Thin-Walled Structures 51 (2012) 64–75
Contents lists available at SciVerse ScienceDirect
Thin-Walled Structures
journal homepage: www.elsevier.com/locate/tws
An experimental investigation on the lateral behavior of knee-braced
cold-formed steel shear walls
Mehran Zeynalian, H.R. Ronagh n
School of Civil Engineering, The University of Queensland, Brisbane, Australia
a r t i c l e i n f o
a b s t r a c t
Article history:
Received 20 January 2011
Received in revised form
16 November 2011
Accepted 16 November 2011
Available online 8 December 2011
Experimental investigations were conducted to evaluate the lateral seismic characteristics of lightweight knee-braced cold-formed steel structures. In all, four full-scale 2.4 2.4 m2 specimens with
different configurations were tested under a standard cyclic loading regime. This paper focuses on the
specimens’ maximum lateral load capacity and deformation behavior and provides a rational estimate
of the seismic response modification factor, R, of knee-braced walls. The study also looks at the failure
modes of the system and investigates the main factors contributing to the ductile response of CFS walls.
That is in order to suggest improvements so that the shear steel walls respond plastically with a
significant drift and without any risk of brittle failure, such as connection failure or stud buckling.
A discussion on the calculated response factors in comparison to those suggested in the relevant codes
of practice is also presented.
& 2011 Elsevier Ltd. All rights reserved.
Keywords:
Cold-formed steel
Light steel frames
Knee-braces
Lateral performance
Response modification factor
1. Introduction
The cold-formed steel (CFS) construction is poised to make a
significant impact in the low rise residual housing industry due to its
unique advantages such as being cost-effective, light-weight and
easy to work with. Although light-weight cold-formed steel walls
are not new and have been used as non-structural components for
many years, their application as load-bearing main structural frames
is relatively new. As a result, appropriate guidelines that address the
seismic design of CFS structures have not yet been fully developed
and the lateral design of these systems is not covered in detail in the
standards of practice. Hence, more research work is required in
order to clarify the many different aspects of the seismic performance of CFS shear walls, including rational estimation of the
response modification factor, R, as well as the achievable ductility
and strength.
Steel framed structures currently in use in Australia, are normally braced using face mounted thin straps, cross braces that are
of the same shape as studs, or compressed cement boards screwed
to the face of the walls. While, these are found adequate in low
seismic regions of Australia, an investigation into the earthquake
resistance properties of CFS have led authors to examine alternative
bracing types that may present a more favorable ductile response.
Knee braces that are specially designed for this purpose are
introduced in the paper and studied in a specially designed testing
n
Corresponding author.
E-mail address: h.ronagh@uq.edu.au (H.R. Ronagh).
0263-8231/$ - see front matter & 2011 Elsevier Ltd. All rights reserved.
doi:10.1016/j.tws.2011.11.008
rig. Of particular interest in this study are the effects of kneeelement length and the use of brackets on the lateral performance.
Knee elements maintain a considerable reserve of post-local buckling strength prior to yielding. Therefore, it is expected that their
presence would facilitate a more ductile response. The brackets also
add to the redundancy of the system and as such increase the
ductility of the system in a similar manner.
2. Past studies
In recent years, there have been many experimental research
studies on the performance of different cold formed lateral
resistance systems mostly on strap-bracing system. However
there has not been any study made on the seismic behavior of
knee-braced cold-formed steel shear walls. Some of these studies
are summarized and presented below.
Fulop and Dubina [1] investigated three full scale 3.6 2.44 m2
X-braced screw connected specimens under cyclic lateral loading.
The walls consisted of cold-formed steel frames and double-sided
110 1.5 mm2 straps. The screw connection configuration was
selected to facilitate yielding along the straps. Double stud
members were chosen as the chords to limit inelastic deformations and ultimate failure of the walls. U profiles were used for the
track to chord connections instead of plates or angles, which
provided more capacity and rigidity for the frames. Local buckling
of the lower track was observed during loading with damage
being concentrated in corner areas. Although plastic elongation
of the strap occurred, the results of the experiments may not
M. Zeynalian, H.R. Ronagh / Thin-Walled Structures 51 (2012) 64–75
necessarily reflect the true ductility of a braced wall because the
unexpected failure of the corners failure had been limited only to
the straps. They suggested the ideal configuration of the corners
would be such 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. [2] conducted experimental and theoretical studies on
the racking performances of CFS walls including frames with single
and double X straps. A total of five full scale 2.45 1.25 m2 frames
consisted of strap braces riveted to the steel framing were tested.
Brace size was either 60 1.0 mm2 or 60 1.2 mm2, which was
installed on both sides of the walls. They investigated the failure
modes and the lateral performances of the walls including: shear
strength and frame’ stiffness. They 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. Subsequent analyses of the test frames using an elastic
slope deflection method were also performed to predict the failure
loads and the initial shear stiffness. They concluded that it is
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.
Gad et al. [3] presented a detailed investigation into the contribution of plasterboard in the seismic performance of CFS X-strap bracing
walls be means of a shaker table together with numerical modeling.
Cyclic loading tests on a real-scale 3D single storey X-strap bracing
structure using shaker table tests were employed to address the
nonlinear element properties as well as to simulate the influence of
boundary conditions. Also, a numerical finite element model was
used to find the theoretical capacity of a four-walled structure, which
was compared with the experimental capacity of the same structure.
The authors focused on comparing the theoretical and the experimental results and provided recommendations for improving the
finite element model. By implementing the FE model, it was found
that contributions to shear capacity from plasterboard and strap
bracing are directly additive. However, considering the different
inherent ductilities of strap braces and gypsum board panels (which
reach their ultimate capacity at different displacements), it would
seem that adding the shear capacity of plasterboard and strap bracing
is irrational, as the Standard for cold-formed steel framing—lateral
design [4] clearly illustrates.
