This document summarizes research on modelling and designing dissipative connections for brace-to-column joints. The behaviour of single-pin and double-pin connection devices is emphasized through theoretical beam models and OpenSees models under monotonic and cyclic loading. The proposed models are calibrated against experimental test results from two specimens. The single-pin device consists of inner and outer plates with a pin running through, while the double-pin device has two pins. The models match the experimental hysteresis loops and energy dissipation, validating the numerical modelling approach.

1. MODELLING AND DESIGN OF DISSIPATIVE CONNECTIONS FOR
BRACE-TO-COLUMN JOINTS
Lucia Tirca; Cristina Caprarelli; Nicolae Danila
Department of Building, Civil and Environmental Engineering,
Concordia University, Montreal, Canada
tirca@encs.concordia.ca; c_caprarelli@encs.concordia.ca;
n_danila@encs.concordia.ca
Luis Calado
IST - Department of Civil Engineering, Instituto Superior Tecnico Lisbon, Portugal
calado@civil.ist.utl.pt
ABSTRACT
In this paper, the behaviour of a dissipative brace-to-column connection
device is emphasized. The computation is carried out for a single- and double-pin
connection device by using the theoretical beam model, the OpenSees beam model
under monotonic loading and cyclic quasi-static displacement loading. The proposed
model was calibrated against experimental test results and the validation was
completed when both the experimental and simulated models provided a match.
1. INTRODUCTION
Concentrically braced frames (CBF) are effective systems, able to provide
strength and stiffness to building structures subjected to earthquake loading. The
system dissipates energy through tension yielding and inelastic buckling of bracing
members, while the remaining framing components behave elastically. In spite of its
efficient stiffness, the behaviour of braces is nonsymetrical. Thus, the amount of
energy dissipated in compression is lower than that in tension and the compression
resistance degrades in the post-buckling range with the number of cycles. To
overcome these draftbacks, while preserving the ability of the CBF system to
respond in elastic range, researchers have proposed an alternative approach
consisting of adding ductile seismic fuses in bracing members and/or their
connections (Tremblay et al., 2011). In addition, the Canadian Design of Steel
Structures standard (CAS/S16, 2009) states that for primary framing members
forming the seismic-force-resisting system of conventional constructions,
connections should be “designed and detailed such that the governing failure mode
is ductile when the member strength does not control the connection design loads”.
Meanwhile, the European seismic code (Eurocode 8, 2005) states: “the overstrength
condition for connections (brace-to-frame) need not apply if the connections are de-
signed to contribute significantly to the energy dissipation capability” of the system.
In this light, authors have carried out research in the field of dissipative connections
placed at each end of CBFs braces (Tirca et al., 2012). These dissipative connec-
tions, shown in Figure 1, consist of single-pin or double-pin devices and are de-
signed and detailed to yield, while braces behave in elastic range. The single-pin

2. device is composed of two outer-plates welded or bolted to column flanges, two in-
ner-plates welded to the brace and a rectangular pin member with rounded corners
running through the four plates. If the single-pin device does not have sufficient ca-
pacity to carry the axial load developed in the brace member, the double-pin connec-
tion should be used. The single-pin device was initially proposed and experimentally
tested in the frame of the European INERD project (Plumier et al., 2006).
Figure 1. Dissipative connections: a) single-pin; b) double-pin; c) detail.
To simulate the behaviour of pin devices, a numerical model was developed
in the OpenSees framework version 2.2.0 (McKena et al., 2009). Thus, in this paper,
the OpenSees model for a single-pin device is calibrated against results obtained
from experimental tests conducted at Instituto Superior Tecnico of Lisbon (IST), Por-
tugal. In addition, a numerical model of a double-pin device is developed with the
aim of preparing for upcoming experimental tests.
2. BEHAVIOUR OF SINGLE-PIN AND DOUBLE-PIN DEVICES
To validate the design method for the single-pin connection device, two nu-
merical models are employed and defined as follows: the simple beam model and
the OpenSees beam model. Regarding the simple beam model, the same approach
considered by Vayas and Thanopoulos (2005) and slightly modified by Tirca et al.
(2012) is used to size the pin cross-section and the connection’s components. By
using data from both models studied under static loading, the authors replicate two
experimental tests conducted at IST Lisbon under quasi-static displacement loading.
The calibration of the model is validated when both the experimental and simulated
models match in terms of hysteresis loops generated from plotting the force versus
displacement, the energy dissipated per cycle and the cumulative dissipated energy.
2.1 Simple beam model
The behaviour of the single-pin device in terms of its capacity to dissipate
energy under cyclic loading is influenced by the length of the pin, L, its cross-
sectional shape and size, as well as the distance between the inner-plates (L-2a), as
is illustrated in Figure 1c. Regarding the shape of the pin, the rectangular cross-
section with rounded corners was chosen instead of a rounded shape due to its lar-
ger moment of inertia. However, the configuration of pin device depends on the size
and depth of the column’s cross-section, which governs the pin’s length. Herein, the
axial force developed in the brace, P, is transferred to the pin through the inner-
plates as uniformly distributed loads, which act along the thickness of the plates. For
simplicity, the pin is considered to behave as a four-point loaded beam, where the
concentrated load P/2 is the resultant of the transferred brace force, as is shown in
Figure 2. When the yielding moment My = WyFy is reached, the pin starts to yield in
a) b) c)

