structural systems are designed to be damage-free under the design basis earthquake (DBE). This paper presents the results of experimental studies on a post-tensioned friction connection for a self-centering moment resisting frame (SC-MRF). The connection consists of a friction device placed below the beam bottom flange, in order to avoid interference with the composite slab, with post-tensioned high strength strands running parallel to the beam. Tests on the connection show it to possess excellent deformation capacity, minimize inelastic deformations in other elements of the connection, and return the structure to its pre-earthquake position. The results of the experimental studies are presented. Based on the experimental results, analytical models were developed in OpenSees. The formulation for these and a comparison with the experimental behavior of the connection are presented. Keywords: Friction, Post-tensioning, Self-Centering Moment Resisting Frame, Steel Moment Connection

INTRODUCTION Damage to conventional steel moment resisting frames (MRFs) 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 high-strength steel strands running parallel to the beam with bolted top and bottom seat angles. Under

1 Bruce G. Johnston Professor of Structural Engineering, ATLSS Center, Dept. of Civil and Environmental Engineering, Lehigh University, PA, USA, jmr5@lehigh.edu 2 Joseph T. Stuart Professor of Structural Engineering, ATLSS Center, Dept. of Civil and Environmental Engineering, Lehigh University, PA, USA, rs0c@lehigh.edu 3 Graduate Research Assistant, ATLSS Center, Dept. of Civil and Environmental Engineering, Lehigh University, PA, USA, mew8@lehigh.edu 4 Visiting Research Scientist, ATLSS Center, Dept. of Civil and Environmental Engineering, Lehigh University, PA, USA, cys4@lehigh.edu 5 Associate Research Fellow, ATLSS Center, Dept. of Civil and Environmental Engineering, Lehigh University, PA, USA, jui205@lehigh.edu

seismic loading, gap opening at the top and bottom beam flanges will occur resulting in yielding of the angles. Angle yielding is the main energy dissipating mechanism for the connection, and the damaged angles will need to be replaced after the earthquake. Prior research has shown that friction energy dissipation devices are effective in PT precast concrete MRFs (Morgen and Kurama 2004) and PT steel MRFs (Rojas et al. 2005). This motivated the further development of a friction energy dissipating device for steel self centering MRFs (SC-MRFs) which would not be damaged and therefore not need to be replaced after a design-level earthquake. This paper presents the experimental study of a PT friction connection for SC-MRFs. In addition, analytical models implemented using OpenSees are presented that describe the hysteretic behavior of the connection.

PT CONNECTION OVERVIEW AND BEHAVIOR Connection Details To exploit the energy dissipation characteristics of friction devices in a beam-to-column PT connection, but eliminate interference with the composite slab, a bottom flange friction device (BFFD) was designed and implemented. A schematic of a PT connection with a BFFD is shown in Fig. 1.

Figure 1. Schematic elevation: (a) frame with PT connections and BFFDs, and (b) connection details.

The BFFD consists of a vertically oriented slotted plate that is shop welded to the bottom beam flange and two outer built-up angles (column angles) that are field bolted to the column. Sandwiched between the two outer angles are brass friction plates on both sides of the slotted plate. The friction plate material is ASTM B-19 UNS half-hard cartridge brass. High strength bolts (referred to as friction bolts) with Belleville disc spring washers provide the normal force, compressing the entire assembly together. The disc-spring washers help to maintain the friction force as shown by Petty (1999) and Morgen and Kurama (2004). The BFFD is intended to be delivered to the site attached to the beam, and, following the post-tensioning of 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 flange and column flange, flange reinforcing plates, and a keeper angle at the beam top flange to prevent transverse and lateral movement of the beam at the column face. Slotted holes in the keeper angle accommodate the gap opening at the beam top flange. Moment-Rotation Behavior The flexural behavior of a PT connection with a BFFD is characterized by gap opening and closing at the beam-column interface under cyclic loading. A conceptual moment-relative rotation relationship (M-θr) for a one-sided connection is shown in Fig. 2, where θr is the relative rotation upon gap opening at the interface between the beam and column.

(a)

PT strands

Anchorage

Beam

ColumnBFFD

Slotted keeper angle

A

Reinforcing plate

(b)

A

Reinforcing plate

Slotted plate welded to beam bottom flange

Brass friction plate at slotted plate/angle interface

PT strands

Friction bolts with Belleville

washers

Section A-A

“Angles” bolted to column

Shim Plates

Under applied loading, the connection has an initial stiffness similar to that of a fully restrained welded moment connection when θr equals zero (events 0 to 2). Once the applied moment overcomes the post-tensioning force, decompression of the beam flange from the column face occurs. This moment is referred 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 of 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 flange, event 2 occurs at a different moment level. This is due to a difference in the distance from the friction force resultant in the BFFD and the center of rotation (COR) of the connection upon gap opening, which results in a different moment contribution from the BFFD.