Serrette and Ogunfunmi [5] investigated the lateral performance
of 2.44 2.44 m2 strap braced frames subjected to lateral monotonic
loading. They tested three specimens with 50.8 0.88 mm2 screwconnected straps on one face, in addition to four specimens with
strap braces on one face and gypsum sheathing board on the other
side. It is also seen that one specimen with braces on both sides of
the wall was investigated. In all cases, they used an 11 mm thick
steel clip angle to the chord studs to act as a hold-down device. In
addition, they implemented cold-formed steel gusset plates to
connect the strap braces to the stud-track corner locations. They
reported that one side strap bracing walls failed by extensive out-ofplane deformation, which is not a favorable scenario in terms
of maintaining lateral stability of the braced frames, nor presents a
ductile performance under inelastic shear deformations. They
reported that gypsum panels provide a substantial increase in shear
capacity compared with the 50.8 mm wide straps though 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 engineers have to pay
adequate attention to strap yield strengths in excess of the minimum specified value, which may result in connection or chord stud
failure.
65
Kim et al. [6] performed a shaker table test on a full-scale twostory one-bay CFS shear panel structure. Each story consisted of
two identical shear walls of 2.8 m length and 3.0 m height
separated from each other by 3.9 m center to center. The two
chords were constructed from three C-sections forming a two-cell
closed section, and columns were welded to steel anchors and
bolted to the slab through top and bottom tracks. A heavy square
RC slab of 4.4 4.4 m2 by 200 mm thickness along with additional mass were placed at the top of each floor level, which made
the total mass at each floor level equal to 256 kN. As the second
story frame was identical to the first story, the damage occurred
mostly in the first story as expected. Connections and anchors to
the base beam were designed for the maximum over-strength of
straps, based on TI 809-07 [7] code; however, no pre-tensioning
was applied to the tension-only straps in spite of explicit
recommendation in the code. The system was completely symmetrical and the centers of mass and stiffness were located at the
same point and parallel to shear walls of the structure, to
preclude torsional and out-of-plane responses. The structure
was then loaded to a normalized accelerogram, which possessed
spectral response acceleration equal to the design response
spectrum around the fundamental period of the test specimen.
The test caused significant yielding in the form of severe nonlinear behavior in the first floor straps along their entire length
and yielding of studs near the anchors. The studs did not develop
full flexural strength due to local buckling and this impaired their
potential contribution to the story shear resistance. The studs’
contribution further decreased (about 15%) due to anchor deformation, which created a gap between the track and the slab. The
results showed that during the large amplitude tests, the X-strap
bracing showed very ductile, but highly pinched, hysteretic
behavior. The results of this study can be considered conservative
because the effect of non-structural gypsum board cladding was
not considered in the test.
Al-Kharat and Rogers [8] studied the inelastic performance of
16 X-strap braced 2.4 2.4 m2 CFS wall studs experimentally. For
this purpose, they tested three different types of X-strap bracing,
which were welded to the double stud chord sections under a
cyclic loading regime. The main factor that was monitored and
changed from one type to other was the cross-sectional area.
Hence, they divided the specimens into light, medium and heavy
strap-braced frame walls. By increasing the lateral drift, the shear
resistance reduced, due to local failure at the hold-down location.
While the main failure mode in the ‘heavy’ group was hold-down
failure, other types of failure (like strap tearing, track buckling
and track-to-chord connection failure) occurred in the ‘medium’
group of braced walls. The authors mentioned that these undesirable failure modes could have been avoided by proper design, as
they would not allow straps to reach yield. Moreover, they
concluded that the ductile performance of CFS walls, which is
reflected in some codes with an R factor of 4, is not reliable and,
for the medium and heavy walls, one should consider R¼3. This is
similar to the provisions of ASCE7-05[9], which provides an R¼3
when adequate seismic research evidence is not available for the
design.
Moghimi and Ronagh [10,11] investigated nine full-scale CFS
walls with four different strap-bracing systems under cyclic
loading, in addition to gypsum board sheathed CFS frames. They
tried to achieve failure of the frames by yielding of the straps,
since this is a desirable ductile failure mode for CFS strap frames.
They reported that gypsum board cladding alone is not reliable,
especially when compressive vertical loads are present. Moreover,
they used brackets at the four corners of the frames where the
chords were connected to tracks and showed that this improved
the walls’ lateral performance characteristics, such as strength,
stiffness and ductility, when either single or double studs were
66
M. Zeynalian, H.R. Ronagh / Thin-Walled Structures 51 (2012) 64–75
used as the chords. They noted that, although using gusset plates
provided ample room for straps to be connected to the panels and
eliminated the possibility of failure in the strap-to-frame connection, this was not a practical method due to the potential esthetic
problems it may cause, such as the unevenness of the covering
plasterboard.
3. Code provisions
One of the pioneer centers working on CFS framing systems is
the American Iron and Steel Institute, AISI. The institute’s efforts
in the development of construction standards started in the 1930s
and culminated in the first publication of the AISI Specification in
1946 [12]. AISI has published several standards, including the
following: Standard for Cold-Formed Steel Framing – Prescriptive
Method for One and Two Family Dwellings [13]; North American
Specification for the Design of Cold-Formed Steel Structural
Members [14]; and a series of standards for cold-formed steel
framing – General Provisions [15], Header Design [16], Lateral
Design [4], Wall Stud Design [17] and Truss Design [18]. Although
the design and construction of cold-formed steel structures shall
comply with the North American Specification [14] and the
General Provisions [15], seismic design regulations have been
stipulated in the Lateral Design [7] along with some design
guidelines for various special shear wall types and strap bracing
[19–21]. The Lateral Design Standard does not enforce any special
rule other than specifications and general provisions for shear
walls when the response modification factor is considered as
being smaller than 3 in design. However, for a response modification factor greater than 3, some additional requirements shall
apply, mainly described for diagonal strap bracing members and
anchorage of braced wall segments that resist uplift as well as
perimeter members at opening. The alternative between R r3,
with no special requirements, or taking the advantages of R43 in
addition to some essential detailing, is permitted only for the
seismic design categories A–C. In the seismic design categories
D–F, using an R equal to or less than 3 is not permitted, and the
designer must use the special seismic requirements with R
greater than 3 to ensure that the system behaves properly in
high seismic regions. Eventually, the code introduces seismic
response modification factors for different basic seismic forceresisting systems; however, it does not cover all available lateral
bracing systems, which are currently used in the CFS residential
industry including the knee-bracing system.
