CARGA DOCENTE POSTGRADO
CONVENIOS VIGENTES PARA LA REALIZACIÓN DE PRÁCTICAS
School of Civil Engineering, Purdue University, West Lafayette, IN, USA [email protected]
Judy Liu
School of Civil Engineering, Purdue University, West Lafayette, IN, USA [email protected]
ABSTRACT
A column base connection was developed for use in steel self-centering moment resisting frames (SC-MRFs). SC-MRFs exhibit negligible residual drift after a seismic event, and damage is limited to replaceable fuse elements. Self-centering behavior is achieved in the column base connection through the use of post-tensioned (PT) bars. The PT bars provide the restoring force in a connection for which the softening behavior is provided by gap opening rather than plastic hinging. The fuse elements in the column base are buckling-restrained steel (BRS) plates, which dissipate energy through yielding.
Large-scale tests on PT column base specimens have demonstrated the ability of the column to self-center with damage limited to the yielding BRS plates. Test parameters included initial post-tension force, initial axial force in the column and column size. Design equations for the PT column base were validated by and further refined based on the test results.
1. INTRODUCTION
Steel self-centering moment resisting frames (SC-MRFs) using post-tensioned (PT) beam-column connections have been developed to eliminate structural damage after earthquakes (Ricles et al. (2001, 2002), Christopoulos et al. (2002), Garlock et al. (2005, 2007)). The SC-MRF has the potential to return to its original position, or self-center, after earthquakes. However, the column bases in SC-MRFs may suffer structural damage due to inelastic deformations after earthquakes; this damage, in turn, may affect the self-centering capability of the frame. In order to overcome these issues, a post-tensioned connection was introduced at column bases for use in SC-MRFs (Chi, 2009). The schematic view of an SC-MRF with PT column base connections is shown in Figure 1. The PT connection consists of high strength PT bars (Dywidag bars), buckling restrained steel (BRS) plates, reinforcing plates, shim plates and Keeper plates. The PT column base is similar to the PT beam-column
connection in that the softening behavior is achieved through gap-opening at the column-grade beam interface rather than yielding in the column. The PT bars provide clamping force to connect columns and beams, and restoring force to close the gaps occurring at the interface of the column and grade beam.
As shown in Figure 1, the PT bars are anchored at mid-height of the first story column and near the bottom of the basement column. Anchorage locations were chosen to avoid congestion with connection details at PT beam-column joints in stories above. Furthermore, the design required sufficient PT bar length to avoid reaching yield and fracture strains even for the gap opening deformations in a Maximum Considered Earthquake (MCE). Location of the PT bar anchorage within the first story was also deliberately chosen so that axial demands from the bars would not compound flexural demands at the top of the first story and lead to plastic hinging.
Figure 2 shows the PT bars and other column base components. Dog-bone shaped BRS plates provide energy dissipation by yielding of a reduced section in tension and compression. Damage in the PT column base connection occurs only in the replaceable BRS plates. Bolted, T-shaped cover plates are used to prevent buckling (i.e., strong axis and weak axis inelastic buckling) of the BRS plates.
The BRS plate and Keeper plate are joined by complete joint penetration (CJP) welding to form one unit. The BRS-Keeper plate unit is bolted to the columns and grade beams. Keeper plates provide additional shear resistance through the slip-critical bolted connection. Meanwhile, the Keeper plates are bevelled at the connection with the BRS plate to allow rotation of the column.
Reinforcing plates provide additional contact area during gap opening. Therefore, bearing stresses in the column flanges can be reduced for strong and weak axis bending. Shim plates are used to fill any gaps between BRS plates and column flanges providing more restraint when the BRS plates are in compression. Shim plates are also used between columns and grade beams to prevent contact with the column web. Meanwhile, large slotted holes in the grade beam flanges are designed to permit lateral movement of the PT bars with gap opening without binding, or ‘kinking’, of the bars.
