Engineering Structures 31 (2009) 2152–2161
Contents lists available at ScienceDirect
Engineering Structures
journal homepage: www.elsevier.com/locate/engstruct
A low-tech dissipative buckling restrained brace. Design, analysis, production
and testing
G. Palazzo a , F. López-Almansa b,∗ , X. Cahís c , F. Crisafulli d
a
National Technological University, Ceredetec, Rodríguez 273, 5500 Mendoza, Argentina
b
Technical University of Catalonia, Architecture Structures Department, Avda. Diagonal 649, 08028 Barcelona, Spain
c
University of Girona, Mechanical and Construction Engineering Department, Lluís Santaló s/n, 17071 Girona, Spain
d
National University of Cuyo, Faculty of Engineering, Mendoza, Argentina
article
info
Article history:
Received 24 October 2008
Received in revised form
24 February 2009
Accepted 17 March 2009
Available online 8 April 2009
Keywords:
Energy dissipators
Buckling restrained braces
Passive control
Testing
Buckling analysis
Fatigue life
abstract
This work aims to foster the mass use of buckling restrained braces, mainly in developing countries.
To reach this goal, two major objectives are pursued: (i) to contribute to a better understanding of the
structural behavior of such dissipators and (ii) to propose cheap and simple yet efficient devices, suitable
for the intended applications. Such devices should be patent free. The research approach consists of three
consecutive stages: (i) designing, producing and testing individually short length dissipators, (ii) taking
profit of the gained experience to design, produce and test individually four larger prototype devices
(near 3000 mm long) and (iii) designing, producing and testing on subassemblies, a number of full scale
dissipators. The two first stages are completed while the third one is in progress; this paper concentrates
on the second stage. The considered devices consist basically of a steel cylinder as dissipative core and a
steel tube filled with mortar as buckling restrainer casing. The design and production issues are accounted
for in an integrated way and all the adopted technical solutions are explained. A numerical analysis of the
buckling behavior is carried out; it allows formulating design recommendations. The experiments consist
of imposing on the prototype devices axial cycling strain up to failure. The results of the tests are described
and discussed; they show that the devices performed satisfactorily. The main conclusion of this work is
that it is possible to obtain a reasonably cheap, efficient, robust, low maintenance and durable prototype
device requiring only a low-tech production process. Further research needs are identified.
© 2009 Elsevier Ltd. All rights reserved.
1. Introduction
Energy dissipators are a convenient option for earthquakeresistant design of buildings and other civil engineering constructions since they absorb most of the input energy, thus protecting
the main structure from damage even under strong seismic motions [1,2]; many applications have been reported [3]. Several types
of devices have been proposed; those based on plastification of
metals (commonly termed as hysteretic) are simple, cheap and reliable and have repeatedly shown their usefulness. Among them,
the buckling restrained braces are one of the dissipators more used
for seismic protection of building frames [4,5]. They consist of slender steel bars connected usually to the frame to be protected either
like concentric diagonal braces as shown by Fig. 1.a or like chevron
braces as shown by Fig. 1.b. Under horizontal seismic motions, the
interstory drifts generate axial strains in such steel bars beyond
∗ Corresponding author. Tel.: +34 93 4016316, +34 606807733; fax: +34 93
4016320.
E-mail address: francesc.lopez-almansa@upc.edu (F. López-Almansa).
0141-0296/$ – see front matter © 2009 Elsevier Ltd. All rights reserved.
doi:10.1016/j.engstruct.2009.03.015
their yielding points; their tension–compression cycles constitute
the hysteresis loops. The buckling of these bars is prevented by
embedding them in a stockiest encasing. Such encasing is usually formed by steel elements [6,7] commonly filled with mortar
(see Fig. 2). Some sliding interface between the steel core and the
surrounding mortar is required to prevent excessive shear stress
transfer, since it would reduce the longitudinal stress in the core
thus impairing the energy dissipation; also, as this interface involves some clearance between the core and the mortar, such a
gap is required to allow the Poisson expansion of the core during
compression.
The buckling restrained braces posses several relevant advantages compared to other hysteretic devices:
• The ratio dissipated energy/added material is the highest in the
comparative devices [8]; the added material includes dissipators, bracing and connections. The degree of plastification is
uniform along the whole body of the core.
• These dissipators constitute themselves as a bracing system and
no additional braces are required to connect each device to the
main frame.
G. Palazzo et al. / Engineering Structures 31 (2009) 2152–2161
2153
• Experiments. A number of tests have been carried out, both
Fig. 1. Building frames protected with buckling restrained braces.
Fig. 2. Common type of buckling restrained brace.
