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Experimental Investigation and Finite-Element Modeling of
an Aluminum Energy Dissipater for Cross-Laminated
Timber Walls under Reverse Cyclic Loading
Kobir Hossain, A.M.ASCE 1; Sriram Aaleti, M.ASCE 2; and Thang N. Dao, M.ASCE 3
Abstract: Cross-laminated timber (CLT) panels with unbonded post-tensioning and a rocking mechanism can be used as a robust lateral
load–resisting system (LLRS). The seismic performance of these systems can be improved further by incorporating external sacrificial energy
dissipating elements. The additional damping provided by the energy dissipaters reduces the structural displacement demand during a designlevel earthquake, and the unbonded post-tensioning provides recentering ability. This study developed a surface mountable, easily replaceable
sacrificial oval metallic element specific to the CLT walls using aluminum was. This connector contributes to the wall system lateral load
capacity. Laboratory testing of the aluminum connectors under cyclic shear loading was performed to characterize the force–displacement
behavior and energy dissipating capacity. A detailed three-dimensional (3D) finite-element analysis (FEA) of aluminum connectors was carried
out to replicate the observed experimental behavior. The experimental results, analytical modeling, and design equations for connector force–
displacement response based on first principles are presented in this paper. The test results showed that the O-connectors can be used as an
effective energy-dissipating element with equivalent damping ratio varying between 20% and 40%. The simplified design equations calculated
the response within 90% of the measured values. DOI: 10.1061/(ASCE)ST.1943-541X.0002978. © 2021 American Society of Civil Engineers.
Introduction
Cross-laminated timber (CLT) is an emerging building material in
the North America, which is produced by laminating cross-oriented
standard-dimension wood planks using glue. Wood structures generally have performed well when subjected to strong earthquakes
(van de Lindt et al. 2018). In recent times, there is growing interest
among the building construction community, especially in the
Pacific Northwest of North America, to use this material for buildings up to 20 stories high (Pei et al. 2014). CLT has been used
successfully as prefabricated walls, floor, and roofing elements
in residential, nonresidential, and commercial structures across
the globe (Iqbal et al. 2015). By taking advantages of CLT compressive strength, dimensional stability, and prefabrication, using
existing designs in the precast concrete (Aaleti and Sritharan 2009;
Sritharan et al. 2015; Rahman and Restrepo 2000; Restrepo and
Rahman 2007) and steel industry for low-damage seismic-resilient
systems, the wood engineering community is investigating the use
of unbonded post-tensioning (PT) to develop a low-damage lateral
load–resisting system with CLT. Pei et al. (2016) found that seismic
resiliency can be achieved by using unbonded post-tensioned CLT
rocking walls, which remain damage-free in moderate earthquakes
and can be repaired easily after large-magnitude earthquakes.
1
Assistant Professor, Dept. of Civil Engineering, Dhaka Univ. of Engineering and Technology, Shimultoly Rd., Gazipur 1707, Bangladesh.
Email: mkhossain@crimson.ua.edu
2
Associate Professor, Dept. of Civil, Construction and Environmental
Engineering, Univ. of Alabama, Tuscaloosa, AL 35487 (corresponding
author). Email: saaleti@eng.ua.edu
3
Associate Professor, Dept. of Civil, Construction and Environmental
Engineering, Univ. of Alabama, Tuscaloosa, AL 35487. Email: tndao@
eng.ua.edu
Note. This manuscript was submitted on December 13, 2019; approved
on December 2, 2020; published online on January 26, 2021. Discussion
period open until June 26, 2021; separate discussions must be submitted
for individual papers. This paper is part of the Journal of Structural Engineering, © ASCE, ISSN 0733-9445.
© ASCE
Several researchers attempted to develop efficient, replaceable
energy-dissipating elements in various forms using steel for
post-tensioned coupled wall system (Fig. 1). Shultz and Magana
(1996) developed a U-shape flexural plate (UFP) connector as
part of the PREcast Seismic Structural Systems (PRESSS) program, to connect two or more unbonded post-tensioned precast
concrete walls along their vertical joints to form a seismicresilient system called a jointed wall system (Priestley 1991). A
similar concept can be adopted easily for CLT wall panels as well,
in which two or more post-tensioned CLT walls are connected
together with energy-dissipating connectors along the vertical
joints. Ganey et al. (2017) used UFP connectors to test jointed
CLT wall system as part of the Natural Hazards Engineering Research Infrastructure (NHERI) Tall Wood research project. As these
PT walls rock under lateral loading, the connectors undergo a relative vertical deformation (Fig. 1), leading these connectors to
experience yielding and provide energy dissipation. This UFP connector was made by bending a steel plate into a U-shape, which
introduced residual stresses into the steel connector during the fabrication process. The residual stresses were difficult to estimate, and
impacted the displacement capacity of connector and predictability
of the failure displacement. Henry et al. (2010) studied different
forms of externally mountable energy dissipaters such as slotted
flexural plates, flexural plates with holes, J-shaped flexural plates,
and oval flexural plates using finite-element modeling (FEM). Their
study, and an experimental investigation by Aaleti (2009), found
that an oval flexural plate, or O-connector, made by cutting the
profile from a mild steel plate can serve as an efficient energydissipating element in a UFP connector. A modified version of the
O-connector further was investigated experimentally by Twigden
and Henry (2015) with different connector proportions (e.g., leg
length to thickness ratio), steel grades, and steel plate cutting and
welding techniques. They found that the strength and stiffness of the
O-connector is affected by the leg length to thickness ratio, cutting
and welding process, and the width at the connector base. Twigden
and Henry also proposed simple design equations for yield, plastic,
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Fig. 1. Jointed rocking CLT wall system: (a) joint wall system; and (b) forces under lateral loads.
