Effect of frame connection rigidity on the behavior of infilled steel...
Transcript of Effect of frame connection rigidity on the behavior of infilled steel...
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Earthquakes and Structures, Vol. 19, No. 4 (2020) 227-241
DOI: https://doi.org/10.12989/eas.2020.19.4.227 227
Copyright © 2020 Techno-Press, Ltd. http://www.techno-press.com/journals/was&subpage=7 ISSN: 2092-7614 (Print), 2092-7622 (Online)
1. Introduction
Infill walls are commonly used in buildings for
structural and architectural purposes. Based on extensive
study since 1950, it has been proved that infills have a
significant effect on the lateral stiffness and strength of
structures as well as energy dissipation during earthquakes.
Therefore, they should not be ignored in the analysis and
design of structures against lateral loads (Moghaddam and
Dowling 1987).
Several models have been proposed to consider the
effects of infill panels on structures in previous five
decades. One of these models is the equivalent diagonal
strut model that was firstly proposed by Polykov (1960) and
Holmes (1961). In this model the infill panel is replaced by
an equivalent diagonal strut that acting in compression to
resist the lateral loading. Several studies such as Stafford-
Smith and Carter (1969) and Mainstone (1971) have been
carried out to developed methods based on an equivalent
strut analogy. This model is also recommended by seismic
guidelines such as FEMA356 (2000) and ASCE41-06
(2006) to model the infills. Some studies (Mander et al.
1993, Dawe and Seah 1989, El-Dakhakhni et al. 2003,
Moghaddam 2004, Moghaddam et al. 2006, Mohammadi
2007, Kaltakcı 2006, Liu and Manesh 2013, Motovali and
Mohammadi 2016, Mohammadi and Motovali 2019,
Mohamed and Romao 2018, Hashemi et al. 2018,
Yekrangnia and Mohammadi 2017) were also focus on the
in-plane behavior of infilled steel frames and several
methods and equations were proposed to predict the
Corresponding author, Assistant Professor E-mail: [email protected]
aAssociate Professor
strength as well as the stiffness of infilled frames. The
proposed models, such as Mainstone (1971) and Flanagan
and Bennet (1999), can estimate the stiffness and strength
of infilled frames, acceptably. From other point of view, the
proposed equations were obtained based on experiments
and analyses of infilled moment resistant frames on which
the beams to columns connections were almost rigid.
However, many infilled frames with semi-rigid and pinned
connections are available in practical cases. Therefore,
using the proposed methods to determine the behavior of
infilled frames without rigid connections is doubtful.
A number of studies have focused on the infilled steel
frames which had not rigid connections. Dawe and Seah
(1989) found out that the infill in a pinned connection frame
has less stiffness and strength as well as lower ductility,
compared with one in a rigid connection frame. Flanagan
and Bennet (1999) preformed a series of experiments on
steel frames with structural clay tile infills. The steel beams
connected to column by double clip angles. The results
show that the stiffness and strength of the specimens were
about half of the values calculated by Mainstone (1971)
formula. Three one-third scale, one-bay, and two-story
specimens with various connection types, including rigid
connection, partially-restrained connection and flush end
plate connection were exerted under reversed cyclic lateral
load (Yan 2006, Peng et al. 2008, Fang et al. 2008). They
reported that the infill specimen which have rigid
connections frame led to shear slip failure mode along the
top interface of base reinforcing cage, the specimen with
semi-rigid connections showed shear slip failure along the
top interface of the second story because low-cycle fatigue
fracture of shear connectors, and the diagonal crush of infill
walls was occurred in the specimen with flush end plate
connections (Sun et al. 2011). Sakr et al (2019) numerically
studied infilled frames with five different beam-to-column
Effect of frame connection rigidity on the behavior of infilled steel frames
Sayed Mohammad Motovali Emami1 and Majid Mohammadi2a
1Department of Civil Engineering, Najafabad Branch, Islamic Azad University, Najafabad, Iran 2International Institute of Earthquake Engineering and Seismology, No. 21, Arghavan St., North Dibajee, Farmanieh, Tehran, Iran
(Received February 17, 2019, Revised June 3, 2020, Accepted October 5, 2020)
Abstract. An experimental study has been carried out to investigate the effect of beam to column connection rigidity on the behavior of infilled steel frames. Five half scale, single-story and single-bay specimens, including four infilled frames, as well
as, one bare frame, were tested under in-plane lateral cyclic reversal loading. The connections of beam to column for bare frame
as well as two infill specimens were rigid, whereas those of others were pinned. For each frame type, two different infill panels
were considered: (1) masonry infill, (2) masonry infill strengthened with shotcrete. The experimental results show that the
infilled frames with pinned connections have less stiffness, strength and potential of energy dissipation compared to those with
rigid connections. Furthermore, the validity of analytical methods proposed in the literature was examined by comparing the
experimental data with analytical ones. It is shown that the analytical methods overestimate the stiffness of infilled frame with
pinned connections; however, the strength estimation of both infilled frames with rigid and pinned connections is acceptable.