The stiffness of the connection after gap opening depends on the elastic axial stiffness of the PT strands. As loading increases, the elongation of the strands produces additional force, thus increasing the moment capacity of the connection. Yielding of the post tensioning may occur at event 4.

Upon unloading at event 3, θr remains constant, where at event 5, the kinetic friction force is zero. Between events 5 and 6, the moment contribution from the BFFD changes direction due to a reversal of friction force in the BFFD, where at event 6 the reversal of the frictional force is complete. Between events 6 and 7, θr reduces to zero as the beam flange comes back in contact with the shim plate but is not compressed. Between events 7 and 8, the moment decreases to zero.

7

2

M

θr0

1

2

3

5

6

7

8

3 4 5 6

Imminent Gap Opening

Decompression

Both Beam Flanges in Contact with Column

Strands Yield Unloading

θr-

Μ +

θr+

Μ −

4

Figure 2. Conceptual cyclic moment-relative rotation response for a one-sided PT connection with a BFFD.

Except for the difference in moment capacity and energy dissipation, a complete reversal in the applied moment will result in a similar connection behavior in the opposite direction of loading, as shown in Fig. 2. As long as the strands remain elastic and no significant beam yielding occurs, the PT force is preserved and the connection will self-center upon unloading. Moment Capacity

The moment capacity M of a PT connection with a BFFD is equal to

rFPdM f2 += (1)

where P, d2, Ff, and r are shown in Fig. 3 and equal to the beam axial force acting through the centroid of the beam section with the flange reinforcing plates, distance from the centroid of the beam section

to the beam flange forces Ct and Cb (see Fig. 3), friction force resultant in the BFFD, and the distance from the COR of the connection to the friction force Ff, respectively. The second term in Eq. (1) is associated with the moment contribution (MFf) due to the friction developed in the BFFD. For a positive moment M+, r+ (see Fig. 3(a)) is used for r in the second term in Eq. (1) to determine +

FfM ,

while −r (see Fig. 3(b)) is used in the second term in Eq. (1) to determine the negative moment

capacity −FfM from the BFFD.

(a) (b)

Figure 3. Free body diagrams of a PT connection with a BFFD: (a) COR+ and (b) COR-.

In the prototype PT frame, the beam axial force P is equal to the sum of the post tensioning force T and any additional axial force Ffd produced by the interaction of the PT frame with the floor diaphragm (Garlock 2002). In the test setup no floor diaphragm existed. At imminent gap opening, the connection moment MIGO overcomes the moment due to P as well as the friction force Ff. Assuming that prior to gap opening P is equal to the initial post tensioning force To in the PT strands, MIGO is determined using Eq. (1):

rFdTM f2oIGO += (2)

where r+ and −r is utilized to determine +IGOM and −

IGOM , respectively. +IGOM and −

IGOM are the imminent gap opening moments under positive and negative moment, respectively. The maximum friction force in the BFFD, Ff, is equal to:

bbf Tn2µF = (3)

In Eq. (3) µ is the coefficient of friction, nb is the number of friction bolts, and Tb is the bolt tension in the friction bolts. The factor of 2 accounts for the two friction surfaces. Upon developing imminent gap opening in the connection, P increases due to the increase in the post tensioning force as the PT strands elongate. The gap opening is related to θr, whereby the post-tensioning force T can be written as a function of θr:

Ff

vb vb Cb

d2

Ff Cb

M - P

V

d1

Ff F -fy F -fx

r -

Beam Column

Centroid of bolts

COR- COR-

Strands not shown for clarity

c.g. (rein. beam section)

Ff Ff

Ct Ct

vt

vt

M+

P

V

d2

Ff F+

fx F+

fy

r+ d1

Beam Column

Centroid of bolts

COR+ COR+

c.g. (rein. beam section)

Strands not shown for clarity

y

x

y

x

bs

bs2ro kk

kkdθTT+

+= (4)

where To is the initial post tensioning force, and ks and kb are the axial stiffness of the PT strands and beam, respectively.

