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 SELFCENTERING 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 posttensioned 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 highstrength 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, [email protected]
Joseph T. Stuart Professor of Structural Engineering, ATLSS Center, Dept. of Civil and Environmental Engineering, Lehigh
University, PA, USA, [email protected]
3
Graduate Research Assistant, ATLSS Center, Dept. of Civil and Environmental Engineering, Lehigh University, PA, USA,
[email protected]
4
Visiting Research Scientist, ATLSS Center, Dept. of Civil and Environmental Engineering, Lehigh University, PA, USA,
[email protected]
5
Associate Research Fellow, ATLSS Center, Dept. of Civil and Environmental Engineering, Lehigh University, PA, USA,
[email protected]
2
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.
(b)
(a)
A
Slotted keeper angle
Reinforcing plate
PT strands
Anchorage
BFFD
PT
strands
Column
Shim Plates
Beam
Friction bolts
with Belleville
washers
Reinforcing plate
Slotted plate welded to
beam bottom flange
Brass friction plate at A
slotted plate/angle interface
Section A-A
“Angles”
bolted to
column
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.
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 posttensioning 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.
M
Unloading
Strands
Yield
3
4
Imminent Gap Opening
2
Decompression
Both Beam Flanges in
Contact with Column
5
1
6
7
0 8
θr
θr7
6
5
4
2
Μ+
Μ−
θr+
3
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
M = Pd 2 + F f r
(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 M Ff+ ,
while r − (see Fig. 3(b)) is used in the second term in Eq. (1) to determine the negative moment
capacity M Ff− from the BFFD.
(a)
(b)
Strands not shown for clarity
Strands not shown for clarity
COR+
vt
vt
Ct
Ct
COR+
Beam
d2
Column
Column
c.g.
(rein. beam section)
r+
Ff
y
d1
+
M
V
Beam
-
COR
vb
d2
vb
Cb
COR-
Cb
Ff
Centroid
of bolts
d
c.g.
1
(rein. beam section)
P
Ff +
F
F+fx fy
Ff
y
x
Centroid
of bolts
r
P
M-
-
V
Ff
Ff F fy
F -fx
x
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):
M IGO = To d 2 + F f r
(2)
+
−
+
−
and M IGO
, respectively. M IGO
and M IGO
are the
where r+ and r − is utilized to determine M IGO
imminent gap opening moments under positive and negative moment, respectively. The maximum
friction force in the BFFD, Ff, is equal to:
F f = 2µnb Tb
(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 posttensioning force T can be written as a function of θr:
T = To + θr d 2
k s kb
k s + kb
(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 ( β E+ ) and negative ( β E− ) moment regions, where:
β E+ =
+
M Ff
+
M IGO
; β E− =
−
M Ff
−
M IGO
(5a,b)
The effective energy dissipation ratio, βE, is calculated as the average value of β E+ and β E− . 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
+
−
and M IGO
were set equal to 0.65 and 0.45 of the nominal plastic moment capacity,
this value, M IGO
+
−
Mpn, of the unreinforced beam section, and M Ff
and M Ff
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
1
2
3
4
5
6
7
Experimental Parameter
Reduced friction force
Design friction force
BFFD improved fillet weld detail
EQ Loading
Bolt bearing – improved BFFD
fillet weld
Assess column angle flexibility
Bolt bearing – BFFD CJP weld
detail
NEES actuator
X
θr,max
(rads)
0.035
0.030
0.035
0.0245
Loading
Protocol
CS
CS
CS
EQ
(%)
12.5
25
25
25
βE
T0,exp
(kN)
2227
2209
2194
2189
Ff,exp
(kN)
242
470
470
470
0.065
CS
25
2209
470
0.035
CS
25
2061
470
0.065
CS
29
2049
541
X
BFFD
PT steel
PT strands
3334 mm
Reaction wall
Beam
Beam
X – Denotes lateral bracing
BFFD
Strong floor
Column
Column
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 beamcolumn 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.
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
0.070
0.060
0.050
0.040
0.030
0.020
0.010
0.000
-0.010
-0.020
-0.030
-0.040
-0.050
-0.060
-0.070
0.030
(a)
(b)
0.020
Rotation, θr (rads)
Rotation, θr (rads)
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 SCMRF, 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).
0.010
0.000
-0.010
-0.020
-0.030
0
20
40
No. of Cycles
60
80
0
20
40
60
80
Time (sec)
Figure 6. θr Loading protocols: (a) cyclically symmetric (CS), and (b) Chi-Chi earthquake (EQ).
