draft - university of toronto t-space · draft 4 compares the hysteretic behavior of conventional...

Draft

Response modification factors for steel buckling restrained

braced frames designed as per NBCC 2010

Journal: Canadian Journal of Civil Engineering

Manuscript ID cjce-2014-0014.R3

Manuscript Type: Article

Date Submitted by the Author: 25-Apr-2016

Complete List of Authors: Moni, Moniruzzaman; The University of British Columbia, School of Engineering Moradi, Saber; The University of British Columbia, School of Engineering Alam, M. Shahria; The University of British Columbia, School of Engineering

Keyword: response-earthquake load < Struct.Eng. & Constr.Mate, structure - steel <

Struct.Eng. & Constr.Mate, structural engineering < Computer Applications

https://mc06.manuscriptcentral.com/cjce-pubs

Canadian Journal of Civil Engineering

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Response modification factors for steel buckling restrained braced frames

designed as per NBCC 2010

School of Engineering, the University of British Columbia, Kelowna, BC, Canada V1V1V7

Moniruzzaman Moni

Graduate Research Assistant

School of Engineering

The University of British Columbia

1137 Alumni Avenue, EME 3213

Kelowna, BC, V1V1V7

Email: [email protected]

Saber Moradi

PhD candidate




Kelowna, BC, V1V1V7


M. Shahria Alam*

Associate Professor, PEng.




Kelowna, BC, V1V1V7

TEL: (250) 807-9397 | Fax: (250) 807-9850 *Corresponding Author


Word count: 9568

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Response modification factors for steel buckling restrained braced frames

designed as per NBCC 2010

Moniruzzaman Moni, Saber Moradi, and M. Shahria Alam*

School of Engineering, the University of British Columbia, Kelowna, BC, Canada V1V1V7

Abstract: This paper evaluates the overstrength, ductility and response modification factors

for low to mid-rise Buckling Restrained Braced Frames (BRBFs) designed as per the

National Building Code of Canada (NBCC) 2010. In addition to nonlinear static pushover

analyses, dynamic time history analyses are performed to assess the seismic performance of

four-, six-, and eight-story BRBFs. Different bracing configurations, including chevron

(inverted-V) and split-X braces, are considered for the building frames with varied frame

span lengths of 6m and 8m. The results confirm that the prescribed design values for

overstrength and ductility factors provide reasonable estimations of the lower bound for these

factors. The response modification factor obtained in this study ranged from 4.8 to 6 for

different frames. The results also indicate that the response modification factor decreases

with the increase of story height and span length. Moreover, bracing configurations may

slightly affect the response modification factor of BRBFs.

Keywords: steel concentrically braced frame, buckling restrained braced frame, split-X

bracing, chevron bracing, seismic overstrength, ductility factor, response modification factor,

force reduction factor, seismic design, NBCC.

*Corresponding Author, Email: [email protected] Tel: +1.250.807.9397, Fax: +1.250.807.9850

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Introduction

Steel concentrically braced frames are commonly used in buildings to resist lateral loads,

such as earthquakes. The design and fabrication of these systems are simple and the required

lateral strength and stiffness can be achieved at a low cost. Under seismic excitations,

conventional steel braces are expected to dissipate energy by yielding in tension and buckling

in compression (Tremblay et al. 1995). However, during past earthquakes, conventional steel

braced frames suffered extensive damage and bracing members, or their connections,

fractured (Tremblay et al. 1996). The poor performance of braced frames are attributed to

several factors, which include limited ductility or energy dissipation capacity, fracture of

connections, unsymmetrical behavior of braces in tension and compression, and buckling of

braces (Sabelli et al. 2003). In particular, the occurrence of buckling in bracing members

leads to a rapid degradation of story shear resistance and stiffness, and, consequently, the

appearance of large deformations under severe seismic loadings (Khatib et al. 1988, as

mentioned in Tremblay at al. 1995).

As an alternative to conventional braces for steel frames, researchers studied the

implementation of Buckling Restrained Braces (BRBs) in buildings (Clark et al. 1999). Figs.

1a, 1b show the components of a typical BRB. The BRB element consists of a ductile steel

core which is encased in a concrete/mortar filled steel tube. The yielding mechanism is

provided by the steel core while the buckling of the core is prevented by the tube (Uang and

Nakashima 2004). BRBs have the potential to exhibit a stable, symmetrical and repeatable

hysteresis while providing adequate ductility (Tremblay et al. 2006). Experimental studies

show that a properly designed BRBF can resist severe earthquakes with insignificant damage

while experiencing no stiffness or strength degradation (Fahnestock et al. 2007). Fig. 1c

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compares the hysteretic behavior of conventional and buckling restrained bracing members.

A brief review of steel BRBFs can be found in Della Corte et al. (2011).

Several researchers have investigated the seismic behavior and design of BRBFs. Chao et al.

(2013) numerically showed the economical use of BRBs in buildings. The frames with a

hybrid bracing system (BRBs at lower story levels) exhibited a similar seismic performance

compared to that of frames having buckling restrained braces at all story levels. Dusicka et al.