CONNECTION DESIGN Connection Rotation In order to design the PT connection with a BFFD, the maximum expected relative rotation, θr,max, under the design earthquake is required. θr,max is used to determine the moment capacity as well as the length of the slotted holes in the BFFD. Under the design earthquake the friction bolts should not bear against the slot at θr,max. Connection rotation data for several Design Basis Earthquake (DBE) and Maximum Considered Earthquake (MCE) ground motions analyzed by Rojas et al. (2005) were examined. A log normal distribution was assumed to determine the probability of exceedance (POE) of θr for the DBE and MCE. A value of θr,max equal to 0.035 radians was selected for the design of the BFFD connection. During the DBE and MCE, the POE for θr of 0.035 radians is less than 1% and 25%, respectively. A summary of the slot design is presented in Wolski (2006). Energy Dissipation Ratio For the SC-MRF to have satisfactory response under the design earthquake, the BFFD must provide sufficient energy dissipation. For the connection, the energy dissipation characteristics are expressed by the effective energy dissipation ratio, βE, which is the ratio of the actual energy dissipation to the energy dissipation for an elastic-plastic connection of the same strength. As previously discussed, the hysteretic behavior of a one-sided PT connection with a BFFD is un-symmetric, as shown in the M-θr curve given in Fig. 2. For a two-sided connection, the overall M-θr behavior would be symmetric. As a result of this unsymmetrical behavior, an effective energy dissipation ratio must be defined for the positive ( +

Eβ ) and negative ( −Eβ ) moment regions, where:

+

++ =

IGO

FfE M

Mβ ; −

−− =

IGO

FfE M

Mβ (5a,b)

The effective energy dissipation ratio, βE, is calculated as the average value of +

Eβ and −Eβ . Seo and

Sause (2005) determined that a structure with a value of βE = 0.25 had good seismic performance. On that basis, a value of βE = 0.25 was used in the connection design for most cases. In order to achieve this value, +

IGOM and −IGOM were set equal to 0.65 and 0.45 of the nominal plastic moment capacity,

Mpn, of the unreinforced beam section, and +FfM and −

FfM selected to be equal to 0.25Mpn and 0.05Mpn, respectively. This would result in a positive moment connection capacity of about 0.82Mpn to be achieved at a θr of 0.035 radians based on Eq. (1). Garlock (2002) designed several SC-MRFs, where the required connection capacity of an exterior PT connection ranged from 0.60Mpn to 0.90Mpn under the DBE. Based on previous work by Petty (1999) and Rojas et al. (2005), the coefficient of friction for a brass-steel interface is taken to be equal to 0.4 in determining the friction force Ff in the BFFD using Eq. (3).

EXPERIMENTAL PROGRAM Test Matrix The focus of the experimental program was to evaluate the performance of the BFFD in a PT connection. Therefore, the beam specimen, reinforcing plates, and post tensioning strands were

designed so that no damage to these elements would occur during the test. The behavior of these elements is well understood from prior experimental research by Garlock (2002). The test matrix for the study is given in Table 1, where θr,max, βE,tar, T0,exp, and Ff,exp are equal to the maximum θr, target value for the effective energy dissipation ratio, measured initial post-tensioning force, and friction force based on the measured friction bolt force and Eq. (3) in each test. The parameters in the experimental study included: friction force 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 of the tests. In most cases, the friction bolts were retensioned before each test.

Table 1. Test Matrix

Test Experimental Parameter θr,max (rads)

Loading Protocol

βE (%)

T0,exp (kN)

Ff,exp (kN)

1 Reduced friction force 0.035 CS 12.5 2227 242 2 Design friction force 0.030 CS 25 2209 470 3 BFFD improved fillet weld detail 0.035 CS 25 2194 470 4 EQ Loading 0.0245 EQ 25 2189 470

5 Bolt bearing – improved BFFD fillet weld 0.065 CS 25 2209 470

6 Assess column angle flexibility 0.035 CS 25 2061 470

7 Bolt bearing – BFFD CJP weld detail 0.065 CS 29 2049 541

NEES actuator

Beam

BFFD

Column

PT strands

3334

mm

X X

X – Denotes lateral bracing

Reaction wall

Strong floor

Figure 4. Test setup. Figure 5. Photo of 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 factor of 3/5 in the test specimen. The scaled beam was a Grade 50 W21x111 section (nominal yield stress of 345 MPa) with a length of 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 of interest of the connection is near the beam-column interface. The test setup boundary conditions included a nearly rigid bearing surface at the beam-column interface. Near the top of the beam an actuator with a cylindrical bearing imposed lateral displacements to the specimen, producing a moment at the beam-column interface. This force boundary condition simulated a point of inflection in the beam in a MRF subjected to lateral loading. Lateral bracing was provided at the top of the beam.