and ultimate strength of the O-connector. However, no analytical
equations were developed to estimate the maximum displacement
capacity of the O-connector, which will be critical for the design
of these resilient rocking systems.
The present study primarily focused on the design and development of an efficient, cost-effective, easy-to-use, replaceable aluminum O-connector for CLT self-centering rocking wall systems.
Elementary analytical equations were formed for different characteristic parameters of the O-connector using the principles of engineering mechanics. Based on the analytical formula and knowledge
gathered in previous studies, an O-connector (Fig. 2) was fabricated
and tested by connecting the CLT walls using different lag-screw
connection configurations under reverse cyclic loading following
a modified ACI ITG 5.1 (ACI 2007) loading protocol. Finite-element
Fig. 2. Schematic of an O-connector, deflected shape, and forces.
© ASCE
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modeling in Abaqus CAE version 6.16 was performed to capture the
observed experimental behavior. The results from the study are presented in subsequent sections.
vertical yield displacement corresponding to the first yield can be
calculated using
ΔVy ¼
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Behavior of O-Connector: Elementary Analytical
Equations
The O-connector was made by cutting an oval profile with two rectangular wings out of a mild steel or aluminum plate. A schematic
of the O-connector is shown in Fig. 2. The connector legs undergo
flexural yielding as shown by the deformed shapes in Fig. 2, when
they are subjected to a relative vertical deformation. Unlike the
UFP connector, which is restrained to roll between two vertical surfaces, the O-connector is attached to the exterior faces of the wall
panels, making it easier to install and repair. The O-connector also
contributes to the system’s moment capacity by transferring shear
force between adjacent CLT panels. The O-connector made from
mild steel previously was used successfully in unbonded PT precast
concrete wall systems (Sritharan et al. 2015; Twigden and Henry
2015).
A relative vertical displacement across the connector legs results
in a bending moment throughout the length of the connector with a
maximum value along the entire length of each straight leg, and
decreases to a zero moment at the vertex of the half-circular part.
For an O-connector, this moment distribution is symmetric about
the vertical centroidal axis. The first yielding occurs along the
straight leg, closer to the base connection region. By applying the
first principles, the moment and shear force corresponding to first
yield can be obtained using Eqs. (1) and (2), respectively
My ¼
σy tw2
6
2σy tw2
Fy ¼
3D
ð1Þ
σy tw2
4
ð3Þ
σy tw2
Fp ¼
D
ð4Þ
Mp ¼
The coupling shear force can be related to the relative vertical
displacement between the connector legs using the Castigliano’s
second theorem. Using this method, it can be found that no horizontal force develops at the panel–connector connection region
when the connector legs are subjected to relative vertical displacement. The majority of the deformation of the O-connector comes
from the flexural deformation of the connector legs. Therefore,
when estimating the displacement corresponding to yield capacity
and failure, the effects of axial and shear forces were neglected. The
© ASCE
ð5Þ
where ΔVy = vertical displacement at first yield; and E = modulus
of elasticity of material. The Supplemental Materials derive the
formulas presented in this section. The initial stiffness (ki ) of the
O-connector can be calculated by combining the Eqs. (2) and (5) as
ki ¼
Fy
4 Etw3
¼
ΔVy 3 πD3
ð6Þ
The horizontal displacement ΔHy of the O-connector at the intersection of the straight leg and the semicircular part can be calculated using Eq. (7), which is same as the displacement at the free
edge of a cantilever subjected to a constant moment throughout the
entire length
ΔHy ¼
M y L2 Fy DL2 3Fy DL2 σy L2
¼
¼
¼
2EI
4EI
Ew
Etw3
ð7Þ
For materials which exhibit strain hardening behavior under
cyclic loading, at the expected maximum strength of the connector,
the stresses will be much higher than yield. In such cases, an estimate of the maximum strength (Fu ) of the connector can be obtained by multiplying the plastic load capacity (Fp ) by the material
overstrength factor, which is defined as the ratio of ultimate stress
(σu ) to the yield stress (σy ) [Eq. (8)]. The maximum displacement
(Δmax Þ corresponding to the failure of the connector can be estimated using the Eq. (9), where εx is the failure strain of the material
(see Supplemental Materials for derivation)
Fu ¼
ð2Þ
where σy = yield strength; w and t = width and thickness of
O-connector legs, respectively; and D = mean diameter of semicircular part of the O-connector. As the relative vertical displacement
between the two legs continues to increase, the strains along the
width of the connector legs further increase beyond yielding, leading to majority of the connector leg cross section experiencing
yielding. The moment capacity at this point is called the plastic
moment, which can be calculated using a uniform compressive
and tensile stress distribution equal to the yield stress of the material
over one-half the width of the O-connector leg. The resulting equations for the plastic moment (Mp ) and corresponding shear force
(Fp ) are
πFy D3 3 πFy D3 π σy D2
¼
¼
16EI
4 Etw3
4 Ew
σu
F ¼
σy p
Δmax ¼
σu σy tw2
σy
D
π
D2
εmax
4
w
ð8Þ
ð9Þ
Experimental Program
Three experimental tests consisting of 12 O-connectors were performed as part of the experimental program. In addition to characterizing the force–displacement response of the connectors, the
effect of number of screws in the O-connector to CLT connection
was investigated.