National Earthquake Hazard Reduction Program, NEHRP, is
another American centers, which has published a few seismic
provisions considering CFS contexts such as FEMA 450 [22] and
FEMA P750 [23]. They specify that the design of cold-formed carbon
or low-alloy steel members to resist seismic loads shall be in
accordance with the requirements of AISI Specifications and AISI
General Provisions. However, the allowable stress and load levels in
AISI are incompatible with the force levels calculated in accordance
with FEMA provisions. Therefore, it is essential to adjust the provisions of AISI for use with the FEMA provisions. It is mentionable that
these modifications affect only designs involving seismic loads.
The provisions affirm that all boundary members shall be designed
to transmit the specified induced axial forces. In addition, connections for diagonal bracing members shall have design strength equal
to or greater than the nominal tensile strength of the members being
connected, or O\ times the design seismic force, in which O\ is the
over-strength factor defined by the code. The pull-out resistance of
screws also shall not be used to resist seismic forces. FEMA 450 gives
the nominal shear strength for shear walls framed with cold-formed
steel members based on different sheathing materials and fastener
spacings at panel edges. Although the code provides the seismic
response modification factors for some CFS framing systems, it does
not cover all of the many different systems currently used in practice.
As a consequence, for systems not mentioned in the code, the
designer has to use the R factor corresponding to ‘‘Steel Systems Not
Specifically Detailed for Seismic Resistance’’, which is 3.
Another US standard on the cold formed steel structures is the
Technical Instructions, TI 809-07 [7]. This code was originally
developed for the design and construction of cold-formed steel
military constructions and is used extensively by the US Army
Corps of Engineers, USACE. The code is primarily based on FEMA
302 [24] though with some modifications in the design load
considering over-strength of straps. TI 809-07 stipulates that
shear panels shall be adequately anchored at their top and bottom
to a floor diaphragm. Furthermore, when it comes to the tying of
two lateral load resisting systems together, walls in orthogonal
direction shall be anchored to the same floor diaphragm. The
chords that support the vertical component of the strap load shall
be selected from a single closed (tubing) section or built-up CFS
section oriented to form a closed cross-section by means of
intermittent welds. Although the code provides some general
recommendations for seismic design of cold-formed steel shear
walls, it mainly focuses on diagonal strap configurations. So, a
seismic response modification factor is suggested only for CFS
shear panels with diagonal strapping, which is 4. The code
mentions that the R factor in the direction under consideration
at any storey shall not exceed the lowest value for the seismic
force resisting system in the same direction considered above that
storey, excluding penthouses. Other structural systems, i.e. dual
systems, may be used in combination with these CFS panels, but
then the smallest R value for all systems in the direction under
consideration must be used for determining the loads applied to
the entire structure in that direction. Dual systems must be used
with caution, particularly if differences in stiffness result in
interaction effects or deformation compatibility problems.
A different structural system may be used in the orthogonal
direction with different R values, and the lowest R value of that
direction shall be used in determining loads in that orthogonal
direction.
Uniform Building Code, UBC 97 [25], and International Building Code, IBC [26], highlight that the design, installation and
construction of CFS structural and non-structural framing shall be
in accordance with AISI. Also, the R factor shall be based on ASCE
7 for the appropriate steel systems, which are designed and
detailed in accordance with the provisions of AISC. Although
UBC allows a maximum height of five storeys for steel stud wall
systems in seismic zones, provided that they comply with some
specifications, IBC limits the use of CFS systems to up to two
storeys in height considering AISI provisions. The codes restrict
the thickness of CFS components to be in between 0.84 mm and
1.10 mm. According to IBC, a minimum of two studs back-to-back
for the chord member is needed and the aspect ratio of the wall
system shall not exceed 2:1. However, for some special applications, a maximum aspect ratio of 4:1 is acceptable. Moreover,
studs shall be a minimum 41 mm (flange) 89 mm (web) with a
9.5 mm return lip, while minimum dimensions for tracks are
32 mm and 89 mm for flange and web, respectively. The code
stipulates that bending in the track, overall buckling in stud and
pull-out of strap connection shall be prevented. Moreover, the
connection of diagonal bracing member and boundary members
shall be designed such that the full tensile strength of the
member, or O\ times the prescribed seismic forces, is developed.
The Australian cold-formed steel structures standard, AS/NZS
4600-05 [27], requires that when cold-formed steel members are
used as the primary earthquake resisting element, the selected
response modification factor shall not be greater than 2, unless
specified otherwise. However, as Australia is located in a low
M. Zeynalian, H.R. Ronagh / Thin-Walled Structures 51 (2012) 64–75
67
seismic zone, wind loads often dominate the design of low-rise
cold-formed steel buildings and therefore such a low value for R
factor does not affect designs. Little research attention has been
paid to the evaluation of R factors in Australia for the same
reason.
A simple but important conclusion from the above review is
that there is not a universal agreement on the value of response
modification factor, R, and in particular, there is no reference in
the codes for the R factor of systems braced with knee-braces.
More studies are required to clarify this matter.
