Eccentric Braced Frame System Performance
E. M. Hines1 and C.C. Jacob2
1
Professor of Practice, Tufts University, Medford, MA 02155; PH (617) 868-1200;
email: [email protected]
2
Graduate Research Assistant, Tufts University, Medford, MA 02155;
email: [email protected]
ABSTRACT
Recent discussions related to the seismic performance of low-ductility steel systems
designed for moderate seismic regions have generated new interest in the costeffective design of ductile systems for such regions. Although eccentrically braced
frames (EBFs) have a well-established reputation as high-ductility systems and have
the potential to offer cost-effective solutions in moderate seismic regions, their
system performance has not been widely discussed. This paper discusses the
historical development of EBFs and their provisions, highlighting previous studies on
EBF system performance. New performance assessment results for EBFs in
moderate seismic regions are compared to previous system studies with the intention
of clarifying the nature of EBF system performance including: story drift capacity,
response to higher mode effects, and frame overturning forces.
INTRODUCTION
Eccentrically Braced Frames (EBFs) are known for their attractive combination of
high elastic stiffness and superior inelastic performance characteristics (AISC 2005).
Since 1993, ASCE 7 has recognized EBFs as high ductility systems, assigning them
Response Modification Coefficients (R-factors) of 8 or 7 depending on whether or not
they contain moment resisting connections at columns away from the shear links
(ASCE 1993). While ASCE 7-88 did not distinguish EBFs from other braced frame
systems with a Horizontal Force Factor (K-factor) of 1.00, or from other braced frame
dual systems with K = 0.8 (ASCE 1990), the 1988 NEHRP Provisions (BSSC 1988)
recommended similar values of R = 8 or 7 prior to their adoption by ASCE 7. Also
prior to adoption by ASCE 7, the 1990 SEAOC provisions recommended Rw = 10 for
EBFs and Rw = 12 for EBF Dual Systems, without distinguishing whether beams
were moment-connected to columns away from shear links.
The development of these early EBF provisions marked the close of an
intensive period of research on EBFs conducted mostly at the University of
California, Berkeley (UCB) under the direction of Professors Popov and Bertero. This
research focused both on behavior and modeling of shear links as components and
systems (Roeder and Popov 1977, 1978, Yang 1982, Malley and Popov 1983, 1984,
Hjelmstad and Popov 1983, 1984, Kasai and Popov 1986a, 1986b, Uang and Bertero
1986, Whittaker et al. 1987, Whittaker et al. 1990, Engelhardt and Popov 1988, 1992,
Ricles and Popov 1994). The primary Berkeley systems tests consisted of two
separate 0.3 scale shake table tests of Concentrically Braced Frame (CBF) and EBF
dual systems (Uang and Bertero 1986, Whittaker et al. 1987, Whittaker et al. 1990).
These shake table tests were designed and conducted as part of the US-Japan
cooperative research program (UCB 1979). During this period of research, designers
also published case studies of EBF designs (Libby 1981, Merovich et al. 1982).
After this initial wave of research and design, relatively little was published
related to EBF design and behavior until the design of shear links for the tower of the
San Francisco-Oakland Bay Bridge East Bay self-anchored suspension span
(McDaniel et al. 2003). This idea of shear links as a general ductile element that can
be replaced after damage, has developed further in recent work by Dusicka et al.
(2009). More recent research into conventional EBFs has focused on updated
material characteristics, as well as new detailing requirements for stiffeners and new
insights into appropriate loading protocols (Richards 2004, Okazaki et al. 2005,
Okazaki and Engelhardt 2007).
While this EBF literature is rich with emphasis on link behavior and detailing
requirements to achieve component ductility, relatively little has been written about
EBF system behavior in light of performance objectives. Discussions leading to the
current AISC design provisions focused mostly on the details of the link itself with an
emphasis on a capacity design philosophy to protect the elastic elements of an EBF
system (Popov et al. 1989). When these discussions were written, however, the 0.3scale Berkeley tests remained the extent of the systems level work completed on
EBFs. In addition to discussing new ideas for shear links in non-traditional EBF
frames as mentioned above, current EBF research has also begun to revisit the
relationship between element deformation and system deformation (Richards and
Thompson 2009).
