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Experimental Study of All-Steel Buckling-restrained Braces under Cyclic
Loading
Ahmad Fayeq Ghowsi & Dipti Ranjan Sahoo Department of civil Engineering, Indian Institute of Technology Delhi, New Delhi-16 (INDIA)
ABSTRACT:
Buckling-restrained braces (BRBs) are the type of braces which capable of yielding in tension and compression
under cyclic loading. BRBs provide the nearly symmetrical hysteretic response under cyclic loading and higher
energy dissipation. Though the all-steel BRBs are considered as cost-effective and light-weight, the main
parameters influence their cyclic performance are the flexibility of steel restraining elements, friction between core
the restrainers, and interlocking mechanism. In this study, the cyclic performance of all-steel BRBs (ABRB) with
angle restrainers has been investigated experimentally. Two reduced-scale ABRB specimens with and without
welded stiffeners are tested under cyclic displacements in accordance with AISC 341-10 (2010) provisions Both
specimens are subjected to axial strain of 3.5%. The main parameters studied are hysteretic response, energy
dissipation response, and displacement ductility. A finite element model has also been developed to predict the
cyclic response of ABRB specimens and to compare the experimental results.
Keywords: Buckling-restrained braces; Cyclic loading; Finite element analyses; Hysteretic energy; Experiment.
1. INTRODUCTION
Conventional steel braced frames (CBFs) used as the lateral load-resisting systems have high stiffness
with less lateral displacement under earthquake and wind loadings. However, the buckling failure of
steel braces can limit their ductility and energy dissipation potential. Buckling-restrained brace (BRB) is
becoming popular because of the high ductility, symmetrical hysteretic behaviour, and good energy
dissipation. A BRB exhibit significant inelastic deformation while yielding in both tension as well as
compression. The restraining mechanism prevents the global buckling of inner core undergoing into the
higher mode of local buckling (Wu et al, 2014; Kersting et al. 2015). This restraining mechanism results
in the superior seismic performance of buckling-restrained braced frames (BRBFs) by developing the
symmetrical hysteretic behaviour in BRBs under tension and compression and providing significant
energy dissipation under earthquakes Clark et al (1999).
The typical BRBs used in USA consisted of hollow square, circular, and rectangular steel sections filled
with cement mortar (Kim et al., 2015). Other BRBs developed till date consisted of all-steel restraining
elements with welded or bolted connections (Xie, 2005; Tremblay et al., 2006; Usami et al., 2008;
Plazzo et al., 2009; Chao and Chen, 2009; Chao and Chen, 2010; Takeuchi et al, 2010; Corte et al. 2014;
Wu and Mei, 2015; Deng et al., 2015; Hoveidae and Rafezy, 2015; Metelli et al., 2016; Khoo et al.,
2016; Shen et al., 2016; Midorikawa et al., 2016; Chen et al., 2016). All-steel BRBs can be made lighter
compares to the conventional BRBs (Dusicka and Tinker, 2013). The big challenge in steel BRB is
minimization of friction between the core and restrainers parts. The friction can cause an increase in the
compressive overstrength of BRBs. Friction can also transfer the load to the casing parts of BRBs which
may cause of global buckling in the BRBs (Judd et al., 2014). More use of welding can cause more
friction between the core and frictions interfaces (Eryasar and Topkaya, 2010; Eryasar, 2009). The
global buckling of BRB may occur due to the weak flexural stiffness of restraint members (Hoveidae
and Rafezy, 2012). Further, the position of stoppers, interlocking, and end rotation may influence the
hysteretic response and energy dissipation potential of all-steel BRBs. Since a steel BRB system is light
in weight, minimizing the friction and end rotation without interlocking has not been explored till date.
Hence, more experimental studies are required.