O-Connector Specifications
The O-connectors tested in the experimental investigation were
fabricated from a 6.35-mm-thick (0.25 in.) 3003-H14 aluminum
plate. The measured nominal yield and tensile strengths for this
aluminum grade were 131 MPa (19 Ksi) and 145 MPa (21 Ksi),
respectively. The O-connectors were extracted from the aluminum
plate by cutting the profile using a water-jet. A schematic of the
O-connector with detail dimensions and a fabricated O-connector
are shown in Fig. 3. Twigden and Henry (2015) suggested a leg
length to thickness ratio of less than 20 for steel O-connector in
order to avoid the onset of premature buckling of the connector.
Considering the lower strength and stiffness properties of aluminum compared with that of steel, for the design of the aluminum
O-connector, the leg length to thickness ratio was 10, which was half
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Fig. 3. Schematic of the O-connector tested in the experimental program: (a) O-connector dimensions; and (b) fabricated O-connector.
that recommended by Twigden and Henry for steel O-connectors.
This resulted in an O-connector with overall width and height of
228.6 mm (9 in.) and 304.8 mm (12 in.), respectively. The width
of the connector legs was 32 mm (1.25 in.), and the clear distance
between two legs was 63.5 mm (2.5 in.). The O-connector had
two rectangular wings at the centerline to facilitate the connection
to CLT panels. The width and height of these wings were 112.7 mm
(4.44 in.) and 50.8 mm (2 in.), respectively. The rectangular wings
contained 6.35-mm-diameter (0.25 in.) holes spaced at 22.2 mm
(0.875 in.) in horizontal direction and 25.4 mm (1 in.) vertical direction, which were used to connect the connectors to CLT using
standard 6.25-mm-diameter (0.25 in.) lag screws. The diameter
of the hole was kept the same as the diameter of lag screws to prevent
any slipping during testing and to have a rigid connection.
Material Properties
The 0.61 × 0.61-m (2 × 2-ft) CLT panels used in this study were
fabricated using graded Douglas fir timber boards in accordance
with ANSI/APA PRG-320 (ANSI/APA 2012). The CLT panels
consisted of five layers, each of which was 25.4 mm (1 in.) thick,
resulting in a total thickness of 127 mm (5 in.). The moisture content at the time of production of the CLT was reported by the manufacturer to be 12% by weight, and the testing presented here was
conducted without controlling the moisture content. The average
compressive strength and modulus of elasticity in compression of
the CLT were determined experimentally as 27.5 MPa (4,000 psi)
and 6,200 MPa (900 Ksi), respectively. Two tensile dog-bone coupons from the same aluminum plate used for the O-connector were
© ASCE
extracted and tested following ASTM B557M-15 (ASTM 2015)
specifications. The test setup, a failed aluminum dog-bone specimen, and the stress–strain diagrams are shown in Fig. 4. The
material properties determined from the aluminum tensile coupon
tests are presented in Table 1.
O-Connector Test Setup
A test setup was designed using 0.61 × 0.61-m (2 × 2-ft) CLT wall
panels and steel plates to apply the desired vertical relative displacement to the O-connector legs using a hydraulic jack (Fig. 5).