Grade 1 2 3 4 5 6 Post-Tensioned Bars
Post-Tensioned Strands or Bars
Figure 1. Schematic view of SC-MRF with PT Column Bases
Connections in Steel Structures VII / Timisoara, Romania / May 30 - June 2, 2012 211 212 Connections in Steel Structures VII / Timisoara, Romania / May 30 - June 2, 2012 PT(Post-Tensioned)
Bars
First Story Column
Keeper Plate BRS (Buckling Restrained Steel) Plate Grade Beam Gap Opening Lateral Load Cover Plate
Figure 2. Configuration of PT column base connection
2. DESIGN AND BEHAVIOR OF PT COLUMN BASE CONNECTION 2.1. Moment-Rotation Relationship
The moment-rotation response of the PT column base connection has the characteristic ‘flag-shaped’ hysteresis of PT connections which have gap opening behavior and energy dissipating elements. When the column moment at the column base overcomes the moment resistance provided by initial PT force and axial force in columns, the connection decompresses, or a gap opening at column-grade beam interface begins to occur. After decompression, the column rotates about the contact surface in column flanges creating relative rotation at column-grade beam interface. As the gap opening increases due to applied moment, the PT bars and BRS plates begin to deform. The PT bars elongate, whereas one of the BRS plates elongates and the other plate shortens. After the decompression occurs, additional axial force from the PT bars as well as BRS plates is developed in the PT column base connection, providing additional moment resistance. As the gap opening increases further, the BRS plates yield. The stiffness of the PT column base connection after decompression is associated with the axial stiffness of the PT bars as well as the axial stiffness of the BRS plates. After the BRS plates form a plastic yielding zone, the stiffness of the connection depends mostly on the axial stiffness of the PT bars. When unloaded, the elastic PT bars provide a restoring force and the gap opening closes, or self- centers, without residual relative rotation.
The design basis earthquake (DBE) connection moment (MDBE_col in( )) is
equal to the sum of the moment from the initial PT force (∆MPTforce), moment from
the initial axial force in column (∆Maxial), moment contribution from the tension BRS
plate (∆MBRS) and moment from the PT force due to PT bar elongation (∆MPT) at
the relative rotation of θr_col DBE( ). The center of rotation (COR) is at the column
flange in compression. The connection moment (MDBE_col in( )) at the relative rotation
of θr_col DBE( ) is expressed as
= ∆ + ∆ + ∆ + ∆
_ ( )
DBE col in PTforce axial BRS PT
M M M M M (1)
The moment contribution of the initial PT force in column (∆MPTforce) at the
relative rotation of θr_col DBE( ) is estimated as
∆MPTforce =T di( 2 _col -hanchor sin(θr_col DBE( ))) (2) where, Ti =initial PT force after jacking loss
2 _ =distance between COR and centroid of the column before decompression
col d
=distance between the column-grade beam interface and top anchorage of PT bar
anchor
h
The moment contribution of the initial axial force in column ( ∆Maxial) at the relative rotation of θr_col DBE( ) is estimated as
∆Maxial =P di( 2 _col -hcolsin(θr_col DBE( ))) (3) where,
=initial axial force in column i
P
= clear length of first story column col
h
The total moment contribution of the tension BRS plate ( ∆MBRS) at the relative rotation of θr_col DBE( ) is estimated as
∆ = _ 3 _ + _ θ _ ( ) 3 _ − _ 3 _
_
( BRS y)
BRS BRS y col BRS p r col DBE col col
BRS i F M F d K d d K (3) where, =
_ elastic stiffness of the BRS plate
BRS i K
=
_ post-yield stiffness of the BRS plate
BRS p K
=
_ yield force of the BRS plate
BRS y F
=
3 _col distance between the center of rotation and the centerline of BRS plate d
The moment contribution of the additional axial force due to PT bar elongation ( ∆MPT ) at the relative rotation of θr_col DBE( ) is estimated as
∆MPT =(KPT)(d2 _col −hanchor sin(θr_col DBE( )))2θr_col DBE( ) (4)
where,
=axial stiffness of the PT bars
PT K
Connections in Steel Structures VII / Timisoara, Romania / May 30 - June 2, 2012 213 214 Connections in Steel Structures VII / Timisoara, Romania / May 30 - June 2, 2012
2.2. Shear resistance
The main contributor to shear capacity of the connection (Vcol) is the friction
force resulting from the axial force of the column at the column-grade beam interface (Vf). The friction force on the contact surface (i.e., column-grade beam interface) is
associated with the axial force developed in the first story column as well as the static friction coefficient of steel. Additional shear resistance (Vk) is provided by the
Keeper plates. The Keeper plates are bolted (i.e., slip critical connection) to the grade beam flanges, and friction resistance is also developed between Keeper plates and grade beam flanges. Therefore, when the shear demand exceeds Vf, the column
flange bears against the Keeper plate, and the shear demand is transferred to the grade beam flange by friction.