PT steel

Column

Beam

BFFD

In an SC-MRF, the elongation of each PT strand is the same due to the placement of the strands across multiple bays (see Fig. 1(a))To replicate this pattern of the PT strand elongation in the one-sided connection test specimen., it was necessary to concentrate the post tensioning strands at the centroid of the beam, as shown in Fig. 4. The post tensioning consisted of two 4-strand bundles and two 5-strand bundles, resulting in a total of 18 strands. The level of post tensioning force ranged from 2049 kN (Test 7) to 2227 kN (Test 1), see Table 1. The PT strands were not retensioned between tests. Differences in the PT force To,exp between tests are due to a loss of post tensioned force in prior tests. The BFFD had eight friction bolts (15.875 mm diameter, A325 bolts). The friction force in the tests ranged from 242 kN (Test 1) to 541 kN (Test 7), see Table 1.

The top and bottom flange reinforcing plates for the connection were designed in accordance with recommendations by Garlock (2002). As shown in Fig. 1(b), the bottom flange reinforcing plate was divided in half and welded to the inside surface of the bottom flange in order to weld the slotted plate directly to the beam bottom flange. Shim plates were used to provide good contact between the beam flanges and column flange. A photo of the test specimen connection region is given in Fig. 5. All tests had a fillet weld detail attaching the BFFD slotted plate to the beam flange, except for Test 7, which used a CJP weld detail. Test 3 had an improved fillet weld detail, consisting of larger fillet welds. Instrumentation The instrumentation for the test specimen included: load cells to measure the applied lateral force and the force in each bundle of post tensioning strands; displacement transducers to measure the lateral displacement of the beam specimen, gap opening and closing at the beam-column interface; and strain gages to measure the strain in the column angles, slotted plate, and the beam flanges. In addition, bolt strain gages were used in order to monitor the friction normal force provided by the friction bolts of the BFFD. The beam in the connection region was white washed to provide visual evidence of yielding. Test Procedure The two loading protocols were included in the test program to evaluate the effect of the displacement history imposed by the actuator. In the cyclically symmetric (CS) loading protocol, an initial six cycles of pre-gap opening displacement were imposed, followed by displacements that produced the θr history shown in Fig. 6(a), where the increment in θr between cycles of different amplitude was 0.005 radians. The first six pre-gap opening displacement cycles were controlled using the actuator displacement as the control feedback. For the remaining cycles the control algorithm imposed actuator displacements such that the θr target was provided (i.e., θr was the control feedback). The displacement history for each test was imposed at a rate of 0.05 Hz, and was terminated when the θr,max given in Table 1 was achieved. The θr history for the earthquake-based (EQ) loading protocol is shown in Fig. 6(b), and has a θr,max = 0.0245 radians. The specimen (Test 4) was loaded at a rate of one-eighth of real-time. The θr history is based on the response computed by Rojas et al. (2005) of a PT connection in a 6-story SC-MRF, where the structure was subjected to the west component of the ground motion recorded at the CHY036 station during the Chi-Chi earthquake record (scaled to the MCE level).

-0.030

-0.020

-0.010

0.000

0.010

0.020

0.030

0 20 40 60 80

Time (sec)

Rot

atio

n, θ

r (ra

ds)

Figure 6. θr Loading protocols: (a) cyclically symmetric (CS), and (b) Chi-Chi earthquake (EQ).

-0.070-0.060-0.050-0.040-0.030-0.020-0.0100.0000.0100.0200.0300.0400.0500.0600.070

0 20 40 60 80

No. of Cycles

Rot

atio

n, θr

(rad

s)

(a) (b)

EXPERIMENTAL RESULTS Cyclic Loading

The moment-rotation (M-θr) response for Test 2 is shown in Fig. 7. The moment at imminent gap opening under positive moment +

exp,IGOM and under negative moment −exp,IGOM was reached at 0.53Mpn

and 0.40Mpn, respectively, where Mpn of the W21x111 beam is 1576 kN-m. This value is less than the targeted value of 0.65Mpn and 0.45Mpn and is due to difficulties in achieving the target level of post tensioning force in the specimen due to the bundling of the strands into four groups, each with a large number of strands (a value of about 80% of the targeted force in the PT strands was achieved). The BFFD provided a moment capacity of +

exp,FfM = 0.21Mpn and −exp,FfM = 0.08Mpn, which was close to

the targeted value of 0.025Mpn and 0.05Mpn, respectively. As the connection rotates, the elastic stiffness of the strands provides an increase in moment capacity. Test 2 developed a maximum connection moment (at the beam-column interface) Mmax,exp of 0.70Mpn at 0.03 radians. After each cycle of loading, θr returned to zero and energy dissipation occurred when the connection was unloaded, demonstrating the self-centering capability and energy dissipation of the connection. Good agreement is seen between the connection predicted M-θr response by Eq. (1) and the measured experimental response, where the width of the hysteresis loops in the prediction by Eq. (1) is based on +

FfM2 and −FfM2 in the first and

third quadrants, respectively, in Fig. 7. Some discrepancy exists between the prediction and experimental result at the unloading portions of the hysteresis loops. This is due to column angle flexibility that is not considered in the theoretical prediction. The flexibility in the column angle was measured in Test 6, and is documented in Wolski (2006). The sum of the measured tension in the friction bolts for Test 2 is shown plotted against θr in Fig. 8. In general, the Belleville washers enabled the pretension force to be maintained reasonably well in the friction bolts.