Keywords: masonry infill; connection rigidity; stiffness; strength; energy dissipation; steel frame
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Sayed Mohammad Motovali Emami and Majid Mohammadi
connection types. They found that the infilled frames with
welded connections had the highest initial stiffness and
load-carrying capacity. However, the infilled frames with
extended endplate connections (without rib stiffeners)
showed the greatest energy dissipation capacity.
Most of the proposed macro models in the literature are
verified only for infilled frame with rigid connections.
Many researchers and engineers ignore the effect of pinned
connection in assessment of infilled frame structures. This
study intends to present an experimental program which
investigates the effect of beam to column connection
rigidity on behavior of masonry infilled steel frames. For
this purpose, four infill specimens as well as one bare frame
were tested by applying cyclic in-plane lateral loading at the
roof level. Two infilled frames were strengthened by
applying the shotcrete on both sides of masonry panel. The
main test variables are the beam to column connection
rigidity and applying the shotcrete to the masonry infills.
Furthermore, the efficiency of some well-known proposed
methods is assessed.
2. Test specimens
Five half scaled specimens consisted of four infilled
frames and one bare frame were tested to investigate the
influence of rigidity of beam to column connections on the
in-plane behavior of the steel infilled frames. The specimen
frames were selected from the first story of the interior bay
of a four-story building. It should be noted that due to
experimental limitation, the axial load of the column and
gravity load on the beam were not applied and only lateral
load was exerted to the specimen during testing as it is
regular in the literature. The prototype building was
designed in accordance with the third edition of Iranian
seismic design code standard No.2800 (2005) and AISC-
ASD01 (2001) steel code of practice. The service dead load
and the live load of the building were assumed as 600 and
200 kg/m2, respectively. The height, length and infill
thickness of the selected frame from the first story were
300, 450 and 20 cm, respectively. The main frame was
made of 2IPE400 section for column and IPE300 standard
section for beam. The scaling method recommended by
Harris and Sabnis (1999) was employed to scale the steel
frame. The scaling ratio was selected based on limitation of
frame height which can be tested in the laboratory. The
practicable frame height was chosen to be 150 cm which
was the half of the main frame height. Consequently, the
scaling ratio was considered as 1:2 of the prototype
dimension. As a result, the height and length of the
specimens were 150 cm length and 225 cm respectively.
Applying the 1:2 scale ratio, the second moment area and
section aria should multiplied by (1/2)4 and (1/2)2,
respectively. Considering the available steel section in
market, the beam and column sections of the frames were
IPBL120 (A=25.3 cm2, Ixx=606 cm4 d=11.4, bf=12, tf=0.8,
tw=0.5 cm) and IPBL180 (A=45.3 cm2, Ixx=2510 cm4
d=17.1, bf=15, tf=0.95, tw=0.6 cm), respectively.