The total axial force in a column (Pcol) is determined by (1) initial PT force
(Ti), (2) additional PT force due to elongation of the PT bars (∆TPT) and (3) initial
axial force in the column (Pi). For an exterior column, the axial force developed by
overturning moment of the SC-MRF should also be considered. The total axial force in a column (Pcol) is
= +( )( 2 _ − sin(θ _ ))θ _ +
col i PT col anchor r col r col i
P T K d h P (5)
The shear resistance provided by friction at the column-grade beam interface (Vf) is
= µ
f col
V P (6)
µ PT 2_col anchor θr_col θr_col
Vf = (Ti + K (d - h sin( )) + Pi) (7)
where, µ =0.35 (AISC, 2005 a)
There are pretension losses in the bolts in first line, or row closest to the BRS plate. Therefore, the shear resistance provided by the Keeper plate (Vk) is calculated
(AISC, 2005 a) as
= φ (µ )
k bolt u sc b s
V N D h T N (8)
where,
Du = 1.13; a multiplier that reflects the ratio of the mean installed bolt pretension
to the specified minimum bolt pretension =hole factor, 1.0 for standard size holes
sc h
=number of bolts excluding the bolts of first line in keeper plate
bolt
N
=number of slip planes, 1 s
N
= pecified minimun fastener tension b
T s
φ =0.85
Therefore, the total shear resistance at a PT column base connection (Vcol) is
= +
col f k
V V V (9)
µ i PT 2_col anchor θr_col θr_col i φ bolt µ u sc b s
Vcol = (T + K (d - h sin( )) + P ) + N ( D h T N )(10)
2.3. Experimental Evaluation
The test program explored PT column base parameters such as the initial PT force, initial axial force applied to the column, column size and loading history. The PT bars that did not yield and BRS plates that did not fracture were reused in the next test. The columns and beams were also used repeatedly since they remained elastic without structural damage (i.e., plastic hinging or local buckling) during the tests. The PTC-1 and PTC-1D tests and results are described herein. The PTC-1 test specimen was the base configuration, or baseline test. The PTC-1D specimen used the same connection configuration, but a higher PT force.
Figure 3 (a) shows the test-setup of PT column base connection subassembly, which represents two-thirds scale PT column base subassemblies based on design of the prototype 6-story 4-bay SC-MRF. One horizontal actuator and two vertical hydraulic actuators were used to impose horizontal cyclic displacement and axial load in the columns. Cyclic lateral displacements based on the AISC loading protocol (AISC, 2005 b) were applied with column axial loads. The distance between the horizontal actuator and grade beam was1.83m and the distance between the grade beam supports was 5.8m. In order to restrain the horizontal movement of the grade beam, one end of the beam was post-tensioned to the strong wall and the other end was simply supported by a column.
W18x86 columns and grade beams were used for the column base subassembly specimens as shown in Figure 3 (b). A992 Grade 50 steels were used for test specimens. Four 31.8mm diameter post-tensioned Dywidag bars were anchored between half-height of the column to close to the bottom of the below-grade column. The PT bars had nominal ultimate strengths of 1030MPa. The PT bar length was 3.75m, and the distance between the PT bars was 178 mm. Two A572 Grade 50 reinforcing plates (19.0 mm thick, 318 mm wide, 940 mm) were welded to column flanges with a 12.7mm fillet welds. A572 Grade 50 BRS plates (reduced section: 9.53 mm thick, 63.5mm inch wide, 63.8 mm long) were bolted to column flanges with 25.4 mm diameter A490 bolts. Cover plates were used to prevent the buckling of the buckling restrained plates. Shim plates are also used between columns and grade beams to prevent contact with and local bearing failure of the column web.
In the PTC-1 test, the initial PT forces before and after applying column axial load were 836.3 kN and 765.1 kN, respectively. The initial axial force in the column was 587.2 kN, based on loads for the prototype building. Once the axial force was applied to the column top, the total initial tension force of the PT bars decreased 8.5% due to shortening of the column. The total initial PT force after the axial loading was 765.1 kN. The lateral loading was applied according to the AISC loading protocol. The maximum applied drift in the PTC-1 test was 0.04 radians. The normalized moment vs. relative rotation response of PTC-1 is shown in Figure 4. The maximum moment achieved in the test was 70% of nominal plastic moment of the column. The maximum force in the PT bar was about 587.2 kN, which corresponded to 87.5% of the yield force of the bar. Figure 5 shows the deformed configuration of PT column base connection at the level of 4% drift. No significant damage (i.e., plastic hinges or local buckling) was observed in the column or grade beam during test.
