international journal of steel structures volume 14 issue 1 2014 [doi 10.1007%2fs13296-014-1006-4]...

8/11/2019 International Journal of Steel Structures Volume 14 Issue 1 2014 [Doi 10.1007%2Fs13296-014-1006-4] Lai, Jiun-Wei

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www.springer.com/journal/13296

International Journal of Steel Structures

March 2014, Vol 14, No 1, 43-58

DOI 10.1007/s13296-014-1006-4

Steel Concentrically Braced Frames usingTubular Structural Sections as Bracing Members:

Design, Full-Scale Testing and Numerical Simulation

Jiun-Wei Lai1,* and Stephen A. Mahin2

1Postdoctoral Researcher, Department of Civil & Environmental Engineering, University of California, Berkeley, USA2Byron L. and Elvira E. Nishkian Professor of Structural Engineering,

Department of Civil & Environmental Engineering, University of California, Berkeley, USA

Director, Pacific Earthquake Engineering Research Center, USA

Abstract

This paper presents the results of experimental and analytical studies carried out on two full-scale, one-bay, two-story steelconcentrically braced frames. Square hollow and round hollow structural sections were used for the bracing components. Thespecimens were designed and detailed according to the 2005 AISC Seismic Provisions, and tested cyclically under displacementcontrol but with a fixed lateral load distribution over height. Numerical computational models including the brace components,gusset plate details and frame members were implemented in OpenSees. Numerical simulations were then performed toinvestigate the cyclic behavior of brace components, brace failure mechanisms and overall system response. Satisfactoryagreement was obtained in comparisons of experimental and numerical results. Premature failures observed suggest that beam-to-gusset plate connections could be pinned to accommodate large rotational demands at this location without the need to formplastic hinges. Test results also showed that for the braced frames having the same configuration, designed for similar base shearcapacities, and subjected to the same roof level displacement history, the braced frame specimen using round tubular sectionsas diagonal braces was able to sustain larger story drifts without brace fracture than the specimen employing square tubularsections. Fracture of the column base in the second specimen, although inconclusive from a single test, suggests more studyis needed of design requirements for column to base plate connections where large variations of axial, bending and shear loadare expected.

Keywords: concentrically braced frames, hysteresis loops, low-cycle fatigue, hollow structural sections, experimental study

1. Introduction

Steel braced frames are considered one of the most

efficient and economical lateral load resisting systems

available to control deformations in civil structures under

wind or earthquake loading. The behavior of braced framesin the elastic range, as expected during wind loading or

minor seismic excitations, has been quite good; however,

a review of the structural performance of steel braced

frames after several major earthquakes has identified

some anticipated and unanticipated damage (AIJ, 1995;

Bonneville and Bartoletti, 1996; Kelly et al., 2000). This

damage has prompted many engineers and researchers to

consider ways of improving the post-elastic behavior of

braced frame systems. One approach has been to increase

the inelastic deformability of the brace by using manufactured

elements, such as buckling restrained braces (Watanabe et

al., 1988) and self-centering braces (Christopoulos et al.,2008). Others have carried out experimental studies (Lee

and Goel, 1987; Tremblay et al., 2002; Roeder and Lehman,

2008) or analytical (Uriz and Mahin, 2008, Chen, 2010)

investigations to assess the ability of braces having different

slenderness and compactness to increase the drift capacity

of braced frames. Another approach has been to reduce

deformation demands by strengthening the system as a

whole (Chen, 2010) or by mitigating local concentrations

of overall system deformation at one or a few stories

(Khatib et al., 1988; Tremblay and Merzouq, 2004).

Although many experimental studies of conventional

buckling brace components and several braced framespecimens have been investigated in the past thirty years

(Black et al., 1980; Ballio and Perotti, 1987; Lee and

Note.-Discussion open until August 1, 2014. This manuscript for thispaper was submitted for review and possible publication on April 29,2012; approved on December 7, 2013. KSSC and Springer 2014

*Corresponding authorTel: +1-510-965-7738E-mail: [email protected]


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44 Jiun-Wei Lai and Stephen A. Mahin/International Journal of Steel Structures, 14(1), 43-58, 2014

Goel, 1987; Bertero et al., 1989; Tremblay, 2002; Roeder

et al., 2004; Yang and Mahin, 2005; Clark et al., 2008;

Roeder and Lehman, 2008; Uriz and Mahin, 2008), the

number of large-scale tests of complete concentric braced

frames needed to assess ultimate system behavior is still

limited.