4. Seismic response modification factor
The term, ‘‘seismic response modification factor’’ was first
introduced by the Applied Technology Council, ATC, in the ATC3-06 report [28] published in 1978. Since that time, other codes
and provisions have adopted similar factors to consider the same
concepts, although with different names [29]. The concept of a
response modification factor is based on the argument that welldesigned structural resistant systems have a ductile behavior and
are able to carry large inelastic deformation without collapse. In
other words, designed seismic strengths given by earthquakeresistant design codes are typically lower than the lateral strength
that is required to keep a structure in the elastic range in the
event of earthquakes. Strength reductions from the elastic
strength demand to real inelastic structural strength are taken
into account using the reduction factors, R. They were considered
to relate the ratio of the forces that would be developed under the
particular ground motions if the lateral framing systems were to
be totally elastic, to the prescribed design forces at the strength
level, which was commonly assumed to be equal to the significant
yield level. So, the R factor is ‘‘ y an empirical response reduction
factor intended to account for damping, over-strength, and the
ductility inherent in the structural system at displacements great
enough to surpass initial yield and approach the ultimate load–
displacement of the structural system’’ [30]. Hence, it is anticipated
that for a low ductility structure, which would not be able to
tolerate any considerable drifts further than the elastic range, the
R factor would be close to 1 and its behavior would be approximately linear. On the contrary, a highly ductile building with a
ductile structural system would be able to endure deformations
significantly better, and therefore is anticipated to have a larger
response reduction factor.
The response modification factor is commonly expressed in
terms of its two main components: ductility reduction factor (Rd)
and structural over-strength factor (O\) [30,31]. The R factor is
defined as
R ¼ Rd O0
ð1Þ
The components of the response modification factor are defined
using Fig. 1, which indicate the actual and the elastic performance of a
structural system as well as the idealized bilinear force–displacement
curve, as
Rd ¼
Ve
,
Vy
O0 ¼
Vy
Vs
ð2Þ
and the R factor can then be regenerated as
R ¼ Rd O0 ¼
Ve Vy
Ve
¼
Vy Vs
Vs
ð3Þ
where Ve, Vy and Vs correspond to the structure’s elastic response
strength, the idealized yield strength and the first ‘‘significant yield’’
strength, respectively.
Fig. 1. General structural response, illustrating FEMA’s concepts.
The evaluation of R factor and its components is a controversial structural concept, which has been discussed for many years;
however, some defined approaches are more popular than others.
In fact, the way that different parameters and an idealized
bilinear curve would be addressed has significant effects on the
estimated R factors. In this research study, the proposed method
by FEMA [22,30,32] is used to evaluate the response modification
factor for knee-braced systems.
Fig. 1 illustrates the general structural response considering both
positive and negative post-yield slope, and the method, which has
been used to idealize a force–displacement curve based on FEMA
356 [32]. The idealized bilinear curve is formed by two lines. The
68
M. Zeynalian, H.R. Ronagh / Thin-Walled Structures 51 (2012) 64–75
line segments shall be located using an iterative graphical method
that balances the size of the areas above and below of the curve. The
initial secant stiffness is calculated using a base shear force equal to
60% of the idealized yield strength of the structure. The second
segment line and the post-yield slope shall be determined by a line
passing through the actual curve at the calculated target displacement, which is addressed as Dt. In this study, based on references
[31,33–36], it is assumed that the target displacement is the
maximum structure’s drift prior to a considerable fall in the
structure’s strength. The code stipulates that the effective yield
strength shall not be taken to be greater than the maximum base
shear force at any point along the actual curve.
4.1. Ductility reduction factor, Rd
Rd has received considerable attention amongst researchers and
depends on the structural properties such as ductility, damping
and fundamental period of vibration, as well as characteristics of
the earthquake ground motion. Newmark and Hall [37] developed
the set of Eqs. (5)–(7) defining Rd in terms of a structure’s ductility,
which is expressed in terms of maximum structural drift, Dmax, and
the drift corresponding to the idealized yielding point, Dn, as
Ductility : m ¼
Dmax
Dy
4.2. Over-strength factor, O\
The over-strength factor is intended to address possible
sources that may contribute to strength beyond its nominal value.
Basically, over-strength results from the following structural
characteristics:
Structural redundancy, which is a representative of the struc
ture’s capacity to redistribute internal forces.
Higher material strength than those prescribed by the designs.
Use of strength reduction factors and load factors in design.
Strain hardening.
Deflection constraints due to serviceability limit state.
Use of oversized members.
Use of multiple loading combinations.
Non-structural elements effects.
Strain rate effect.
FEMA 450 [30] has categorized the over-strength factor into
three main components including: the design over-strength, O\,
the material over-strength, OM, and the system over-strength, OS;
and suggested a typical range for each.
ð4Þ
5. Objective and scope of research
8
m
>
< Rd ¼ p
ffiffiffiffiffiffiffiffiffiffiffiffiffi
¼
2m1
R
Newmark and Hall :
d
>
:R ¼1
d
T 4 0:5 s
0:1 o T o 0:5s
ð5Þ2ð7Þ
T o 0:03 s
The Newmark and Hall method has been widely adopted by
other researchers, and the offered equations have been verified by
different real seismic records. In studies by Nassar and Krawinkler
[38] and Miranda and Bertero [39], it has been shown that Rd
is dependent on the ground motion frequency as well as the
ground’s soil type.
One potential lateral resistant system for CFS structures is the
knee-braced system, which uses elements similar to studs or
noggins at an angle that runs in between the studs to form a
knee-brace. The behavior of these systems is not completely
understood as yet, because most previous studies have been
conducted on the strap-bracing system and shear walls with panel
sheathing, as can be seen in the literature and codes. The aim of the
current research is to evaluate the lateral seismic performance of
different configurations of knee-braced systems including an estimation of the seismic response modification factor for different CFS
Fig. 2. Testing rig diagram and notation convention.
M. Zeynalian, H.R. Ronagh / Thin-Walled Structures 51 (2012) 64–75
knee-braced configurations followed by a comparison with the
recommended code values for the R factor.
It is necessary to mention that the walls studied here are
unlined, and the positive effect of gypsum board on the lateral
performance of the frame under cyclic loading is ignored. This is
due to the fact that post-earthquake observations of timber frame
structures in the Northridge earthquake have shown that many
gypsum board shear walls failed under imposed dynamic load [5].
Also, some design codes [40] have recommended neglecting the
gypsum board’s contribution and relying only on the bare steel
frames.
6. Test setup
6.1. Testing rig and instrumentation
The general configuration of the testing rig is shown in Fig. 2.