3. bending under the point load Py/2 = My/a. At this stage, characterized by the yielding
of the extreme fibres of the pin’s cross-section, the static deflection of the pin is:
δy = (My/6EI)aL(3 - 4a/L) (1)
where EI is the flexural stiffness, Wy is the section modulus and Fy is the yield
strength of the pin. In Eurocode provisions, the corresponding Fy symbol is fy.
Figure 2. Behaviour of simple beam model: a) elastic; b) plastic; c) tri-linear curve.
By considering the small deflection theory, the pin’s deflection at yield is δI = Ia,
where I is the rotation at yield. By definition, I = kIlp, where kI is the yielding curva-
ture, computed as kI = 2εI/h and lp is the length of the plastic hinge which may be
approximated with the height, h, of the pin’s cross-section. The strain corresponding
to the static yield stress is two to five times the yield strain εy (Ziemian, 2010) with an
average of 3εy and the dynamic yield stress is 10% larger. Thus, εI is expressed as:
εI = 1.1x3εy. Theoretically, the yielding moment My = WyFy is reached under the two
Py/2 loads in accordance with Eq. (2), while the pin’s deflection at yield in given in
Eq. (3). After the attainment of Mp, some clamping starts developing at the pin’s
ends and end bending moment is generated (Figure 2b). By equating the external
work, Pδ/2 = P(a)/2, with the internal work (M1 + M2), the magnitude of the ulti-
mate load carried by the beam, PII, is given in Eq. (4). It is estimated that the ultimate
flexural capacity of the pin, Mu, is Mu = WpFu, where Fu is the steel ultimate strength.
Under the two-point loads Pu/2, the ultimate strain εu is approximated as being equal
to εu = 1.1x50εy = 0.1 and the corresponding value of the ultimate plastic rotation, u,
becomes u = kIIlp =0.2 radians, while the ultimate deflection, δII is given in Eq. (5).
PI = Py = 2My/a (2)
δI = Ia = 2(1.1x3εy)a (3)
PII = Pu = 2(M1 + M2)/a ~ 4Mu/a (4)
δII = δu = 1.15(0.2a) (5)
The numerical coefficient 1.15, given in Eq. (5) symbolizes the ratio between the
length of the plastic hinge and the cross-sectional height. During the incursions in
plastic range, the magnitude of load PII may slightly increase due to material over-
strength, to a value PIII, while the maximum deflection of pin at failure is estimated to
be δIII = 0.4a. By employing Eqs. (2) to (5) and the parameters at failure: PIII and δIII,
the pin response follows a tri-linear curve (Figure 2c).
2.2 OpenSees beam model for single-pin device
The purpose of developing the OpenSees beam model is to simulate the behaviour
of the pin in its outer-plate supports. Thus, until the yielding moment is reached, the
pin behaves as a simply supported beam. Then, during the plastic response, the de-
a) b) c)