-1.0

-0.5

0.0

0.5

1.0

-0.04 -0.02 0.00 0.02 0.04

Rotation, θr (rads)

Nor

mal

ized

Mom

ent,

M/M

p,n

imminent gap opening

imminent gap opening

ExperimentalTheoretical - Eq. (1)

Figure 7. Moment-rotation response, Test 2. Figure 8. Total friction bolt force, Test 2.

The post tensioning force-rotation response for Test 2 is shown in Fig. 9. The theoretical post-tensioning force for the specimen is calculated using Eq. (4). Good agreement between the experimental and theoretical values is seen in Fig. 9. The initial post tensioning force is 2209 kN at θr = 0 radians and increases linearly to 2972 kN at a magnitude of θr = 0.030 radians. At the end of a loading cycle, the post tensioning force returns to the original value. The specimen was designed so that the post tensioning would not yield up to a magnitude of θr = 0.070 radians.

No significant damage to the beam occurred during the Test 2. However, due to the seating of the beam, bearing yielding at the end of the beam flanges occurred. Also, some minor web yielding occurred at the location of the slotted plate. Neither of these affected the global response of the connection. Test 2 achieved a measured effective energy dissipation ratio βE,exp of 17.9%, based on the

0

500

1000

-0.040 -0.020 0.000 0.020 0.040Rotation, θr (rads)

Fric

tion

Bol

t Ten

sion

For

ce, N

(kN

)

cycle of loading with an amplitude of θr = 0.030 radians. A summary of the test results for Test 2, along with all tests, are given in Table 2.

1500

2500

3500

-0.04 -0.02 0.00 0.02 0.04

Rotation, θr (rads)

PT F

orce

, T (k

N)

Eq. (4)

Experiment

To

Figure 9. Post-tensioning force, Test 2. Figure 10. Moment-rotation response, Tests 1 and 2.

Table 2. Experimental Results

Test a

np

IGO

MM

.

,exp+

a

np

IGO

MM

.

,exp−

a

np

Ff

MM

.

,exp+

anp

Ff

MM

.

,exp−

anpM

M

.

max,exp+

,expEβ c

(%)

1 0.43 0.36 0.11 0.04 0.66b 14.5 2 0.53 0.40 0.21 0.08 0.70 27.9 3 0.53 0.40 0.21 0.08 0.72 27.2 4 0.54 0.41 0.21 0.08 0.65 28.6 5 0.50 0.37 0.18 0.07 1.04b 24.1 6 0.52 0.37 0.21 0.08 0.77b 31.1 7 0.58 0.40 0.25 0.10 1.22b 34.7

a Mp,n = nominal plastic moment capacity of W21x111 section equal to 1576 kN-m b Indicates tests where slotted plate went into bearing against friction bolts c Based on cycle with θr = 0.030 radians, prior to friction bolt bearing

Effect of Friction Force

The effect of the level of friction force in the BFFD was evaluated by comparing the response of Tests 1 and 2. In Test 1, the friction force Ff,exp was 242 kN, which was 51% of that of Test 2. It is evident in Fig. 10, where the M-θr response of the two tests is compared, that the reduction in friction force 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 of the connection upon gap opening. The reduced moment capacity is due to the reduction in +

exp,FfM and −exp,FfM , which in Test 1

were 52% and 50% of the corresponding values in Test 2. As given in Table 2, +exp,IGOM and

−exp,IGOM in Test 1 was 0.43Mpn and 0.36Mpn,, representing a 19% and 10% reduction compared to the

+exp,IGOM and −

exp,IGOM of Test 2. The effective energy dissipation ratio βE,exp achieved by Test 1 was

14.5%, which is 54% of the βE,exp of Test 2.

-1.0

-0.5

0.0

0.5

1.0

-0.04 -0.02 0.00 0.02 0.04

Rotation, θr (rads)

Nor

mal

ized

Mom

ent,

M/M

p,n

Test 1Test 2

Effect of Loading History

The M-θr response for Test 4, with the EQ loading protocol is shown in Fig. 11, where it is compared to the response of Test 2. As stated earlier, the EQ θr history is from an analysis of a 6-story MRF under the Chi-Chi earthquake record (scaled to the MCE level). This history was chosen, since as shown in Fig. 6(b), there are several non-symmetrical cycles of θr 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 frequency of loading of about 0.5 Hz. Test 2 had a loading frequency of 0.05 Hz.