The general properties of the specimens are summarized
in Table 1. The bare frame as well as two infill specimens
had rigid connections of beam to column, while the two
others had pinned connections. The first column of Table 1
shows the name of the specimens. The bare frame was
named BF, while in the infill specimens, the names start
with letters M or S2 indicated the material of infill panel;
the former stand for “Masonry” infills and the later stand
for masonry infills with “Shotcrete” on both sides. The
second part of specimen names denotes the type of beam to
column connections; RC represents Rigid Connection and
PC indicates Pinned Connection. The last part, 1B, shows
that the specimens have 1 Bay. Dimensions of the infill
panels were 207.9 cm in length, 138.6 cm in height and 10
and 15 cm thickness for specimens with masonry infill
panel and masonry panel strengthened by shotcrete,
respectively, as shown in Fig. 1(a). The strengthened infill
panels include 10 cm clay masonry brick and 2.5 cm
shotcrete applied to each side of the masonry infills.
Moreover, a mesh of Ø2.5 mm@10 cm was utilized in
middle part of each shotcrete layer.
3. Test setup
The test setup is illustrated in Fig. 1(a). In-plane cyclic
lateral load was applied by a hydraulic actuator. The
maximum capacity of actuator was 500 kN with stroke of
±150 mm. The actuator was connected to a stiff triangle
support attached to the strong floor of laboratory. The
positive and negative directions of lateral loading, which
will be used in the following of the paper, are shown in Fig.
1(a). A bracing system was attached to the two ends of top
frame beam to prevent undesirable out-of-plane movement,
as shown in Fig. 2. All specimens were constructed and
tested in the structural laboratory of International Institute
of Earthquake Engineering and Seismology (IIEES). The
lateral load was exerted to a loading beam which is
connected to the frame through shear keys. These shear
keys were welded to the top beam and columns of the
infilled frame, shown in Fig. 1(b). The corresponding
arrangement leads to an approximately uniform distribution
of lateral loading along the top beam of frame as it is done
in the practical cases in which the lateral load of earthquake
Table 1 Summary of specimens
Specimen Column Beam Infill Beam to column connection
BF IPBL 180 IPBL 120 - rigid
M-RC-1B IPBL 180 IPBL 120 Masonry rigid
S2-RC-1B IPBL 180 IPBL 120 Masonry+2layers shotcrete rigid
M-PC-1B IPBL 180 IPBL 120 Masonry Pinned
S2-PC-1B IPBL 180 IPBL 120 Masonry+2layers shotcrete Pinned
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Effect of frame connection rigidity on the behavior of infilled steel frames
at the floor level distributed to the lateral resisting elements.
Relative lateral displacement of the specimens was
measured by two LVDTs installed along the top and bottom
beams of the frames, as shown in Fig. 1(a).
Due to the available group holes of the strong floor and
fix distance between them, the columns base plates were
arranged in such a way that its behavior is different in each
direction of loading. Noted that, the base plates are fixed
when the specimen is loaded in the positive direction but
they can rotate when the lateral loading is applied in the
negative direction, as shown schematically in Fig 1(c) and
1(d).
The rigid connections were provided with two plates
dimensions of which are 18×10×0.8 cm at top and bottom
of the beam flanges. The flange plates were connected to
the column using complete joint penetration (CJP) welding
and the fillet welding with thickness of 5 mm was used to
connect the plates to the beam flanges. Moreover, two 12 ×
8 × 0.6 cm plates were used to connect the web of beam to
the column face using fillet welding. The pinned connection
is fabricated by the application of just mentioned web
plates.
Fig. 1 Test setup: (a) schematic view, dimension in mm; (b) detail of shear key in the lateral loading setup; (c) rigid
connection of column base plate in the positive direction; (d) rotation of base plate when load is applied in the negative
direction; (e) rigid connection; (f) pinned connection
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Sayed Mohammad Motovali Emami and Majid Mohammadi
A 2 cm gap is provided between the beam and column to
prevent possible bending moment transfer in pinned
connection. The details of rigid and pinned connections are
illustrated in Fig. 1(e) and 1(f), respectively.