Since the overall behavior of braced frames is sensitive

to relative proportions, strengths and stiffnesses of members

and local details, system tests are needed to assess fully

the adequacy of current code provisions and suggested

improvements. As such, integrated experimental and

analytical studies are carried out to examine likely seismic

behavior of representative concentrically braced steel frame

systems, and the ability of current analysis methods to

simulate this behavior. In this study, two full-scale, one-

bay, two-story steel concentrically braced frames were

constructed and tested under a series of cyclic lateral

displacement excursions increasing in amplitude up to a

maximum roof drift ratio about 4%. In a companion study

of code-compliant special concentric braced frames (Lai

et al., 2010), nonlinear dynamic analyses showed that

under the most severe hazard level considered (i.e. 2%

probability of exceedence in 50 years), the median

expected maximum story drift ratio is about 3.3%.

2. Design and Analysis of Frame Specimens

2.1. Selection of brace configuration and preliminary

analysis

As part of a George E. Brown, Jr., Network for

Earthquake Engineering Simulation (NEES) Small Group

Project entitled International Hybrid Simulation of

Tomorrows Braced Frame Systems, a coordinated set of

large-scale tests were carried out on various configurations

of concentrically braced frames representative of systems

used in western North America. These tests included two-

story and three-story double story X-braced frames testedat the National Center for Research in Earthquake

Engineering (NCREE) in Taiwan (Clark et al., 2008;

Lumpkin et al., 2010), a three-dimensional frame testedat the University of Minnesota (Palmer et al., 2010), and

two-story frames with diamond-shaped brace configurations

(with a V configuration in the lower story and an

inverted-V shape in the upper story) tested at University

of California, Berkeley. This paper focuses on two of the

Berkeley test specimens. The diamond brace configuration

used for these specimens was selected to complement

other tests carried out in the overall program and to focus

attention on floors where gusset plates are used to

connect braces to columns. Due to space and test rig

limitations, typical story height and beam span were

selected as 2,743 mm and 6,096 mm, respectively, as

shown in Fig. 1. In one specimen, square HSS sections

were used for the braces, while circular HSS sections

were used in the other specimen.

2.2. Design of test rig

Several configurations were considered and carefully

evaluated during the design of the test setup (Lai, 2009).

An overview of the final test setup is shown in Fig. 2.

Thirty reconfigurable reaction blocks (ten blocks per

stack) were grouted together and post-tensioned horizontally

and vertically over a strong floor to create an integrated

reaction wall. The maximum base shear capacity of the

test setup is 4,003 kN (with 2,669 kN applied at the upperlevel and 1,334 kN at the lower level), assuming the load

applied by the lower actuator is half that acting in the

upper one. An Atlas 6,672 kN actuator with 304.8 mm

stoke was attached at each floor level. This stroke capacity

corresponds to about 5% of the total height of the test

specimen. A heavy built-up beam (Fig. 2) was provided

between the specimen and the laboratory strong floor to

spread out concentrated reaction forces at the base of the

specimen. Four additional stiff load transfer beams were

provided below the top flange of the cellular strong floor

to spread out the concentrated uplift forces. Out-of-plane

support of the test specimen was provided along the topof both beams and at the beam-to-column connections by

a stiff and strong transverse support frame shown in Fig.

Figure 2. Overview of the final test setup.

Figure 1. Dimension of test specimen.


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Steel Concentrically Braced Frames using Tubular Structural Sections as Bracing Members: Design, Full-Scale Testing ... 45

2. The lateral supports were designed to move longitudinally

with the test specimen. Details of the test setup design are

summarized in a report by Lai (Lai, 2009).

2.3. Design of braces

For the ideal condition where the top floor is subjected

to twice the lateral force as the lower floor, the braces

were selected to protect the test setup such that story

shears would not exceed 4,003 kN and 2,669 kN in the

lower and upper stories, respectively. By assuming the

braces resist about 80% of the maximum permitted story

shear, using a system over-strength factor of 2 as

stipulated in the AISC Seismic Provisions (AISC, 2005b)

and considering the geometry of the bracing system, the

maximum permitted brace forces were estimated. Detailing

requirements from the AISC Specification (AISC, 2005a)

and AISC Seismic Provisions (AISC, 2005b), such as

limitations on brace slenderness ratio and width-thickness

ratio, were imposed to finalize the brace size and the detailing

of the specimen. For instance, net section reinforcing

plates designed in accordance with AISC Seismic Provisions

(AISC, 2005b) were welded on all tubular brace connection

regions, as shown in Fig. 3, to prevent possible premature

fractures (Yang and Mahin, 2005).