• A relevant experience is available since a number of individual and subassemblage tests have been carried out [7,9–20]
and many realizations have been reported, mostly in Japan [6],
Taiwan [7], Canada [21] and the United States [9]. Preliminary versions of design codes have been proposed [22–24]
and many references about design procedures are available
[14,16,17,25–31].
• Since the dissipative part of the device can encompass nearly
the whole length of the brace, the required strain is rather low.
Therefore, the plastic excursion is rather moderate, possibly
providing high fatigue resistance.
In spite of the relevant existent background about the buckling
restrained braces, there are still some open questions which
require further research:
• Design and production. Although a number of devices based
on axial plasticity of steel bars are commercially available, no
full details about them have been reported, perhaps partially
for confidentiality reasons. In particular, the solutions for the
sliding interface between the steel core and the mortar have
been reported only scarcely [7,16,17] in the technical literature.
Also, most of the relevant production issues have not been
deeply discussed.
• Buckling analysis. The buckling design of the mortar-steel
coating is based usually on simple second-order models [9,17].
Some of their parameters are not usually selected from the
actual parameters of the device but merely from semi-empirical
considerations; hence, the obtained results cannot be very
accurate and it is uncertain than they are on the safe side. In
other words, only over-conservative designs of the casing are
feasible and it is even doubtful that the actual safety factor is
greater than 1.
individually and on subassemblies accounting for the main
frame. Perhaps the only relevant thing missing is extensive
information about the inner final condition of the devices.
• Structural behavior. The structural behavior of the device
is rather complicated because of the coexistence of several
coupled issues, mainly: (i) joint behavior of three materials
(inner and outer steel, mortar and the sliding interface),
(ii) plastic cyclic behavior of the core, (iii) partial sliding
between the core and the encasing mortar and (iv) large
strains and displacements. A reliable and accurate numerical
model considering these issues has not been reported. This
omission requires that the design is based on over-conservative
approaches and prevents the proposal of innovative and daring
solutions.
• Effectiveness. Although several parametric studies have been
reported in the technical literature [32,33], their authors still
indicate a number of open questions. It is noted that most of
the existing studies refer to steel buildings while this research is
rather oriented to concrete frames, very common in developing
countries.
This work belongs to a research project aiming to promote
the mass use of patent free buckling restrained braces for
seismic protection of buildings in developing countries. The
research approach consists of: (i) designing, producing and testing
individually five short length dissipators (about 400 mm long)
[34,35], (ii) taking advantage of the gained experience to design,
produce and test individually four larger prototype devices (near
3000 mm long), (iii) deriving a simplified model of the buckling
behavior of these devices, (iv) developing a complex numerical
model of their structural behavior, (v) designing, producing and
testing on subassemblies a number of full scale dissipators and
(vi) performing a numerical parametric study about the seismic
efficiency of such devices. The first three stages are completed,
while the last three are still in progress. This paper deals with the
second and third stages, which correspond to the first three open
questions. A description of the research follows; such description
is organized according to the aforementioned questions.
• Design and production. A buckling restrained brace dissipator
is designed and a number of prototypes are produced; such
device is rather similar to the existing ones (see Fig. 2). Main
concerns of the design are: (i) efficient, simple, robust, low
maintenance and durable device, (ii) low cost, (iii) simple
manufacturing and (iv) easy to find materials.
• Buckling analysis. A simple yet reasonably accurate second
order analysis is performed. The geometrical imperfections and
the nonlinear behavior of the core are explicitly considered in a
simplified way.
• Experiments. Individual testing has been carried out in the
University of Girona, Spain; the experiments consist of cycling
axial loading until failure.
2. Design and production
Beyond efficiency, the following qualities are sought in the
proposed devices:
• Simplicity. The device should be robust, durable and virtually
maintenance-free.
• Low cost. It should be kept in mind that the use of energy
dissipators has to compete with other solutions and that in
developing countries the economical issues are crucial.
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G. Palazzo et al. / Engineering Structures 31 (2009) 2152–2161
Fig. 3. Considered prototype of a buckling restrained brace.
Fig. 4. Pictures of a prototype of a buckling restrained brace.
• Easy production. Neither protected nor complex technologies
are acceptable; in particular, neither big production facilities
nor highly skilled and experienced workers should be required
and the manufacturing should be fast. Moreover, the product
has to be robust with respect to manufacturing errors. Any
developing country should be able to produce the devices by
itself.
• Basic materials. Only materials that are easy-to-find, replaceable and widely spread in the construction world should be
used. In particular, no particular requirements about the steel
of the core are suitable.