In Fig. 11 the connection in Tests 2 and 4 appear to have performed in a similar fashion to previous tests, and as before, the self-centering capability was demonstrated after each cycle of loading. The rounding of the hysteresis loop upon unloading was observed again due to the flexibility of the BFFD column angles. Table 2 shows that the moments at imminent gap opening, exp,IGOM , moment

contribution from the BFFD, exp,FfM , and the effective energy dissipation ratio βE,exp are nearly the

same for the two tests. The connection in Test 4 developed a smaller maximum moment +expmax,M of

0.65Mpn than Test 2 (where +expmax,M = 0.70Mpn) because Test 4 was subjected to a smaller value of

θr,max of 0.0245 radians. In general, the connection in Test 4 did not appear to be effected by the difference in load history and loading rate, and performed well under the applied earthquake loading.

-1.0

-0.5

0.0

0.5

1.0

-0.04 -0.02 0.00 0.02 0.04

Rotation, θr (rads)

Nor

mal

ized

Mom

ent,

M/M

p,n

Test 2Test 4

-1.40

-0.70

0.00

0.70

1.40

-0.080 -0.040 0.000 0.040 0.080

Rotation, θr (rads)

Nor

mal

ized

Mom

ent,

M/M

p,n

Test 2Test 7

Friction boltsgo into bearing

Friction boltsgo into bearing

Friction boltsfail in shear

Figure 11. Moment-rotation response, Tests 2 and 4. Figure 12. Moment-rotation response, Tests 2 and 7.

Effect of Bolt Bearing

The effect of bearing of the friction bolts on the edge of the slotted holes in the BFFD was evaluated by comparing the response of Tests 2 and 7. Shown in Fig. 12 is the M-θr response for Tests 2 and 7. The initial force To,exp in the PT strands was slightly smaller in Test 7 (2049 kN), while the friction force Ff,exp due to the friction bolts was slightly higher (541 kN) in Test 2, see Table 2. As a result the moment contribution from the BFFD, +

exp,FfM and −exp,FfM , and at imminent gap opening, +

exp,IGOM

and −exp,IGOM , 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 of θr of about 0.035 radians, the moment capacity of the connection would initially increase due to the bolt bearing force developed in the BFFD. The result of bolt bearing led to deforming the friction bolts, where upon unloading the connection the bolts were elongated and bent, and therefore suffered a loss in their pretension force. The bent bolts did not go into bearing until the maximum amplitude of θr from the previous cycles was surpassed. Consequently, in subsequent cycles of the same amplitude of θr, the friction force in the BFFD would be reduced due to the loss of tension force in the friction bolts, leading to a loss in moment capacity of the connection. In subsequent cycles with a greater magnitude of θr, the friction

bolts would go into bearing and increase the moment developed in the BFFD. The loss in tension in the friction bolts led to a pinching in the hysteretic response and a reduction in the energy dissipation capacity of the BFFD. In Test 7, the CJP weld detail for the BFFD attachment to the beam flange resulted in the bolt shear capacity being achieved without failure of the BFFD weld detail. Upon shearing the bolts in Test 7, which occurred at θr = +0.065 radians, the connection did not dissipate energy but continued to self center due to the post tensioning force in the PT strands remaining intact. In Test 5, which used a fillet weld detail to attach the slotted plate of the BFFD to the beam, the fillet weld developed a low cycle fatigue failure when the friction bolts went into bearing.

ANALYTICAL MODELING OF PT CONNECTIONS WITH A BFFD

Analytical models of a PT connection with a BFFD were developed using the OpenSees computer program (Mazzoni et al., 2006). Since the friction force in the BFFD changes direction due to the kinematics under the cyclic loading, it was necessary to consider a two-dimensional formulation to model the friction force in the BFFD in order to obtain the correct direction of the friction force resultant. The analytical model for the frictional force resultant included a bidirectional plasticity-based model, and a directional velocity-based model. The experimental data was used to evaluate the accuracy of each of these models. The formulations for each are described below. Bidirectional Plasticity-Based Model The two components of the friction force in the BFFD (see Fig. 3) define the friction force vector Ff, where Ff = {Ffx, Ffy} T. The direction of the friction force resultant is equal to that of the instantaneous velocity vector, v& , where:

vvFF ff &

&⋅= (6)

The force-deformation behavior for the friction force is modeled using an elasto-perfectly plastic model with a large elastic stiffness, ki. The maximum friction force that can develop, Ff, was given previously by Eq. (3), and is equated to the yield force Fy to define the diameter of the yield surface. The yield function Φ(Ff) for the bi-directional plasticity model is:

( ) yF−= ff FFΦ (7)

where Ff is determined from Eq. (8):

( )pf vvF −⋅= ik (8)

In Eq. (8) v and vp are the total and the plastic deformation vectors, respectively.