2.4. Design of columns

A tributary gravity load (computed based typical design

dead and live loads for office occupancies and a tributaryfloor area of 18.6 m2) was included in the column design.

The column axial force due to overturning was estimated

by dividing the maximum overturning moment permitted

by the test set up at the base level by the moment arm

between the two columns. Accordingly, the estimated

axial force was 214 kN from the tributary gravity loading

and 3,003 kN from overturning. The demands of bending

moment in the columns were calculated from structural

analysis. Since the specimen was only two-stories tall, a

single piece column extended over both stories. Because

tributary gravity loads contributed only a minor portion of

the total column axial load, these loads were not imposedduring the tests.

2.5. Design of beams

The design approach used for the upper and lower

beams differed slightly. The roof beam was designed

assuming a maximum axial force of 2,669kN (correspondingto the maximum force permitted in the upper actuator).

The bending moment demands for the top beam were

extracted from structural analysis results, considering a

vertical unbalanced force produced by the two braces

intersecting at the beams midspan, as required by the

AISC Seismic Provisions (2005b). For the lower beam,

the maximum axial force was calculated to be 1,415 kN

under the loading conditions shown in Fig. 4 (for

Specimen TCBF-B-1). Bending moments in the lower

beam were calculated from structural analysis. No vertical

unbalanced load was required for the lower beam level

due to the brace configuration.

2.6. Design of gusset plates

All gusset plates were designed for out-of-plane buckling

considering the uniform force method suggested in AISC

Specification (AISC, 2005a). Typical details used (Fig. 5)

incorporated 30-degree tapers and a plastic hinge fold gap

equal to twice the thickness of the gusset plate. To explore

the possibility of simplifying field erection, a single piece

gusset plate was attached to each column at the lower

level. This plate was intended to be welded to the column

in the shop, and to the beam and braces in the field. Two

finger plates were shop welded to each of these gusset

plates to simulate the flanges of a beam continuing to thecolumn face. The fingerplates extend slightly beyond the

ends of the gusset plate tapers (Fig. 6) to facilitate welding

of the beam to the gusset plate.

2.7. Design of connections

All connections were designed considering the maximum

probable force in the interface using the capacity design

approach outlined in the AISC Seismic Provisions (2005b).

2.8. Design of base plates

Base plates and end plates were designed according to

the AISC steel design guide (Fisher and Kloiber, 2006).Table 1 as well as Figs. 7 and 8 summarize the final

Figure 4. The load condition for lower beam.

Figure 3. The net section reinforcing plate.


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member sizes and the material types used. The members

satisfy 2005 AISC requirements for compactness, as can

be noted in Table 2, and very nearly satisfy those in the

draft 2010 edition for highly ductile members. In interpreting

results, it is useful to note that the round HSS brace

sections selected satisfy the compactness requirement by

Figure 7. Member sizes of test specimen TCBF-B-1.

Figure 8. Member sizes of test specimen TCBF-B-2.

Figure 5. Typical gusset plate detail.

Figure 6. The one-piece gusset plate.

Table 1. Name, member size, and material type of the specimen components

NameColumn & Beams Braces

Section and Material b/t (h/tw) Section and Material b/t(D/t) kL/r

TCBF-B-1 W1296 (Column)W24117 (Roof Beam)W2468 (Lower Beam)

(ASTM A992)

6.76 (17.7)7.53 (39.2)7.66 (52.0)

HSS 555/16HSS 663/8

(ASTM A500B)14.214.2

5147

TCBF-B-2HSS 51/2HSS 61/2

(ASTM A500B)10.812.9

6055

Table 2. AISC Seismic Provision Limitations

Seismic ProvisionLimitations

Wide Flange HSS

Flange (b/t) Web (h/tw) Square (b/t) Round (D/t)

