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Journal of Constructional Steel Research 63 (2007) 460474www.elsevier.com/locate/jcsr

Inelastic performance of cold-formed steel strap braced walls

M. Al-Kharat, C.A. Rogers

Department of Civil Engineering and Applied Mechanics, McGill University, Montreal QC H3A 2K6, Can ada

Received 8 May 2006; accepted 27 June 2006

Abstract

The inelastic performance of sixteen 2.44 m 2.44 m cold-formed steel strap braced walls was evaluated experimentally. The performance

was affected by the holddown detail, which in many cases did not allow the test specimens to reach or maintain a yield capacity and severelydiminished the overall system ductility. Test-based Rd Ro values of 3.65, 2.11 and 1.72 indicate the low ductility levels, which were not

adequate to warrant the use of a seismic response modification coefficient of R = 4.0 in design. Capacity design of the SFRS elements must

account for the overstrength of the strap material.c 2006 Elsevier Ltd. All rights reserved.

Keywords: Cold-formed steel; Strap brace; Ductility; Inelastic; Seismic; Performance

1. Introduction

The use of cold-formed steel as the main framing element

in a structure is becoming more popular for the construction

of low- to mid-rise buildings across Canada, including areas

with a high seismic hazard. In order to maintain the integrity

of these structures when subjected to horizontal forces due

to an earthquake the use of diagonal flat steel strap cross

bracing may be a practical solution (Fig. 1). The straps act as a

vertical concentric bracing system, which transfers the lateral

forces from the roof and floor levels to the foundation. The

overall lateral strength, ductility and stiffness of this bracing

system may not be related solely to the steel straps; many

other elements in the lateral load carrying path can play a role,

such as the strap connections, the gusset plates (if needed), the

anchorage including holddown and anchor rod, etc.In Canada earthquake loading may often dictate the design

of the lateral force resisting system in a building in areasof high seismic hazard, such as found along the west coast

of the country as well as in the Saint Lawrence and Ottawa

River valleys. The 2005 National Building Code of Canada

(NBCC) [1] requires that seismic loading also be considered

in other areas of the country, where in the past it has not been

Corresponding address: Department of Civil Engineering and AppliedMechanics, McGill University, 817 Sherbrooke St. W., Montreal, QC H3A 2K6,Canada. Tel.: +1 514 398 6449; fax: +1 514 398 7361.

E-mail address: [email protected] (C.A. Rogers).

Fig. 1. Cold-formed steel strap braced walls under construction.

of significant concern for design engineers. This is due, in

part, to a change in the seismic hazard information used for

design. Seismic forces, which were previously based on a 10%

in 50 year probability of exceedance, i.e., corresponding to a

return period of 475 years, are now based on a uniform hazardspectrum having a 2% in 50 year probability of exceedance,

i.e., approximately a return period of 2500 years [2]. The 2005

NBCC also comprises a capacity based philosophy for seismic

design, where a fuse element in the seismic force resisting

system (SFRS) is selected to dissipate earthquake derived

energy. This energy dissipating element is expected to enter

into the inelastic range of behaviour, whereas the remaining

components of the SFRS are designed to carry the forces

associated with the probable capacity of the fuse element,

i.e., they should remain essentially elastic or experience only

0143-974X/$ - see front matter c 2006 Elsevier Ltd. All rights reserved.

doi:10.1016/j.jcsr.2006.06.040
http://www.elsevier.com/locate/jcsrmailto:[email protected]://dx.doi.org/10.1016/j.jcsr.2006.06.040http://dx.doi.org/10.1016/j.jcsr.2006.06.040mailto:[email protected]://www.elsevier.com/locate/jcsr

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M. Al-Kharat, C.A. Rogers / Journal of Constructional Steel Research 63 (2007) 46 0474 461

minor plastic damage. It is generally assumed that the straps

act as the fuse element in the SFRS of braced cold-formed steel

structures.

Guidelines that address the seismic design/inelastic perfor-

mance of cold-formed steel structures are not provided in the

2005 NBCC or in the Canadian Standards Association (CSA)

S136 Standard for the Design of Cold-Formed Steel StructuralMembers [3]. In contrast, seismic design information for cold-

formed steel structures is available in the US. ASCE 7-05 [4]

allows for the use of a seismic response modification coeffi-

cient of R = 4.0 for strap braced bearing wall systems, which

indicates a reliance on a moderate level of ductile/inelastic per-

formance of the SFRS as well as some overstrength. Use of

this R value necessitates that the material specific seismic de-

sign and detailing requirements of the American Iron and Steel

Institute (AISI) Lateral Design Standard [5] and the AISI Spec-

ification [6] be met. Even if not detailed for seismic resistance

ASCE 7-05 allows for an R of 3.0 to be used for the design

of strap braced walls. The AISI Lateral Design Standard states

that boundary members, chords, collectors and connections of abraced wall must be proportioned to transmit the induced forces

and the amplified seismic loads. Vertical chord members are

required to have the nominal strength to resist amplified seis-

mic loads, but not loads greater than what the system can de-

liver. The strength of brace connections need be the lesser of

the nominal tensile strength of the brace or the amplified seis-

mic load. Furthermore, strap bracing is to be designed in ac-

cordance with the AISI Specification or the AISI Standard on

General Provisions [7], which for the most part do not contain

any relevant seismic detailing information. Typically, the AISI

Standards and Specification are written in terms of strength

requirements for seismic design; however, no mention of ex-pected ductility requirements or recommended ductile connec-

tion/anchorage details is made. The US Army Corps of Engi-

neers has also published a document that addresses the seis-

mic design of cold-formed steel structures, TI 809-07 [8]. The

intent of this document is to ensure that ductile building sys-

tem performance is attained during large seismic events. Duc-

tile performance requires that the strap members of a braced

wall are first able to yield and then maintain this level of load

carrying capacity while being subjected to significant plastic

deformations. The failure of columns and connections must not

occur. The TI 809-07 provisions for seismic design are similar

to what is found in ASCE 7-05 and the AISI Lateral Design

Standard, except that additional prescriptive requirements for

material properties of the braces, as an example, exist.

2. Objectives and scope of research

Due to the lack of codified seismic design guidance in

Canada for cold-formed steel structures a research project

was undertaken to evaluate the inelastic performance of steel

framestrap braced walls that are not designed following a strict

capacity based design philosophy. The main objectives were to

determine the ductility of common strap braced walls by means

of physical testing and to assess the inelastic performance

with respect to the ASCE7-05 R-value of 4.0; that is the

ability of the flat straps to yield over extended displacements

without extensive damage to the other components in the

SFRS. Three typical wall configurations were tested; light,

medium and heavy in the context of cold-formed steel. Due

to this research being in its initial stages the investigation

involved only the assembly testing of representative strap

braced walls under lateral in-plane loading. A total of sixteen2.44 m 2.44 m walls with standard non-seismic details

were tested using monotonic and reversed cyclic loading

protocols. The performance of the walls was expected to

match that of a SFRS for which an appropriate capacity based

design approach had been implemented. That is, gross cross-

section yielding of the tension braces was the anticipated

failure mode, while the remaining elements in the SFRS were

expected to carry the brace force with no or only minor plastic

deformation. A comparison of the failure mode, ductility, shear

strength and shear stiffness characteristics of the strap walls is

presented.