The test setup consisted of a steel reaction frame, hydraulic jack,
and a total of three five-ply CLT panels, including two 0.61 ×
0.61-m (2 × 2 ft) outer panels and one 0.61 × 0.305-m (2 × 1-ft)
intermediate panel. The vertical reaction frame was post-tensioned
to the strong floor using two 37-mm-diameter (1.5 in.) posttensioning bars tensioned to 266.9 kN (60 kip) each. In addition,
a 2.13-m-long (7 ft), 406-mm-deep (16 in.) steel reaction beam was
simply supported on 100-mm-thick (4 in.) steel plates and posttensioned to the strong floor using a 37-mm-diameter (1.5 in.)
post-tensioning bar tensioned to 266.9 kN (60 kip). The steel reaction beam mimicked the foundation in a real structure and was
used to anchor the outer CLT panels. A 25-mm-diameter (1 in.)
hole was drilled at the center of the outer CLT panels through
the entire height of the panel and a 19-mm-diameter (0.75 in.)
B7 threaded rod in combination with a 550-kN (120-kip) centerhole hydraulic jack was used to anchor the panels to the steel reaction beam with a constant compression force of 133.4 kN
(30 kips). The outer and intermediate CLT panels were connected
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Fig. 4. Aluminum coupon test setup and measured stress–strain response: (a) test setup; (b) tensile fracture; and (c) stress–strain response.
Table 1. Aluminum tensile coupon test results
Specimen ID
1
2
0.2% offset yield strength
[MPa (Ksi)]
0.2% offset yield strain
(mm/mm)
Ultimate strength
[MPa (Ksi)]
Rupture strength
[MPa (Ksi)]
Modulus of elasticity
[GPa (Ksi)]
132.4 (19.2)
131.7 (19.1)
0.0035
0.0040
148.0 (21.5)
147.9 (21.5)
115.6 (16.8)
113.4 (16.4)
75.25 (10913)
69.64 (10100)
Fig. 5. O-connector test setup: (a) test setup for O-connector testing; and (b) close-up of Test specimen 1 and instrument.
© ASCE
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Fig. 6. Loading protocol for O-connector test.
together with O-connectors on both faces. The connectors were attached to the CLT panels with 6.35-mm-diameter (0.25 in.) standard lag screws driven symmetrically about the connector axes. The
CLT–O-connector connection was designed following the NDS
design specifications (AWC 2015). Details of this connection
are provided in the next section. To apply a direct shear force to
the O-connector without subjecting it to any eccentric loading, four
O-connectors were tested together in aforementioned test setup.
Additionally, this arrangement provided a more accurate average
of the connector response, allowing for variations in the manufacturing process and producing a broader validation than testing a
single connector. The double-acting hydraulic jack with a 445kN (100-kip) load cell was attached to the intermediate CLT panel
using high-strength threaded rods. The intermediate panel was
moved up and down using the hydraulic jack to apply a relative
displacement between the two legs of the O-connector, emulating
relative displacements expected for connectors in a typical jointed
rocking CLT wall system. Small 25-mm-wide (1 in.) aluminum
plates around the connector legs were used in Tests 2 and 3, providing restraint to prevent any out-of-plane buckling of the connector legs [Fig. 3(b)]. These plates did not constrain the in-plane
movement of the connector.
The displacement of the connectors was measured using
two different instruments: LVDTs and an NDI (Waterloo, Ontario)
Optotrak three-dimensional (3D) noncontact digital distance measurement system. In addition, in Test 2, two strain gauges were used
on opposite sides of a straight leg of one connector to monitor the
critical strains at the two extreme faces of the connector. In Test 3,
five strain gauges were used, four of which were placed on opposite
faces of two straight legs, and one of which was placed at the vertex
of a connector. The total load carried by the four connectors was
measured using a 445-kN (100-kips) load cell. Data from all the
instruments was collected continuously at 20-Hz frequency using
a standard data acquisition system.
Loading Protocol
CLT to O-Connector Connection
The O-connectors were connected to CLT panels using 6.35 ×
76.2-mm (¼ × 3-in:), hex-head lag screws [Fig. 7(c)]. The lag screw
dimensions are listed in Table 2. The mechanical connections between O-connector and CLT panel using lag screws were designed
following National Design Specification (NDS) 2015 (AWC 2015)
and the CLT Design Handbook (CLT Handbook 2013). NDS treats
lag screws as a dowel bearing–type fastener and uses the European
Yield Limit Model to calculate the design capacity of a single fastener, known as the reference design value in shear. The Yield Limit
Model considers different failure mechanisms, such as crushing in
main member (CLT in this case), crushing in side member (aluminum O-connector base plate), rotation of fastener, plastic hinge and
crushing in main member, plastic hinge and crushing in side
member, and two plastic hinges per shear plane, for calculating
the capacity of a wood–wood or wood–metal connection using a
dowel bearing fastener. The lowest among the values given by these
yield limit equations is considered as the reference design value.