2005Seismic

Compactness ps =7.22

ps=52.6 (Column, Ca=0.38)ps=52.3 (Roof Beam, Ca=0.39)ps=53.4 (Lower Beam, Ca=0.35)

ps=16.1 ps=27.7

2010

Highly Ductilehd =7.22md =9.15

hd=47.3 (Column, Ca=0.38)md=52.6 (Column, Ca=0.38)hd=47.1 (Roof Beam, Ca=0.39)md=52.3 (Roof Beam, Ca=0.39)hd=47.8 (Lower Beam, Ca=0.35)

md=53.4 (Lower Beam, Ca=0.35)

hd=13.8md=16.1

hd=24.0md=27.7

Moderately

Ductile


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a far greater margin than do the square sections. All wideflange beams, columns and braces in the specimens were

ASTM A992 steel sections. All braces were made of

ASTM A500 Grade B steel. The 19 mm thick gusset

plates, 51 mm thick base plates, 51 mm stub beam end

plates, 13 mm shear tabs, 16 mm finger plates, 16 mm

continuity plates, 10 mm washer plates for all-thread

anchor rods and brace reinforcing cover plates were made

of ASTM A572 Grade 50 steel plate. Beam web stiffener

plates, lifting lugs, shim plates and miscellaneous parts

were made of ASTM A36 steel plates. High strength

structural fasteners that satisfy the ASTM A490 standard

were used at beam-column connections and the one-piece

gusset plate-to-beam web splices. High strength, all-thread

anchor rods (ASTM A193 Grade B7) were used at

column bases and gusset-to-floor beam base plates.

Figures 9(a) and 10(a) show the photo of specimen

TCBF-B-1 and TCBF-B-2 before testing. To reduce

overall cost of specimen fabrication, the top beam and

two columns in Specimen TCBF-B-1 were reused in

Specimen TCBF-B-2.

3. Loading History

The displacement of the roof beam was monitored and

used to control the overall motion of the specimens. The

lower level actuator was force controlled to have half of

the load applied at the upper level. The resulting lateral

force pattern is a typical inverted triangular distribution.

The test protocol was adapted from the Appendix T of

the AISC Seismic Provisions (AISC, 2005b). An additional

six cycles corresponding to one half of the elastic design

drift (0.5Dbe) and two cycles at the elastic design drift

(Dbe) were added to the beginning of the test protocol.

Figure 11 shows a plot of the cyclic test protocol in terms

of roof displacement and roof drift ratio. Specimen

movement towards the east side of the laboratory (Fig. 1)

is defined as a positive displacement.

During the test process, loading was paused to document

major events, such as brace fracture, weld cracking, or

significant yielding or local buckling of members. Testing

was terminated following any cycle in which both braces

at a single story were completely fractured.

Figure 9. Specimen TCBF-B-1.

Figure 11. Loading protocol for Specimens TCBF-B-1 and TCBF-B-2.

Figure 10. Specimen TCBF-B-2.


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4. Instrumentation

More than two hundred instruments, including linear

strain gages, strain gage rosettes, linear variable differential

transformers (LVDTs), wire pots and tilt-meters wereinstalled and monitored throughout the entire test. The

specimen was whitewashed to help in visual detection of

yielding and damage.

Multiple time lapse digital images were taken using

high-resolution digital single-lens reflex (DSLR) cameras

and stored using desktop computers. Four Canon EOS 5D

Mark-II DSLR cameras were connected to the data

acquisition system and triggered to take still photos every

5 mm of roof displacement. Three Canon EOS D1 DSLR

cameras were connected to desktop computers and shot

still images every 10 seconds continuously throughout the

tests. Additional high definition (HD) videos captured

global and certain local behavior of individual braces. A

three-dimensional Leica HD laser scanner was also used

to capture the specimens deformed shape throughout the

cyclic testing.

5. Test Results

In many respects, Specimens TCBF-B-1 and TCBF-B-

2 behaved as expected. The braces all buckled out-of-

plane (see Figs. 9(b) and 10(b) for details) as intended.

The net section reinforcing plates at the brace-to-gusset

plate connections achieved their purpose, with no weld or

other yielding or fractures noted in these areas. In thegusset plates, the expected yield pattern was developed

within the 2t fold line width provided (Figs. 12(a) and

12(b)). However, as discussed later, significant damage

occurred at the ends of the lower level beam and at the

base of the columns that limited the ultimate displacement

capacity of the specimens. A more detailed description of

the testing process and key observations is provided by

Lai (Lai, 2009).