4. formed pin member causes bearing pressure to the contact surface of the outer-
plate hole which is the pin’s support. In this stage, bending moment is generated at
both pin ends and its magnitude is incremented until the pin reaches its failure
mechanism. Therefore, the OpenSees beam model was built to simulate the behav-
iour of the pin member acting as a four-point loaded beam, as previously described.
The model shown in Figure 3 consists of eight nonlinear beam-column elements with
distributed plasticity and four integration points per element. The pin’s cross-section
is made up of 60 fibers. Among them, 12 fibers were assigned along the height of
the cross-section, h, and 5 along its width, b, as illustrated in Figure 3. The length of
the pin, Lpin, is the clear span between the outer-plates, which act as supports.
Herein, the pin’s supports (outer-plates) are modelled as rigid links of length H,
which represents the free length. To allow rotation between the pin member and the
support (rigid link), a zero-length spring is added at both pin ends. The material as-
signed to the pin and rigid link is Steel02, which is also known as Giuffre-Menegotto-
Pinto material. To simulate the deformation of the pin in the outer-plate supports, a
calibrated Pinching4 material, explained below, is assigned to both zero-length
springs. The length and thickness of the outer-plates influence the behaviour of the
connection and the deflection of the pin controls the deflection of outer-plates. When
the pin member behaves elastically, both links act as cantilever members with a
stiffness Kl = 3ElIl/H
3
, where ElIl is the flexural stiffness of the link. The Pinching4
material represents a pinched force-deformation response and it allows users to
simulate the transition phase from a shear connection to a semi-rigid connection
when the beam is loaded below its elastic bending capacity.
Figure 3. OpenSees beam model for single-pin device
The Pinching4 material is calibrating by using data from two experimental
tests conducted at IST Lisbon, and the involving specimens, shown in Figure 4, are
P-A9 and P-3. The difference between them is the distance between the inner-
plates. In both cases, the pin is made of steel with the following characteristics: Fy =
396 MPa and Fu = 558 MPa, while the pin’s cross-sectional dimensions are 60x40
mm. The tri-linear curve of specimen P-A9 is built by using the theoretical values
computed with Eqs (2) to (5) and is plotted in Figure 5a. To investigate the correla-
tion between the theoretical tri-linear curve and that resulted from the OpenSees
beam model, an incremental analysis is performed. Pairs of applied forces and de-
flections recorded at the beam’s mid-span are plotted and shown in Figure 5b to-
gether with the theoretical tri-linear curve. In addition, at each incremental loading
application, the stress and strain corresponding to each one of the 12 fibers record-
ed at beam’s mid-span are plotted (Figure 6). Thus, when the force Py =145 kN,
computed with Eq. (2), is applied to the OpenSees beam model, the strain recorded
in the extreme fiber of the cross-section is εy and the corresponding stress is Fy. The
maximum strain developed in the fibers is approximately 60εy and is reached under
the applied force, PII =612 kN, as computed with Eq.(3). The corresponding stress
recorded in the same fibers is Fu. Thus, the theoretical and the OpenSees beam
Zero-length spring b
h
fibers

5. model show a good correlation and the stress and strain diagrams validate the theo-
retical equations previously devised.
Figure 4. The geometry of samples P-A9 and P-3.
Figure 5. Tri-linear curve of P-A9 device: a) theoretical, b) OpenSees model.
Figure 6. Strain and stress diagram of modeled P-A9 connection device
2.3 Validation of the numerical model against experimental test results
The two selected specimens P-A9 and P-3 were tested on a box stand un-
der the ECCS cyclic quasi-static loading protocol. The displacement loading applied
to the P-A9 sample has 25 cycles with a rate of loading of 0.45 mm/s and a maxi-
mum displacement in the last cycle of 40mm. The displacement loading protocol ap-
plied to the P-3 sample has 21 cycles, a rate of loading 0.33 mm/s and a maximum
displacement of 45 mm. In both cases, three consecutive cycles reach the same
displacement amplitude. The force-displacement hysteresis loops that characterize
a) b)a) b)
50
15
8040 80
30
P-A9
15
40
70
P-3
7070
30
a) b)
a) b)