The considered dissipator consists basically of a slender solid
bar (cylinder) as dissipative steel core and a round thin-wall steel
tube filled with high strength mortar (without shrinkage) as casing
buckling restrainer. Two two-halved steel connectors are placed at
both ends to ensure a proper anchoring to the frame. Fig. 3 shows
a plan view of the device, an elevation of one of their ends and two
front views; the left front view includes a steel connector while
the right one shows a bare core end. Fig. 4 shows some images of a
particular device. Fig. 4.a and b displays side and front views of one
of the ends, respectively; the steel connectors are not incorporated.
Fig. 4.c contains two pictures of a connector and Fig. 4.d shows their
two halves.
Figs. 3 and 4 show that the two end steel connectors consist
of two mirror halves; they are milled from a solid cylinder. The
connection is based mainly on friction through pre-tensioned
bolts; since welding can impair the fatigue strength, it is only used
in the outer parts, where most of the stress has been transferred
from the core to the connectors. When the core is tensioned and
reaches its maximum extension their ends protrude beyond the
protection of the casing; when the motion reverts, the core is
compressed and both naked ends are in serious risk of buckling. To
prevent this, four trapezoidal steel plates (see Figs. 3 and 4.c) are
welded to each of the connectors; they slide in cruciform-shaped
grooves carved in the mortar, as shown by the right Front View in
Fig. 3 and by Fig. 4.b.
Both the core and the tube have a constant cross section
because of simplicity and availability. A relevant decision was
to select the section of the core; in the technical literature
mainly flat rectangular and cruciform sections have been proposed
[9,16] but round sections have been also considered [36]. In the
aforementioned previous tests of short dissipators the core had a
rectangular section and some cracks were detected in the mortar
near the corners [34,35]; hence, for these devices it was decided
to use a circular section for the core. Additional advantages that
support this choice are the facility of placing the sliding layer, the
G. Palazzo et al. / Engineering Structures 31 (2009) 2152–2161
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Table 1
Main geometrical parameters of prototypes D1, D2, D3 and D4.
Devices
Lco (mm)
Lcn (mm)
Ltu (mm)
Ldi (mm)
dco (mm)
dtu (mm)
ttu (mm)
dcn (mm)
D1 & D2
D3 & D4
2808
2808
200
270
2422
2152
2466
2196
10
22
90
115
3
3
80
85
equal buckling strength in any direction (compared to flat sections)
and the lack of risk of torsional buckling (compared to cruciform
sections). The tube is also round for simplicity and coherence;
moreover, in rectangular tubes the confinement of the mortar is
not fully effective in the middle of the sides (this can be relevant to
avoid local buckling of the core). The core can be made of ordinary
construction steel. It is well known that the surface evenness
reduces the risk of crack propagation and provides higher fatigue
strength; however, for the sake of simplicity and of moderate cost,
no surface treatment is required.
A key issue of the design is to ensure a proper sliding between
the core and the surrounding mortar to avoid relevant shear stress
transfer. In the proposed device, the sliding is ensured by a threelayer interface: the steel core is coated with Teflon r , lubricated
with grease and wrapped with rubber. The purposes of the rubber
are: to provide shear flexibility, to guarantee an even sliding
surface and to allow the transversal expansion of the core when
compressed. The thickness of the rubber layer plays a significant
role in the design: if the layer is too thin it will inhibit lateral
(Poisson) expansion of the core, conversely, if it is too thick it will
allow excessive local buckling and reduce fatigue life of the brace.
In the tested devices, 1.7 mm thick rubber has been selected, both
for availability reasons and for being a common value in similar
devices. The Teflon is selected, because of its high strength and
low friction coefficient, as an additional measure to provide further
sliding capacity.
Four prototype devices (termed D1, D2, D3 ad D4) have been
produced in Barcelona during June 2006 according to the described
technology (see Fig. 3). The total length of the devices is limited to
3 m because of restrictions in the testing laboratory. The values of
the geometrical parameters (Fig. 3) are summarized in Table 1.
Table 1 shows that dissipators D1 and D2, as well as D3 and
D4 are designed alike, to compare their results. For all the devices
the difference between the length of the dissipative segment of
the core Ldi and the length of the tube Ltu is 44 mm (22 mm each
side); it is intended to allow enough slide of the core with respect to
the casing. This value is about six times the yielding displacement;
hence, this design largely allows ductility ratios (quotient between
the yielding and the maximum displacements) slightly above 5.
The diameters of the core have been conservatively selected to
provide more slender bars than in usual full size devices. The
restraining casing has been designed from the approach suggested
by [9]. For both the tube and the core, ordinary construction steel
S275 JR has been used [37]; its yielding point is fy = 275 MPa
while the ultimate strength is fu = 410 MPa. Commercially
available mortar without shrinkage has been used; the expected
compressive strength ranges between 45 and 50 MPa.