5.1. Overall behavior

The peak actuator forces (Figs. 13 and 14) throughout

the test in both experiments were all less than the maximumforces permitted for each actuator, which were 2669 kN

for upper level actuator and 1334 kN for lower level

actuator. Thus, no excessive overturning moment was

developed during the test that would overload the test

setup or reaction floor. These figures illustrate that the

degradation of the peak story shear forces occurs rapidly

once the crack in the brace initiated (Figs. 13 and 14) andalso points out that the peak story shear forces degrade

more slowly with cycling for Specimen TCBF-B-2 than

for Specimen TCBF-B-1.

Specimen base shear versus roof displacement hysteresis

loops are presented in Figs. 15 and 16. Loops for both

specimens are fairly stable and repeatable during the early

cycles. However, there is a reduction of load capacity

during repeated cycles to the same displacement. This

cyclic strength deterioration increases with increasing

displacement amplitude.

A more detailed assessment of the hysteretic characteristics

of the specimens can be made by examining the relation

between story shear and story deformations (or story

drifts). Figures 17 and 18 indicate that lateral drifts were

larger in the lower story, especially for Specimen TCBF-

B-1. Interestingly, the individual story deformation excursions

are not symmetric even though the roof displacements are

symmetrically applied. This is mainly associated with the

unequal distribution of story drifts due to the weak story

mechanism that occurs once the braces buckle. The

distribution of drift is also influenced to a smaller extent

by the configuration of the braces and the way that

actuators are attached to the specimen.

5.2. Behavior of bracesBrace axial force versus axial deformation hysteresis

loops are plotted in Figs. 19 and 20. All four braces in

both specimens yielded in tension and buckled in

compression. Since load cells were not installed in the

braces, brace axial forces were estimated in several ways

using strain gauge measurements from portion of the

braces and adjacent elements that remained essentially

elastic in conjunction with elementary mechanics and

equilibrium considerations. The different methods considered

produced similar results and best estimates are plotted

(see Lai and Mahin, 2013 for more details). Minor

deformation hardening during inelastic elongation of thetubular braces is noted in all four braces in both

specimens. The peak compression strength decreased

Figure 12. The yield patterns in the first story gusset plates after testing for both specimens.


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significantly from cycle to cycle. The braces buckled

laterally, and formed plastic hinges in the gusset plates(Fig. 12) and at midspan. The midspan plastic hinge

locally buckled on the compression-most (inside) face of

the section. With increased cycling and deformation,

rupture initiated in the locally buckled region and

propagated during further cycling until complete fracture

of the section occurred. This behavior is representative of

that observed in past component tests (Black et al., 1980;

Lee and Goel, 1987; Tremblay, 2002; Yang and Mahin,

2005). At the end of tests, both braces in the lower story

of both specimens had completely fractured, while the

braces in the upper story had not. A partial fracture was

observed in the upper story east brace in SpecimenTCBF-B-1 (upper part of Fig. 19). No cracks initiated in

the upper story braces in Specimen TCBF-B-2.

The out-of-plane displacements at the mid-span of each

brace are shown in Figs. 21 and 22. The maximum brace

out-of-plane displacements for Specimen TCBF-B-1 wereclosed to 380 mm in the lower story and 240 mm in the

upper story. For Specimen TCBF-B-2, the maximum

brace out-of-plane displacements were close to 500 mm

in the lower story and 340 mm in the upper story. These

brace out-of-plane displacements were as large as about

eight times the axial deformations recorded in the braces

(Figs. 19, 20, 21 and 22). This potential out-of-plane

deformation should be considered when braces are placed

near safety related nonstructural components, such as

stairways, or cladding elements that may pose a falling

hazard.

Figure 21 and the lower part of Fig. 22 show that duringthe last cycles of response out-of-plane displacements

were developed at the peak tension loading. In earlier

Figure 15. Base shear vs. roof displacement relationshipfor Specimen TCBF-B-1.

Figure 16. Base shear vs. roof displacement relationshipfor Specimen TCBR-B-1.

Figure 13. Actuator force and story displacement timehistory for Specimen TCBF-B-1.

Figure 14. Actuator force and story displacement timehistory for Specimen TCBF-B-2.