This new research, coupled with questions related to the efficacy of EBF
designs for moderate seismic regions (Hines 2009), raises questions related to EBF
system behavior that ought to be discussed in light of the performance assessment
tools that have evolved out of the structural engineering profession’s response to the
Northridge Earthquake (SAC 2000, ATC 2009). For the calibration of these tools at
the systems level, the 0.3-scale Berkeley EBF dual system test provides the most
important experimental data to date. This paper discusses the development of nonlinear dynamic EBF models calibrated based on the Berkeley tests and used to
develop performance assessments for buildings in moderate seismic regions. These
performance assessments are based on the ATC-63 approach (ATC 2009) with
modifications for moderate seismic regions as recommended by Hines et al. (2009).
EBF SHAKE TABLE TESTS AT BERKELEY AND THE R-FACTOR
In 1990, Whittaker, Uang and Bertero concluded from shake table tests of CBF and
EBF dual systems at the University of California, Berkeley, that the current “response
modification factors assumed by the ATC and SEAOC for these dual systems are
non-conservative” (Whittaker et al. 1990, p. 145). Table 1 lists the R-factors
recommended by various model codes around the time of the Berkeley tests and
reports. The systems in Column (1) not identified previously are the Concentric
Brace Dual System (CBDS) and the Eccentric Brace Dual System (EBDS). Columns
(2) and (3) list values for CBDS and EBDS discussed by Whittaker et al. based on the
1984 version of ATC 3-06, and the 1986 version of the SEAOC provisions. The
values in Column (2) for the CBF and EBF were filled in by the authors based on the
1978 version of ATC 3-06 (ATC 1978). Columns (3) and (7) list Rw-factors, which
Whittaker et al. converted to equivalent R-factors by dividing by 1.25. Column (4)
lists the R-factors recommended for general use by Whittaker et al. on page 146 of
their report, and Column (5) lists R-factors estimated by Whittaker et al. on page 140,
based on the actual test units at UCB. Columns (6) and (7) list the R- and Rw-factors
from BSSC and SEAOC mentioned in the introduction to this paper.
Table 1. R- and Rw-Factors related to Berkeley Shake Table Tests.
System
ATC 3-06
(1984)
SEAOC-Rw
(1986)
UCB
Rec.
UCB
U. Bound
BSSC
(1988)
SEAOC-Rw
(1990)
(1)
CBF
CBDS
EBF
EBDS
(2)
5
6
5
6
(3)
(4)
2
2.5
4
5
(5)
(6)
5
6
8/7
8/7
(7)
8
10
10
12
10
12
4.5
6
Table 1 shows the remarkable transition of the EBF R-factor from R = 4 as
recommended by Whittaker et al. to R = 7 (for frames without moment connections
between beams and columns away from the shear links), which has been the standard
since the early 90s (ASCE 1993). The authors are not aware of a document in the
literature explaining this transition. Anecdotal explanations, however, have suggested
that code committees were interested in distinguishing EBFs from CBFs as more
ductile systems, and hence, the ATC 3-06 R-factor of 5 for the EBF was raised to 7.
In other words, the recommendations by Whittaker et al. may have been perceived as
too conservative and inconsistent with conventional wisdom. Clearer understanding
of this transition is important for future work on EBFs because the widely accepted
standard of R = 7 for EBFs cannot be easily traced to specific test results or analyses.
Whittaker et al. (1987, 1990) clarified that the Berkeley EBF test structure
was designed to relate to the full-scale prototype structure tested pseudodynamically
in Japan. This structure, in turn, had been designed to accommodate both 1979
Uniform Building Code (UBC) and the 1981 Japanese Aseismic Code (JAC). As a
result of the high forces prescribed by these two codes, the prototype structure and the
0.3-scale Berkeley structure were significantly stronger than an EBF or an EBF dual
system as prescribed by later US model codes.