The circular yield surface provides the magnitude of Ff during plastic flow, where according to the associated plastic flow rule, the incremental plastic deformation vector dvp is normal to the yield surface during plastic flow:

( )

( ) nFF

FF

vf

f

f

fp ⋅λ=⋅λ=

∂Φ∂

⋅λ=d (9)

In Eq. (9) n is the outward normal vector of the yield surface defined by Φ(Ff), and λ is the magnitude of plastic deformation, where λ ≥ 0. Eq. (9) indicates that the direction of the incremental plastic deformation vector is in the same direction as Ff during plastic flow. Hence, from Eq. (6), the following can be written:

p

pfff v

vF

vvFF

d

d⋅≈⋅=

&

& (10)

Eq. (10) is an approximation since the bidirectional plasticity model formulation does not result in truly rigid plastic behavior, which Eq. (6) assumes. A more detail discussion about the bidirectional plasticity model can be found in Huang (2002).

Directional Incremental Velocity-Based Model

From Eq. (6), the difference ∆Ff in the friction force vector Ff at time t and t+∆t can be expressed as:

( ) ( ) ( )( )

( )( )

−

++

⋅=−+=tt

ttttttt

vv

vvFFFF ffff &

&

&

&

∆∆∆∆ (11)

Performing a Taylor series expansion of Eq. (11) at ∆ v& =0, and truncating the higher order terms yields the following relationship between ∆Ff and the change in the instantaneous velocity v&∆ :

vCvv

FF f

f &&&&&

&&&

&∆⋅=∆⋅

−−

⋅≈∆ 2xyx

yx2y

3 vvvvvv

(12)

where v&∆ is { yx v,v && ∆∆ }T, and v&∆ equals ( )tt ∆+v& - ( )tv& . 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 ∆Ff and summing the result with the friction force vector from the beginning of the time step to obtain the friction force at the end of the time step. Description of Analytical Models An analytical model for the post tensioned subassembly test specimen was developed using the OpenSees computer program. This model was used to conduct cyclic nonlinear pushover analyses of the test specimen. In this model, the nonlinear beam column element in OpenSees (nonlinearBeamColumn) was used to model the beam and the column. The effect of axial, flexural and shear deformations 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 flanges and the column face was modeled using two zero length elements (zeroLength) located at the beam flanges at the beam-to-column interface. 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 surface element (surface) was used to model the bidirectional friction force in the BFFD, where the bidirectional friction force is based on the bidirectional plasticity model described above. Alternatively, the zero length element was used to model the bidirectional friction force in accordance with the directional incremental velocity-based model described above.

A modulus of elasticity E of 200 GPa was used for the beam and column elements of the analytical model with a large yield stress, thereby assuming elastic behavior of the members during the analysis. For the post tensioning strand element, an E of 199.5 GPa was used. For the column angle element, the stiffness observed from the result of Test 6 was used to define the property in the y-direction of the BFFD (see Fig. 3). The stiffness in the x-direction of the BFFD model was determined to be twice that in the y-direction, by matching the M-θr relationship of the analytical prediction with that of the test

result. A large initial stiffness was assumed in the BFFD element (≈150 times the column angle element in the y-direction), with the yield force (i.e., maximum friction force) set equal to Ff,exp.

The construction sequence of the test specimen had the post tension force applied before the BFFD is installed. Consequently, the BFFD element was activated in the OpenSees model after the initial post tensioning force was applied to the model. Cyclic loading analyses were subsequently performed using the displacement history that was applied to the test specimen. In the model with the bidirectional plasticity formulation, the cyclic loading analysis was performed using a static analysis procedure. However, the model with the directional incremental velocity-based formulation 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 of the beam), and a ground acceleration history was applied to the base of the test specimen to achieve the target displacement amplitudes at the end of the beam. A small mass was added to the nodes of the BFFD element and mass proportional damping was used in order to avoid high frequency errors in the velocity at these nodes. Validation of Models The analytical models with the BFFD based on the bidirectional plasticity and the directional velocity were verified by conducting analyses of the test specimens, and comparing the computed response with the experimental behavior. The M-θr results from the analysis of Test 2 are given below in Fig. 13, where they are compared to the experimental results of Test 2.