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cycles, the out-of-plane displacements generally returned

to zero as the brace was loaded in tension. However, once

ruptures initiated at the midspan of a brace, the center of

the remaining material at this section shifted from the

mid-depth of the section. As a result of this eccentricity,

the brace displaced laterally in the direction opposite insign from that occurring during the compression phase of

the cycle. This local bending at the ruptured section

during the tension phase of a cycle is believed to accelerate

the complete fracture of the section. This phenomenon

can be observed in both experiments where the brace

fractured or cracked in the specimen (Fig. 21 and the

lower part of Fig. 22).

5.3. Behavior of columns, beams and connections

During cycles with small lateral displacement, the axial

forces in the east- and west-side columns were nearly of

equal magnitude but opposite in sign. This can be seen inFigs. 23 and 24. Once braces buckled and began to loose

compression capacity, the internal forces in the frames

redistributed so that the tension braces still developed

their full tensile capacity. The unbalance between the

peak compression and tensile forces developed in the

braces resulted in the peak compression forces in the

columns becoming far greater than the peak tensile forces.

The column axial compression force drop gradually withthe deterioration of the compression capacity of the

contiguous brace, and rapidly as the tension brace begins

to rupture. Even with the complete fracture of both braces,

the remaining beams and columns act as a moment-

resisting frame, and some variation of column axial loads

occurred during continued lateral displacement.

Note that in TCBF-B-2 specimen, the CJP weld

connecting on the outermost flange of the west column to

the thick base plate fractured suddenly in the early

portion of the planned test protocol; at a roof drift ratio of

about 0.9%. The fracture initiates in the vicinity of the

heat-affected zone in the base plate and is shown in Fig.25. The column base then underwent emergency repair

using a large cover plate on the fractured flange (which

Figure 18. Story shear vs. story drift relationship forSpecimen TCBF-B-2.

Figure 17. Story shear vs. story drift relationship forSpecimen TCBF-B-1.


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also suffered a small amount of local buckling) and

stiffeners around the column base as shown in Fig. 26.

The modification of the column base for the west-side

column changed that columns stiffness and moved the

potential plastic hinge location upwards.

The strong axis bending moment in the columns at top

and bottom ends in each story were estimated from

readings of strain gages located away from potential plastic

hinge regions. These readings reveal that the columns at

both stories in Specimen TCBF-B-1 remained essentially

elastic throughout the entire experiment, except at the

column bases. Minor flaking of whitewash was alsonoted at the column bases. During the TCBF-B-2 test,

significant yielding (identified through Lders lines seen

in Figs. 25 and 27) occurred in the lower story columns

and also at the bottom end of the west side column in the

upper story (Fig. 28). The peak base shear and column

axial loads in this specimen were slightly higher than

those in Specimen TCBF-B-2. Fracture may have been

also associated with the cumulative effects of prior

inelastic actions that occurred at the column base during

testing of TCBF-B-1. However, as seen in Fig. 25, the

pattern of yield lines, and observed distortion of the

specimen during the tests, suggests that the column base

was subjected to torsional and out-of-plane bending as a

result of the eccentric transfer of forces from the buckledbraces to the column.

The total column shear forces estimated at each story

Figure 19. Estimated brace axial forces vs. brace axial deformations for Specimen TCBF-B-1.

Figure 20. Estimated brace axial forces vs. brace axial deformations for Specimen TCBF-B-2.


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for both specimens are shown in Figs. 29 and 30. Almost

symmetric shear force response was found in Specimen

TCBF-B-1, while un-symmetric response was found in

Specimen TCBF-B-2 after the installation of the repair. It

is believed that this asymmetry is due to local strains in

the gages near the repair exceeding yield (Fig. 27(b)).

From the relationships plotted between total column shear

force and story shear force in Figs. 31 and 32, the

columns took at the beginning of the tests about 17% of

total story shear at both stories. After the braces buckled,

the columns took a greater and greater portion of the total

story shear. A slope of unity in these plots suggests thatthe columns took the entire story shear, as is observed for

the later cycles for the lower story. It is also interesting to

note that the lower story column webs yielded for both

specimens, as identified from significant flaking of white

wash and from shear strain values derived from rosette

gages installed on the columns web. The webs in the

upper level columns remained elastic. The distribution of

whitewash flaking can be seen in Figs. 27(b) and 28(a)

for the west-side column.