(2013) studied an ultra-lightweight buckling-restrained brace which weighs 27% of a

traditional mortar-filled tube and 41% all-steel buckling-restrained brace configurations.

Palmer et al. (2013) examined the bidirectional behavior of BRBFs through experimental

tests. BRBs can also be used in conjunction with other damping or recentering devices (for

e.g. Miller et al. 2012).

There are several studies proposing and investigating the seismic design procedures for

BRBFs. Choi et al. (2006) studied the performance based design of BRBFs using a modified

energy-balance concept. The study by Bosco and Marino (2013) proposed and numerically

validated a design method for BRBFs. Lin et al. (2013) introduced a seismic design method

for corner gusset plates in steel BRBFs. There are some other studies aimed at evaluating the

design factors specifically for BRBFs (among others, Asgarian and Shokrgozar 2009).

Several studies have confirmed that the use of BRBs can improve the seismic response of

buildings. As a result, design guidelines and standards address the specifications for the

design of BRBFs. Most design guidelines allow for the reduction of design forces when using

the static equivalent force procedure (e.g., ATC-3 1978, as mentioned in Rainer 1987; NBCC

2010). In 2010, force modification factors for BRBFs were added to the NBCC 2010

(Mitchell et al. 2010). The force modification factor (R) includes two characteristics of a

structural system, including ductility and reserve strength. This design concept relies on the

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inherent overstrength and ductility of the structure. In general, the structure can provide a

higher amount of strength than its predefined design value and it can sustain large inelastic

deformations without collapse (Kim and Choi 2005). The ductility and energy absorption of

the structure, its ability to withstand load, and its stiffness under reversed cyclic loading are

among the structural features supporting this concept (Mitchell et al. 2003). The 2010 NBCC

uses two separate force modification factors:

i) the overstrength factor (Ro) accounts for the dependable portion of reserve strength in

the structure, as mentioned in the 2010 NBCC. This factor can be calculated from the

ratio of the actual lateral strength (Vy) to the design lateral strength (Vd). Fig. 2

illustrates the base shear-roof displacement relationship generated from the pushover

response of a structure. The design and actual strengths along with the maximum roof

displacement (∆max) and the roof displacement at the yield points (∆y) are indicated in

Fig. 2.

ii) the ductility-related force modification factor (Rd) reflects the capability of the

structure to dissipate energy through inelastic behavior. There are several methods to

obtain the ductility factor. In this study, the method proposed by Miranda and Bertero

(1994) was used to calculate (Rd). To calculate the ductility factor (Rd), soil type,

ductility ratio (µ), and the natural period of the structure are considered.

The design base shear can be greatly reduced for a structural system having higher ductility

and overstrength factor. Consequently, this reduction leads to a decrease in the member sizes

of the structure. Hence, a more economical design can be obtained by accepting some

damages during an earthquake. The evaluation of the response modification factor is essential

in the seismic design of buildings as it shows the trade-off between inherent favourable

structural characteristics, such as ductility and accompanying damage, and the initial cost of

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the structure (Rainer 1987). Previous research has shown that the reserve strength can

significantly affect the seismic behavior of BRBFs (Ariyaratana and Fahnestock 2011).

The 2010 NBCC prescribes 1.2 and 4 as the overstrength and ductility factor of BRBFs.

These are regardless of buildings height, span length, and bracing configuration. In this

paper, the seismic design factors, including ductility, overstrength, and response modification

factors for BRBFs designed as per NBCC 2010 were examined. In order to include the effects

of buildings height and span length, four-, six-, and eight-story frames with different span

lengths of 6m and 8m were considered in the study (herein, span length is the bay length of

BRBF). In addition, two different bracing configurations, including inverted-V chevron and

split-X were used for the frames. The overstrength and ductility of the BRBFs were evaluated

by performing nonlinear static pushover analyses. Furthermore, nonlinear time history

analyses were conducted to assess the dynamic responses of the frames. The capacity/demand

ratios of the BRBFs were obtained and discussed.

Design of frames

Twelve frame buildings with buckling-restrained braces were designed as per NBCC 2010

and CSA-S16-09 (CSA 2009) and their overstrength factors, ductility factors, and response

modification factors were evaluated. Fig. 3 shows the plan and elevation view of the steel

frames along with the span and height dimensions. All the frames have three bays in each

direction and a story height of 4 m. The total heights of the BRBFs considered here remain

less than 40 m (i.e. the height restriction for BRBFs specified in CSA-S16-09). The general

purpose structural program, SAP2000 (v15.0) was used to analyze and design the 3D

building models. The buildings were assumed to be located on a stiff soil (site class D) in

Vancouver. In the design process, the ductility and overstrength factors of 4.0 and 1.2 were

considered, respectively. A normal seismic importance factor (i.e. I=1.0) were assumed for

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the buildings. The dead and live loads were considered as uniformly distributed loads of 4.8

and 1.9 kN/m2, respectively. The design was carried out assuming steel buckling restrained

braces for the frames. Modulus of elasticity, yield strength, and strain hardening of steel were

assumed to be 200,000 MPa, 350 MPa, and 0.5%, respectively. Table 1 lists the member

sizes for different steel BRBFs. The core steel area for the buckling-restrained bracing

members was determined based on the force in the bracing members from the analysis results

in SAP program. The analytical values were also manually verified through a static analysis.