4. Material properties
All of the infill walls were constructed by an
experienced mason to minimize workmanship effects. The
brick masonry units were pre-soak before using for the
construction of the infills in Accordance with Iranian
National Building code-part 8 (2005) which cause an
improvement in the bond strength of the mortar-brick
interface. Solid brick units with a dimension of 20×10×5
cm were utilized in the infill. Twelve Standard masonry
prisms were made during the infill construction. These
prisms had the same curing time of the panels and were
tested in the same time of the infilled frames testing. Each
prism consisted of three brick units and two layers of mortar
in which the height to thickness was 2. The mean
compressive strength, fʹm and the modules of rapture Em of
the standard masonry prisms were measured as 9.5 MPa and
1800 MPa, respectively, as per ASTM C1314 (2004). The
mortar mixture were composed of 1 part cement type II and
6 parts sand. Twelve 50 mm standard cube of mortar were
tested to determine compressive strength of the mortar in
accordance with ASTM C-109 (2002). The mean mortar
compressive strength was obtained 8.3 MPa with standard
deviation of 1.2 MPa.
Six steel coupon specimens were supplied to determine
steel properties of the frames and tested in accordance with
ASTM E8/E8M (2009). These specimens were provided
from the beam and column sections. The mean yield and
ultimate stress of the steel were 294 and 488 MPa, with
corresponding strains of Ԑy=0.00162 and Ԑu= 0.161
mm/mm, respectively. The mean module of elasticity, Es for
the steel was determined 185 GPa.
Fig. 3 Displacement pattern applied
5. Loading protocol
A displacement control loading proposed by FEMA461
(2007) was applied to the specimens. The applied
displacement history consists of 28 repeated cycles of step-
wise increasing deformation amplitude. The displacement
controlled cycles start from an amplitude of 1.7 mm which
is gradually increased by multiplying 1.4 to the previous
amplitude until the last cycle amplitude reaches 135 mm.
Each cycle was applied twice in order to determine stiffness
degradation and strength deterioration. The applied
displacement history is presented in Fig 3. The test was
continued up to the lateral displacement of 135 mm
(corresponding to drift of 9%) unless a severe damage was
observed in the specimen, test setup or instruments.
6. Experimental results
6.1 Specimen BF behavior
The first specimen was bare frame with rigid
connections. The load-displacement relation is shown in
Fig. 4(a). The initial stiffness was 9.5 kN/mm in the positive
direction which was slightly more than the theoretical value
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pla
cem
ent
(mm
)
Cycle No.
(a) (b)
Fig. 2 Bracing system to prevent out of plane movement (a) side view. (b) top view
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Effect of frame connection rigidity on the behavior of infilled steel frames
9.1 kN/mm. The initial stiffness was obtained 7.45 kN/mm
in the negative direction. Yielding in the specimen started at
the drift of 1.7%, in which plastic hinge was created at the
column in the base and both ends of the top beam. The
yielding was obviously observed through the spalling of
plaster.
The peak load was 254 kN and 215 kN in the positive
and negative direction, respectively, both occurred in the
drift of 3.6%. After this drift the load was reduced as the
result of damage in the beam to column connections. The
beam-column connection was completely failed at the drift
of 5.3% and the test was terminated subsequently. It should
be noted that the difference of the stiffness or the strength
for positive and negative directions is attributed to the
difference in the rigidity of columns base plates, as depicted
in Figs. 1(c) and 1(d); at the positive direction the base
plates were rigid, while in the negative direction the base
plates were free to rotate. By comparing the initial stiffness
of specimen BF with that of analytical model, it is found out
that the rotational rigidity of column-base plate connections
in negative direction is equal to 1.5e4 kN.m/rad. The
envelope of hysteresis curve with indicated important
observation is illustrated in Fig. 4(b).