3. Literature review of previous research on strap bracedwalls

Previous experimental and analytical research on the

performance of cold-formed steel strap braced walls was

reviewed to establish in-part the scope and methods of study for

the investigation described in this paper. Information from this

past research, summarized below, was used to select the wall

configurations and the test methods. In addition, the findings of

these studies were used to define the best case scenario of wall

performance in which inelastic deformations are limited to the

strap braces.

Adham et al. [9] evaluated the lateral load versus deflectionbehaviour of six 2.44 m 2.44 m cold-formed steel planar

frames sheathed with steel straps and gypsum. Straps, 50.8 mm

and 76.2 mm in width with three different thicknesses (0.84,

1.09 and 1.37 mm) were screw connected to the framing

elements. Most walls were constructed with X straps as well as

gypsum panels on both sides. Holddowns were bolted to each

test specimen at the base to limit uplift of the cold-formed steel

frame. Adham et al. showed that stud buckling will lead to a

severe degradation in the shear load that can be applied to the

wall; however when this mode is properly addressed in design

strap braced systems are effective in dissipating energy under

reversed cyclic loading.

Serrette and Ogunfunmi [10] also investigated the perfor-mance of 2.44 m 2.44 m strap braced frames through experi-

ments of walls under lateral in-plane loading. Screw connected

walls constructed with 50.8 mm 0.88 mm straps on one face

were tested (3 specimens), in addition to walls with strap braces

on one face and gypsum sheathing board on the other (4 speci-

mens). A single test specimen with braces on both sides of the

wall was also included in the study. In all cases, it was neces-

sary to bolt an 11 mm thick steel clip angle to the chord studs

to act as a holddown device. Cold-formed steel gusset plates

were used to connect the strap braces to the studtrack cor-

ner locations. It was shown that walls with bracing on one side

alone failed by excessive out-of-plane deformation, which is

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462 M. Al-Kharat, C.A. Rogers / Journal of Constructional Steel Research 63 (2007) 460474

not a favourable scenario in terms of maintaining lateral stabil-

ity of the braced frame, nor ductile performance under inelas-

tic shear deformations. Serrette and Ogunfunmi reported that

gypsum panels provide a substantial increase in shear capac-

ity compared with the 50.8 mm wide straps; however the use

of gypsum panels and strap braces together is not practical. It

was also noted that in the design of X-braced walls the engi-neer must be concerned with strap yield strengths in excess of

the minimum specified value, which may result in connection

or chord stud failure.

Barton [11] and Gad et al. [1214] investigated the

earthquake performance of strap braced cold-formed steel wall

structures as used in the Australian residential construction

industry. The impact of steel strap braces, as well as non-

structural components such as plasterboard and brick veneer, on

wall performance were evaluated through experimentation and

analyses. The research involved racking and dynamic (shake

table) testing of planar wall and 3D one room house specimens.

Relatively small strap braces were installed, 25 mm wide

1 mm thick, compared with previous studies by Adhamet al. [9] and Serrette and Ogunfunmi [10]. Ductility and

overstrength concerns were investigated given the possible

impact of non-structural components. Hysteretic load versus

deflection behaviour of the braced steel frame alone was

first obtained, followed by tests of sheathed walls and the

3D single-storey structures. In general, the steel frames were

able to perform well under seismic loading and the non-

structural components made a significant contribution to the

lateral bracing of the frames. It was reported that the pinched

force versus deformation behaviour was caused by elongation

of the straps, deformation of the connections, as well as initial

slack in the system. Screw failure was typically observed inracking tests. Stiffness of the bare steel frame was mainly

due to the strap braces and not the stud to track connection

detail even if welded. Dynamic shake table tests showed that

yielding of the braces could take place, in addition to slip

and in most cases failure of the brace connections. A 3D

finite element study was also completed, which included the

bare steel frame accounting for the brace, brace connection

and tensioner unit behaviour, as well as the effect of adding

a plasterboard lining. This allowed for different length walls

and boundary conditions for the non-structural components

to be evaluated. These studies showed that for single family

dwellings the non-structural components significantly increase

the strength and stiffness of strap braced wall systems. It is

possible that the use of relatively small brace members by

Barton and Gad et al. allowed for the plasterboard lining to

become dominant with respect to resisting lateral in-plane loads

and providing shear stiffness to the steel framing. A ductility

related response modification coefficient for seismic design

(R = 1.53.5) was recommended based on various yield

displacement models by Park [15] and subsequent nonlinear

time history dynamic analysis. A formulation was put forth to

predict the period of vibration for strap braced structures. An

evaluation of overstrength, which is highly dependent on the

non-structural components and their boundary conditions, was

also provided.

Fulop and Dubina [16] tested three X bracedscrew

connected wall specimens (3.6 m long 2.44 m high)

under in-plane lateral loading. Of the three wall specimens

one was tested monotonically and two cyclically. The walls

were constructed of a cold-formed steel frame connected to

110 mm wide 1.5 mm thick straps located on each side.

The screw connection configuration was selected to facilitateyielding along the length of the brace, i.e., to avoid net section

fracture of the strap through the screw holes. Chord members

were constructed of double stud members such that inelastic

deformations and ultimate failure of the walls would be limited

to the braces. U profiles were placed in the tracks at corner

locations to increase the holddown capacity and rigidity. Local

buckling of the lower track was observed during loading with

damage being concentrated in corner areas. Plastic elongation

of the strap did take place; however because of the unexpected

failure of the corners the results of the experiments may not

necessarily reflect the true ductility of a braced wall if yielding

(and failure) had been limited to the straps. Fulop and Dubina

suggested that the ideal configuration of the corners would besuch that the uplift force is directly transmitted from the brace

or corner stud to the anchoring bolt, without inducing bending

in the bottom track. Failure to strengthen the corners can have a

significant effect on the initial rigidity of the system and can be

the cause of larger than expected in-plane shear deformations

of the wall and premature failure of the braced frame.

Tian et al. [17] completed an experimental and theoretical

study on the racking strength and stiffness of cold-formed steel

walls, including frames with single and double X straps. A

total of five planar frames, 2.45 m in height 1.25 m in

length, composed of strap braces riveted to the steel framing

were tested. Brace size was either 60 mm 1.0 mm or60 mm 1.2 mm, and for all but one of the specimens

braces were installed on both sides of the wall. Monotonic

loading of all tests was carried out, which included single step

and three step protocols. Deformation behaviour and failure

modes were observed, and shear strength and stiffness of

the frames were measured. Tian et al. reported that frames

with straps on both sides have the best racking performance.