The production cost in Barcelona during 2006 of the four
prototypes D1, D2, D3 and D4 has been 3272.28 e including
16% VAT. The material cost is 737.11 e and the labor and local
transportation costs are 2535.17 e; some tasks were carried out
directly by the authors of this work and are not considered. Also,
the cost of the experiments is not included. It is noted that, under
normal manufacturing conditions in developing countries, the
labor cost can be dramatically reduced.
A deeper description of the design and production issues is
available in [35].
3. Buckling analysis
This section presents a simplified model of the second
order behavior of buckling restrained braces. This model allows
designing the buckling restrainer system (casing). However, the
casing of the tested devices was designed according to previously
existing models because this one was not completely developed.
This study shows that the proposed model provides more slender
devices.
In any buckling restrained brace, three types of flexural modes
are feasible [38]:
• Buckling of the core which does not involve the buckling of
the casing; rather the core behaves as a column embedded in
an elastic medium. This phenomenon is commonly termed as
rippling. For small lateral displacements, the medium is the
rubber, which is extremely flexible, being unable to provide
any relevant restraint. Conversely, larger deflections involve the
mortar; [9] have shown that the critical load is several orders of
magnitude higher than the maximum possible axial load in the
steel core.
• Local buckling of the naked core ends. When the core is elongated, it protrudes from the casing; when compressed, instability can arise. This phenomenon can be easily described by
conventional Euler analysis; therefore, no additional considerations are included here.
• Global buckling of the whole device. The buckling of the core
induces relevant overall bending of the casing.
An analysis of the third type of modes is presented next. It is
based on second order formulations, typical in steel structures [39].
The proposed model accounts, in a simplified way, for all
the relevant issues: the initial geometrical imperfections, the
nonlinear behavior of the core and the interaction between the
core and the mortar.
The following geometrical imperfections are considered:
• Initial gap (a) between the core and the surrounding mortar. It
is conservatively assumed that this gap is constant along the
length of the core and is equal to two times the rubber thickness
(a = 3.4 mm). This assumption is equivalent to neglect the
transversal stiffness of the rubber.
• Initial eccentricity of the core duct (eco ) due to out-ofstraightness. The observation of the split tested specimens (see
Fig. 14) shows that this parameter is relevant and, hence, cannot
be neglected.
Fig. 5 describes the i-th buckling mode; it is assumed that its
shape is composed of near-straight equally-distributed segments
(with wave length li = Ltu /i) joined by plastic hinges leaning
alternatively on both sides of the hole housing the core. P is
the axial compressive force, Fi is the interaction force between
the core and the mortar and M is the bending moment in the
corners of the core. Since the interaction forces Fi are close and,
hence, nearly counteract each other, it might seem reasonable to
neglect the transversal bending flexibility of the casing. Under such
assumption, the equilibrium equations show that the maximum
shear force Vi and bending moment Mi in the casing are Vi =
Fi /2 = 2P ei /li and Mi = Fi li /4 = P ei . Hence, for high buckling
modes the casing undergoes extremely large shear forces and,
therefore, the assumption that its lateral flexibility is negligible
must be discarded. By considering such an effect [9] have shown
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G. Palazzo et al. / Engineering Structures 31 (2009) 2152–2161
Fig. 5. High buckling mode of the core.
The constant value k is given by k2 = P /(Eca Ica + Eco Ico ); since the
core yields, its bending stiffness can be neglected compared to the
one of the casing and ky P /Eca Ica . By integrating twice, a secondorder differential equation is obtained; its general solution is
y = A sin k x + B cos k x +
∞
X
qi sin
i =1
πx
li
.
(4)
A and B are unknown constant values and qi are also unknown final
eccentricities. By imposing the initial conditions y (0) = 0 and
y(l1 ) = 0, it follows that A = B = 0; since sin(π x/li ) are linearly
independent functions it follows that the eccentricities qi are given
by
qi =
Fig. 6. Lateral interaction between the core and the casing.
that, under ideal conditions, the critical axial load of the brace is
Pcr = π 2 (Eco Ico + Eca Ica )/L2k ; Lk is the effective length of the device
and Eco Ico and Eca Ica are the stiffness (elastic moduli and moments
of inertia) of the steel core and of the casing, respectively. This can
be also concluded by noting that, if the bending stiffness of the core
is neglected, its buckling situation is roughly equivalent to the one
of a liquid column compressed axially by a frictionless piston [39].