The following formula was used to obtain the core steel area for the buckling-restrained

braces:

where is the axial force in the bracing member (in N) and is the yield strength of

steel material (in MPa). As an example, for the 4 story 6m span, the brace force is 329 kN,

thus the brace core area will be:

Table 3 lists the story shear and axial forces of the bracing members under earthquake

loading (equivalent static force analysis) as well as seismic weight of each floor. From Table

3, it is observed that the seismic load distributions of the bracing members are almost the

same for frames with different bracing configurations (less than 5% variation). However, as

seen in Table 1, the axial forces in BRX braces for buildings with the same span length are

larger compared to BRC braces, particularly at lower stories. Here, unlike BRC, BRX

configuration attracts more gravity forces because it connects two alternate levels in between

two column nodes where axial forces are being partially transferred through braces. Hence,

braces in BRX experience more forces compared to BRC.

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Analytical modeling of frame structures

The finite element program, SeismoStruct (v7.0.3) was used to model the buckling restrained

braced frames and perform 2D analyses. The external braced frame shown in Fig. 3 was

considered for the numerical analyses. A uniaxial bilinear stress-strain model with kinematic

strain hardening was used to capture the steel behavior. The strain hardening parameter (i.e.,

the ratio between the post-yield stiffness and initial elastic stiffness of steel material) was

assigned as 0.5%. Displacement-based frame elements with fiber sections were employed to

model the beam and column members. The buckling restrained braces were modeled using

truss elements having bilinear hysteretic behavior (with strain hardening of 2%). Only the

steel core of BRB was modeled neglecting the other parts, such as concrete and debonding

materials. Moreover, the behavior of a BRB was assumed to be similar in tension and

compression. The cross sectional areas of steel core considered for the buckling restrained

braces are provided in Table 1.

Modal analysis

Eigenvalue analyses were performed to determine the natural periods of the BRBFs. Table 2

presents the fundamental periods of the frame structures obtained from modal analysis along

with the values calculated as per NBCC 2010. Eq. [1] is the empirical equation proposed by

NBCC 2010:

[1] T = 0.025 hn

Where T is the fundamental period of the structure in (sec) and hn is the height of the

structure in meter. It can be observed that the equation provided in the code underestimates

the period of the BRBFs. It should be also noted that the fundamental periods of the

structures are not affected by varying span length and bracing configuration.

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Nonlinear static pushover analyses

Static nonlinear pushover analyses were carried out to evaluate the overstrength factor (Ro)

and ductility (µ) of the BRBFs. Lateral loads with a triangular distribution over the building

height were considered at each story level, in which the horizontal load is zero at the base of

the building and peak load is applied at the roof level. Fig. 4 shows the pushover response

curves for different BRBFs. The pushover analysis continued until the maximum interstory

drift in the frame reached the design drift limit of 2.5% or until non-convergence happened.

As can be seen, the elastic stiffness and ultimate strength of the building increases by

increasing the span length.

In most cases, similar base shear capacities were observed for the same BRBFs having

different bracing configuration (with chevron- or X-braces). The maximum difference was

observed as 10% for four-story BRBFs with 6m span. The inter story drift distributions of the

frames are depicted in Fig. 5 for four-, six- and eight-story frames, respectively. Here, the

inter-story drift represents the relative movement of the floor level either at the stage of

collapse or at the code specified maximum allowable story drift (i.e. 2.5%), whichever

governs.

Overstrength factors

As depicted in Fig. 2, overstrength factor (Ro) is the ratio of the maximum base shear

capacity or actual response to the design base shear. The overstrength factors were calculated

using the pushover curves. Table 4 lists important characteristics derived from the pushover

response. The displacement ductility (µ) which is defined as the ratio of the maximum

displacement to the yield displacement was also calculated from the pushover curve. Here,

the maximum displacement (∆max) is defined as the displacement corresponding to the

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maximum base shear or when the maximum interstory drift reaches 2.5%. The displacement

at the yield point (∆y) is observed from the idealized pushover curve. The design base shear

values (Vd) for the BRBFs are also listed in Table 4. The base shear strength is higher for a

similar BRBF with greater bay length where the longer-bay BRBF is designed with higher

steel core areas (see Table 1).