Compression failure of the chord stud members was observed

in the double sided specimens. Rivet failure at the brace to

frame connection was also observed. It appears that the walls

were not designed such that inelastic behaviour was limited

to the braces given the connection and chord stud failures that

were reported. Subsequent analyses of the test frames using an

elastic slope deflection method was completed to predict the

failure loads and initial shear stiffness. Tian et al. concluded

that it was possible to accurately predict the shear loads that

were measured during testing; however the in-plane shear

deformations of the walls could not be precisely determined

with their calculation method.

Pastor and Rodrguez-Ferran [18] presented the develop-

ment of an hysteretic model that can be used for the nonlin-

ear inelastic dynamic analysis of X-braced cold-formed steel

frames. The model captures the behavioural characteristics

of this framing type that have been observed during experi-

ments, including pinching and stiffness degradation of the force

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Fig. 2. Schematic drawing of displaced strap braced wall specimen in test frame.

Fig. 3. Schematic drawing of light strap braced test wall with corner detail.

versus deformation hysteresis as well as slack of the braces. The

use of this model assumes that the strap braced wall is able to

maintain its load carrying capacity over extensive and repeated

in-plane inelastic displacements. For the model to be valid the

walls also must be designed such that the strap enters into and

remains in the plastic range prior to buckling of the chord studs.

Further to this research, Casafont et al. [19] evaluated the seis-

mic performance of the screwed connections that are commonly

used for the straps of such braced walls. It was shown that the

straps were able to maintain their yield capacity over extended

inelastic displacements prior to failure of the brace by net sec-

tion fracture at the first line of screws and by tilting of the screw

fasteners. However, in cases where tilting, bearing and pull out

of the screws was observed then ductile yielding of the braces

was not obtained. A design criterion to induce a tiltingnet sec-

tion fracture failure mode, and hence ductile behaviour in the

strap braces, is provided by Casafont et al.

4. Test program

Assembly tests of sixteen strap braced stud wall specimens

(2.44 m 2.44 m) were carried out using a test frame

designed specifically for in-plane shear loading (Fig. 2). These

walls were not designed following a capacity based seismicdesign approach; rather the elements were selected given

typical wind loading levels where all of the components in the

lateral load carrying path were expected to remain elastic. The

predicted factored lateral in-plane resistance of the three wall

configurations in a wind loading situation was approximately

20 kN (light), 40 kN (medium) and 75 kN (heavy), respectively.

Schematic drawings of the three test wall configurations,

including an exterior and interior view of the corner connection

details and holddowns, are provided in Figs. 3 (light), 4

(medium) and 5 (heavy). A listing of the nominal design

(minimum specified) dimensions and material properties of

the test specimens with details of member components is

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Table 1

Matrix of strap braced wall tests (nominal design dimensions and material properties)

Specimen properties Test specimens

Light Medium Heavy

1A-M, 1B-M, 2A-C, 2B-C, 3A-M, 3B-M, 4A-C, 4B-C, 5A-M, 5B-M, 6B-C

1C-Ma 2C-Cb 3C-M 4C-C 5C-M

Strap bracing

Thickness (mm) 1.22 1.52 1.91

Dimensions (mm) 58.4 101 152

Grade - Fy (MPa) 230 230 230

Chord studs

Thickness (mm) 1.22 1.52 1.91

Dimensions (mm) 92 41 12.7 152 41 12.7 152 41 12.7

Grade - Fy (MPa) 230 345 345

Interior studs

Thickness (mm) 1.22 1.22 1.22

Dimensions (mm) 92 41 12.7 152 41 12.7 152 41 12.7

Grade - Fy

(MPa) 230 230 230

Tracks

Thickness (mm) 1.22 1.52 1.91

Dimensions (mm) 92 31.8 152 31.8 152 31.8

Grade - Fy (MPa) 230 345 345

Gusset plates

Thickness (mm) NA 1.52 1.91

Dimensions (mm) NA 250 250 300 300

Grade - Fy (MPa) NA 230 230

a Monotonic protocol.b CUREE reversed cyclic protocol.

Fig. 4. Schematic drawing of medium strap braced test wall with corner detail.

provided in Table 1. Note: the measured member dimensions

and material properties provided in Al-Kharat and Rogers [20]

may vary from these nominal values. The walls were braced

with diagonal flat straps installed in an X configuration on

both sides; a configuration that has been shown to have better

performance characteristics than single sided braced walls [10].

The braces specified for the medium walls were similar to those

used by Fulop and Dubina [16], whereas the heavy walls had a

gross cross-sectional area approximately 26 times that of the

straps found in any of the previous studies [914,1619]. Chord

stud members were composed of double C-section shapes stitch

welded front-to-front, while the remainder of the single interior

C-section studs were placed at a nominal spacing of 406 mm.

One row of 1.22 38 12.7 mm continuous bridging was

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Fig. 5. Schematic drawing of heavy strap braced test wall with corner detail.

welded in place through the web knockouts at the mid-height

of the walls. All steel framing was ASTM A653 [21] material,

either Grade 230 or 345 MPa (Table 1). Connections between

the studs and tracks were made with No. 1016 wafer-head self

drilling/self tapping screws.

The light walls were constructed of straps connected

directly to the stud framing by No. 1016 wafer-head self

drilling/self tapping screws, whereas the medium and heavy

walls comprised of straps that were fillet welded to the gusset

plates, which were in turn welded to the stud and track members

(Figs. 4 and 5). The welded connection detail had not been

used in any of the previous studies on strap braced walls [914,

1619]. L shaped holddowns with a factored uplift capacity of

35 kN were welded to the interior face of the chord studs of thelight walls and then connected to the test frame with a 15.9 mm

diameter ASTM A307 [22] equivalent threaded rod (Fig. 3).

Note that a 12.7 mm diameter threaded rod was instead used for

the first test to be carried out (1B-M). The L shaped holddowns

were fabricated of a vertical steel plate (364260 mm) which

was welded to a horizontal plate (20 64 70 mm). The load

path for the light walls traced from the straps to the chord studs

and then directly to the holddowns.In contrast, flat plate holddowns were placed within the

upper and lower tracks at the four corner locations of the

medium and heavy walls (Figs. 4 and 5). Walls 3A-M, 3B-M

and 5B-M had plates measuring 1990127 mm, whereas for

walls 3C-M, 4A-C, 4B-C, 4C-C, 5A-M and 6B-C plates 19

127 203 mm in size were installed in an attempt to increase

the holddown uplift capacity. Test specimen 5C-M was fitted

with modified holddowns that were fabricated from a C13010

channel section fillet welded to a 19 90 127 mm plate [20].

The holddown plates for the medium and heavy walls were

attached to the loading beam and reaction frame by means of

19 mm diameter ASTM A325 [23] equivalent threaded rods.