ANALYTICAL MODEL CALIBRATION AND COMPARISON OF
BERKELEY TESTS TO US STANDARDS
As part of the analytical model calibration process, the authors developed a model of
the 0.3-scale Berkeley EBDS (UCB). A full report of the model and its observed
behavior can be found in Jacob (2010). Table 2 lists the design base shears for the
prototype according to the codes referenced by Whittaker et al. (1990) and according
to ASCE 7-05. Table 3 lists member sizes for the UCB prototype design. Future
work will include evaluation of a model designed according to the ASCE 7-05
standard for comparison to the stronger UCB design.
Table 2. Prototype Base Shear Coefficients for UCB Tests.
Base
Shear
Coefficient
(1)
Nominal
EBF
MRF
Total
UBC
(1979)
(2)
0.113
125% =
0.141
50% =
0.056
0.197
JAC
(1981)
(3)
N/A
66% =
0.130
34% =
0.067
0.197
UBC
(1985)
(4)
0.113
125% =
0.141
25% =
0.028
0.169
ATC 3-06
(1984)
(5)
0.133
90% =
0.120
25% =
0.033
0.153
SEAOC
(1986)
(6)
0.075
90% =
0.068
25% =
0.019
0.087
ASCE
(2005)
(7)
0.124
100% =
0.124
25% =
0.031
0.155
Table 3. UCB EBF Prototype.
Story/ Floor Beam/ Link 6/R W16x31 5/6 W16x31 4/5 W18x35 3/4 W18x35 2/3 W18x40 1/2 W18x40 *Weak axis orientation Columns Interior Exterior* W10x49 W10x49 W10x49 W10x49 W12x72 W10x60 W12x72 W10x60 W12x106 W12x79 W12x136 W12x106 Braces TS8x6x0.313 TS8x6x0.313 TS8x6x0.375 TS8x6x0.375 TS8x6x0.375 TS8x6x0.375 Figure 1 shows a favorable comparison of story displacement plots for the
authors’ UCB model and the UCB test results under the “Taft-57” acceleration input.
For clarity, displacement response is shown only for the time window of 4 to 10
seconds where the largest displacements were observed. Figure 2 compares Level 2
shear link hysteresis loops for the UCB test and the UCB model, showing relatively
consistent inelastic behavior between the test and the model. Note that test data
available for the Whittaker et al. (1987) report provided only the brace vertical forces,
i.e. the link shear plus the backspan shear. Hence, for comparison, the UCB model
response is also plotted with respect to the brace vertical forces.
Roof
1.8
0.9
0.0
-0.9
Level 6
-1.8
1.8
0.9
0.0
-0.9
Level 5
0.9
0.0
-0.9
Level 3
Level 4
-1.8
1.8
Level 2
Displacement (in.)
-1.8
1.8
0.9
0.0
-0.9
-1.8
1.8
0.9
0.0
-0.9
-1.8
1.8
0.9
UCB Test
UCB Model
0.0
-0.9
-1.8
4
5
6
7
8
Time (seconds)
9
Figure 1. Story Displacements for UCB Test Results and UCB Model.
10
UCB Test
Brace Vertical Force (kips)
40
UCB Model
40
20
20
0
0
-20
-40
-0.10
-20
-0.05
0.00
0.05
0.10 -0.10
-0.05
0.00
0.05
-40
0.10
Link Shear Strain (radians)
Figure 2. Level 2 Shear Link Hysteresis for UCB Model and UCB Test Results.
PERFORMANCE ASSESSMENT OF 9-STORY EBF FOR BOSTON,
MASSACHUSETTS
Based on the modeling techniques calibrated from the Berkeley shake table tests
(Jacob 2010), a 9-story EBF was modeled on the design by Hines (2009) for Boston,
Massachusetts. The intent of this design was to reduce all link capacities to the
minimum required by code, thereby reducing the capacity design requirements for the
braces and columns. This design philosophy resulted in shear links whose sizes were
controlled by wind loads. In the upper stories of the building, several shear links
were allowed to be up to 6 ft long W10x19s. While these upper links appeared
remarkably small, they satisfied the letter of the code and raised the question as to
their performance under higher mode effects. Hines et al. (2009) demonstrated that
higher mode effects affected the upper story behavior significantly in low-ductility
CBF systems.