2. SCOPE AND OBJECTIVES
In this study, an experimental study has conducted on all-steel angle BRB (ABRB). ABRB is an all steel
BRB which uses four angle restrained the core to resist global flexural as well as rotation the brace and
forced the core to the higher mode buckling. In this study, a cyclic test of two ABRB conducted to
investigate the hysteretic behaviour under both axil and rotational demands. The sub-assemblages of
ABRB specimens are subjected under quasi-static displacement control loading in accordance with
AISC 341-10 (2010) provisions. A finite element model has been developed and validated using the
experimental results.
3. DESIGN OF TEST SPECIMENS
Two ABRB specimens of same dimensions with two different stoppers detailing are considered in this
study. Figure 1 shows the component of ABRB in which the BRB core of rectangular core cross-section
and cruciform shape of ends and transition zones are used. The core cross-section of ABRB specimens is
40 mm x8 mm and the length of core is 1000 mm. Figure 2 shows the combined assembly of ABRB
specimens with cross-section details. 8 mm diameter bolts at a spacing of 30 mm on centres are used
along the length of specimens. The restrainer angles are attached to each other using bolted connections.
A spacer (gap control) plate is placed between every two angles to limit the gap between the core and
restrained parts. The cruciform shaped end regions are designed to remain elastic even at the ultimate
load of the core. These angles are extended to cover almost ends portions to prevent the possible end
rotations. Additional stiffening plates are welded to the angle restrainer. To minimize the friction, the
core plate is wrapped with a 1mm thick Polytetrafluoroethylene (PTFE) sheets.
a) ABRB core dimension (mm), (b)Orientation of gap control plates
(c) Angle restrainers
Figure 1. Various components of ABRB specimen
(Section a-a) (Section b-b) (Section c-c)
Figure 2. Details of ABRB assembly
Figure 3 shows the test set-up and overall ABRB assembly subjected under cyclic loading. The total
length between the work point to work point of braces is 2.45m, with a column high 1.75m. The brace is
fixed at both ends and not allowed to rotate. The bottom column and bottom of braced end is connected
to a plate which is fastened to the rigid floor. A servo-controlled hydraulic actuator of 500 kN capacity is
used to apply the cyclic loading to the ABRB specimens.
unbounded
material
ABRB Core
Figure 3. ABRB test set-up
3.1 Material testing
A material of grade Fe410 with specified yield stress of 250 MPa is used as the steel core of the
specimens. Coupon tests are carried out to determine the tensile stress-strain characteristics of the plates.
Figure 4 shows the coupon test results. The measured yield and ultimate stress values are 269 MPa and
397 MPa, respectively.
0.00 0.04 0.08 0.12 0.16 0.200
100
200
300
400
Str
ess (
MP
a)
Strain (%)
Figure 4. Tensile stress-strain characteristics of core plate
3.2 Design of strength of specimens
Normal and shear design load on bolts are computed based on recommendation of Chen-Wu (2014).
Bolts used are of high strength of grade 8.8 with 8 mm diameter. The maximum compressive axial
strength in steel BRB for the purpose of transferring load trough the higher mode buckling can defined
as follows:
yy PRP max (1)
Where, Ry is the overstrength factor, ω is the strain-hardening adjustment factor, β is the compression
strength adjustment factor, and Py is the axial yield strength of steel. Table 1 summarizes the assumed
design parameters used in this study. The core area of ABRB is 320 mm2 and the over-strength factor is
computed as 1.076.