No direct connection was made from these holddown plates

to either the braces, gusset plates or the chord studs. Thus the

uplift forces in the medium and heavy walls were transferred

from the braces, through the gusset plates, to the track flanges

and web, and finally to the holddown plate and threaded rod.

Shear anchors (19 mm diameter ASTM A325 bolts [23])

were placed along the top and bottom tracks as indicated in

Figs. 35. All top tracks were drilled to accommodate the ten

shear anchors and two anchor rods, which connected the tracks

through an aluminium spacer to the loading beam. Similarly,

the bottom tracks contained four shear anchors and two anchor

rods, which connected the wall through an aluminium spacer

to the testing frame. The function of the top shear anchors was

to uniformly transfer the load from the loading beam to the top

track, whereas the function of the interior bottom shear anchors

was to connect the wall to the testing frame in a more realistic

fashion.

The testing frame was equipped with a 125 mm stroke

250 kN dynamic actuator. Displacement controlled monotonicand reversed cyclic protocols were used in testing. The testing

frame incorporated external beams to prevent out-of-plane

buckling of the wall specimen, such that only lateral in-

plane displacement would take place, as shown in Fig. 2.

Measurements consisted of strap width (Table 2), in-plane

wall displacements, strains in the steel straps, acceleration of

the loading beam assembly and the shear load at the wall

top. The LVDTs, strain gauges, load cell and accelerometer

were connected to Vishay Model 5100B scanners which were

used to record data using the Vishay System 5000 StrainSmart

software.

The monotonic loading procedure consisted of a steady

rate of displacement (2.5 mm/min) starting from the zero

load position. The CUREE ordinary ground motions reversed

cyclic loading protocol [24,25], run at 0.5 Hz, was chosen

for the testing of the strap braced walls. Previous research

at McGill University on cold-formed steel walls braced with

wood sheathing also incorporated this loading protocol [26].

It was selected because it was anticipated that the dynamic

behaviour of the strap braced walls would resemble in some

ways that of the wood sheathed walls and because a direct

comparison of results would be possible. In a best case

scenario, where the braces are able to maintain their yield

capacity, and given the range of displacement available from the

actuator, no decrease in the wall resistance would be expected.

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Table 2

Average measured brace widths

Specimen Positive wall displacementa Negative wall displacementb

Front brace Back brace Front brace Back brace

(mm) (mm) (mm) (mm)

1A-M 58.6 58.5

1B-M 58.2 58.2 1C-M 58.3 58.7

2A-C 58.5 58.8 58.5 58.9

2B-C 58.5 58.4 58.4 58.4

2C-C 58.5 58.5 58.6 58.5

3A-M 101.2 101.3

3B-M 101.5 100.8

3C-M 101.3 101.0

4A-C 101.7 100.9 101.5 101.4

4B-C 104.1 104.3 104.3 104.2

4C-C 101.6 102.3 104.8 102.4

5A-M 152.2 152.6

5B-M 152.3 152.9

5C-M 152.4 152.2

6B-C 152.4 152.4 152.4 152.6

a Braces under tension during wall displacement in the positive direction.b Braces under tension during wall displacement in the negative direction.

Hence, it was not possible to rely on the 80% post peak-load

definition of the reference deformation [24,25]. Instead, the

yield displacement of the wall, y , was incorporated in the

calculation of the reference deformation for the determination

of the displacement amplitudes for the loading cycles. It

was assumed that = 2.667y , where y was obtained

from the nominally identical monotonic wall tests. Additional

information on the test program is provided by Al-Kharat and

Rogers [20].

4.1. Material tests

Material tests were carried out for the straps, chords and

tracks according to ASTM A370 [27] requirements. Coupon

tension tests were conducted at a cross-head rate of 0.5 mm

per minute in the elastic range, which was increased to a rate

of 4 mm per minute beyond the yield point. A 50 mm gauge

length extensometer was used to measure the extension of the

coupon and to calculate percentage of elongation, yield stress

and ultimate stress. Table 3 contains a listing of the minimum

specified (nominal design value) material yield stress, Fyn , and

thickness, as well as the measured yield stress, Fy , ultimate

stress, Fu , percent elongation and ratio of Fu /Fy , in addition

to the ratio of measured to nominal yield stress, Fy /Fyn . To

determine the base metal thickness of the material, the zinc

coating was removed with a 10% hydrochloric acid (HCL)

solution after testing. All of the steels used in the construction

of the test walls met the requirements of the North American

Specification for Cold-Formed Steel Members [3,6]. That is,the ratio of Fu /Fy was greater than 1.08, and the elongation

over a 50 mm gauge length exceeded 10%. It should be noted

that the 1.22 mm Grade 230 MPa steel was measured to have

a yield stress 54% greater than the minimum nominal specified

value, Fy /Fyn .

4.2. Modes of failure

In terms of ductile seismic performance, the desirable mode

of failure of a cold-formed steel braced wall system is generally

that of gross-cross section yielding of the straps, which form the

fuse element in the SFRS. The other elements and connectionsin the seismic force resisting system are expected to carry

the force associated with the strap yielding load level. The

strap braces should be able to enter into the inelastic range

of behaviour such that ground motion induced energy can be

dissipated. Ideally, the braces would be able to maintain their

yield capacity over extended lateral inelastic displacement of

the wall without failure of the connections, gusset plates, tracks,

chord studs or holddowns.

In general, the overall performance of the tested walls

under lateral loading was not governed by the yielding of the

straps, as indicated by the strain gauge measurements that were

taken [20]. Rather, failure of or extensive damage to the tracks,

chord studs, gusset plates, holddown threaded rods and straps

(due to net section fracture) was often observed depending on

the wall configuration being tested. These undesirable modes

of failure prevented the straps from maintaining their yield

load, or from yielding altogether. Thus the ductility and energy

absorption ability of the SFRS was reduced in comparison

to what could theoretically be expected given the material

properties of the strap braces and what inherently would be

assumed when a seismic response modification coefficient of

R = 4.0 is selected in design. A summary of the dominant

failure modes is provided below. More detailed information can

be found in Al-Kharat and Rogers [20].

Table 3

Material properties of strap and frame members

Member Nominal grade

(MPa)

Nominal thickness

(mm)

Base metal thickness

(mm)

Yield stress (Fy )

(MPa)

Ultimate stress (Fu )

(MPa)

Fu /Fy % Elng. Fy /Fyn

Strap 230 1.22 1.16 353 440 1.24 33 1.54

Strap 230 1.52 1.48 279 350 1.25 40 1.21

Strap 230 1.91 1.83 262 346 1.32 38 1.14

Track 230 1.22 1.22 320 380 1.19 31 1.39

Stud 230 1.22 1.23 336 398 1.19 35 1.46

Track 345 1.52 1.59 330 400 1.21 35 0.96

Stud 345 1.52 1.56 329 397 1.21 39 0.95

Track 345 1.91 1.94 348 474 1.36 37 1.01

Stud 345 1.91 1.91 352 489 1.39 35 1.02

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Fig. 6. Typicaltrackand connection failure modesat holddown location in light

walls.