The top-level beam behaved as expected. Vertical

deflections developed at the mid-span of the beam. For

both specimens, the peak deflection was about 5 mm (less

than 1/1000 beam span) and the top beam remained elastic

(confirmed by strain gage readings). The maximumunbalanced force applied to the upper beam was estimated

from strain gage readings on the adjacent beams to be

Figure 21. Estimated brace axial forces vs. brace out-of-plane displacements for Specimen TCBF-B-1.

Figure 22. Estimated brace axial forces vs. brace out-of-plane displacements for Specimen TCBF-B-2.


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remaining flange. This suggests that a simple pin connection

at this location might be acceptable.

5.4. Panel zone and gusset plates

No web doubler plates were provided in the panelzones. In both specimens, the lower floor level panel

zones were attached to large gusset plates and did not

yield, while the panel zones in the roof beam-column

connections yielded in both tests (detected by whitewash

flaking and readings from strain rosettes). This inelastic

deformation in the upper level panel zone was compatible

with the plastic hinging noted at the ends of the lower

level beam. No significant adverse effects on system

behavior of either specimen resulted from this yielding.

The one-piece-gusset plates formed a yield line,

perpendicular to the axis of the brace yielded as expected,

near the 2t yield line region in the first and second storygusset plates (Figs. 12, 33 and 34). In the TCBF-B-2 test,

eleven linear strain gages were attached on one face of

Figure 28. Second story column yield patterns forSpecimen TCBF-B-2.

Figure 27. Column base yield patterns for SpecimenTCBF-B-2.

Figure 29. Time history of the sum of column shear

forces in both stories for Specimen TCBF-B-1.

Figure 30. Time history of the sum of column shearforces in both stories for Specimen TCBF-B-2.

Figure 31. Story shear component from two columns vs.total story shear forces for Specimen TCBF-B-1.

Figure 32. Story shear component from two columns vs.total story shear forces for SpecimenTCBF-B-2.


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the one-piece-gusset plate located on the east side of thefirst story. These were used to monitor the axial stain

distribution in the tapered region of the gusset plate.

Figure 35 shows plots of the difference in strains on

corresponding locations on opposite sides of the gusset

plate. The increase in these strains with distance from the

centerline of the brace suggests that the braces contribute

to in-plane frame action.

6. Numerical Simulation of Test Results

In the computational phase of this study, a low-cycle

fatigue sensitive material model (Uriz and Mahin, 2008)

implemented in the computer analysis framework OpenSees

(McKenna, 1997) was used. All wide flange beams,

columns and tubular braces were modeled using force-

based nonlinear beam-column elements with initial

transverse imperfections (about 1/1000 of the member

length). Corotational geometric transformations were used

to capture member geometric nonlinearities under large

deformation (i.e., to simulate member lateral buckling).Fiber sections were used to model the geometric cross

sectional shape of members. The total number of

elements used to represent each brace was 24, and 64

fibers were used to represent each square HSS and round

HSS, as shown in Fig. 36(a). The uniaxial Giuffre-

Menegotto-Pinto steel material with initial elastic tangent

of 200 GPa and a strain-hardening ratio of 0.003 was

used. Yield strength of the steel material was based on the

mill certificate report. Rigid end zones were assumed in

the model connections and gusset plates. Figure 36(b)

schematically illustrates the two-story braced frame

specimen model used with OpenSees.

A series of material calibration trials were done to

identify low-cycle fatigue and other properties for the

braces using existing experimental data on tubular braces

(i.e., Yang and Mahin, 2005). Two typical calibration

results under different loading histories are shown in Figs.

37 and 38. From the plots we can clearly see that the

overall cyclic behaviors in the component tests are

Figure 35. The bending strain time history in the tapered gusset plate at eastern side of Specimen TCBF-B-2.

Figure 33. Plastic hinges formed in the lower beam oSpecimen TCBF-B-1.

Figure 34. Plastic hinges formed in the lower beam oSpecimen TCBF-B-2.


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captured well by the OpenSees low cycle fatigue model.

Using the input parameters obtained from the calibration

results, analyses of the two-story specimens were performed

using the recorded top-level displacement history as

Figure 36. Illustration of OpenSees Two-Story Braced Frame Model.