Each of the yield limit equations includes the dowel bearing strength
of either a main member or a side member. The reference design
value for each lag screw was calculated to be 578 N (130 lb). In
Test 1, a total of eight lag screws were used at each base of the
leg [Fig. 7(a)]. In Tests 2 and 3, a total of six lag screws were used
at each base [Fig. 7(b)].
Test Observations and Results
The O-connectors were tested under displacement control loading.
The connectors were subjected to a displacement history, in which
the peak connector displacements (Fig. 6) were selected following
the ACI ITG 5.1 loading protocol for testing and validation of posttensioned rocking wall behaviors. The loading started with three
© ASCE
cycles of 2.54 mm (0.1 in.), after which each loading displacement
was increased by almost 25% and each loading step was repeated
for three complete cycles, except the last loading cycles. The hydraulic jack was operated using a manual hydraulic pump, and the
rate of loading was controlled by observing the vertical displacement measured by LVDTs. The loading procedure was stopped several times during the test to observe condition of the connectors and
to take pictures after a specified displacement had been applied.
Reverse cyclic loading tests were conducted to obtain the force–
displacement (F-Δ) response and energy dissipation capacity of
the connectors and to verify the analytical equations for practical
use. The hysteretic force–displacement responses from all the
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Fig. 7. Screw connections for O-connector tests: (a) eight-screw connection in Test 1; (b) six-screw connection in Tests 2 and 3; and (c) screw used for
O-connector tests. (Images by authors.)
Table 2. Lag screw dimensions
Property
Nominal diameter
Root diameter
Length
Tapered tip length
Height of head
Value [mm (in.)]
6.35
4.40
76.2
4.06
4.36
(0.25)
(0.173)
(3.0)
(0.16)
(0.172)
three tests are shown in Figs. 8–10. The deformed shapes of a connector at 12.5 mm (0.5 in.), 25.4 mm (1 in.), and at the displacement when the O-connector experienced significant out-of-plane
buckling also are shown in these figures. In Test 1, the O-connectors
experienced premature out-of-plane buckling at a displacement
level of 12.7 mm (0.50 in.), and the test was terminated at that
loading cycle. Based on the observations from Test 1, small aluminum plates were added as restraining plates in Tests 2 and 3 to
Fig. 8. F-Δ response and deformed shape of O-connector Test 1: (a) force–displacement response; (b) deformed shape of O-connector at 7.5 mm; and
(c) deformed shape of O-connector at 15 mm.
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Fig. 9. F-Δ response and deformed shape of O-connector Test 2: (a) force–displacement response; (b) deformed shape of O-connector at 12.5 mm;
(c) deformed shape of O-connector at 25.4 mm; and (d) deformed shape of O-connector at 31.75 mm.
Fig. 10. F-Δ response and deformed shape of O-connector Test 3: (a) force–displacement response; (b) deformed shape of O-connector at 12.5 mm;
(c) deformed shape of O-connector at 25.4 mm; and (d) deformed shape of O-connector at 35.5 mm.
prevent the onset of local buckling [Figs. 9(b) and 10(b)]. With
these restraining plates, the O-connectors in Tests 2 and 3 were able
to undergo large displacement cycles up to 32 mm (1.25 in.) while
reaching their ultimate load carrying capacities [Figs. 9(a) and
10(a)]. The F-Δ responses obtained from Tests 2 and 3 had stable
hysteretic loops for each loading cycle until failure initiated by
outward buckling of the unrestrained semicircular part of the Oconnector. However, no fracture occurred at this displacement level
except signs of yielding on the surfaces. Yielding of O-connectors’
straight legs was observed at a vertical displacement of 19 mm
(0.75 in.) (Fig. 11). Yielding occurred only in the straight legs of
the O-connector, whereas the semicircular part remained elastic,
supporting the expected the moment distribution along the Oconnector length used to derive the analytical equations.
© ASCE
Energy Dissipation
The energy dissipation for a cycle of displacement is calculated by
estimating the total area enclosed by the force–displacement response corresponding to that displacement cycle. Fig. 12(a) shows
the energy dissipated by the connectors at different displacement
cycles from all three tests. Because the connectors in Test 1 experienced out-of-plane buckling at small displacements, the calculated energy dissipation capacity of the O-connector from that
test was lower than that obtained from other tests. The approximate
total energy dissipation per connector before failure due to buckling
was calculated to be 1,136 J (835 ft-lb), 3,854 J (2,843 ft-lb) and
4,235 J (3,124 ft-lb) for Tests 1, 2, and 3, respectively. The low
energy-dissipation capacity of the O-connector in Test 1 compared
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Fig. 13. Calculation of equivalent damping ratio.