Strain gauge measurements showed that yielding of the

straps occurred in the light walls; however, this was always

combined with the progressive compression failure of the

track and/or failure of the chord-to-track connection (Fig. 6).

This failure mode was similar to that reported by Fulop and

Dubina [16] for their strap braced wall tests. Fracture of a brace

occurred in only one wall (Test 1A-M) after approximately

30103 rad of shear deformation. In the first test to be carried

out (Test 1B-M) tension fracture of the 12.7 mm dia. anchorrod took place because, although adequate for the assumed 20

kN wind loading design level, the threaded rod was not able to

carry the force associated with the actual yield capacity of the

braces. The anchor rod size was increased to 15.9 mm dia. for

all subsequent tests of light walls to avoid this mode of failure.

Yielding of the straps occurred in the medium size walls

only when the larger holddown plates were installed. Even

so, the straps were not able to maintain their yield force level

due to extensive damage to the area adjacent to the holddown,

specifically in the track and gusset plates. Specimens 3A-M

and 3B-M, which were the first of this series to be tested,

were outfitted with 19 90 127 mm holddown plates. Thepunching shear capacity of the tracks around these plates was

not adequate. For the remainder of the medium strap braced

wall specimens a larger holddown plate, 19 127 203 mm,

was installed in an attempt to alleviate the punching shear

failure mode. This was successful to some degree; however

punching shear failure of the tracks, as well as permanent

deformation of the gusset plates and chord studs were still

observed (Fig. 7). Furthermore, the gusset plates created a

rigid corner element that would rotate in-plane due to the lack

of stiffness in the holddown/track area and the anchor rod

(Figs. 7 and 8). Local buckling of the chord studs on the uplift

side of the wall was caused by the extensive corner rotation

and the resulting applied moment on the framing member(Fig. 8). In one case (3C-M) punching shear failure of the

bottom track was observed along with fracture of the strap brace

(Fig. 7). The in-plane rotation of the bottom wall corner caused

excessive tensile stresses on the lower side of the strap brace

that ultimately resulted in its failure.

The heavy walls in the test study were not able to

demonstrate yielding of the strap braces along their length.

Extensive damage to the frame and gusset area adjacent to

the holddown plate was typically observed (Fig. 9); modes of

failure that would not be expected under a capacity based design

approach. Punching shear failure of the track occurred in all

tests, which did not allow the braces to reach their yield capacity

Fig. 7. Typical punching shear failure mode at holddown location in medium

walls.

Fig. 8. Medium wall post-test deformations and flexural failure of chord studs.

Fig. 9. Typical punching shear failure mode at holddown location in heavy

walls.

in tension. It was also common to observe the chord studs

being pulled in towards the centre of the wall due to the loss

of compression resistance in the track and gusset plates after

punching shear failure had taken place. Pull-out of the screws

that connected the interior studs to the bottom tracks was alsowitnessed, mainly due to the large deformations experienced by

the walls. Similar to the medium walls, rotation of the corner

connections took place, which led to moment induced local

buckling of the chord studs (Fig. 8).

The failure modes that were observed were mainly due to the

fact that the selection of holddowns and anchor rods, as well as

other elements in the SFRS, was not based on an estimate of

the yield capacity of the strap braces. Instead, each of the SFRS

elements were chosen given the expected factored lateral force

on the wall, which was assumed to be equal to the factored

capacity; 20 kN (light), 40 kN (medium) and 75 kN (heavy).

The actual lateral capacity of a braced wall is typically higher

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Fig. 10. Measured and predicted wall strength and stiffness.

than the factored design level; hence, in order to ensure that the

braces yield in tension along their length and that the yield load

level is maintained into the inelastic range it is important that

a capacity based approach be implemented in design. Although

the braces in the light walls did reach and maintain their yield

plateau, the inelastic performance of these walls could have

been improved by reinforcing the tracks, selecting a thicker

track section, or with the use of a corner detail that transferred

the horizontal brace forces into the supporting foundation by

means of tension. The medium and heavy walls did not exhibit

the inelastic behaviour that would be expected if a hysteretic

model, such as the one developed by Pastor and Rodrguez-

Ferran [18], were utilized for the nonlinear inelastic dynamicanalysis of X-braced cold-formed steel frames. Nor did the

observed inelastic failure modes match that which would be

associated with the use of a seismic response modification

coefficient of R = 4.0 as recommended in ASCE 7-05 [4].

4.3. Measured and predicted performance parameters

The maximum load level reached by each braced wall

regardless of the failure mode was defined as the measured

yield strength, Sy . The measured initial elastic shear stiffness,

Ke, was defined as the secant stiffness from the zero load level

to the 40% of maximum load level, S0.4, as recommended

in ASTM E2126 [25] (Fig. 10). These measured values werecompared with predicted wall properties, which were calculated

using the minimum specified (nominal) brace dimensions and

material properties (Table 1), as well as the measured brace

dimensions (Table 2) and material properties (Table 3). None of

these prediction methods are code specific. Given that the topic

of this paper is the inelastic response of strap braced walls, it is

the measured and predicted yield strengths that are of primary

concern, not the initial elastic stiffness or the factored shear

capacity. A schematic drawing that illustrates the measured and

predicted wall properties is shown in Fig. 10 for monotonic

wall test 1-AM. In a similar fashion the outer envelope of the

hysteretic loops was used to obtain the measured properties of

the reversed cyclic tests. Note: the position of the predicted

strengths, Syn and Syp , with respect to Sy may vary from what

is illustrated depending on the particular wall being analysed.

The predicted nominal lateral yield strength, Syn , of the wall

was based on the tension yield strength of the braces determined

using their nominal area (width thickness) as well as the

minimum specified (nominal) yield stress (230 MPa) (Table 1).

The nominal tension yield capacity of the brace was adjusted

for the inclined position of the strap members with respect to

the horizontal. The predicted nominal lateral shear stiffness of

the wall, Kn , was calculated based on the axial stiffness of the

two tension brace members, which was also adjusted for their

inclined position with respect to the horizontal. In this case thenominal design width, thickness and length of the strap braces

(Table 1) and E = 203 000 MPa were utilized. The reduction

in shear stiffness of the wall assembly due to the flexibility of

the brace connections and holddown was not accounted for.

The predicted values Syn and Kn represent the nominal (not

factored) design parameters that an engineer would typically

be able to determine using minimum specified member sizes

and material properties without the aid of test results and

measurements.

The lateral shear strength and stiffness parameters of each

test wall were also predicted using the measured width (Table 2)

and base metal thickness (Table 3) of the strap braces, as wellas the measured yield stress (Table 3) and the CSA S136 [3]

specified Youngs modulus (E = 203 000 MPa). Syp is the

predicted lateral yield strength of the wall, which is typically

reached when the strap braces yield in tension. Kp is the

predicted lateral shear stiffness of the wall, again obtained from

the initial elastic axial stiffness of the strap braces alone.