Table 1. Assumed design parameters
Description Value
Plastic Poisson’s ratio (ᵞ) 0.5
Expected maximum core strain (c) 0.04
Width of ABRB core (wc) 40 mm
Core thickness (tc) 8 mm
Gap between core and restrainers on strong side (Ss) 2 mm
Gap between core and restrainers on weak side (Sw) 2 mm
Center-to-center distance between two bolts (Lc) 100 mm
Center-to-center distance between two continues bolts (Lw) 100 mm
Material overstrength (Ry) 1.076
strain-hardening adjustment factor (ω) 1.54
compression strength adjustment factor (β) 1.04
Maximum load can be carrying by the ABRB at the ultimate level, max 137.9 P kN
Design of bolts
The wave length and the wave shape within BRB core produce a lateral force over the restrainers which
should be considered in the design on the weak and strong axis. The maximum tensile load demand over
the bolts through the higher mode buckling on the strong axis surface of the core is given by (Wu 2014).
max
4 213.2 S c c
S
c
S wN P kN
L
(2)
Maximum tensile strength (Ft) of 8 mm bolt with using bolt stress Pt as 560 MPa is computed as follows:
28.14 13.2 t t boltF P A kN kN
The load from the higher mode of buckling of BRB acting on the weak surface axis over the bolts, which
can cause shear failure, is computed as follows:
max
4 211.5 w c c
w
w
S tN P kN
L
(3)
Maximum shear strength (V) of the bolt using bolt strength Pv as 375 MPa is given by
18.85 11.5 v boltV P A kN kN
ABRB core design strength
The design axial strength of ABRB is given by
yy PRP (4)
Where, is taken 0.9 as design strength factor.
Accordingly, the design axial strength is computed as 124 kN.
4. EXPERIMENTAL RESULTS
Figure 5(a) shows the test set-up used in the cyclic testing of ABRB specimens. LVDTs are used for
measuring the axial deformation as well as lateral displacement of specimens. The horizontal load from
the actuator has been inclined in the axial direction of brace and assumed that the angle as constant
angle. As shown in Figure 5(b), the selected loading protocol consisted of two cycles at each
deformation of axial strain of 0.5, 1, 1.5, 2, 2.5, 3, and 3.5% with an increment of 0.5% after every two
cycles. The strain rate of loading is 0.25mm/sec for the first four cycles and 0.5 mm/sec for the last 5
cycles.
0 5 10 15 20 25 30 35-4
-3
-2
-1
0
1
2
3
4
Str
ain
(%
)Time steps
(a) (b)
Figure 5. (a) ABRB assembly with instrumentations and (b) loading protocol
ABRB with welded stoppers performed well for the loading cycles up to 3% of axial strain. The stable
hysteretic response is noted in the first cycles of 3.5% axial strain as shown in Figure 6(a). Tensile
fracture on the second cycle of 3.5% as shown in Figure 6(b). Load control test has been done for the
purpose of effective stiffness of the ABRB. The effective stiffness of ABRB is calculated as follows:
(FEMA-356, 2000)
FFkeff (5)
Where, Keff is the effective stiffness, F+ is the maximum in positive load, F- is the minimum in negative
of compressive load, + is the maximum deflection in elastic range, and - is the minimum deflection of
brace in elastic range. For ABRB with wilding stopper, the effective stiffness is 45.1 kN/mm.
-40 -30 -20 -10 0 10 20 30 40-200
-150
-100
-50
0
50
100
150
200
Ax
ial
forc
e (k
N)
Axial displacement (mm)
ABRB with welded stopper
(a) (b)
Figure 6: Test results of ABRB without stopper (a) Hysteretic response, (b) core fracture
Figure 7 shows the hysteretic response and fracture of brace core. ABRB without welded stopper
performed well up to 3% of axial strain. Though stable hysteretic is noted in compression cycle of 3.5%
axial strain, the brace core fracture is noted in the tension cycle. The effective stiffness of ABRB without
welded stoppers is noted as 43.6 kN/mm.