Watanabe et al. and Black, Makris and Aiken [4,9] propose that
the axial design load of the casing is equal to this critical value
multiplied by a safety factor. This factor accounts for the initial
imperfections, the yielding of the core and the interaction between
the core and the mortar; however, the given criteria to select
their values are not related to such issues. A modification of the
approach by Watanabe et al. and by Black, Makris and Aiken [4,9]
is presented next; it considers these three issues, and in particular
incorporates explicitly the initial imperfections.
Fig. 6 describes the buckling interaction between the core and
the casing. The upper sketch represents the initial position of the
core (dashed line, y0 ) and the final one (solid line, y). The lower
sketches represent, separately, the final bent configurations of
the casing and of the core; the distributed interaction forces are
described by an unknown law p(x).
The initial position of the core is described by the Fourier series
decomposition:
y0 =
∞
X
ei sin
i=1
πx
li
=
∞
X
ei sin
π ix
l1
i=1
.
(1)
Eco Ico (yiv − yi0v ) + Py00 = p.
(2)
By adding both equations, the unknown interaction forces are
eliminated and, taking into account Eq. (1), a single equation is
derived
yiv + k2 y00 =
∞
X
i=1
ei
4
π
li
−
P
PE
.
(5)
PE is the first critical Euler load of the casing; if the end connections
are hinged it is given by PE = π 2 Eca Ica /l21 . Eq. (5) for i = 1 shows
that loads below the critical one can largely amplify the bending of
the core, possibly leading to collapse. The contribution of the first
mode to the maximum bending moment in the casing is the value
of Eca Ica e1 (y00 − y000 ) in the mid section:
M1 = Eca Ica e1
P
PE
2
π
l1
1−
P
PE
=
P e1
1−
P
PE
.
(6)
By neglecting the higher modes contribution, Eq. (6) allows
designing the casing. Axial load P is the maximum feasible force
in the core considering strain hardening effects and the difference
between expected and nominal yield strengths of the core. It is
noted that, because of the friction, the casing will also likely carry
some compression; the experiments (see Fig. 12) show that its
demand is negligible.
By assuming conservatively that e1 = 10 mm, in the tested
dissipators the casing is able to largely resist this demand. In
devices D1 and D2, the safety margin for the bending moment
is bigger than 16, even neglecting the contribution of mortar; in
devices D3 and D4, such margin is bigger than 5. These calculations
show that the design of the casing for devices D1 and D2 is clearly
over-conservative; if a tube with thickness ttu = 3 mm and
diameter dtu = 63 mm is considered, the safety margin is still
bigger than 6.
4. Experiments
The first term is given by e1 = eco + a; for the other terms it can be
conservatively assumed that ei = a (see Fig. 5). The second order
equilibrium differential equations of the casing and of the core can
be written as
Eca Ica (yiv − yi0v ) = −p
ei
i2
sin
πx
li
.
(3)
4.1. General description
The four prototypes were tested during July 2006 in the
University of Girona, Spain. The experiments are individual
(i.e. there are no subassemblages accounting for the frame) and
consist of imposing cycling axial deformation until failure. A
comprehensive description is available in [35]. The objectives of
the tests are (i) to assess the performance of the proposed devices,
(ii) to learn about their structural behavior, (iii) to characterize
their hysteretic behavior and (iv) to obtain experimental results
useful to calibrate the numerical models to be developed. An
G. Palazzo et al. / Engineering Structures 31 (2009) 2152–2161
2157
Fig. 7. Testing rig for dissipators D1, D2, D3 and D4.
Fig. 8. Testing rig for dissipator D1.
additional objective is to increase the available information about
the fatigue strength of buckling restrained braces; that information
might be useful to other researchers to develop models of such
capacity. The experiments are designed to reach these goals whilst
accounting for the time, budget and availability constraints.
followed. The average values of the compressive strength and
deformation modulus are fm = 39.92 MPa and Em = 17.52 GPa,
respectively.
4.2. Characterization of materials
Dissipators D1, D2, D3 and D4 were placed horizontally, fixed
by one of their ends, and connected by the other end to a servocontrolled hydraulic jack. Fig. 7 displays two sketches (plan view
and elevation) while Fig. 8 shows a picture of the testing rig of
dissipator D1.
Fig. 7 shows that both end connections are pinned with respect
to a vertical axis, i.e. the device is free to rotate in a horizontal plane.
This assemblage is aimed to simulate hinged connections among
the dissipator and the main frame (Fig. 1); such a solution has been
adopted for simplicity and for avoiding the influence of bending
moments in the end of the device [16].