These figures show that the analytical models adequately capture the M-θr behavior of the connection in Test 2. The reduction in stiffness in the M-θr response due to column angle flexibility 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 of θr. This is due to using a fixed location for the contact point where the gap elements were defined in the model. In the experiment it was observed that the COR moves slightly toward the extreme fiber of the reinforced beam flange during the tests as the beam rotates, causing the distance between the COR and the friction force resultant in the BFFD, and therefore connection moment to increase as the connection rotates with increasing θr.

-1

-0.5

0

0.5

1

-0.04 -0.02 0 0.02 0.04-1

-0.5

0

0.5

1

-0.04 -0.02 0 0.02 0.04

Nor

mal

ized

Mom

ent

M/M

p,n

Nor

mal

ized

Mom

ent

M/M

p,n

Rotation (rad)θr Rotation (rad)θr

ExperimentalAnalytical

ExperimentalAnalytical

Figure 13. Comparison of M-θr relationships of analytical models and experimental response from Test 2.

SUMMARY AND CONCLUSIONS

A post-tensioned moment connection with a bottom flange friction device (BFFD) for use in a self-centering moment resisting frame (SC-MRF) was developed and experimentally investigated. The test

(a) Bidirectional plasticity model (b) Directional incremental velocity model

results demonstrate that the BFFD provides excellent energy dissipation while the PT connection provides stiffness, strength, and deformation capacity under cyclic and earthquake loading. In addition, the connection self-centers without residual drift as long as the PT strands remain elastic. During the tests, the magnitude of maximum friction force remained relatively constant and the brass friction plates provided a good friction surface. It was also observed that the simple design model presented needs to be improved in order to include the flexibility of the column angles in the BFFD. The models implemented using OpenSees enabled the column angle flexibility to be accounted for, and consequently improved predictions for the connection moment-relative rotation.

The OpenSees connection models are currently being used to analyze SC-MRF systems with PT connections with a BFFD under seismic loading conditions. These analyses will be used to assess the behavior of the models in a SC-MRF and to study the seismic performance of these frames.

ACKNOWLEDGEMENTS This paper is based upon work supported by the National Science Foundation under Grant No. CMS-0420974, within the George E. Brown, Jr. Network for Earthquake Engineering Simulation Research (NEESR) program and through Grant No. CMS-0402490 (NEES Consortium Operation). Any opinions, findings, conclusions, and recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.

REFERENCES Garlock, M. 2002. “Full-Scale Testing, Seismic Analysis, and Design of Post-Tensioned Seismic

Resistant Connections for Steel Frames”. Ph.D. Dissertation, Department of Civil and Environmental Engineering. Lehigh University, Bethlehem, PA.

Huang, W-H. 2002. “Bi-directional Testing, Modeling, and System Response of Seismically Isolated Bridges”. Ph.D. Dissertation, Department of Civil and Environmental Engineering. University of California, Berkeley, CA.

Herrera, R. 2006. “Seismic Behavior of Concrete Filled Tube Column-Wide Flange Beam Frames”. Ph.D. Dissertation, Dept. of Civil and Environmental Engineering. Lehigh Univ., Bethlehem, PA.

Mazzoni, S., MacKenna, F., and Fenves, G. L., 2006. OpenSees Command Language Manual, PEER, University of California, Berkeley, CA.

Morgen, B. and Kurama, Y.C. 2004. “A Friction Damper for Post-Tensioned Precast Concrete Moment Frames,” PCI Journal, 49(4), 112-132.

Petty, G. 1999. “Evaluation of a Friction Component for a Post-Tensioned Steel Connection”. M.S. Thesis, Department of Civil and Environmental Engineering. Lehigh University, Bethlehem, PA.

Ricles, J., Sause, R., Garlock, M., and Zhao, C. 2001. “Post-Tensioned Seismic-Resistant Connections for Steel Frames,” Journal of Structural Engineering, 127(2), 113-121.

Rojas, P., Ricles, J.M. and Sause, R. 2005. “Seismic Performance of Post-Tensioned Steel MRFs with Friction Devices,” Journal of Structural Engineering, 131(4), 529-540.

Seo, C.-Y. and Sause, R. 2005. “Ductility Demands on Self-Centering Systems under Earthquake Loading,” ACI Structural Journal, 102(2), 275-285.

Wolski, M. 2006. “Experimental Evaluation of a Bottom Flange Friction Device for a Self Centering Seismic Moment Resistant Frame with Post-Tensioned Steel Moment Connections” M.S. Thesis, Department of Civil and Environmental Engineering. Lehigh University, Bethlehem, PA.