Each specimen was installed on the rig between the fixed support
beam at the bottom and a rigid loading beam at the top, using
four M16 high-strength bolts in the vicinity of the chords and the
69
middle of the tracks either side. The bolts were tightened by a
torque wrench to a torque of about 190 N m, corresponding to
about 53 kN tension in the bolt. A strong combination of washers
and nuts was used to ensure that there was no possibility of slip
between the tracks and the beams. Also, as shown in the figure,
four hold-down angles were used at the four corners of the wall in
order to reduce the possibility of overturning and to provide a
proper load path from the braces to the wall chords and studs. An
accurate Horizontal Drift (HD) transducer was used to evaluate
the horizontal displacement of the top track. To evaluate the
amount of uplift, four transducers were placed at the four corners
of the walls between the frame and tracks. Also, one load-cell
was used to measure the racking resistance. All data from the
transducers and load-cell were analyzed and transferred to the
computer using Lab View Signal Express software [41]. The load–
displacement curve of each frame was then plotted.
6.2. Loading protocol
The cyclic loading regime that has been used in this study is
based on Method B of ASTM Standard [42], which was originally
Specimen N1
Specimen N2
Specimen N3
Specimen N4
Fig. 3. General configuration of specimens N1–N4.
70
M. Zeynalian, H.R. Ronagh / Thin-Walled Structures 51 (2012) 64–75
developed for ISO (International Organization for Standardization) standard 16,670. This loading regime consists of one full
cycle at 0.5, 1, 2, 3 and 4 mm, and three full cycles at 8, 16, 24, 32,
40, 48, 56, 64 and 72 mm, unless failure or a significant decrease
in the load resistance occurs earlier. The mentioned lateral
amplitudes are corresponding to 1.25%, 2.5%, 5%, 7.5%, 10%, 20%,
40%, 60%, 80%, 100%, 120%, 140%, 160% and 180% of the ultimate
lateral displacement of the walls.
It is worth noting that Method B of ASTM E2126-07 stipulates
that the amplitude of cyclic displacements has to be selected based
on fractions of monotonic ultimate displacement. If this was applied
here, the loading regime would vary for different specimen types
since each specimen had its own ultimate displacement. However,
as set out earlier, one of the current research objectives has been a
comparison between different types of knee-braced configurations
of the shear walls, which would necessitate the use of identical
cyclic amplitudes for different walls. Hence, Method B is used in this
study with lateral amplitude independent of monotonic testing.
Moreover, although 75 mm, or 3.125%, inter-storey drift ratio was
the maximum amplitude of the actuator, it was considered adequate, since the maximum allowable storey drift ratio specified by
the Standard FEMA 450 is 2.5% [22]. The average loading velocity
was about 2 mm/s, which is compatible with the ASTM E2126-07
recommendation that the loading velocity must be in the range of
1–63 mm/s.
Table 1
Mechanical properties of the C-section stud.
Nominal grade
Nominal thickness
Elastic modulus
Yield stress, Fy
550 MPa
0.55 mm
169 GPa
592 MPa
Yield strain
Ultimate stress, Fu
Ultimate strain
Fu/Fy
0.45%
617 MPa
2.86%
1.04
7. Experimental program
The program consisted of testing four 2.4 2.4 m2 full-scale
frames to investigate the hysteretic lateral performance of different configurations of knee-braced walls shown in Fig. 3.
Specimens N1 and N3 included concurrent knee-braced system and brackets in the four interior corners of the wall. This was
to investigate the effects of brackets on the frames performance.
In order to reduce the number of geometric variants, the length of
knee elements and brackets
pffiffiffi were considered equal. The kneeelements length was 300 2 mm, which is equal to 13 times the
half wave-length (HWL)pof
ffiffiffi local buckling of the stud section in
specimen N1, and 200 2 mm (eight times the local buckling
HWL) in specimen N3. The diagonal elements were connected
to the middle of elements exactly as shown in Fig. 3.
These walls were tested in the Structural Laboratory of the
School of Civil Engineering at the University of Queensland using
a specially made testing rig illustrated previously. All of the frame
elements, such as top and bottom tracks, noggins, studs and
KNEE-elements were made by an identical C-section of dimensions 90 36 0.55 with a lip of 6.6 mm. The section structural
material properties are shown in Table 1, and the detailed section
geometry is shown in Fig. 4.
All components were connected together at each flange using
just one rivet with the shear strength capacity and tensile
strength capacity of 3.3 kN and 3.8 kN, respectively.
The effects of different components, such as different configurations or numbers of knee-elements, use of double studs, etc.,
were monitored and investigated in this research by changing
them from one specimen to another.
8. Experimental results
Based on the observations made during the tests, the common
failure mode for all of the specimens was plastic local buckling in
the knee-elements to studs connections (as shown in Fig. 5),
which was followed by rivet pull-out for specimens N2 and N4.
The rivet pull-out failure did not happen in specimens N1 and N3
due to the presence of brackets, which brings about more
structural flexibility and higher energy dissipation through studs’
deformations, rather than rivet pull-out phenomenon.
As depicted in Fig. 3, the first specimen, N1, consisted of a wall
panel with four brackets in the interior corners. To prevent
buckling in the side chords, double studs sections were used.
Fig. 4. Detailed dimension of stud C 90 36 0.55 in mm.
Fig. 5. Plastic local buckling in the knee-elements to studs connection.
M. Zeynalian, H.R. Ronagh / Thin-Walled Structures 51 (2012) 64–75
2500
Shear Resistance (KN)
Interestingly, the panel performance was perfect and no failure
mode was observed up to the end of the test that was corresponding to maximum drift cycle of 74 mm, though some plastic
local buckling occurred in the knee-elements’ connections at the
central part of the frame, which was followed by plastic bending
in the middle of the brackets. The hysteretic envelope curves and
load–deflection Hysteretic Cycles for all Specimens are presented
in Figs. 6–10. The envelope curves are derived from the load–
deflection hysteretic cycles, which are obtained from racking tests
using accurate transducers and Lab View software [41].