Figs. 7 and 8 show that the registered magnitudes are: axial
force in the jack (sensor 7), displacement of the actuator (sensor
6), longitudinal displacements of the steel connectors (sensors 2
The mechanical properties of the steel of the core have been
obtained from tension tests following [37] on four specimens with
diameter 10 and 22 mm (coupon testing). An extensometer was
incorporated to three specimens to determine the elastic modulus.
The average values of the yielding point, ultimate strength and
Young’s modulus are fy = 303.75 MPa, fu = 425.31 MPa and
Eco = 210.91 GPa, respectively; the main disagreement with the
nominal characteristic values lie in the yielding point (303.75 MPa
instead of 275 MPa).
The experiments about the mortar consist of compressive
testing of two specimens cut from the previously tested dissipators
D1 and D3 (coupon testing). European regulations [40] were
4.3. Testing rig
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G. Palazzo et al. / Engineering Structures 31 (2009) 2152–2161
and 1), longitudinal displacements of the end sections of the tube
(sensors 8 and 9), transversal horizontal and vertical displacements
of the mid section of the tube (sensors 3 and 4, respectively) and
axial strains of the casing (sensors 16 and 17). At dissipator D1,
two additional strain gauges were fixed near the end sections of
the tube (sensors 18 and 19). Gauges 16 and 17 were placed at
opposite ends of a horizontal diameter of the mid section so as to
obtain the axial forces and the horizontal bending moments in such
section. The axial elongations of the core that were given by the
difference between channels 1 and 2 and by channel 6 differ due to
the flexibility of the supports and of the interposed elements; after
eliminating such effect, the fit among both measures is excellent.
The time was also recorded but is not considered relevant, as the
behavior of the dissipator is assumed to be rate-independent for
the range of considered velocities.
4.4. Imposed displacements
The imposed displacements consisted of two consecutive
phases: growing-amplitude cycles and constant-amplitude cycles
until failure; in the second phase the amplitude on either the
tension or compression side is 5∆y , ∆y being the yielding
displacement. The values of ∆y are estimated as 3.83 mm for
dissipators D1 and D2 and 3.37 mm for dissipators D3 and D4;
correspond to the measured yielding points. In devices D1 and
D2 the maximum imposed amplitude corresponds to a strain
level of approximately 8 × 10−3 and inter-story drift ratios of
about 2% in diagonal braces (Fig. 1.a) and 1.6% in chevron braces
(Fig. 1.b). The loading histories are intended to evaluate the energy
dissipation capacity under moderate constant ductility demand.
The first fifteen imposed cycles of devices D1 ad D2 are displayed in
Fig. 9; they encompass the first phase (growing-amplitude cycles)
and part of the second one (constant-amplitude cycles).
Fig. 9. Initial loading cycles of dissipators D1 and D2.
4.5. Testing results
The tests were conducted without major problems; the order of
the experiments was D1, D2, D4 and D3. The main incident was a
premature failure of dissipator D4 by local buckling of the naked
core ends as the trapezoidal steel plates were not rigid enough; to
avoid this, in the device D3, two sliding supports were added near
the end connections to prevent the lateral displacements of the
casing. Also, the rotation capacity of the two pinned connections
(Fig. 7) proved to be damaging for the behavior of the dissipator D1
as relevant rotations were observed; the situation for dissipators
D2, D3 and D4 was improved by inserting steel wedges and can
sheets that transformed the hinged connections in near-clamped
ones. It is noted that both the additional supports and the clamped
connections are feasible in real applications.
The most representative tests results are summarized next.
Fig. 10 displays hysteresis loops for dissipator D2. Positive
values of force correspond to tension and of displacement to
elongation. The first and last loops have been eliminated since they
are mostly irregular. To facilitate the interpretation of Fig. 10 an
ideal bilinear hysteresis loop fitting the inner registered loops is
also drawn in dashed lines.
The following trends can be observed from Fig. 10:
• The hysteretic behavior is stable. The force amplitude decreases
after the first cycles but tends to stabilize quite fast. This is
due to a progressive detachment between the core and the
surrounding mortar.
• Every time the force in the jack changes its sign, the plot exhibits
a near horizontal jump; it means that the jack keeps moving
without any relevant force change. This slide is due to the gap
in the pin-joint connections between the dissipator and the end
supports (see Fig. 7); obviously, this undesirable effect should
be minimized in real applications.
Fig. 10. Regular hysteresis loops for dissipator D2 (channel 7 vs. channel 6).
• The observed buckling of the core (see Fig. 14) does not affect
the plots.