The ductility, , defined as the ability of the strap braced

wall system to maintain its yield capacity while attaining

significant inelastic lateral deformations, was also determined

(Eq. (1)).

=0.8

syp(1)

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Table 4

Summary of monotonic test results

Specimen Sy Ke Ductility () 0.8 Energy Syp Kp Sy /Syp Sy /Syn Ke/Kp Ke/Kn(kN) (kN/mm) (mm/mm) (rad 103) (kN mm) (kN) (kN/mm) (%) (%) (%) (%)

1A-M 31.97 1.29 3.01 32.3 2086 33.93 4.00 94 126 32 28

1B-M 30.39 1.59 2.32 20.2 1123 33.73 3.98 90 120 40 35

1C-M 31.96 1.48 3.88 36.7 2810 34.03 4.01 94 126 37 32Avg 31.44 1.45 3.07 29.7 2006 33.90 4.00 93 124 36 32

SD 0.909 0.152 0.782 8.547 846 0.153 0.015

CoV 0.029 0.104 0.255 0.287 0.422 0.005 0.004

3A-M 55.37 2.34 1.57 16.2 1478 58.88 9.20 94 110 25 24

3B-M 48.29 2.99 1.28 10.3 1332 58.84 9.20 82 96 33 31

3C-M 55.12 2.56 3.10 29.2 3610 58.77 9.19 94 109 28 27

Avg 52.93 2.63 1.98 18.5 2140 58.83 9.20 90 105 29 27

SD 4.017 0.331 0.978 9.644 1275 0.056 0.006

CoV 0.076 0.126 0.493 0.520 0.596 0.001 0.001

5A-M 82.93 3.61 2.21 25.9 5622 103.4 17.20 80 88 21 20

5B-M 59.79 5.97 1.78 12.7 1943 103.6 17.22 58 63 35 33

5C-M 81.23 3.85 2.09 23.0 3537 103.4 17.18 79 86 22 22

Avg 74.65 4.48 2.03 20.5 3701 103.5 17.20 72 79 26 25

SD 12.90 1.299 0.222 6.944 1845 0.108 0.020

CoV 0.173 0.290 0.109 0.339 0.499 0.001 0.001

Table 5

Summary of reversed cyclic test results

Specimen Sy Ke Ductility () 0.8 Energy Syp Kp Sy /Syp Sy /Syn Ke /Kp Ke/Kn(kN) (kN/mm) (mm/mm) (rad 103) (kN mm) (kN) (kN/mm) (%) (%) (%) (%)

2A-C (+ve) 35.26 1.27 4.11 45.1 10 167 34.00 4.01 104 139 32 28

2A-C (ve) 35.29 1.08 3.10 40.1 104 139 27 23

2B-C (+ve) 34.50 1.18 3.83 45.1 10 571 33.83 3.99 102 136 30 26

2B-C (ve) 34.47 1.18 3.83 48.0 102 136 30 26

2C-C (+ve)a 38.97 2.26 6.33 38.9 5 967 33.91 4.00 115 153 56 49

2C-C (ve) 35.49 1.22 4.22 46.7 . 105 140 31 27

Avg 35.00 1.19 3.82 44.0 8 902 33.91 4.00 103 138 30 26SD 0.48 0.07 0.44 3.637 2 550 0.08 0.01

CoV 0.014 0.059 0.114 0.083 0.286 0.002 0.002

4A-C (+ve) 59.47 2.36 1.98 20.3 19 006 58.98 9.22 101 118 26 25

4A-C (ve) 60.07 2.09 1.89 21.9 102 119 23 22

4B-C (+ve) 62.31 2.27 2.23 24.4 18 663 60.64 9.48 103 124 24 24

4B-C (ve) 60.59 2.05 1.87 22.6 100 120 22 21

4C-C (+ve) 55.69 2.21 2.00 22.3 18 513 59.80 9.35 93 110 24 23

4C-C (ve) 56.40 2.43 2.26 22.9 94 112 26 25

Avg 59.09 2.24 2.04 22.4 18 727 59.81 9.35 99 117 24 23

SD 2.55 0.15 0.17 1.355 253 0.74 0.12

CoV 0.043 0.067 0.082 0.060 0.013 0.012 0.012

6B-C (+ve) 87.13 3.79 2.01 22.6 26 051 103.5 17.2 84 92 22 21

6B-C (ve) 83.56 3.48 1.88 22.9 81 88 20 19

Avg 85.35 3.64 1.95 22.7 26 051 103.5 17.2 83 90 21 20

a 2C-C (+ve) not included in calculation of statistical parameters.

where 0.8 is the failure displacement in the post-peak range

that corresponds to a wall resistance of 80% of the maximum

level measured (Fig. 10). In an ideal case where failure is

limited to yielding of the brace members, no reduction in shear

strength should take place; and hence, the failure displacement

would be defined as the maximum in-plane displacement

reached by the wall as limited by the stroke of the actuator.

It was however typical for the walls in this study to experience

some decrease in shear resistance due to failure modes other

than yielding of the strap braces. The elastic yield deformation,

syp, was calculated using the measured elastic stiffness, Ke,

and the predicted lateral yield strength of the wall, Syp (Fig. 10).

A summary of the test results and predicted wall properties is

found in Tables 4 and 5.

4.4. Comparison of measured and predicted performance

4.4.1. Light walls

An average yield strength of Sy = 31.44 kN, equal to 93%

of the predicted value based on the measured properties of the

brace members (Sy /Syp ), was attained for the light walls tested

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Fig. 11. Cyclic resistance versus displacement curve of 58.4 mm (light) strap

braced wall 2A-C.

monotonically (Table 4). The full predicted capacity was not

reached most likely because of the increase in Fy due to the

strain rate effect that occurred during testing of the coupons.

The estimated strain rate for the coupons was 0.0667 /min,

which was 92 times greater than the approximate strain rate

determined for the monotonically tested strap walls (0.000725

/min). The average measured yield strength of the cyclic tests

was 35.0 kN, which was 3% higher than the predicted Sypvalue (Table 5). A higher yield capacity was measured because

the walls, which were tested at a frequency of 0.5 Hz, would

have reached a much higher strain rate than experienced by the

monotonic tests. This would likely have elevated the yield stress

of the strap braces.