Fig. 11. Yielding of O-connector at four legs in O-connector Test 3.
to Tests 2 and 3 indicates the necessity of out-of-plane buckling
restraint to enhance its energy dissipation capacity. The equivalent
viscous damping ratio at each peak displacement cycle, defined as
the ratio of energy dissipated by the connector in that displacement
cycle to the available potential energy in that cycle multiplied by 4π
(Fig. 13) (Blandon 2004) was calculated. The calculated equivalent
damping ratios for the connectors in all the three tests are shown in
Fig. 12(b). The damping ratio of the connector increased with displacement, and it varied between 18% and 42% depending on the
vertical displacement level. Gavric et al. (2015) found the equivalent viscous damping ratio for standard hold-downs, such as
WHT540 and WHT440 under shear loading to be 19.84% and
21.38% respectively. Similarly, Gavric et al. (2015) found that
the equivalent viscous damping ratios for steel angle brackets,
such as BMF90 × 116 × 48 × 3 and BMF100 × 100 × 90 × 3,
was 22.75% and 17.49% respectively. The damping ratio of the
O-connector was higher than those of the aforementioned standard
hold-downs and angle brackets. Baird et al. (2014) tested a UFP
connector made of 8-mm-thick (5=8 in:) 320-MPa (45-Ksi) steel
plate with outer dimensions of 136 mm (5.35 in.), similar to the
outer dimensions of the O-connector tested in this study. The measured yield and maximum force capacity of the UFP connector
were 6.4 kN (1.41 k) and 12.5 kN (2.81 k), respectively. The
UFP connector had equivalent viscous damping ratios between
3% and 47% depending on the vertical deflection. The maximum
energy dissipation ratio of the O-connector was 10% lower than
that of the UFP connector. However, at the lower displacements,
for example, at 29 mm (1.15 in.) vertical displacement, the Oconnector had a higher damping ratio (42%) than the UFP connector (32%). The O-connector had similar performance in terms of
energy dissipation capacity compared with that of a UFP connector
with similar force capacities. Therefore, this O-connector can be
used as a significant source of energy dissipation and damping
for building construction with CLT. The seismic performance of
CLT buildings with the O-connectors will be similar to that with
UFP connectors.
Discussion of Results
Stiffness and Strength Calculations
Using Eqs. (2), (7), and (8), the yield load capacity of the Oconnector calculated based on the determined material properties
was 5.87 kN (1,320 lb) with a vertical (ΔVy ) and horizontal (ΔHy )
yield displacement of 0.81 mm (0.032 in.) and 0.46 mm (0.018 in.),
respectively. The ratio of vertical to horizontal yield displacement
Fig. 12. (a) Energy dissipation of O-connectors; and (b) equivalent damping ratio of O-connectors.
© ASCE
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was calculated as 1.77, with the horizontal displacement calculated
at the intersection of the straight leg and the half-circular part. The
maximum load capacity of the O-connector was calculated based
on a fully plastic section as 8.81 kN (1,980 lb); from the measured
F-Δ behavior of Tests 2 and 3, the yielding of the O-connectors
was found to occur at approximately 88% of the calculated yield
force; however, the displacements at yield obtained from the
tests were approximately 3 times higher than the calculated yield
displacement. The yielding of the O-connectors occurred at the first
cycle of displacement loading, which was 2.54 mm (0.1 in.), and
this was confirmed with the measured strain in the straight legs.
This difference in the yield displacement might be due to the base
rotation and/or the connection slack between the lag screws and the
holes. Although the diameter of the hole was same as the diameter
of lag screw, some of the holes were not perfectly circular because
they were tapped using a hand drill and some degree of inaccuracy
was unavoidable in that process. However, once the gaps between
the lag screws and cylindrical surface of the holes were closed, the
connectors engaged themselves to carry force. The base rotation
was associated with this connection slack as well because of the
small vertical movement of lag screws. For Tests 2 and 3, the base
rotations were found to be considerable. The base rotation increased the relative vertical displacement, and therefore should be
incorporated in the analytically derived formula.
In the tests, when the connectors were unloaded from a peak
displacement level, the force decreased from its peak value to zero
with a small change in vertical displacement compared with the
total displacement, and the stiffness and strength decreased during
the repeated loading cycles. This might have been due to the local
buckling of the connector in addition to the repetition of loading
(Bauschinger effect). When the cross section of straight legs became fully plastic, there was no increase in force, but the displacement increased until the legs reached failure strain. Therefore,
analytically the force–displacement response after plastic hinge formation was a horizontal straight line.
The peak force–peak vertical displacement responses at each
loading cycle for Tests 2 and 3 are shown in Fig. 14. Based on
the experimental results, a bilinear force–vertical displacement relationship (Fig. 14) is proposed for practical use. The bilinear
elastic-plastic force–displacement model predicts the force developed in the connector for a design vertical displacement at the base
of the connector. The inclined part of the model is formed by connecting the origin and the analytical yield point until it meets the
backward projection of the horizontal ultimate load–displacement
line. After the intersecting point, the force–displacement response
is a horizontal line until it reaches the failure displacement value.