The overstrength factors, defined as the ratio between the actual base shear capacity (Vy) and

the design base shear, are also provided for all the frames. The base shear capacity is

observed by performing pushover analysis and it is shown in Table 4. From this table, it is

observed that the actual base shear capacity of the BRBFs is increased for buildings with

longer spans. In almost all cases, higher BRBFs showed greater base shear capacities. The

actual base shear capacity is used to calculate the over strength factor of the considered

frames. Fig. 6 shows the overstrength factors for the BRBFs with chevron inverted-V and X-

braces, ranging from 1.20 to 1.48, which means that the lateral capacities are from 1.20 to

1.48 times the design base shear. The minimum overstrength factor observed in this study is

found to be the same as the code prescribed value. A higher overstrength factor than the

code-specified design overstrength value (i.e. Ro = 1.2) indicates the conservative view of the

NBCC 2010. It is important to note that in seismic design codes, a conservatively lower Ro is

stated to account for several uncertain factors influencing the reserve strength in a building.

These factors, which may not be explicitly considered in numerical studies, include the

effects of member sizes exceeding the design requirements, effects of structural redundancy,

effects of non-structural elements, and uncertainty associated with determining the actual

material yield strength, resistance and strain hardening (Elnashai and Sarno 2008; Mitchell et

al. 2003).

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In general, the overstrength factor decreases with increase in the bay length and the building

height. Moreover, almost similar overstrength factors were obtained for buildings with

different bracings, where the maximum variation was 10.44%. Therefore, the overstrength of

the BRBF buildings considered in this study can be considered independent of the bracing

configuration. The brace length, angle of brace inclination, and bay size are the same in both

frames with either chevron inverted-V or X-braces, half of them are in tension and half in

compression at any given time. Therefore, it is reasonable to expect essentially similar

behavior for these buildings.

Ductility factors

In this section, the ductility factors (Rµ) for the BRBFs were obtained using the equations

proposed by Miranda and Bertero (1994). This method includes characteristics such as soil

conditions, ductility (µ) and natural period of the structure (Τ). For stiff soil:

[2]

[3]

The ductility factors calculated based on this method are provided in Fig. 7. It can be

observed that BRBFs with longer spans typically result in a higher ductility factor. The

highest ductility factor was obtained as 4.18 for four-story BRBFs with 8m span length and

X- braces. The smallest amount of ductility factor was 3.97 for six-story BRBFs of 6m span

with chevron braces. When comparing the ductility factors for BRBFs of the same height

with different bracing configurations, the maximum difference was 5%. Therefore, the

bracing configuration does not affect the ductility factor of the BRBFs considered in this

paper.

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Response modification factors

The response modification factor for the BRBFs was obtained by multiplying the

overstrength factor with the ductility factor for each frame, which are listed in Table 5. The

response modification factors for the frames with chevron braces and X-braces are compared

in Fig. 8. Generally, lower response modification factors were obtained for BRBFs with

higher heights. All the BRBFs, showed response modification factors equal or higher than the

NBCC 2010 prescribed value of Rµ Ro=4.8 for BRBFs. Among the BRBFs considered, the

six and eight-story 6m-span chevron braced frame exhibited a minimum response

modification factor equal to the prescribed value of 4.8 in the 2010 NBCC. Based on the

results, the maximum response modification factor was obtained as high as 6.17 for four-

story X-BRBF with 6m span length. When comparing the response modification factors for

BRBFs of the same height with different bracing configuration, a maximum difference of

11% was observed. Hence, the response modification factor of BRBFs may be slightly

affected by the bracing configuration. It can be also concluded that the response modification

factor decreased with the increase of story height and span length.

Nonlinear time history analysis

To assess the seismic performance of the BRBFs, nonlinear dynamic time history analyses

were performed for the 2D frames. Nine real records and an artificial ground motion

developed by Atkinson (2009) for Vancouver were used. Some characteristics of the selected

ground motion records are presented in Table 5. These records were chosen as they could

represent the seismic events for the location of the designed structures. The ratio between the

peak ground acceleration (PGA) and peak ground velocity (PGV) which indicates the

frequency content of a seismic motion is around 1.0 for the western part of Canada

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(Naumoski et al. 1988). As can be seen in Table 6, the PGA/PGV ratio of the records varies

between 0.8 and 1.2. In the following sections, the seismic performance of the BRBFs is

discussed in terms of interstory drift demand, roof drift demand, and base shear demand.

Inter-story drift demand

The inter-story drift demands were calculated from the dynamic time history analyses of the

frame buildings under the ensemble of earthquake data. For the sake of brevity, the drift

demand distribution plot is presented only for four-story chevron BRBFs (Fig. 9). In this

figure, the demand values are illustrated for different earthquake records as well as the

average interstory drift demand over the height of the buildings. Based on the average drift

demands for the four-story chevron BRBFs (Fig. 9), the maximum demand was generated at

the first floor level for the four-story chevron BRBF with 8m span, while the BRC frames

with less span lengths of 6m experienced the peak demand at their second floor levels.

By changing the bracing configuration to X-braces, the concentration of the drift demands

remains on the same story level, except for the four-story X-BRBF frame with 6m span

length.

For the six-story chevron-BRBFs with 6m span lengths, the peak average demand was

produced at the 5th

floor level, whereas in the case of the 6BRC frame with 8m span length,

the 2nd

story level exhibited the maximum interstory demand.