Figure 37.Square HSS brace axial force-axial displacementrelationships (test vs. OpenSees).

Figure 38.Round HSS brace axial force-axial displacementrelationships (test vs. OpenSees).

Figure 39. Test results vs. OpenSees cyclic pushoverresults for Specimen TCBF-B-1.

Figure 40. Test results vs. OpenSees cyclic pushoverresults for Specimen TCBF-B-2.


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input. The numerical results obtained are compared with

the actual test results for both specimens in Figs. 39 and

40. It is clear that the overall behaviors of two braced

frame specimens are well predicted by the simulation

models, including the deterioration and member failure.

7. Conclusions

Based on the experimental and analytical results

presented, several conclusions can be drawn. It should be

recognized, however, that these are based on two

specimens, each of which includes unique details. As

such, these conclusions may not apply to other brace

configurations, other braces having different slenderness

and compactness ratios, or material properties.

When designed for similar base shear capacity and

subjected to the same loading protocol, the specimen(TCBF-B-2) with braces fabricated from round tubular

sections exhibits better displacement capacity than the

more traditional specimen (TCBF-B-1) that used square

tubular sections as braces. The peak base shear developed

in inelastic cycles was also observed to degrade slower

and local buckling of the braces occurred later in

Specimen TCBF-B-2 specimen under the same test

sequence. The particular round HSS braces used satisfied

AISC requirements for compactness by a far greater

margin than did the square HSS braces. This selection of

a size for the hollow round brace was a consequence of

using a small diameter circular section with a strength

and slenderness similar to that used for the square HSS

brace.

For the inverted triangular pattern of lateral load used

in design and imposed during the tests, story drifts

tended, once brace buckling initiated, to be larger in the

lower level than in the upper story. This concentration of

damage is associated with braces at each level buckling at

different times and degrading at different rates during the

test. This difference is a consequence of the finite number

of sizes from which to pick bracing members satisfying

design requirements, and small differences between the

boundary and initial conditions for the as-built specimens

and the analytical models used in design. Because thestory with the greatest lateral displacement tends have its

strength deteriorate more, damage tends to concentrate

eventually in a single story. In both specimens, selection

of brace sizes as close to the expected demands resulted

in initial lateral buckling of braces in both stories.

However, because of the slower deterioration of strength

exhibited by the compact round HSS braces, the distribution

of lateral displacement for Specimen TCBF-B-2 was

more uniform than for Specimen TCBF-B-1.

The gusset plate details performed as intended. However,

at large lateral displacements, frame action resulted in

plastic hinges at the faces of the gusset plate used toattach the beam to the column. The single-piece gusset

used worked well, but the complexities of the connection

of the beam to the gusset plate may have accelerated local

buckling and fracture of the beam at this location. A

pinned beam-to-gusset detail might be advisable to avoid

such local damage. Test results indicate large axial forces,

including large tensile forces, develop in the beams as a

result of the unbalance in horizontal force components of

the braces joining at the ends of the beam and shortening

of the beam plastic hinge regions. More study is needed

to better understand the required axial strength and

stiffness of beams in concentric braced frames.

The columns from Specimen TCBF-B-1 were reused

for Specimen TCBF-B-2. The failure at one of the

column base welds may be an indication of inadequate

workmanship, or possibly low-cycle fatigue. The behavior

of this particular connection is complicated due to the

absence of a gusset plate at the base of the column to

assist in transferring axial load to the base plate, and thepresence of torsional and out-of-plane bending in the

column associated with the out-of-plane buckling of the

braces at the level above. More study is warranted.

The numerical model implemented in OpenSees was

able to match the experimental results with considerable

accuracy. The key to this modeling was the use of fiber-

based models that captured the brace hysteretic loops

well, and the use of an empirically calibrated low-cycle

fatigue model to capture the progressive rupture the

bracing elements. Such fiber models do not directly

account for the effects of local buckling, and their use

requires careful validation using relevant test results.

Acknowledgment

This research is supported by National Science

Foundation (NSF) under grant number CMMI-0619161.

Financial Support from NSF is greatly appreciated. The

conclusions and opinions expressed in this paper are only

those of the authors and do not necessarily represent the

views of the sponsor. Tests would not have been possible

without the assistance of the Herrick Corporation; their

help on fabricating and erecting the test specimens are

greatly appreciated.

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