For specimen N2 (presented in Fig. 3), after the application of
the lateral loads, early plastic local buckling occurred in the kneeelements connections; however the frame lost its capacity only
after the rivet pull-out at the end of diagonal braces. This was
1500
500
-100
-50
-40
2500
500
1500
20
-1500
-2500
Lateral Displacement (mm)
40
60
N1
N3
80
N2
N4
Shear Resistance (KN)
2500
500
-500 0
-100
-50
-500 0
50
100
-1500
Fig. 10. Load–deflection hysteretic cycles for specimen N4.
1500
-50
500
-2500
Lateral Displacement (mm)
Fig. 6. Hysteretic envelope curve for all specimens.
-100
100
Fig. 9. Load–deflection hysteretic cycles for specimen N3.
1500
-20 -500 0
50
-2500
Lateral Displacement (mm)
Shear Resistance (KN)
Shear Resistance (KN)
-60
-500 0
-1500
2500
-80
71
50
100
-1500
-2500
Lateral Displacement (mm)
considered as the main failure mode of the frame and was
corresponding to the third cycle of 56 mm drift in the upward
cyclic loading. Next specimen was N3 (shown in Fig. 3). It was
similar to specimen N1 with a smaller length for knee-elements
and brackets.
Again for specimen N3, no specific failure mode was observed
up to the end of the test. The only phenomenon was plastic local
buckling in the knee-elements’ connections followed by plastic
bending in the brackets. The major failure mode for the last shear
wall, N4, was a plastic global buckling in the longer Knee
elements, which followed by the rivet pull-out corresponding to
the second cycle of 48 mm drift.
Fig. 7. Load–deflection hysteretic cycles for specimen N1.
9. Evaluation of R factor
Shear Resistance (KN)
2500
1500
500
-100
-50
-500 0
50
-1500
-2500
Lateral Displacement (mm)
Fig. 8. Deflection hysteretic cycles for specimen N2.
100
The specimens’ hysteretic envelope curves are used to determine the response modification factors by following these steps:
Firstly, the idealized bilinear curve is evaluated using the method
presented in FEMA 356 [32]. The idealized curves of Specimens
N1–N4 in the positive side of the envelope curves are depicted in
Figs. 11–14. Secondly, the ductility reduction factor, Rd, is evaluated via the first part of Eq. (2). The equation requires both Vs
and Vn, which can be estimated based on Fig. 1. Vs is calculated
based on the concept of equal energy and Vn is evaluated using
the idealized bilinear curve, which is explained in detail in part
4 of this paper. A comparison between the ductility reduction
factors obtained this way and those calculated based on Newmark
and Hall’s formulations is presented in Table 2 where a good
agreement is evident between the two methods. For the calculation of Rd based on Newmark’s method, the ductility factor, m, is
72
M. Zeynalian, H.R. Ronagh / Thin-Walled Structures 51 (2012) 64–75
Shear Resistance (N)
2500
Table 2
Ductility reduction factors, Rd.
2000
1500
1000
0
20
40
60
Lateral Displacement (mm)
80
2500
Shear Resistance (N)
N2
N3
N4
la
rb
Graph (Ve/Vy)
Newmark’s method Eq. (6)
Differences (%)
1.88
1.88
0
1.83
1.90
3.7
1.98
1.97
0.5
1.66
1.67
0.6
1.84
1.86
1.1
0.132
0.130
–
b
Fig. 11. Idealized bilinear curve for specimen N1.
2000
1500
1000
500
0
0
20
40
60
80
Lateral Displacement (mm)
Fig. 12. Idealized bilinear curve for specimen N2.
2500
Shear Resistance (N)
N1
a
500
0
2000
1500
1000
500
0
0
20
40
60
Lateral Displacement (mm)
80
2500
2000
1500
1000
500
0
0
20
40
60
Lateral Displacement (mm)
Fig. 14. Idealized bilinear curve for specimen N4.
m: average.
s: standard deviation.
calculated using Eq. (4), which requires the idealized bilinear
curve to be drawn first in order to determine Dmax and Dy. Here
Eq. (6) can be used, as the fundamental period of CFS structures is
usually assessed to lie in between 0.1 and 0.5 s [3]. The third step
is to establish the over-strength factor, O\, using the second part
of Eq. (2), employing Vy and Vs.
The authors here have made use of reverse calculations in
order to find out the design capacity of the tested frames looking
at the mechanism with the smallest failure load, which happens
in this case to be the rivet pull-out as observed in the tests.
According to the design formulas of AS4600, the design pull-out
capacity of the rivets used in this experiment is 705 N. This value
is basically the ultimate pull-out resistance of one rivet reduced
by a capacity reduction factor of 0.5 as advised in AS4600. Kneebraces are connected to studs using two rivets on the side flanges
and therefore the capacity of every knee-bracing element under
pull-out failure mechanism is taken to be 1410 N. In order to
relate this capacity to the lateral load applied to the frame, a
model is generated in SAP2000 [43] using normal frame elements
capable of flexure and axial tension or compression. To illustrate
this, the model of specimen N2 is shown in Fig. 15 and its lateral
defection in Fig. 16. Using the model, the lateral load at which the
first element reaches its pull-out capacity is derived and recorded
as VS. Having this information, the values of O\ and R factors are
then calculated. These are listed in Table 3 for all specimens.
The R factors presented in Table 3 indicate that the response
modification factors for knee-braced systems would range
between 2.80 and 3.61; with the average being 3.18. These values
show that the prescribed value of 3 for the R factor of CFS frames
as advised in some design codes (such as AISI and FEMA) is
reasonable while the suggested R factor of 2 in the Australian
standard (AS4600), is too conservative (Figs. 17–19).
10. Conclusion and recommendation
Scrutinizing the obtained outcomes and comparing the results
to other experiments performed both by the authors and by other
researchers, it is concluded that although knee-braced cold
formed frames have relatively high maximum drifts, Dmax, their
strengths are not as high as strap bracing systems. Hence, the use
of a knee-stud bracing system is possible only in low seismic
regions where the earthquake loads, and thus the required lateral
resistance capacity, are not high.