6. the behaviour of samples P-A9 and P-3 are shown in Figure 7. In both cases the
failure of the pin occurred in the compression side at one of the two points of load
application, as shown in Figure 8. Thus, in the case of specimen P-A9, when the
distance between the outer-plate and the inner-plate is larger than the distance be-
tween the inner-plates, the failure occurs in the longer pin segment at the external
face of the inner-plate. In the case of specimen P-3, the failure occurred in the mid-
dle segment at the internal face of the inner-plate. For both specimens, same stiff-
ness degradation occurred during reloading. Although both specimens reached the
same deformation in bending of 35 mm, the corresponding ultimate tensile forces
(615kN for P-A9 and 670kN for P-3) differ by 10%. On the other hand, for both
specimens, the capacity in tension is larger than that in compression by 12%. This
difference in strength is due to out-of-plane bending of outer-plates which implies an
increased distance between the pin’s supports in the outer-plate hole. In this case
the outer-plates deflect toward exterior as is shown in Figure 8b. Thus, the thickness
of outer-plates influences the behaviour of the connection.
Figure 7. Hysteresis loops recorded from the OpenSees model vs. experimental test
results: a) P- A9, b) P- 3.
Figure 8. Failure mechanism of specimens P-A9 and P-3.
For the modelling of connections, the Pinching4 uniaxial material defined in
the OpenSees library (Mazzoni et al., 2007) is employed. This material model is able
to simulate the cyclic degradation of stiffness during unloading or reloading and the
degradation of strength. Meanwhile, it could be defined for a hardening-type or sof-
tening-type load-deformation response envelope. Thus, by analyzing the hysteretic
response of specimens P-3 and P-A9, the unloading stiffness degradation model for
P - A9
Failure
of pin
Failure
of pin
Inflection point
P - 3

7. a hardening-type response envelope is used and calibrated against the aforemen-
tioned experimental results. For Pinching4 material calibration, three floating points
are required to be defined in tension and three in compression. Floating point values
(1) and (2) are 0.5 and 0.35 respectively. The first floating point (1) represents the
ratio of the force at which pinching begins, 301 kN, to the total hysteretic force de-
mand, 615 kN. Similarly, the second (2) represents the ratio of displacement where
pinching begins, 12 mm, to the total hysteretic displacement demand, 35 mm. The
third (3) floating point value is the value of force at negative unloading, 17 kN, to the
total load during monotonic testing, 615 kN, resulting in a value of 0.03. Therefore,
as shown above, the pinching curve is built by multiplying certain values of the skele-
ton curve, better known as the tri-linear curve, with the above floating point values
defined for the tension side. For the compressive side, the floating points corre-
sponding to (1) and (3) are reported to a total compressive force of 549 kN. Thus,
the three floating points in tension and compression are shown in Figure 9.
Figure 9. Pinching4 material definition.
The validation of the OpenSees model against the experimental results rec-
orded for specimens P-A9 and P-3 is expressed in terms of normalized energy dis-
sipated per cycle and the normalized cumulative energy, as shown in Figures 10 and
11. The hysteresis response of the specimen P-A9 during the last cycle shows fail-
ure in compression after a tentative failure in tension before reloading. As illustrated
in Figure 10a, the proposed computer model is not able to simulate this type of sof-
tening that occurred during the last cycle and shows a large discrepancy in terms of
Figure 10. Energy dissipated per cycle for specimens: a) P-A9 and b) P-3.
-40 -20 0 20 40
 (mm)
-600
-400
-200
0
200
400
600
Force (kN)
(ePf1, ePd1)
(ePf2, ePd2) (ePf3, ePd3)
(ePf3*0.69, ePd3*0.45)
(*, ePd3*0.03)
a) b)