LVDT
BRB
-40 -30 -20 -10 0 10 20 30 40-200
-150
-100
-50
0
50
100
150
200
Ax
ial
forc
e (k
N)
Axial displacement (mm)
ABRB without welded stopper
(a) (b)
Figure 7. Test results of ABRB without stopper (a) Hysteretic response, (b) core fracture
The theoretical elastic stiffness of ABRB can be calculated as follows:
contryi
c
kkk
k111
11 (6)
Where,
yi
yi
yiL
EAk is elastic stiffness of ABRB core portion,
con
concon
L
EAk is stiffness of end portions
of ABRB, and tr
trtr
L
EAk is the stiffness of transition portions. The overall theoretical stiffness is
56.32 kN/mm. A comparison of theoretically computed and experimentally observed values of elastic
stiffness of ABRB specimens has been summarized in Table 2. Experimental values are found to be
about 20% smaller than the theoretical ones. The difference between the theoretical and experimental
stiffness values may be due to the non-inclusion of the influence of gussets plates, bolts, and others
components of ABRB specimens.
Table 2. Comparison of elastic stiffness
Specimen name Theoretical Stiffness
cK1 (kN/mm)
Computed Stiffness, eK1 (kN/mm)
Difference (%)
ABRB with stopper 55.6
45.1 -19.1
ABRB without stoppers 43.6 -22.2
Post-yield stiffness of ABRB can be expressed as follows:
cc KK 12 (7)
Where, 2
cK is the post-yield (secondary) stiffness, 1
cK is the elastic stiffness, and is the ratio of
post-yield stiffness ratio.
The value of is computed as 2.79% for ABRB specimen with welded stoppers and 2.98% for ABRB
specimens without stoppers. These values are found to be 10-15% higher than the conventionally
assumed values of 2% for BRBs. The maximum tensile force, maxT and the maximum compressive
force, maxC are also determined from the experimental results. These axial strengths are computed
corresponding to the peak deformed position of specimens. The compressive adjustment factor, β can
expressed as follows:
peak
peak
T
C (8)
Where, Cpeak is the peak compressive and Tpeak is the peak tension force after first significant yield. The
strength hardening adjustment factor of ω is given by.
yscysc
peak
AF
T (9)
Where Fysc is the yield stress of core plate and calculated based on coupon test result, and Aysc is the brace
area of ABRB core. The hardening adjustment factor and compressive adjustment factor has been
compared in Table 3.
Table 3. Comparison of strength adjustment parameters
Specimen nP (kN) maxT (kN) maxC (kN) β ω βωmax
ABRB with stopper 124 148 188 1.27 1.49 1.89
ABRB without stoppers 124 151 172 1.14 1.38 1.57
5. FINITE ELEMENT MODELING
Finite element ABRB models are developed in ABAQUS CAE (2010) platform to predict their cyclic
response under two different stopper consideration. Steel cores of BRB are modelled using eight-node
solid (C3D8R) elements having reduced-integration technique. Combined isotropic and kinematic strain
hardening properties is considered for the non-linear material modelling elastic and plastic material to
account for their cyclic hardening behaviour. The stoppers are modelled as the same as the core
segments on both sides of weak surfaces of ABRB models, which are provided at centre of the core to
keep safe from creeping of the core in the casing. One millimetre gaps are provided on each side. The
restrainers are also modelled as eight-node solid (C3D8R) elements with reduced-integration technique
and with elastic properties. Surface-to-surface contact with tangential behaviour having friction
coefficient of 0.1, normal behaviour as hard contact and the tangential behaviour used with penalty
friction formulation. In normal behaviour, the maximum stiffness value is used as default with stiffness
scale factor of one, Initial/Final stiffness ratio as 0.01, upper quadratic limit scale factor as 0.03, lower
quadratic limit ratio as 0.3333, and the zero clearance at which contact pressure is zero. The restrainer
parts are connected by tie constraints with each other and considered to remain elastically during
analysis.
The material yield stress at zero plastic strain is taken as 269 MPa as found from excremental results for
ABRB with weld stoppers and without stoppers. The combined hardening parameters used in the
ABAQUS modelling are: C1 =10 GPa, γ1 = 48, Q∞ = 45 MPa and b = 4 (Korzekwa and Tremblay,
2009). An initial imperfection of total BRB length/1000 is assigned based on the first mode of buckling
scaling. The same loading protocol as used in experiment has also been applied to the ABRB models.