According to current research results and by comparing the
associated envelope curves in Figs. 6–10, the following conclusions can be made:
Fig. 13. Idealized bilinear curve for specimen N3.
Shear Resistance (N)
Specimen’s name
80
1. Having a larger enclosed area in the hysteretic curves of kneebraced frames represents a more favorable lateral response
for these frames as frames with larger enclosed curves
dissipate more energy.
2. Using brackets at four interior corners of a knee-braced
wall panel improves the lateral performance of the panel
considerably, including both the shear strength and the panel
M. Zeynalian, H.R. Ronagh / Thin-Walled Structures 51 (2012) 64–75
73
Fig. 15. SAP2000 model of K4, 3D view.
Fig. 16. Lateral deflection of K4.
Table 3
The evaluated response modification factors based on FEMA provisions.
No.
Specimens
Dy (mm)
Dmax (mm)
O0
Rd
R
1
2
3
4
N1
N2
N3
N4
33.0
24.4
30.2
24.4
74.8
56.5
74.0
46.4
1.62
1.78
1.83
1.68
1.88
1.83
1.98
1.66
3.05
3.26
3.61
2.80
1.73
0.095
1.84
0.132
3.18
0.346
Average
Standard deviation
ductility. Besides supporting the chords and the tracks
against buckling by reducing the buckling length of the
members, one great advantage of using brackets is to use
the plastic bending capacity of the brackets as an additional
energy dissipating mechanism in the frame. It is necessary to
mention that using double stud sections for the chord
members is essential to improve the lateral performance of
the walls when brackets are incorporated as it increases the
chord buckling capacity.
3. It is noted that the frame performance depend on the
accuracy of the manufacturing of LSF elements. Existing gap
74
M. Zeynalian, H.R. Ronagh / Thin-Walled Structures 51 (2012) 64–75
2.2
2.1
2.0
5.
1.9
1.8
N1
N2
N3
N4
6.
Fig. 17. Maximum strength of the specimens (KN).
4.0
3.0
7.
2.0
8.
1.0
9.
0.0
N1
N2
N3
N4
Fig. 18. Maximum lateral drift ratio (%).
6.0
R factors
Average R
5.0
4.0
3.0
specific failure modes were observed during the tests and the
ultimate drifts were approximately similar, the maximum
shear load for specimen N3, which had shorter knee-elements
was higher than that of N1. As is evident in Fig. 6, the area,
which is enclosed by the Equivalent Energy Elastic Plastic
(EEEP) curve and the capacity of energy dissipation for
specimen N3 is higher than other specimens.
Comparing the envelop curves of specimens N2 and N4, it is
seen that a shorter knee-element leads to a greater shear
strength for the wall but at the expense of a lower ductility.
That is because larger knee-elements provide more post-local
buckling reserve, which allows the walls to deform further
under the lateral loads.
Investigating the test results and the final failure modes for
different specimens, a suggestion would arise with regard to
preventing the brittle failure of the walls (with no bracket)
associated with rivet pull-out, and this is to use appropriate
washers under the rivets or use a rivet with a wider head.
This suggestion has been implemented in the current study
and confirmed by the favorable results [44].
Considering the evaluated R factors, while the prescribed
value of R ¼3 for a knee-braced system in AISI is reasonable,
the R¼2 suggested by AS4600 seems to be too conservative.
A combination of different structural characteristics and
dissipating energy mechanisms affect the R factor. While
the strength and maximum drift of one specimen can be
higher than the other, the R factor could be lower.
Considering the aforementioned results and comparing those
with the results of strap bracing performed by Moghimi and
Ronagh [11], it is concluded that the performance of kneebracing systems under cyclic loads is not satisfactory. That is
because, even after preventing some undesirable failure modes
like rivet pull-out and shear failure mode in the rivets, there still
remains the buckling failure mode in the knee-elements, which is
an undesirable failure. Based on the graphs shown in Figs. 7–10,
which show that there is neither adequate ductility nor a
measurable energy dissipating mechanism for the knee-braced
system, it is concluded that knee-bracing is not a preferable
lateral resistant system, especially in medium to high seismic
regions.
2.0
1.0
References
0.0
N1
N2
N3
N4
Fig. 19. R factor.
(the lack of continuity of the web element) in the kneeelements to stud elements connections causes the early plastic
local buckling in the connections that finally leads to undesirable failure modes such as tearing in the connections; and as
such the real capacity of frame cannot be utilized. Also, as the
bending capacity of studs is low, it is essential to connect
different knee-elements at the same point or as close to each
other as possible to prevent any lever arm and bending moment
development in the studs.
4. The performance of the Knee Brace lateral resistant system
would be improved
pffiffiffi by decreasing the length of knee-elements from 300 2 mm (13 times the half
pffiffiffi wave-length of
local buckling of the stud section) to 200 2 mm (eight times
the local buckling half wave-length). In another word,
although the lateral performances of both specimens N1
and N3, which include the brackets were acceptable and no
[1] Fulop LA, Dubina D. Performance of wall-stud cold-formed shear panels
under monotonic and cyclic loading—Part I: experimental research. ThinWalled Structures 2004;42(2):321–38.
[2] Tian YS, Wang J, Lu TJ. Racking strength and stiffness of cold-formed steel
wall frames. Journal of Constructional Steel Research 2004;60(7):1069–93.
[3] Gad EF, Duffield CF, Hutchinson GL, Mansell DS, Stark G. Lateral performance
of cold-formed steel-framed domestic structures. Engineering Structures
1999;21(1):83–95.
[4] AISI. Standard for cold-formed steel framing—lateral design. Washington,
DC: American Iron and Steel Institute; 2004.
[5] Serrette R, Ogunfunmi K. Shear resistance of gypsum-sheathed light-gauge steel
stud walls. Journal of Structural Engineering New York 1996;122(4):383–9.
[6] Kim TW, Wilcoski J, Foutch DA, Lee MS. Shaketable tests of a cold-formed
steel shear panel. Engineering Structures 2006;28(10):1462–70.