A comparison of the measured yield strength reached, Sy ,

by each of the light walls with the factored design resistance

(20 kN) including both monotonic results as well as the results

of positive and negative excursions for the reversed cyclic

tests gave a ratio of 1.66. The test-to-nominal predicted shear

capacity, Sy /Syn , listed in Tables 4 and 5 was 1.24 and 1.38

for the monotonic and reversed cyclic tests, respectively; which

indicates that the test walls were able to reach the expected

nominal design shear strength. However, using the nominalshear strength of the wall based on the brace yield capacity

did not provide for an accurate estimate of the actual force in

the SFRS when the straps yield. An increase in the nominal

prediction of between 1.2 and 1.4 is necessary to determine a

more realistic force level for the brace connections, holddowns,

chord studs, etc. in a capacity based design context because

the actual yield stress of the strap material is higher than the

minimum specified 230 MPa.

The light walls were able to perform in a ductile manner;

that is, they were able reach and maintain their yield capacity

throughout most of the reversed cyclic loading protocols;

however, often the resistance decreased in the latter stages of

Fig. 12. Cyclic resistance versus displacement curve of 58.4 mm (light) strap

braced wall 2B-C.

each cycle. This reduction in load was caused by the damage

that occurred at the holddown/track-to-chord stud connection

locations (Fig. 6). An example of this can be seen in Fig. 11,

where for the negative load/displacement region of test 2A-C

there is a significant decrease in load above the 30 103

rad displacement level compared with test 2B-C (Fig. 12).

On average the light walls reached a 0.8 (Fig. 10) shear

deformation of 34.5 103 rad and 44.0 103 rad for

the monotonic and reversed cyclic tests. Note; the monotonicaverage was calculated without using the result from test wall

1B-M because it failed prematurely due to the fracture of the

12.7 mm dia. threaded anchor rod. These shear deformation

measurements correspond with an average ductility of 3.07 and

3.82 for the monotonic and reversed cyclic tests, respectively.

A test-based estimate of the ductility related seismic force

modification factor, Rd, can be defined as shown in Eq. (2) [28].

An average Rd of 2.48 was obtained for the light strap braced

walls. Furthermore, Mitchell et al. [29] recommended that the

overstrength related seismic force modification factor, Ro, can

be estimated by considering the product of the average Sy /Syn

ratio and the inverse of the resistance factor, 1/. CSA S136 [3]specifies that = 0.9 for gross cross section yielding design of

a tension member. For comparison purposes the ASCE 7-05 [ 4]

defined R-value can be thought of as the product of the ductility

related, Rd, and overstrength related, Ro, force modification

factors as found in the 2005 NBCC [1]. The resulting overall

average Ro factor of 1.47 and the Rd factor noted above provide

for an R value of 3.65 for the light walls. This test-based

estimate of the seismic response modification coefficient is

between the R = 3.0 and 4.0 recommended by ASCE 7-05.

Reinforcement of the track member of the wall, such that it is

capable of carrying the strap yield forces, would likely improve

the ductility such that the test-based R is at a level of 4.0

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or higher.

Rd =

2 1. (2)

In terms of predicted stiffness levels, none of the walls

were able to reach the expected 4.00 kN/mm. As is illustrated

in Fig. 11, Ke was substantially lower than Kp. In a similar

fashion the nominal stiffness, Kn , was also not reached byany of the light walls. This can also be seen in the Ke/Kpand Ke/Kn ratios provided in Tables 4 and 5. These predicted

stiffness values were based solely on the dimensions and

material properties of the straps. From observations of the large

deformations and damage at the holddown locations, as well as

the measured stiffness values, it is apparent that in this case the

flexibility of the holddowns and brace connections has caused a

decrease in the stiffness of the test walls. The predicted lateral

in-plane elastic stiffness of the braced wall cannot be based

solely on the axial stiffness of the straps.

4.4.2. Medium wallsA performance ratio of Sy /Syp = 90%, which corresponds

to an average monotonic lateral resistance of 52.93 kN

was measured for the medium walls (Table 4). The 10%

shortcoming in the ratio of Sy /Syp is again likely due to the

strain rate used for the monotonic wall testing compared with

that used for the coupons. The early onset of punching shear

failure in the tracks may also have limited the capacity of the

wall. Similar findings were obtained for the reversed cyclic tests

except that a higher average resistance of 59.09 kN was reached

(Table 5). This resulted in a performance ratio of Sy /Syp =

99%. The increased load levels can be attributed to the strain

rate effect experienced by the strap braces. Nonetheless, as isshown in Figs. 13 and 14, these walls were unable to maintain

their load carrying capacity due to punching shear failure of

the tracks (Fig. 7). No yield plateau was observed; instead

a sharp peak resistance was recorded, followed by a sudden

degradation in load carrying ability. The fuse element in the

seismic force resisting system ultimately was the holddown

plate/anchor rod/track connection in combination with the strap

braces.

A comparison of Sy for the medium walls with the factored

design resistance (40 kN) for the monotonic and reversed

cyclic tests gave a ratio of 1.40. The test-to-nominal predicted

shear capacity, Sy /Syn , listed in Tables 4 and 5 was 1.05 and

1.17 for the monotonic and reversed cyclic tests, respectively;which shows that the wall was able to reach the expected

nominal design shear strength. However, the nominal shear

strength of the walls based on the brace yield capacity did not

provide for a precise estimate of the actual force in the SFRS

when the straps yield, although the estimate was improved

compared with the light walls. An increase in the nominal

prediction of approximately 1.2 is necessary to determine a

more realistic force level for the brace connections, holddowns,

chord studs, etc. in a capacity based design context. Note that

this increase is somewhat lower than that recommended for the

light walls, mainly because of the significantly higher material

yield strength, Fy , that was measured for the braces of the

Fig. 13. Monotonic resistance versus displacement curve of 101 mm (medium)

strap braced wall 3C-M.

Fig. 14. Cyclic resistance versus displacement curve of 101 mm (medium)

strap braced wall 4B-C.

light walls compared with the nominal (minimum specified)

230 MPa (Table 3).

The medium walls attained a 0.8 (Fig. 10) shear deforma-

tion of 18.5 103 rad and 22.4 103 rad for the monotonic

and reversed cyclic tests. The corresponding average ductility

for the monotonic and reversed cyclic tests was 1.98 and 2.04,

respectively. These ductility measurements provided an average

Rd value of 1.71 for the medium walls. An overstrength related

Ro value of 1.23 was also obtained, which when combined with

the Rd value results in a test-based R value of 2.11, far below

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Fig. 15. Monotonic resistance versus displacement curve of 152 mm (heavy)

strap braced wall 5A-M.

that specified in ASCE 7-05 [4]. The punching shear mode of

failure did not allow for the yield capacity of the braces to be

maintained; thus, the flat plate holddown detail used for the

medium walls did not provide for a sufficient level of ductility

to warrant a seismic response modification coefficient equal to

4.0 or even 3.0. It is recommended that the flat plate holddown

detail not be used for braced walls with unlipped channel track

sections because of the lack of a direct connection between the

straps and anchor device.The average Ke of 2.63 kN/mm for the monotonic tests was

well below the expected stiffness, Kp = 9.20 kN/mm, due to

the flexibility of the flat plate holddown detail, as well as the

extreme damage that occurred (Fig. 7). Likewise, the nominal

elastic stiffness, Kn , was also not reached by any of the test

walls.