This 9-story model served as the basis for performance assessments as
outlined by ATC-63 (ATC 2009) and modified for moderate seismic regions: to refer
to scale factor as opposed to spectral acceleration, to allow a richly varying suite of
motions, and to allow for direct assessment of soil amplification (Hines et al. 2009).
The ground motion suite for Site Class D in Boston was adapted from the work
developed by Sorabella (2006) and used by Hines et al. (2009) for assessment of
chevron braced CBFs in Boston.
Figure 3 shows two fragility curves resulting from this performance
assessment. Each curve is shown both in its raw form, as taken from the incremental
dynamic analysis (IDA) results of 15 ground motions, and in its smoothed form
assuming βRTR = 0.4 and βTOT = 0.53. The curves labeled “Reqd.” in Figure 3 reflect
IDA results that were terminated once the first shear link reached its allowable
rotation as defined by the AISC Seismic Provisions (AISC 2005). The curves labeled
“Tests” in Figure 3 reflect IDA results that were terminated once the first shear link
reached its allowable rotation as interpreted by test results reported by Okazaki and
Engelhardt (2007). The performance level represented by these curves relates to
allowable inelastic link rotation and not to system collapse. Therefore, these curves
may not be compared directly to other results for CBFs in Boston which included
reserve system capacity and carried IDAs up to the models’ system collapse.
The performance implied by these two fragility curves does not meet the
recommended 10% threshold. If link rotations are only allowed to reach the levels
prescribed by the AISC Seismic Provisions, there is a 78% chance of the model not
performing as intended. If the rotation limits are relaxed to correspond more closely
to test results, there is a 25% chance of the model not performing as intended.
1.00
0.80
Probability
Reqd.
Reqd. (data)
0.60
Tests
Tests (data)
0.40
0.20
0.00
0
1
2
3
4
5
6
Scale Factor
7
8
9
10
Figure 3. Fragility Curves for EBF Performance Assessment.
All of the IDA results represented in Figure 3 reflect rotation limits at Levels
7 and higher, precisely in the region of the long shear links, and precisely where the
structure is most heavily affected by higher mode effects. The results in Figure 3
suggest that all EBF designs for moderate seismic regions may not necessarily
provide the level of performance implied by the value R = 7 in ASCE 7. Future
analytical work should address the effects of shortening these links, strength
degradation of links that exceed allowable inelastic rotations, and the effects of
system reserve capacity.
CONCLUSIONS
The performance assessments presented in this paper suggest that some EBFs may
ultimately rely on system reserve capacity in order to survive an MCE event in a
moderate seismic region. While Hines (2009) demonstrated that the 9-story EBF
frame in question could be designed to satisfy the AISC Seismic Provisions without
exceeding the weight of a similar R = 3 CBF structure, the resulting performance
does not appear to be substantial improvement on a low-ductility CBF with an
adequate reserve system.
The actual behavior of EBFs in all seismic regions, and their expected
performance according to probabilistic methods such as ATC-63, remains the subject
of future research. The apparent discrepancy between the recommendations of
Whittaker et al. (1990) and the code prescribed R-factor for EBFs underscores this
need for further research and discussion regarding EBF performance levels. While
Popov et al. (1989) reported that a 6-story EBF designed as a demonstration of the
new U.S. code provisions performed within acceptable limits under several strong
motions, these results do not necessarily imply adequate probabilistic performance
according to newer methods. They also do not imply adequate performance of
structures with longer links, which may be considered inferior, but may not be
explicitly prohibited by codes.
In the same paper, Popov et al. underscored the need for further analysis to
determine the capacity design loads on EBF columns. As the AISC Seismic
Provisions still require EBF columns to resist overstrength loads from all links
yielding simultaneously, there is strong incentive to design links that are as weak as
possible. For the Boston structure discussed in this paper, the longer, weaker links at
the top of the building experienced problems due to higher mode effects.
Interestingly, such higher mode effects will generally benefit column design criteria
by reducing building overturning forces. It is therefore advisable to study the
relationship between EBF system ductility and column overstrength demands with the
aim of ensuring maximum link rotation capacity while minimizing overturning
forces.
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