6.2 Specimen M-RC-1B behavior
The second specimen was a masonry infilled frame with
Fig. 6. Practical stiffness of infilled frames (Motovali
Emami and Mohammadi (2016))
rigid connections of beam to column. The hysteresis curve
of the specimen is depicted in Fig. 5(a). The stiffness of
infilled frames remains almost constant after occurrence of
interface cracking up to infill cracking. In other words the
interface cracking normally occurs at the first few cycles of
earthquake shaking, in very small story drifts. The stiffness
of infilled frame is very high before the interface cracking.
Just after that, the stiffness of the infilled frame is reduced
to the practical stiffness which was firstly proposed by
Mohammadi (2007). Although the issue of the appropriate
(a) (b)
Fig. 4 (a) Lateral load-drift relation, (b) backbone curve for specimen BF
(a) (b)
Fig. 5. (a) Lateral load-drift relation, (b) backbone curve for specimen M-RC-1B
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Late
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oad
(kN
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Drift (%)
BF
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oad
(kN
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Drift (%)
Begining of beam to column connection
damage
Beam to column connection failure
Beam to column connection failure
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oad
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M-RC-1B
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oad
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Occurrence of inclined cracking
Terminate the test due to excessive out of plane movement
Occurrence of inclined cracking
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Sayed Mohammad Motovali Emami and Majid Mohammadi
Fig. 8 Cracking pattern and failure mode at the end of the
test of specimen M-RC-1B
stiffness value for infilled frames widely investigated in
literature, the authors believe that the practical stiffness
represents the actual stiffness of infilled frame during a
moderate earthquake. Furthermore, the practical stiffness
does not depend on the contact properties of the infill to the
frame, which may vary considerably even in similar
specimens, as shown in (2007). The practical stiffness is the
slope of a line tangent to the load-displacement envelope
curve after the occurrence of interface cracking, as
illustrated in Fig. 6. The practical stiffness of the specimen
was obtained 10.64 and 8.4 kN/mm in the positive and
negative directions, respectively. The maximum strength
was 325 and 218 kN in the positive and negative directions
which were occurred at the drift of 5.1% and 3.5%,
respectively.
The backbone curve of the specimen is depicted in Fig.
5(b). The most significant events that occur during the test
are shown in Fig. 5(b). The inclined cracking was initiated
at the drift of 1.1% at approximately 65˚ against horizontal
axis in both directions. The cracks were propagated through
the infill panel which lead to formation of two compression
struts in each direction of loading as schematically depicted
in Fig. 7. The struts were initiated at top of windward
column and bottom of leeward column and continued to the
opposite beam at approximately 65˚. In Fig. 7, by increasing
the drift, the color of cracks becomes darker. The test was
stopped at the drift of 7.4%, due to out of plane movement
of the specimen in the negative direction. This event has
exacerbated the difference between the strength of the
specimen in positive and negative directions. As it can be
seen in Fig. 8, the predominant failure mode of the
specimen was diagonal cracking and no corner crushing can
be observed at the end of the test.
6.3 Specimen S2-RC-1B behavior
This specimen was similar to specimen M-RC-1B but
two 2.5 cm thickness layers of shotcrete were applied on
both sides of the masonry infill. The load-lateral drift
relationship and corresponding backbone curve are shown
in Fig. 9. The practical stiffness values were 80 and 53
kN/mm in the positive and negative directions, respectively.
The interface cracking was occurred at the initial cycles of
loading. The cracking pattern could not be observed on the
infill panel because shotcrete layers covered the masonry
infill panel. The first major damage observed in the
specimen was due to corner crushing in the left bottom of
the infill panel at the drift of 0.68%, which coincided with
the peak lateral load. The maximum lateral strength values
were 458 and 405 kN in the positive and negative
directions, respectively. By increasing the amplitude, the
corner crushing occurred in other corner of infill panel as
well as developing of two plastic hinges at the top and
bottom of columns. Fig. 10 shows the corner crushing of the
infill and the plastic hinge of the columns in the specimen at
the end of the test.