This model is presented mathematically as
Yield force; Fy ¼
Elastic vertical displacement; ΔV ¼
ð10Þ
3 πFv D3
4L
1
þ
4 Etw3
πD
3
for Fv < Fy
2
Plastic force; ΔVy < ΔV ≤ Δmax
3
for Fv ¼ Fp ¼ Fy
2
Maximum vertical displacement; Δmax ¼
π
D2
εmax
4
w
ð11Þ
ð12Þ
ð13Þ
The strain at the legs of the O-connectors was measured in Tests
2 and 3. The peak strain versus peak vertical displacement at each
displacement cycle of the connector is shown in Fig. 15. The measured strains beyond 0.03 mm=mm were not useful because the
strain-measuring limit of the strain gauge was 0.03. Although these
strain variations with respect to vertical displacement did not have a
specific correlation, a linear relationship between strain and vertical
displacement is useful to predict the ultimate displacement capacity
of the O-connector. From the principle of engineering mechanics,
the relationship between displacement and curvature for an elastic
system was used to develop a relationship between plastic displacement and curvature. Because the curvature is obtained by dividing
the strain by the depth of the neutral axis, the displacement can be
calculated from the strain. The ultimate vertical displacement
capacity calculated using Eq. (13) was 35.8 mm (1.41 in.), whereas
the test results indicated no fracture at a vertical displacement of
32 mm (1.25 in.) while experiencing out-of-plane buckling. This
design equation can be used to predict conservatively the maximum
displacement capacity of O-connector before fracture. The yield
Fig. 14. Peak force–vertical displacement plot.
© ASCE
2σy tw2
3D
Fig. 15. Peak strain versus peak vertical displacement plot.
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Fig. 17. FEM of the test configuration and the O-connectors: (a) FEM
assembly; and (b) FEM at 38-mm (1.5-in.) vertical displacement.
Fig. 16. Measured peak vertical displacement and measured corresponding horizontal displacement.
force can be calculated from the material and cross-sectional properties of the connector using Eq. (10), and Eq. (11) can be used to
calculate the yield displacement. Any displacement corresponding
to a force smaller than 1.5Fy is calculated using Eq. (11) as well.
Relationship between Vertical and Horizontal
Displacement
As one base of the O-connector moves up and down relative to the
other base, the connector legs and the semicircular parts move in
horizontal direction. Appropriate prediction of the horizontal displacement at the intersection of straight leg and half-circular part
for a given relative vertical displacement of the O-connector is important before using the connection in building system. Knowing the
associated horizontal displacement beforehand allows the designer
to provide enough room for lateral movement that will occur during
an earthquake or severe wind event. The relationship between vertical and horizontal displacement of the O-connector was determined. The ratio of the analytical vertical to horizontal yield
displacements is
ΔyV π D2
¼
ΔyH 4 L2
ð14Þ
which equaled 1.77 for the geometry of the O-connector tested in the
experimental program. From the measured experimental results, this
ratio was found to be very close to 1.77 (Fig. 16). This supports the
validity of analytical equations derivation, and Eq. (14) provides an
effective way to calculate the expected horizontal lateral displacement associated with the relative vertical displacement for a given
connector.
Three-Dimensional Finite-Element Analysis
To better understand the observed hysteretic behavior of the aluminum O-connector tested in the experimental program, a detailed
finite-element model for the test configuration was developed using
Abaqus 2016 (Fig. 17). The FEM of the test configuration was constructed using three-dimensional deformable elements. Because no
© ASCE
damage was observed in the CLT panels during testing, the CLT
panels were modeled with an elastic material using the measured
properties of the CLT described in the section “Material Properties.” The material behavior of the O-connector was represented
using a multilinear nonlinear material model with the stress–strain
response obtained from the aluminum tensile coupon test results.
A combined kinematic/ isotropic hardening property was used
to simulate the material model. The material model parameters,
such as modulus of elasticity, yield strength, failure stress, and corresponding strain, were taken from the measured properties from the
coupon tests (Table 1). No failure criteria were used in the aluminum
material definition, so the stress–strain response showed no strength
loss beyond the ultimate strain of 0.16 mm=mm. This did not affect
the results of the analysis, because a strain limit of 0.095 (60% of
ultimate strain.) was used to determine the ultimate displacement
capacity for each connector. The CLT panels were meshed using
linear 3D stress elements with eight nodes (i.e., C3D8R in Abaqus)
and one integration point per element. The mesh size was approximately 50.8 mm (2 in.). The O-connectors were meshed using
a four-node 3D stress elements (C3D4), and the mesh size was
3.175 mm (0.125 in.).