For all the six-story BRBFs with X-braces (i.e. 6BRX), the peak interstory drift demands

were generated in the 4th

floor level.

The 3rd

, and 4th

floor experienced the peak average interstory drift demand in the eight-story

chevron-BRBFs with the span lengths of 6m and 8m, respectively.

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In all the eight-story X-BRBFs, the peak interstory demand was in the 4th

floor. Generally, it

can be mentioned that the interstory drift demand concentration shifts to higher story levels as

the height of the BRBF increases. For the BRBFs of the same height, the story level at which

the drift demand concentration occurred either shifts to lower stories or remain unchanged

when increasing the span length.

Roof drift demand

Figs. 10 and 11 show the roof drift demands for both types of BRBFs of different stories and

span lengths under various earthquake records. In general, the roof drift demand increases for

BRBFs of lower stories. The roof drift demand for BRBFs with chevron braces is almost the

same as that of BRBFs with X-braces. Fig. 12 depicts the roof drift capacity/demand ratios

for the frames with different heights and span lengths. The global drift of the building at the

maximum base shear from the pushover analysis was considered as the drift capacity of the

frame. Further, the drift demand is defined as the average of the maximum drifts at the roof

of the building subjected to earthquakes scaled to represent the design spectrum. As can be

seen in Fig. 12, all the designed BRBFs possess higher roof drift capacities than their

demands under earthquakes. The roof drift capacity demand ratio is higher for 8m span for

both four- and six-story chevron and X- braced frames. However, in the case of eight-story

frames, a higher capacity/demand ratio is observed for 6m span frames.

Base shear demand

The calculated base shear demands based on the nonlinear time history analyses of the

BRBFs are depicted in Figs. 13 and 14 for chevron and X-braced frames with different

heights and span lengths. The maximum base shear generated in the building frame subjected

to the earthquake loading was considered as the base shear demand value. In Figs. 13 and 14,

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the base shear capacities of the frames were also indicated. The average base shear demands

for frames of 6m long span are less compared to that of 8m span frame for each story type.

Therefore, it can be stated that the frames with larger span lengths experienced higher base

shear demands. In addition, the demand generally increases with increasing the number of

stories. The results also show that the base shear demand is not much affected by the bracing

configuration of the BRBFs analyzed in this study. The capacity demand ratios in terms of

base shear is presented in Fig. 15. As can be seen, the capacity/demand ratios for the 6m span

frames is higher compared to those of 8m span frames in case of four- and six-story frames.

The base shear capacity demand ratio is higher for 8m span in case of eight-story chevron and

X-braced frames. In addition, the base shear capacity/demand ratio decreases with the

increase of building height for the chevron braced frames but it may remain same for X-

braced frames. Fig. 15 also indicates that all the BRBFs possess higher base shear capacities

compared to the base shear demands generated under the earthquake excitations.

Conclusions

This paper numerically evaluated the force reduction factors for steel Buckling Restrained

Braced Frames (BRBF) designed as per the 2010 NBCC. Four-, six-, and eight-story

buildings with different span lengths of 6m and 8m were designed and analyzed. Two

different bracing configurations, including chevron inverted-V and split-X braces, were also

considered for the BRBFs. Overstrength, ductility, and response modification factors for

twelve BRBFs were assessed by performing nonlinear static pushover analyses. Eigen value

analyses were also performed to obtain the natural periods of the BRBFs. In order to examine

the seismic performance of the designed BRBFs, nonlinear time history analyses were

conducted using several ground motion records. Capacity/demand ratios of the BRBFs in

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terms of interstory drift, roof drift, and base shear were obtained and discussed. The

following conclusions are drawn:

• The equation provided in the 2010 NBCC underestimated the natural periods of the

BRBFs. The fundamental periods of the structures were not affected by varying span

length and bracing configuration.

• The elastic stiffness and maximum base shear capacity of the BRBFs increased when

the span length of the building was increased. In almost all cases, higher BRBFs

showed greater base shear capacities.

• The overstrength factors obtained for the BRBFs ranged from 1.20 to 1.48. These

overstrength values are higher than those prescribed in the 2010 NBCC for BRBFs

(i.e., 1.2). In general, the overstrength factor decreased with the increase in the span

length and the increase in the building height. The overstrength of the BRBF

buildings considered in this study was independent of the bracing configuration.

• The ductility factors for BRBFs calculated based on the method by Miranda and

Bertero (1994) were in the range of 3.97 to 4.18. All the ductility factors are equal or

higher than 4, which is stated in the 2010 NBCC for BRBFs. In general, it can be

noted that BRBFs with longer spans possess a higher ductility factor. Furthermore,

the bracing configuration of the BRBFs may affect the ductility factor.

• The response modification factors obtained from the multiplication of the

overstrength and ductility factor were in the range of 4.8 to 6.0. The combined use of

overstrength and ductility factor, provided in the 2010 NBCC, results in a response

modification factor of 4.8 (=1.2×4.0). Therefore, it can be concluded that the code

prescribed value of 4.8 is somewhat a lower bound for the response modification

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factor of the BRBF. Additionally, the results indicate that the response modification

factor decreased with the increase of story height and span length. The response

modification factor may be slightly affected by the bracing configuration.