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 M IGO
,exp and under negative moment M IGO ,exp 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 M Ff
,exp = 0.21Mpn and M Ff ,exp = 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 2 M Ff+ and 2 M Ff− 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.
0.5
Friction Bolt Tension Force, N (kN)
Normalized Moment, M/Mp,n
1.0
imminent gap opening
0.0
imminent gap opening
-0.5
Experimental
Theoretical - Eq. (1)
-1.0
-0.04
-0.02
0.00
0.02
0.04
Rotation, θr (rads)
Figure 7. Moment-rotation response, Test 2.
1000
500
0
-0.040
-0.020
0.000
0.020
Rotation, θr (rads)
0.040
Figure 8. Total friction bolt force, Test 2.
The post tensioning force-rotation response for Test 2 is shown in Fig. 9. The theoretical posttensioning 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
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.
3500
Normalized Moment, M/Mp,n
1.0
PT Force, T (kN)
Experiment
2500
Eq. (4)
To
1500
-0.04
0.5
0.0
-0.5
Test 1
Test 2
-1.0
-0.04
-0.02
0.00
0.02
-0.02
0.04
0.00
0.02
0.04
Rotation, θr (rads)
Rotation, θr (rads)
Figure 9. Post-tensioning force, Test 2.
Figure 10. Moment-rotation response,
Tests 1 and 2.
Table 2. Experimental Results
Test
+
M IGO
,exp
M p .n
a
−
M IGO
,exp
M p .n
a
M Ff+ ,exp
M p .n
a
M Ff− ,exp
M p .n
a
+
M max,exp
M p .n
a
β E ,exp 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 M Ff+ ,exp and M Ff
,exp , which in Test 1
+
were 52% and 50% of the corresponding values in Test 2. As given in Table 2, M IGO
,exp and
−
M IGO
,exp in Test 1 was 0.43Mpn and 0.36Mpn,, representing a 19% and 10% reduction compared to the
+
−
M IGO
,exp and M IGO ,exp 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.
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, M IGO ,exp , moment
contribution from the BFFD, M Ff ,exp , 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 M max,
exp of
+
0.65Mpn than Test 2 (where M max,
exp = 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.
1.40
Normalized Moment, M/Mp,n
Normalized Moment, M/Mp,n
1.0
0.5
0.0
Test 2
Test 4
-0.5
-1.0
-0.04
-0.02
0.00
0.02
Friction bolts
go into bearing
0.70
Friction bolts
fail in shear
0.00
-0.70
0.04
Rotation, θr (rads)
Figure 11. Moment-rotation response, Tests 2 and 4.
Test 2
Test 7
Friction bolts
go into bearing
-1.40
-0.080
-0.040
0.000
0.040
0.080
Rotation, θr (rads)
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, M Ff+ ,exp and M Ff− ,exp , and at imminent gap opening, M IGO
,exp
−
and M 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 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 plasticitybased 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:
v&
Ff = Ff ⋅
(6)
v&
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:
Φ (Ff ) = Ff − F y
(7)
where Ff is determined from Eq. (8):
(
Ff = k i ⋅ v − v p
)
(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:
dv p = λ ⋅
∂Φ (Ff )
F
= λ ⋅ f = λ ⋅n
∂ (Ff )
Ff
(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:
Ff = Ff ⋅
dv p
v&
≈ Ff ⋅
v&
dv p
(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:
 v& (t + ∆t )
v& (t )
−
v& (t )
 v& (t + ∆t )
∆Ff = Ff (t + ∆t ) − Ff (t ) = Ff ⋅ 



(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& :
∆Ff ≈
Ff
v&
3
 v& 2y
⋅
− v& x v& y
− v& x v& y 
 ⋅ ∆v& = C ⋅ ∆v&
v& 2x 
(12)
where ∆v& is { ∆v& x , ∆v& y }T, and ∆v& equals v& (t + ∆t ) - v& (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 ∆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.
1
0.5
0
-0.5
Experimental
-1
-0.04
Analytical
-0.02
0
0.02
0.04
Normalized Moment M/Mp,n
Normalized Moment M/Mp,n
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
Experimental
Analytical
-0.02
Rotation θr (rad)
(a) Bidirectional plasticity model
0
0.02
0.04
Rotation θr (rad)
(b) Directional incremental velocity model
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 selfcentering moment resisting frame (SC-MRF) was developed and experimentally investigated. The test
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. CMS0420974, 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.
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