4.4.3. Heavy walls

The monotonic tests 5A-M, 5B-M and 5C-M (heavy walls)

had the lowest performance ratio of all the strap braced walls

that were included in the study. An average capacity of 74.65

kN was measured, which corresponds to an Sy /Syp ratio of72% (Table 4). Yielding was seen in some areas of the braces,

based on strain gauge measurements; however the overall yield

capacity of the brace was not reached at any time (Fig. 15). As

was observed for the medium walls, punching shear failure of

the track controlled the wall resistance, stiffness and ductility

(Fig. 9). Given the poor results of the monotonic tests only

one reversed cyclic test was completed (6B-C) (Fig. 16).

The average maximum resistance of the negative and positive

displacement cycles was 85.35 kN (Table 5). This provided a

performance ratio ofSy /Syp = 83%, somewhat higher than the

monotonic tests, but not adequate when compared to the shear

load associated with brace yielding.

Fig. 16. Cyclic resistance versus displacement curve of 152 mm (heavy) strap

braced wall 6B-C.

A comparison of Sy for the heavy walls with the factored

design resistance (75 kN) for the monotonic and reversed

cyclic tests gave a ratio of 1.07. The test-to-nominal predicted

shear capacity, Sy /Syn , listed in Tables 4 and 5 was 0.79 and

0.9 for the monotonic and reversed cyclic tests, respectively,

which shows that the walls were not even able to attain their

expected nominal design shear strength. Punching shear failure

of the track members limited the amount of force that could be

transferred to the brace members; hence, the strap braces did

not at any time reach their potential tensile yield capacity whilebeing tested.

Punching shear failure of the track once again controlled the

behaviour of the wall. As found for the medium strap braced

walls, the flat plate holddown detail was inadequate to allow

for the wall to maintain its yield capacity, and hence to act

in a ductile fashion. This can be seen in the measured 0.8(Fig. 10) shear deformation of 20.5 103 rad and 22.7

103 rad reached by the monotonic and reversed cyclic tests.

The average ductility calculated using these shear deformation

values for the monotonic and reversed cyclic tests was 2.03 and

1.95, respectively; which was similar to the medium walls. An

average Rd value of 1.72 was obtained; however, because theSy /Syn ratio was below 1.0, no overstrength existed and as such

Ro = 1.0. The product of Rd and Ro gives a test-based R

value of 1.72, again significantly lower than that specified in

ASCE 7-05 [4] for strap braced bearing wall systems. It is again

recommended that the flat plate holddown detail not be used for

braced walls with unlipped channel track sections because of

the lack of a direct connection between the straps and anchor

device.

The measured initial elastic stiffness, Ke, was in the range

of 20%26% of the expected Kp and Kn values (Tables 4 and

5). This finding can again be attributed to the flexibility of the

flat plate holddown detail.

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5. Conclusions and recommendations

In general, the strap braced test walls, as constructed, were

not able to maintain a yield level load carrying capacity over

extended displacements, with the exception of the light walls.

Moreover, the heavy walls were not able to even reach the

load level associated with gross cross-section yielding of thebraces. The extensive damage to the holddown/gusset/chord

stud/track location in almost all test walls showed that the

inelastic deformations were not limited to the brace elements of

the lateral force resisting system. Furthermore, punching shear

failure of the tracks severely reduced the inelastic performance

of the medium and heavy walls.

Given the results of testing, it is not possible to consider the

walls to have performed in the ductile fashion that would have

been associated with a response modification coefficient ofR =

4.0 and assumed if a capacity based design approach had been

followed. The medium and heavy walls did not even possess

the ductility and overstrength to validate the use of R = 3.0, as

allowed in ASCE7-05 when seismic details are not incorporatedin the design of a structure. However, the fact that the test

walls were designed and constructed without capacity based

concepts in mind does indicate that the inelastic performance

could possibly be improved if additional design steps were

taken. This is most evident for the light walls in which a test-

based RdRo value of 3.65 was attained. In contrast, however,

the medium and heavy walls were only able to exhibit a test-

based Rd Ro value of 2.11 and 1.72, respectively; which is

approximately half of the ASCE7-05 upper R-value specified

for cold-formed steel strap braced bearing wall systems.

An estimate of the force in the SFRS due to brace yielding

needs to account for the possible overstrength of the strapmaterial, such that failure or plastic deformation of other

elements in the lateral load path is avoided. The nominal

capacity of the strap members (Ag Fy ) does not indicate

the true force level that may be reached in the system. This is

due to the actual yield strength of the cold-formed steel strap

members, which in the case of this study reached as high as

1.54 times the minimum specified 230 MPa.

It is recommended that supplementary tests of similar size

strap braced walls be carried out, for which the elements

in the seismic force resisting system are selected based on

the probable yield capacity of the strap braces. An accurate

estimate of the yield stress of the brace material is needed,

which accounts for both the effects of the higher than minimum

nominal yield stress due to the manufacturing processes and the

strain rate under seismic loading. Furthermore, the holddown

detail needs to be improved, such that the probable brace loads

can be carried with minimal rotation and inelastic damage to

the track, chord studs, gusset plate, anchor rod and holddown

itself. In terms of recommendations for designers, at the very

least it is necessary that a capacity based design approach be

implemented for the selection of SFRS elements. The use of

corner holddown plates placed in the bottom and top tracks of

a strap braced wall does not provide for an adequate transfer of

brace induced forces due to the possibility of punching shear

failure. Moreover this holddown failure mode is not ductile

in nature, and hence does not allow for the strap brace yield

capacity to be maintained. Additional research that includes

more specific detailing requirements for strap braced walls is

ongoing.

Acknowledgements

The authors would like to acknowledge the support provided

by the Canada Foundation for Innovation and the Canadian

Sheet Steel Building Institute. Test specimens were generously

supplied by Genesis by KML Ltd. of Cambridge, ON, Canada.

A thank you is also extended to the students K.E. Hikita,

A. Frattini, T.L.W. Lim and Z. Fu for their assistance in carrying

out the braced wall tests.

References

[1] National Research Council of Canada (NRCC). National Building Code

of Canada. Ottawa (ON, Canada); 2005.

[2] Heidebrecht AC. Overview of seismic provisions of the proposed 2005

edition of the National Building Code of Canada. Canadian Journal of

Civil Engineering 2003;30(2):24154.

[3] Canadian Standards Association S136. North American specification for

the design of cold-formed steel structural members. Mississauga (ON,

Canada); 2001.

[4] American Society of Civil Engineers ASCE 7. Minimum design loads for

buildings and other structures. Reston (VA, USA); 2005.

[5] American Iron and Steel Institute. Standard for cold-formed steel framing

lateral design. Washington (DC, USA); 2004.

[6] American Iron and Steel Institute. North American specification for the

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