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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