• The plastic tension loading branches are curved, yet tend
to become flat horizontal near the corner. This can be also
observed in the plastic compression loading branches but
their end segments exhibit a rather sudden increase leading
to a sharper peak and even to a reversal in the curvature
of the branch. This fact is common to most of the buckling
restrained braces; it is due to the higher mortar contribution
during the core buckling because of the rising of the friction
forces. This effect is rather unwelcome since it does not raise
remarkably the area encompassed by the hysteresis loops while
the increase of force is more relevant.
Fig. 11 displays the superposition of the regular hysteresis loops
for dissipator D3 and of the stress–strain plot for a steel specimen
obtained from coupon test.
Plots from Fig. 11 show that:
• The elastic branch of the specimen and the unloading tension
branches of the device are near parallel. Hence, the elastic
tension stiffness of the steel core is similar to the one of the
dissipators. This can be also concluded by observing the first
cycles (not shown in Fig. 11) [35]. It confirms that, under
tension, the friction forces between the core and the casing are
not relevant.
G. Palazzo et al. / Engineering Structures 31 (2009) 2152–2161
Fig. 11. Comparison between stress–strain plots for the 22 mm core bar and for
dissipator D3.
2159
Fig. 13. Horizontal bending moment in the mid section of the casing of dissipator
D2 ([channel 16 − channel 17]/2).
Table 2
Main results of the experiments.
Fig. 12. Axial force carried by the casing of dissipator D2 ([channel 16 + channel
17]/2).
• The yielding point of the core fits roughly the inner loops. It
confirms the first observation from Fig. 10 since such loops
correspond to a full detachment between the core and the
mortar.
• The plastic tension branch of the specimen is flat, showing
that the strain hardening for monotonic loading is not reached.
Conversely, the plastic tension branch of the device is curved.
Such discrepancy can be explained in two ways. First, the
specimen underwent a simple elongation test where all the
fibers yielded simultaneously; on the contrary, the core of
the device was curved due to local buckling (see Fig. 5) and
the yielding of the fibers was not simultaneous. For higher
elongation strains the plots become horizontal, showing full
plastification of the core section. Second, after several cycles of
forced displacements, the steel of the core might have entered
in the strain hardening zone.
Figs. 12 and 13 show the ‘‘time histories’’ of the axial force and
of the horizontal bending moment in the mid section of the casing
of device D2. The longitudinal force and the bending moment
have been obtained from the semi-sum and the semi-difference,
respectively, of strain gauges 16 and 17 (see Fig. 8). In both cases,
linear elastic behavior of the section has been assumed.
Device Buckled
ends?
No. of cycles
Normalized
dissipated energy
Cumulative
plastic ductility
D1
D2
D3
D4
160
131
387
73
3492
2928
8856
1485
2454
1976
6662
1124
NO
NO
NO
YES
Comparison between Figs. 10 and 12 show that the axial
forces carried by the casing are less than 10% of the jack force.
It confirms that the three-layered sliding core–mortar interface
performs reasonably well. Apart from that, the plots from Fig. 12
show a significant drift, since the average values of the force tend
to shift from near zero in the initial instants to tension in the final
instants. Apparently this means that the steel tube tends to remain
permanently tensioned after the test; however, this is unfeasible
since at each cycle some compressive stresses are transferred
during the compression phase (through friction, see Fig. 5) and
are released during the tension phase (yet perhaps only partially).
Importantly, since this phenomenon cannot be seen in Fig. 13,
it cannot be attributed to any malfunction of the strain gauges.
Conversely, a more feasible explanation is as follows: the outer
steel might be longitudinally compressed because of the mortar
shrinkage while the gauges were stuck; hence, the drift shown in
Fig. 12 would represent only the progressive detachment between
the tube and the mortar.
A comparison between the maximum bending moment in
Fig. 13 and the value provided by Eq. (6) is performed next. The
axial force P is obtained from Fig. 10 and the initial eccentricity e1 ,
according to after-test observation, is assumed as e1 = 3.4 mm;
hence:
M1 =
P e1
1−
P
PE
=
25 × 3.4
1−
25
375
= 91 kN mm.
This result can be considered as a preliminary verification of the
proposed model. It is noted that the contribution of the higher
modes is hard to estimate since their short wavelengths generate
high sensitivity to the longitudinal positioning of the sensors.
Obviously, further research is needed.
The analysis of the results of the other devices provides similar
conclusions to those derived from Figs. 10–13 [35]. Table 2 presents
a summary of the results of tests for dissipators D1, D2, D3 and D4.
The irregular values corresponding to behavior near or after failure
are not accounted for.
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G. Palazzo et al. / Engineering Structures 31 (2009) 2152–2161
Fig. 14. Mortar and core of dissipator D1 after testing.