• From the nonlinear time history analyses of the BRBFs, it was observed that the

interstory drift demand concentration shifts to higher story levels as the height of the

building increases. When increasing the span length of the BRBFs of the same

height, the concentration of drift demand either remained on the same story level or

shifted to lower heights.

• The base shear demand of the BRBFs generally increased as the building height and

span length increased. Moreover, the capacity/demand ratios of the BRBFs showed

that all the frames considered in this study exhibited higher roof drifts as well as base

shear capacities compared to the demand values.

Further studies can be done to assess the response modification factors for BRBFs with

different design details such as floor height. To confidently evaluate the response

modification factors for BRBFs, more accurate modeling details associated with the buckling

restrained braces can be also included in the analysis and design of such buildings.

Acknowledgement

The financial contribution of Natural Sciences and Engineering Research Council (NSERC)

of Canada through Discovery Grant was critical to conduct this research and is gratefully

acknowledged.

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buckling‐restrained braces. Steel Construction, 4(2): 85-93.

Dusicka, P., and Tinker, J. 2013. Global Restraint in Ultra-Lightweight Buckling-Restrained

Braces. Journal of Composites for Construction, 17(1): 139-150.

Elnashai, A. & Sarno, L. Di, 2008. Fundamentals of earthquake engineering, John Wiley &

Sons, Ltd, Publication.Fahnestock, L.A., Sause, R., and Ricles, J.M. 2007. Seismic

response and performance of buckling-restrained braced frames. Journal of Structural

Engineering, 133(9): 1195-1204.

Kim, J., and Choi, H. 2005. Response modification factors of chevron-braced frames.

Engineering Structures, 27:285–300.

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steel frames. Earthquake Engineering Research Center, University of California,

Berkeley, Calif., Report NO. UCBIEERC-88/01.

Lin, P.C., Tsai, K.C., Wu, A.C., & Chuang, M.C. 2013. Seismic design and test of gusset

connections for buckling‐restrained braced frames. Earthquake Engineering &

Structural Dynamics. doi: 10.1002/eqe.2360

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308-327.

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Mitchell, D., Paultre, P., Tinawi, R., Saatcioglu, M., Tremblay, R., Elwood, K., Adams, J.,

and DeVall, R. 2010. Evolution of seismic design provisions in the National building

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validation of a nickel–titanium shape memory alloy self-centering buckling-restrained

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ON Canada. EERG Report 88-01.

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Palmer, K.D., Roeder, C.W., Lehman, D.E., Okazaki, T., and Shield, C. 2013. Experimental

Performance of Steel Braced Frames Subjected to Bidirectional Loading. Journal of

Structural Engineering, 139(8): 1274-1284.

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Sabelli, R., Mahin, S., and Chang, C. 2003. Seismic demands on steel braced frame buildings

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Tremblay, R., Filiatrault, A., Timler, P., and Bruneau, M. 1995. Performance of steel

structures during the 1994 Northridge earthquake. Canadian Journal of Civil

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Earthquake Engineering: Recent Advances and Applications, CRC Press, Boca Raton,

FL.

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List of Tables

Table 1. Design summary of different types of buildings (combined loading).

Table 2. Fundamental period of the structures.

Table 3. Storey Shear, bracing forces, and building weight under earthquake loading

(equivalent static force analysis).

Table 4. Overstrength factor and ductility.

Table 5. Response modification factor for model structures.

Table 6. Ensemble of ground motion records.

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Figure Captions

Fig. 1. (a) Typical buckling restrained bracing element and (b) cross section A-A and (c)

Hysteretic behavior of conventional bracing and bucking restrained bracing members

under cyclic loading.

Fig. 1. Lateral load–roof displacement relationship of a structure (Alam et al. 2012, with

permission).

Fig. 3. (a) Plan of the buildings; and elevation of the (b) 4 story (c) 6 story and (d) 8 story

buildings.

Fig. 4. Pushover response curves for (a) four-story (b) six-story and (c) eight-story BRBFs

with chevron-braces (left) or X-braces (right).

Fig. 5. Interstory drift distributions for (a) four-story (b) six-story and (c) eight-story BRBFs

with chevron-braces (left) or X-braces (right).

Fig. 6. Overstrength factor of BRBFs with: (a) chevron bracing; (b) X-bracing.

Fig. 7. Ductility factor of the BRBFs with: (a) chevron bracing; (b) X-bracing.

Fig. 8. Response modification factor of BRBFs with: (a) chevron bracing; (b) X-bracing.

Fig. 2. Inter-story drift demand for 4-story chevron braced (a) 6m span and (b) 8m span.

Fig. 10. Roof drift demand for (a) 4-story, (b) 6-story and (c) 8-story chevron braced frame

Fig. 11. Roof drift demand for (a) 4-story, (b) 6-story and (c) 8-story X-braced frames.