Ductile damage has been considered for the prediction of fracture of brace cores in the analytical model.
Figure 8 shows finite element assembly of the ABRB specimens and their final deformed states.
Figure 9 shows the comparison of predicted hysteretic response with the test results. The predicted
hysteresis loops matched very well with the test results. The peak strengths at each axial strain levels
also matched well with test results. The finite element models predicted the brace core fracture at the
same cycle of 3% axial strain in tension.
Figure 8. FEM assembly of ABRB
-40 -30 -20 -10 0 10 20 30 40-200
-150
-100
-50
0
50
100
150
200
EXP
FEM
Axia
l fo
rce
(kN
)
Axial displacement (mm)
ABRB with welded stopper Fracture
-40 -30 -20 -10 0 10 20 30 40-200
-150
-100
-50
0
50
100
150
200
EXP
FEM
Ax
ial
forc
e (k
N)
Axial displacement (mm)
ABRB without welded stopper Fracture
(a) (b)
Figure 9. Comparison of hysteretic response of ABRB model (a) with stopper and (b) without stopper
Figure 10 shows the comparison of backbone curves of hysteretic response and energy dissipation
response of ABRB with weld stoppers. The predicted backbone curve matched reasonable well with the
experimental results though some minor deviation in noted in the tension part. This resulted some
difference in the energy dissipation response. The similar comparison for ABRB specimen without
stopper has been shown in Figure 11. A better match is obtained between the predicted and experimental
results in terms of backbone curves and energy dissipation. ABRB models with stoppers showed better
axial resistance and energy dissipation response. In addition, ABRB specimen with stopper also
exhibited the maximum ductility and cumulative displacement ductility (Table 4).
-40 -30 -20 -10 0 10 20 30 40-200
-150
-100
-50
0
50
100
150
200
Exprimental
FEM
ABRB with welded stopper
Axia
l fo
rce
(kN
)
Axial displacement (mm)
0 2 4 6 8 10 12 140
50
100
150
200
250
Experimental
FEM
Com
ula
tive
ener
gy
(kN
-mm
)
Number of cycles
ABRB with welded stopper
(a) (b)
Figure 10. comparison of numerical with experimental ABRB with welding (a) backbone curve (b) energy
-40 -30 -20 -10 0 10 20 30 40-200
-150
-100
-50
0
50
100
150
200
Exprimental
FEM
ABRB without welded stopper
Axia
l fo
rce
(kN
)
Axial displacement (mm)0 2 4 6 8 10 12 14
0
25
50
75
100
125
150
Experimental
FEM
Com
ula
tive
ener
gy
(kN
-mm
)
Number of cycles
ABRB without welded stopper
(a) (b) Figure 11. compression of numerical with experimental ABRB without stopper (a) backbone curve (b) energy
Table 4. Compression of displacement ductility
Brace type Maximum Ductility
Cumulative Ductility
ABRB with weld stoppers 38.28 779
ABRB without weld stoppers 34.99 647
6. CONCLUSIONS
Based on experimental and analytical studies, the following conclusions can be drawn.
The proposed all-steel BRB exhibited the excellent axial strength, hysteretic response, and
energy dissipation. As compared to conventional BRB, ABRBs are light in weight.
The use of welded stoppers in the brace core significantly influence the overall cyclic response
of ABRB specimens. The welded stoppers help in enhancing the deformability prior to their
fracture.
ABARB specimens with and without stoppers exhibited stable hysteretic energy till 3% core
strain. The core fracture is noted at 3.5% axial strain level for the ABRB specimens.
The post-yield stiffness ratio of ABRB specimen is found about 2.8%. The maximum
displacement ductility of about 40 can be obtained in the ABRB specimens.
The proposed finite element model successfully captured the hysteretic response and fracture
behaviour of ABRB specimens.
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