The restraint conditions were idealized to reduce computational time. The lag screw connections between CLT panels and
O-connectors were modeled in finite element analysis (FEA) using
tie constraints. Each screw was modeled using an equivalent square
area, with each side 2 times the diameter of screw. The tie constraints were allowed to rotate to some degree to simulate the rotation of the connector wings observed in the experiments. This was
done by defining a rotational constraint ratio (CR). The rotations of
the connector wings at the connection region were measured using
the NDI system, a noncontact 3D displacement measurement system
in the experiments. Based on the measured rotation of the connector
wings in Test 2, a rotational constraint ratio of 50% was used to
simulate the observed rotation at the connection region. Similarly,
for Test 3, a rotational constraint ratio of 25% was used, based on the
experimental observations. The rotational constraint ratio was
chosen by trial and error to match the measured rotation of the connector wings. The post-tensioned outer CLT panels were simulated
by coupling the bottom surfaces of the CLT panels to a reference
point, where the fixed boundary conditions were applied. The
top face of the interior CLT panel was coupled in all degrees of
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Fig. 18. Experimental and FEA results for F-Δ response: (a) O-connector Test 2; and (b) O-connector Test 3.
freedom to a reference point which was used to control the loading.
The displacement-controlled loading was applied by defining
a displacement boundary condition on the reference point and
restraining movement of the intermediate CLT panel in all degrees
of freedom except the vertical. The experimentally measured reversed cyclic loading history was applied on the reference point
in the same increments as in the experimental testing. The FEM
analyses produced force–displacement curves from the output at the
reference point as well as the local stress and strain values for each
element.
The predicted force–displacement responses of a single connector from the FEA of Tests 2 and 3 configurations are plotted alongside the test results in Fig. 18. The F-Δ responses show the impact
of the connection flexibility on the overall response of the connector. The FEM accurately predicted the connector response when the
connection flexibility is considered. The FEM accurately predicted
the loading and unloading stiffness and only marginally underestimated the connector strength.
Fig. 19. Measured and calculated strains in a critical location of a
connector.
© ASCE
The measured and FEA predicted peak strains in the connector
from Tests 2 and 3 are plotted with connector vertical displacements in Fig. 19. The vertical displacement of the FEA results
was related linearly to the strain beyond yielding of the connector,
which was supported by the experimental results. The strain beyond 0.03 mm=mm in experimental results was not usable because
it was beyond the strain-measuring limit of strain gauges. This observation about the linear relationship between strain and vertical
displacement supports the analytical equation for calculating the
ultimate displacement capacity of the O-connector.
Conclusions
This paper presented the development of an oval aluminum energy
dissipater (O-connector) for coupled post-tensioned CLT wall systems. Three test specimens, each containing four O-connectors,
were tested under reversed cyclic loading to characterize the response of the O-connectors. A detailed 3D finite-element model
of the test configuration was developed in Abaqus and validated using the experimental results. The following conclusions were drawn
based on the experimental and finite-element analysis results:
1. The aluminum O-connector has a stable hysteretic force–
displacement response and can provide sufficient amount of energy dissipation by undergoing comparatively large vertical
displacement.
2. The premature out-of-plane buckling of the O-connector legs
have a significant influence on the force–displacement response
of the connector, as shown by Test 1. This problem can be overcome easily by adding a simple restraining plate, as shown in the
second and third tests.
3. A small amount of rotation in the O-connector–CLT connection
is expected when they are connected together by means of lag
screws. Metal–CLT (wood) connections with lag screws should
not be considered as fixed; rather, they should be considered as
flexible connections with a relative degree of fixity. This flexibility can be captured by defining the degree of rotational constraint for the connection region in finite-element models. A
rotational constraint ratio of 0.25–0.5 seems to provide reasonable predictions for overall force–displacement response.
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4. The finite-element analysis model accurately predicted both the
connector strength and critical strains. The capacity of the connector predicted by the FEA model was 3% more than the measured response.
5. Analytical expressions based on the first principles for predicting the force–displacement response of the O-connector were
developed. The values predicted using the analytical expressions
were within 88%–92% of the measured O-connector forces.
Thus, these analytical expressions can be used for designing
O-connectors for coupled rocking wall systems.
Data Availability Statement
Some or all data, models, or code generated or used during the study
are available in a repository online in accordance with funder data
retention policies. The repository is accessible at https://www
.designsafe-ci.org/data/browser/public/designsafe.storage.published//
PRJ-2485.
Acknowledgments
The authors acknowledge the financial support from National
Science Foundation (NSF) for this research under Grant No. CMMI
1537788. The authors thank Collin Sewell, research engineer at the
Large Scale Structures Laboratory at The University of Alabama,
and several undergraduate students for helping with test setup and
testing. The opinions, findings, and conclusions expressed in the
paper are those of the authors, and do not necessarily reflect the
views of NSF.
Supplemental Materials
Figs. S1 and S2 are available online in the ASCE Library (www
.ascelibrary.org).
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