In the PTC-1D test, a relatively high PT force was applied at the connection to have the PT bars yield at relatively low drift level. The purpose of the PTC-1D
Connections in Steel Structures VII / Timisoara, Romania / May 30 - June 2, 2012 215 216 Connections in Steel Structures VII / Timisoara, Romania / May 30 - June 2, 2012
test was to investigate the effect of PT bar yielding at an early stage on the behavior of the PT column base connection. The initial PT forces before and after applying column axial load were 1356.7 kN and 1285.5 kN, respectively. The initial axial force in the column was 587.2 kN. The lateral loading was applied according to the AISC loading protocol. The maximum applied drift in PTC-1D test was 0.04 radians. Each PT bar had an average tension force of 339.2 kN, which was about 51% of the yield force of the bar. The normalized moment vs. relative rotation response of PTC-1D is shown in Figure 6. The maximum moment achieved in this test was 77% of nominal plastic moment of the column. No significant yielding was observed in the column and beam during the test except for localized yielding in the panel zone and yielding of the column web. At about 3.4% drift, the PT bars began to yield near the ends of the bars. The loss of the total PT force was about 395.9 kN, which corresponded to 31% of the total initial PT force. However, no significant degradation occurred during 4% drift cycles. Even as the PT bars yielded, the column did self-center upon unloading.
(a) (b) Figure 3. Test-setup and specimen
-0.04 -0.02 0.00 0.02 0.04 -1.0 -0.8 -0.6 -0.4 -0.20.0 0.2 0.4 0.6 0.8 1.0 M / M pn
Relative Rotation (rad)
Figure 4. Normalized moment vs. relative rotation response of PTC-1
(a) (b)
Figure 5. Deformed configuration of PT column base connection (PTC-1)
-0.04 -0.02 0.00 0.02 0.04 -1.0 -0.8 -0.6 -0.4 -0.20.0 0.2 0.4 0.6 0.8 1.0 M / M pn
Relative Rotation (rad)
Figure 6. Normalized moment vs. relative rotation response of PTC-1D 2.4. Verification of design equations
The connection moments predicted by the equations presented earlier compare well with the connection moments from the post-tensioned column base connection subassembly tests. These comparisons are shown for PTC-1 (Figure 7) and PTC- 1D (Figure 8). It is noted that the decompression moment corresponds to event (a) in Figure 7 and Figure 8, the connection moment at initiation of BRS plate yielding corresponds to event (b), the connection moment at relative rotation of 0.02 radians corresponds to event (c) and the connection moment at relative rotation of 0.04 radians corresponds to event (d), respectively. Equation (1) is used for events (b) – (d); the column rotation for BRS plate yielding is predicted based on geometry of the PT column base and the BRS plate yield strain. Event (a) is based on Equation (2) and (3), with corresponds to an assumed zero rotation.
Connections in Steel Structures VII / Timisoara, Romania / May 30 - June 2, 2012 217 218 Connections in Steel Structures VII / Timisoara, Romania / May 30 - June 2, 2012 -0.04 -0.02 0.00 0.02 0.04 -800 -600 -400 -200 0 200 400 600 800 (b) (c) (d) (a) Design equation Mom ent (k N-m )
Relative Rotation (rad)
Experimental data
Figure 7. Comparison of moment vs. relative rotation of PTC-1
-0.04 -0.02 0.00 0.02 0.04 -1000 -800 -600 -400 -2000 200 400 600 800 1000 (d) (c) (b) (a) Experimental Data Mo ment (k N -m )
Relative Rotation (rad) Design Equation
Figure 8. Comparison of moment vs. relative rotation of PTC-1D 3. SUMMARY AND CONCLUSIONS
This paper presented a post-tensioned column base connection for use in steel self-centering moment resisting frames. The PT column base connection consists of PT bars, BRS plates, reinforcing plates, Keeper plates and shim plates. The PT bars provide clamping force and restoring force for the connection, and the BRS plates dissipate energy by yielding. Keeper plates provide additional shear resistance for the PT column bases. The moment-rotation behavior of the PT column base connection is characterized by gap opening and closing at the column-beam interface and yielding of the BRS energy dissipating elements. Results for a pair of PT column base tests demonstrated effects of a higher initial PT force. Design equations were verified with the moment-rotation test results of post-tensioned (PT) column base connection subassemblies subjected to cyclic lateral displacement and axial loading and showed good agreement with the experimental data.
ACKNOWLEDGMENTS
This research was financially supported by the National Science Foundation, CMMI-0420974, in the George E. Brown, Jr. Network for Earthquake Engineering Simulation Research (NEESR) program. Material donations and other support were provided by Steel Dynamics, Inc., Prospect Steel, Benchmark Fabricated Steel, and Nucor Fastener.
REFERENCES
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