Fig. 12. Roof drift capacity/demand ratio of (a) chevron braced frames and (b) X-braced

frames.

Fig. 13. Base shear demand for (a) 4-story, (b) 6-story and (c) 8-story BRBFs with chevron

braces.

Fig. 14. Base shear demand for (a) 4-story, (b) 6-story and (c) 8-story BRBFs with X-braces.

Fig. 15. Base shear capacity/demand ratio of (a) chevron braced frames and (b) X-braced

frames.

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Tables

Table 1. Design summary of different types of buildings (combined loading).

Story

ID

Span

length

(m)

Floor

level

Braced bay

Interior

columns

Braced bay

exterior

columns

Steel girder

Axial force

for bracing

(BRC)

BRB steel

core area

(mm2)

(BRC)

Axial

force for

bracing

(BRX)

BRB steel

core area

(mm2)

(BRX)

4

6 1~2 W460×113 W410×74 W410×46 329 1044 388 1231

2~4 W460×60 W360×51 W410×46 218 692 207 657

8 1~2 W530×150 W460×106 W410×54 497 1577 581 1844

2~4 W530×74 W410×74 W410×54 330 1048 379 1203

6

6

1~2 W530×150 W530×101 W410×46 495 1571 589 1869

2~4 W530×72 W410×54 W410×46 303 1152 513 1628

5~6 W460×60 W360×51 W410×46 185 587 263 834

8

1~2 W610×415 W460×128 W410×54 762 2177 814 2325

2~4 W530×109 W410×85 W410×54 590 590 776 2217

5~6 W530×74 W410×60 W410×54 320 320 423 1208

8

6

1~2 W530×248 W410×106 W410×46 514 1631 605 1920

2~4 W530×101 W410×85 W410×46 450 1428 583 1850

5~6 W410×74 W410×67 W410×46 350 1111 459 1457

7~8 W410×46 W410×46 W410×46 220 698 250 794

8

1~2 W920×725 W460×128 W410×54 779 2473 844 2680

2~4 W610×155 W410×85 W410×54 701 2225 794 2520

5~6 W610×101 W410×60 W410×54 350 1746 602 1911

7~8 W530×74 W410×60 W410×54 326 1035 291 923

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Table 2. Fundamental period of the structures.

Span length

(m) 6 8

Bracing BRC BRX BRC BRX Empirical equation

# Story

4 0.57 0.57 0.57 0.57 0.4

6 0.72 0.72 0.72 0.72 0.6 8 0.92 0.92 0.92 0.92 0.8

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Table 3. Storey shear, bracing forces and building weight under earthquake load

(equivalent static force analysis).

Storey ID Bracing

type Storey

level Storey shear from seismic

load ( kN) Brace axial forces for

seismic load ( kN) Weight of building

(kN)

6m Span 8m Span 6m Span 8m Span 6m

Span 8m Span

4

BRC

4 305 544 118 177 1360 2419

3 240 425 214 320 1360 2419

2 165 286 254 400 1360 2419

1 95 145 318 481 1360 2419

BRX

4 305 544 118 176 1360 2419

3 240 425 214 321 1360 2419

2 165 286 261 391 1360 2419

1 95 145 321 485 1360 2419

6

BRC

6 312 504 118 190 1360 2419

5 275 468 229 359 1360 2419

4 220 393 316 482 1360 2419

3 165 304 390 596 1360 2419

2 112 207 394 633 1360 2419

1 58 110 472 719 1360 2419

BRX

6 312 504 115 189 1360 2419

5 275 468 227 363 1360 2419

4 220 393 311 478 1360 2419

3 165 304 393 604 1360 2419

2 112 207 383 620 1360 2419

1 58 110 477 723 1360 2419

8

BRC

8 316 550 116 178 1360 2419

7 225 385 207 316 1360 2419

6 195 325 267 430 1360 2419

5 164 260 335 536 1360 2419

4 134 220 381 591 1360 2419

3 96 165 424 680 1360 2419

2 65 115 435 683 1360 2419

1 35 60 501 763 1360 2419

BRX

8 316 550 113 174 1360 2419

7 221 385 205 314 1360 2419

6 190 325 265 424 1360 2419

5 160 260 342 537 1360 2419

4 130 220 388 574 1360 2419

3 96 165 414 667 1360 2419

2 65 115 449 686 1360 2419 1 35 60 505 770 1360 2419

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Table 4. Over-strength factor and ductility.

Storey Bracing

types

Span

length (m)

Actual

strength Vy (kN)

Design

strength Vd (kN)

Over-

strength factor Ro

Maximum

displacement ∆max (mm)

Yield

displacement ∆y (mm)

Ductility

µ

4

BRC 6 1080 805 1.34 235 50 4.70

8 1736 1400 1.24 250 53 4.72

BRX 6 1190 805 1.48 260 55 4.73

8 1680 1400 1.20 245 50 4.90

6

BRC 6 1385 1142 1.21 275 67 4.10

8 2397 1986 1.21 290 67 4.33

BRX 6 1440 1142 1.26 265 63 4.21

8 2393 1986 1.20 290 69 4.20

8

BRC 6 1473 1230 1.20 440 120 3.67

8 2504 2080 1.20 380 102 3.73

BRX 6 1575 1230 1.28 575 153 3.76

8 2493 2080 1.20 425 115 3.70

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Table 5. Response modification factor for model structures.