In Table 2, ‘‘Buckled Ends?’’ refers to the local buckling of the
naked core ends. The dissipated energy is the area encompassed
by the hysteresis loops normalized with respect to the elastic
energy corresponding to the yielding displacement (1/2 k ∆2y ,
where k is the axial stiffness). This energy cannot be considered the
ultimate energy dissipation capacity since it is highly dependent
on the loading history [41]. The ‘‘Cumulative plastic ductility’’ [9]
is a dimensionless normalized expression of the cumulative
plastic deformation: Σ |∆+ − ∆− |/∆y where ∆+ and ∆− are
the maximum and minimum values of the plastic displacement,
respectively. The sum is extended to all the plastic excursions.
Results from Table 2 show that, apart from the premature
failure of the dissipator D4, the devices performed properly. The
performance was significantly better in dissipator D3 than in
devices D1 and D2. Such difference might be due to two reasons:
(a) the observed permanent curvatures of the core (see Fig. 14)
are smaller in D3 and (b) in such device the local buckling of both
naked core ends was restrained by the aforementioned additional
sliding supports. It is noted that such supports are feasible in real
applications, like those shown in Fig. 1.
4.6. Observations after tests
Excluding dissipator D4, the failure came for breakage of the
core near the mid section. After pulling out the broken core,
the dissipator was split longitudinally in two halves to observe
the actual condition of the mortar. Fig. 14 displays views of
representative parts of device D1; Fig. 14.a and b refer to the mortar
while Fig. 14.c and d correspond to the core. The other tested
devices provide similar results [35].
Fig. 14.a and b show that the mortar is in good condition,
even in the near vicinity of the core; it means that the transversal
compressive forces due to high buckling modes (Fig. 5) were
not able to locally damage the mortar. According to Fig. 14.a
some eccentricity of the core hole due to out-of-straightness was
observed; it ranged between 5 and 10 mm. Both values fit those
considered for the buckling analysis. The cover of the core (Teflon,
grease and rubber) is in good condition. Fig. 14.c and d show that
the core is bent; it is shaped roughly like a warped sinusoidal wave
whose wavelength ranges between 100 and 200 mm and whose
amplitude reaches 2 mm. Given that the lateral forces exerted by
the core were unable to bend the casing and that the surrounding
mortar is not damaged, is obvious that only the compression of the
rubber layer allows this permanent curvature. As expected, such
observed permanent deformation was bigger for the 10 mm core
bars (D1 and D2) than for the 22 mm ones (D3 and D4). This seems
to indicate that the rubber layer is too thick for devices D1 and D2
and perhaps also for D3 and D4.
5. Conclusions
This work belongs to a larger research project whose main
objective is to promote the mass use of patent free energy
dissipators for seismic protection of buildings in developing
countries. With this aim, a simple dissipative buckling restrained
brace has been designed, produced and tested. The design and
production issues have been considered in an integrated way.
All the adopted technical solutions, namely the sliding interface
between the core and the mortar, are revealed. A buckling
analysis approach is described. Laboratory tests of four prototype
devices are carried out. Such experiments consist of cyclic axial
deformation until failure; a wide set of magnitudes are measured
to investigate the performance of the devices and to collect a
set of results able to calibrate a numerical model currently being
developed. Main conclusions are listed next.
• It is feasible to design buckling restrained braces that are efficient, robust, virtually maintenance-free, durable, reasonably
cheap, easy to produce and made of basic and easily replaceable
materials. It is noted that no particular smoothening operation
of the yielding core is required.
• The buckling design of the casing of the tested devices was
based on an existing model; it is over-conservative since the
proposed buckling analysis approach allows designing slender
tubes, particularly for dissipators D1 and D2. A preliminary
experimental verification of the proposed buckling analysis
approach is presented.
• The tests showed that, in general, the devices performed
properly, without relevant shear stress transfer to the casing
and with stable hysteretic behavior. It is noted that the inner
observation of the tested devices showed that the mortar was
not damaged by the lateral pushing of the core during its local
buckling.
Acknowledgments
The Argentinean ‘‘National Technological University’’ and
‘‘Banco Río’’ (Argentina), supported the stay of Mr. Palazzo in
Barcelona and part of the testing cost (‘‘Programa de Becas
de Postgrado’’ and ‘‘Proyectos de Investigación Científica para
el Perfeccionamiento Docente’’). The assistance of the Technical
University of Catalonia and of the University of Girona is
gratefully acknowledged. Mr. O. Montenegro (Technical University
of Catalonia, Barcelona) tested the mortar of the prototypes; his
help is appreciated.
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