6.4 Specimen M-PC-1B behavior
This specimen was a pinned frame with masonry infill
panel. The hysteresis behavior curve of this specimen is
shown in Fig. 11(a). The practical stiffness of this specimen
was reduced by 57% in comparison with M-RC-1B and was
(a) Left loading (b) Right loading
Fig. 7 Cracking pattern and formation of compression strut in specimen M-RC-1B
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Effect of frame connection rigidity on the behavior of infilled steel frames
measured 5.6 and 3.6 kN/mm in the positive and negative
directions, respectively. The peak load of the specimen was
290 kN at the drift of 5.5% in the positive direction and 185
kN at the drift of 3.7% in the negative direction. The major
observed damage in the infill panel was inclined cracking.
This cracking was initiated at the drifts of 0.57% and 0.68%
in the positive and negative directions, respectively, as
shown in Fig. 11(b). The damage in the plate of pinned
connections was initiated at the drift of 3.5%. Afterward,
the pinned connections of the top beam were completely
failed (as shown in Fig. 12) at the drift of 5.5% and 4.8% in
the positive and negative directions, respectively and
therefore the test was terminated. The most important
events and their corresponding drifts during the test are
shown in Fig. 11(b). The cracking pattern of the infill panel
and their corresponding drifts in each direction are shown in
Fig. 13. One can observe that similar to specimen M-RC-
1B, two inclined compression struts have been developed in
the infill panel.
6.5 Specimen S2-PC-1B behavior
The last specimen was similar to specimen S2-RC-1B,
but the connections of beam to column were pinned. The
hysteresis behavior and the corresponding backbone curve
are depicted in Fig. 14. The practical stiffness values were
52 and 32.7 kN/mm in the positive and negative directions,
respectively. The peak lateral load was 293 kN in the
(a) (b)
Fig. 9.(a) Lateral load-drift relation, (b) backbone curve for specimen S2-RC-1B
Fig. 10. Failure mode of specimen S2-RC-1B
(a) (b)
Fig. 11 Lateral load-drift relation; (b) backbone curve for specimen M-PC-1B
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oad
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oad
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Occurrence of corner crushing
Occurrence of corner crushing
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oad
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Occurrence of inclined cracking
beam to column connection failure
Occurrence of inclined cracking
beam to column connection failure
Begining of damage in connection plate
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Sayed Mohammad Motovali Emami and Majid Mohammadi
positive direction and 248 kN in the negative direction,
which were occurred at the drifts of 0.56% and 0.7%,
respectively.
The initiation of damage in the plate of pinned
connection also occurred in these drifts. Consequently, the
increasing trend of strength was stopped and the strength of
the specimen remained almost constant or diminished until
the end of the test. The connections of top beam to columns
were completely failed at 2.5% and 2.3% drifts in the
positive and negative directions, respectively. Fig. 15 shows
the pictures of failed pinned connection at the two ends of
top beam. The behavior of the specimen after failure of
pinned connections is distinguished by dashed line in the
backbone curve in Fig. 14(b). The predominant failure
mode of the specimen after the occurrence of first
connection failure is illustrated in Fig. 16. One can see that
no major damage could be observed in the infill panel.