Storey Bracing

types

Span

length

(m)

Over-

strength

factor, Ro

Ductility

Reduction

Factor, Rµ

Response

Modification Factor

4

BRC 6 1.34 4.04 5.4

8 1.24 4.06 5.0

BRX 6 1.48 4.06 6.0

8 1.20 4.18 5.0

6

BRC 6 1.21 3.97 4.8

8 1.21 4.16 5.0

BRX 6 1.26 4.06 5.1

8 1.20 4.05 4.9

8

BRC 6 1.20 4.02 4.8

8 1.20 4.08 4.9

BRX 6 1.28 4.11 5.3

8 1.20 4.05 4.9

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Table 6. Ensemble of ground motion records.

No. Earthquake Station Magni-

tude PGA (g)

PGA/PGV (sec

-1)

Data Source

1 Artificial (ART) - 6.5 0.35 - Atkinson (2009)

2 ATS, Kocaeli, 199/08/17 ATS-UP, 150 7.8 0.67 0.93 PEER*

3 BTS, Kocaeli, Turkey

1999/08/17

Botas 7.8 0.62 1.0 PEER*

4 Chi-Chi,Taiwan. 1999/09/20 CHY-006 7.6 0.63 0.81 PEER*

5 ChiChi-longt,Taiwan.

1999/09/21 Unknown 7.6 0.43 1.13 PEER*

6 Chi-Chi,Taiwan. 1999/09/20 CHY019-E 7.6 0.63 0.83 PEER*

7 Chi-Chi,Taiwan. 1999/09/20 CHY019-N 7.6 0.7 1.0 PEER*

8 Victoria, Mexico 6/9/1980 3:02 VICT/HPB0006.4 0.95 0.86 PEER*

9 Loma Prieta 1989/10/18 00:05 16 LGPC 6.9 1.11 - PEER*

10 Chi-Chi,Taiwan. 1999/09/20 TTN042-N 7.6 0.65 1.0 PEER*

* http://peer.berkeley.edu (PEER strong ground motion database 2007)

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(a)

A

A

(b)

Steel core

Debonding

material

Steel jacket

Concrete

mortar

(c)

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Fig. 2. Lateral load–roof displacement relationship of a structure (Alam et al. 2012, with permission). 123x77mm (220 x 220 DPI)

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Fig. 3. (a) Plan of the buildings; and elevation of the (b) 4 story (c) 6 story and (d) 8 story buildings. 73x97mm (216 x 216 DPI)

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500

1000

1500

2000

2500

3000

0 100 200 300 400 500 600

Base shear (kN)

Roof displacement (mm)

6 BRC

6m span

8m span

0

500

1000

1500

2000

2500

3000

0 100 200 300 400 500 600

Base shear (kN)


6 BRX6m span

8m span

0

500

1000

1500

2000

2500

3000

0 100 200 300 400 500 600

Base shear (kN)


8 BRC6m span

8m span

0

500

1000

1500

2000

2500

3000

0 100 200 300 400 500 600

Base shear (kN)


8 BRX6m span

8m span

0

500

1,000

1,500

2,000

2,500

3,000

0 100 200 300 400 500 600

Base shear (kN)


4 BRC 6m span8m span

0

500

1000

1500

2000

2500

3000

0 100 200 300 400 500 600

Base shear (kN)


4 BRX 6m span8m span

(a)

(b)

(c)

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Fig. 5. Interstory drift distributions for (a) four-story (b) six-story and (c) eight-story BRBFs with chevron-braces (left) or X-braces (right).

158x218mm (96 x 96 DPI)

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0

1

2

4 story 6 story 8 story

Overstrength factor

BRC 6m span 8m span

0

1

2


Overstrength factor

BRX 6m span 8m span

(a) (b)

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1

2

3

4

5


Ductility factor

BRC 6m span 8m span

0

1

2

3

4

5


Ductility factor

BRX 6m span 8m span

(a) (b)

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0

0.2

0.4

0.6

0.8

16m span

8m span

Ro

of

drift

dem

and

(%

)

0

0.2

0.4

0.6

0.8

16m span

8m span

Ro

of

drift

dem

and

(%

)

0

0.2

0.4

0.6

0.8

1

6m span

8m span

Ro

of

drift

dem

and

(%

)

(b)

(c)

(a)

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0

0.2

0.4

0.6

0.8

16m span

8m span

Roofdrift demand (%)

0

0.2

0.4

0.6

0.8

1 6m span

8m span


0

0.2

0.4

0.6

0.8

1 6m span

8m span


(a)

(b)

(c)

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