8. energy dissipated. However, in the case of specimen P-3, a close correlation was
observed. Thus, the OpenSees model is able to replicate the response during the
last cycle, as shown in Figure 10b. Regarding the cumulative energy dissipated by
both samples, the P-3 pin was subjected to 21 cycles, while the P-A9 pin to 25 cy-
cles. Under similar conditions it is expected that the connection device with a larger
distance between inner-plates posses a larger dissipative energy capacity. In order
to improve the OpenSees model, it is required to wrap the Fatigue material to the
Pinching4 material. The Fatigue material accounts for the effect of low-cyclic fatigue
and does not influence the force-deformation relation of the initial material. The algo-
rithm is based on the Coffin-Manson relationship in the log–log domain and the
damage value is accumulated into the material in accordance with Miner’s rule.
Figure 11. Cumulative energy dissipated by specimens: a) P-A9 and b) P-3.
2.4 Numerical modelling of the double-pin device
When a larger axial force is required in brace members and the capacity of
single-pin device cannot satisfy the demand, the connection with two pins acting in
parallel is proposed and is illustrated in Figure 12. Due to the symmetry of a double-
pin connection, the study can be conducted on half of the device and its behavior is
reduced by the single-pin OpenSees beam model as is shown in Figure 3. For sim-
plicity, two small pins of rectangular shape 40x35 mm are used herein and the flex-
ural stiffness is similar with that of an equivalent single-pin 60x40 mm. By employing
two pins in the same connection, each pin is able to carry half of the force trans-
ferred by the brace, while undergoing the same deflection as per the equivalent sin-
gle-pin device. In this example, the same connection device geometry as that con-
sidered for the sample P-A9 is selected. The theoretical curve proposed for the dou-
ble-pin model is an equivalent tri-linear curve shown in Figure 13a. It is obtained by
doubling the forces PI, PII, and PIII which characterize the behavior of a single-pin
placed in parallel, while experienced the same deformation as per the equivalent pin.
The strain corresponding to one pin belonging to the double-pin device is shown in
Figure 13b.
Figure 12. Double-pin connection device.
a) b)

9. Figure 13. Double-pin connection device: a) theoretical tri-linear curve; b) strain
experienced by one pin.
Thus, by doubling pins, the connection load-carrying capacity doubles, while
the deflection remains the same due to the increasing of the flexural stiffness.
2.5 Fatigue of pin connection devices
The method applied to summarize data as recorded from testing P-3 and P-
A9 under cyclic loading (Plumier et al., 2006) was based on S-N line approach which
is in agreement with Eurocode 3 provisions. In Figure 14, the collected test data of
P-3 and P-A9 samples are plotted in the fatigue resistance curves obtained
according with Eurocode 3. These fatigue resistance curves adopted in Eurocode 3,
are built using a statistical analysis of constant amplitude fatigue test data. In the
case of the P-3 and P-A9 samples, a variable amplitude (ECCS) loading history was
used. However, the direct assessment of the fatigue resistance in not possible and
reference should be made to the cycle-counting method (rainflow) and to a suitable
damage accumulation rule. Thus, the linear damage accumulation rule proposed by
Minner was employed for calculation of an effective value, Seq, which was adopted
instead of S, as an argument in the fatigue failure prediction function. From Figure
14 it is possible to see that the P-3 device is on line 90 of EC3 while P-A9 is on line
80 of EC3. It seems that fatigue behaviour of the pins increases with larger
distances between the inner-plates. This evidence agrees with the dissipated energy
of the pins illustrated above.
EC3 - 100
EC3 - 90
EC3 - 80
EC3 - 71
3,00
3,20
3,40
3,60
3,80
4,00
1,00 1,20 1,40 1,60 1,80 2,00
Log ( S )
Log ( N )
EN1993-1-9
P-3
P-A9
Figure 14. Fatigue resistance curves according to Eurocode 3 with detail category.
Equivalent pin
a) b)

10. 3. CONCLUSIONS AND GENERAL RECOMMENDATIONS
In this paper, the behaviour of a dissipative brace-to-column connection de-
vice is emphasized. The computation is carried out for single- and double-pin con-
nection devices by using the simple beam model, the OpenSees beam model under
monotonic loading and cyclic quasi-static displacement loading. The proposed
model was calibrated against experimental test results. From this study, the follow-
ing recommendations are proposed:
i) The simple beam model can be used for preliminary design applications.
ii) The dissipative energy capacity of connection devices increase if larger dis-
tance between the inner-plates is provided.
iii) Fatigue strength curves like the ones of Eurocode 3 allow predicting the
stress range and number of stress cycles to fatigue failure. Low-cyclic fatigue failure
is not the typical failure mode for these devices.
iv) An OpenSees model calibrated against experimental test results is devel-
oped and may be used for analyzing CBFs with dissipative pin connection devices.
ACKNOWLEDGMENTS
Financial support from the NSERC (Natural Sciences and Engineering Research
Council of Canada) is gratefully acknowledged.
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