[7] TI809-07. Design of cold-formed loadbearing steel systems and masonry
veneer/steel stud walls. US Army Corps of Engineers, Engineering and
Construction Division, Washington, DC, 1998.
[8] Al-Kharat M, Rogers CA. Inelastic performance of cold-formed steel strap
braced walls. Journal of Constructional Steel Research 2007;63(4):460–74.
[9] ASCE7-05. ASCE 7-05 minimum design loads for buildings and other
structures. USA: ASCE; 2005.
[10] Moghimi H, Ronagh HR. Better connection details for strap-braced CFS stud
walls in seismic regions. Thin-Walled Structures 2009;47(2):122–35.
[11] Moghimi H, Ronagh HR. Performance of light-gauge cold-formed steel strapbraced stud walls subjected to cyclic loading. Engineering Structures
2009;31(1):69–83.
M. Zeynalian, H.R. Ronagh / Thin-Walled Structures 51 (2012) 64–75
[12] Larson JW. AISI standards for cold-formed steel framing. In: Proceedings of
the 18th international specialty conference for cold-formed steel structures.
October 2006.
[13] AISI. Standard for cold-formed steel framing—prescriptive method for one
and two family dwellings. Washington, DC: American Iron and Steel
Institute; 2001.
[14] AISI. North American specification for the sesign of cold-formed steel structural
members. Washington, DC: American Iron and Steel Institute; 2001.
[15] AISI. Standard for cold-formed steel framing—general provisions. Washington,
DC: American Iron and Steel Institute; 2004.
[16] AISI. Standard for cold-formed steel framing—header design. Washington,
DC: American Iron and Steel Institute; 2004.
[17] AISI. Standard for cold-formed steel framing—wall stud design. Washington,
DC: American Iron and Steel Institute; 2004.
[18] AISI. Standard for cold-formed steel framing—truss design. Washington, DC:
American Iron and Steel Institute; 2004.
[19] AISI. Design of cold-formed steel shear walls. Steel Framing Alliance; 1998.
[20] AISI. Performance of cold-formed steel-framed shear walls: alternative
configurations. Research report RP 02-7, Revision 2006. Washington, DC:
Steel Framing Alliance; 2002.
[21] AISI. Code of standard practice for cold-formed steel structural framing.
Practice guide CF06-1. Washington, DC: American Iron and Steel Institute;
2006.
[22] FEMA-450. NEHRP recommended provisions for seismic regulations for new
buildings and other structures—Part 1: provisions. USA: Building Seismic
Safety Council; 2003.
[23] FEMA-P750. NEHRP recommended seismic provisions for new buildings and
other structures. USA, Washington, DC: Building Seismic Safety Council;
2009.
[24] FEMA-302. NEHRP recommended provisions for seismic regulations for new
buildings and other structures. In: FEMA 302. Building Seismic Safety
Council, 1998.
[25] UBC, Uniform Building Code. In: International conference of building officials.
California, USA, 1997.
[26] IBC. International Building Code. International Code Council; 2006.
[27] AS/NZS4600. Cold-formed steel structures, AS/NZS 4600. Australian Building
Codes Board; 2005.
[28] ATC-3-06, A.T.C. Tentative provisions for the development of seismic regulations for buildings. 1984 second printing. National Science Foundation,
[29]
[30]
[31]
[32]
[33]
[34]
[35]
[36]
[37]
[38]
[39]
[40]
[41]
[42]
[43]
[44]
75
National Bureau of Standards: 555 Twin Dolphin Drive, Suite 550, Redwood
City, California 94065, USA, 1978.
ATC-19, A.T.C. ATC-19 structural response modification factors. National
Center for Earthquake Engineering Research, 555 Twin Dolphin Drive, Suite
550, Redwood City, California 94065, USA, 1995.
FEMA-450. NEHRP recommended provisions for seismic regulations for new
buildings and other structures—Part 2: commentary. USA: Building Seismic
Safety Council; 2003.
Uang C-M. Establishing R (or Rw) and Cd factors for building seismic
provisions. Journal of Structural Engineering 1991;117(1):19–28.
FEMA-356. Pre standard and commentary for the seismic rehabilitation of
buildings. USA, Virginia: American Society of Civil Engineers; 2000.
Park R. Evaluation of ductility of structures and structural assemblages from
laboratory testing. Bulletin of the New Zealand National Society for Earthquake Engineering 1989;22(3):155–66.
Gad EF, Chandler AM, Duffield CF, Hutchinson GL. Earthquake ductility and
overstrength in residential structures. Structural Engineering and Mechanics
1999;8(4):361–82.
Maheri MR, Akbari R. Seismic behaviour factor, R, for steel X-braced and
knee-braced RC buildings. Engineering Structures 2003;25(12):1505–13.
Kim J, Choi H. Response modification factors of chevron-braced frames.
Engineering Structures 2005;27(2):285–300.
Newmark N, Hall W. Earthquake spectra and design. Berkeley, CA: Earthquake Engineering Research Inst.; 1982.
Nassar AA, Krawinkler H. Seismic demands for SDOF and MDOF systems.
United States, 1991. p. 224.
Miranda E, Bertero VV. Evaluation of strength reduction factors for earthquake-resistant design. Earthquake Spectra 1994;10(2):357–79.
US Army Corps of Engineers. TI 809-07, Technical instructions, Design of
cold-formed loadbearing steel systems and Masonry Veneer/Steel Stud Walls.
Washington, DC 20314-1000, 1998.
LabVIEW. LabVIEW SignalExpress. Austin, Texas: National Instruments Corporation; 2007.
ASTM E2126-07. Standard test methods for cyclic (reversed) load test for
shear resistance of walls for buildings. USA, 2007. p. 13.
CSI. SAP2000 advanced 14.1.0. Computers and Structures, Inc.; 2009.
Zeynalian M, Ronagh HR. Performance of K-braced cold-formed steel shear
walls subjected to lateral cyclic loading. In: The fourth international conference on structural engineering, mechanics and computation. Cape Town,
South Africa, 2010.