7. Comparison of the specimens
A comparison between the hysteresis envelopes of the
Fig. 12. Failure of pinned connection in specimen M-PC-1B
(a) Left loading (b) Right loading
Fig. 13 Crack pattern and formation of compression strut in specimen M-PC-1B
(a) (b)
Fig. 14 (a) Lateral load-drift relation (b) backbone curve for specimen S2-PC-1B
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oad
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oad
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beam to column connection failure
beam to column connection failure
beginning of damage on beam to column
connection plate
beginning of damage in beam to column connection plate
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Effect of frame connection rigidity on the behavior of infilled steel frames
Fig. 16 Failure mode of specimen S2-PC-1B
specimens is illustrated in Fig. 17(a). Table 2 summarizes
the key values for stiffness (K) and strength (P) parameters
of the specimens and their corresponding infill to strength
stiffness (λh). In this table, the sign + and – refer to the
positive and negative directions, respectively. Moreover, the
subscripts in, cr, p and m represent the initial, first major
cracking, practical and maximum values, respectively, and
K0.5Pm shows the secant stiffness at 0.5Pm. The λh is a non-
dimensional parameter expressing the relative stiffness of
infill to the frame which can be determined by (Stafford-
Smith and Carter 1969)
col
colfe
mh h
hIE
tE 41
inf
inf
4
2sin
(1)
Where, hcol is the height of the column, Em is the
modulus of elasticity of the infill panel, tinf is the thickness
of the infill, θ is the angle of the infill diagonal with respect
to the horizontal, Efe and Icol are the modulus of elasticity
and flexural rigidity of the columns, respectively and hinf is
the height of the infill panel. One should be noted that the
connection rigidity of surrounding frame have not effect on
the λh parameter. The module of elasticity of multilayer
infill panels (the specimens with masonry + shotcrete infill)
is calculated by the following formula
n
i
i
n
i
ii
t
t
Et
E
1
1
)( (2)
Where, ti and Ei are the thickness and module of
elasticity of i-th layer, respectively.
According to Table 2, comparing the infill specimens
with bare frame shows that the presence of infill improved
the in-plane stiffness and lateral strength of the system. The
peak load of specimens M-RC-1B and S2-RC-1B were
respectively 1.3 and 1.8 times of specimen BF in positive
direction. Comparing to bare frame, the masonry infill and
shotcreted masonry infill panels increased the initial
stiffness of specimens M-RC-1B and S2-RC-1B by 3.7 and
10 times, respectively. While, the secant stiffness K0.5Pm of
them increased by 1.45 and 8.5 times, respectively. It
should be noted that, the marginal difference between the
peak loads of specimens M-RC-1B (218 kN) and BF (215
kN) in the negative direction is attributed to the loss of the
strength of specimen M-RC-1B due to out of plane
movement in the negative direction as previously
mentioned.
By comparing the values presented in Table 2, it is
obvious that the stiffness and strength of infilled frames
depends directly on the connection rigidity of surrounding
frame. Comparing to specimens with rigid connections, M-
RC-1B and S2-RC-1B, the practical stiffness of specimens
with pinned connections, M-PC-1B and S2-PC-1B, were
averagely decreased by 52% and 36%. Moreover, the
maximum strength of M-PC-1B and S2-PC-1B were
respectively reduced by 11% and 37% (with respect to the
same infilled frame with rigid connections). According to
the results, the difference between the strength of specimens
due change in frame connection (PC to RC) with higher λh
is more notable than specimen with lower λh. It can be
attributed to occurrence of damage at lower drift in pinned
connection of specimen with higher λh=3.4 (S2-PC-1B) in
comparison with the specimen with lower λh=2.4 (M-PC-
1B). Consequently, the damage in the connections of the
surrounding frame leads to reducing the maximum strength
of the system.
The potential of specimens to dissipate energy in the
structures can be characterized using damping. The
damping of infilled frames is caused by opening and closing
of cracks and sliding of masonry materials along the cracks
and bed joints as well as nonlinear response of the
surrounding frame due to inelastic deformation of the
structure. The amount of damping in actual structures is
usually represented by equivalent viscous damping. The
(a) (b)
Fig. 15 Failure of pinned connections of top beam in specimen S2-PC-1B at (a) left side, (b) right side
235
-
Sayed Mohammad Motovali Emami and Majid Mohammadi
most common method for defining equivalent viscous
damping is to equate the energy dissipated in a vibration
cycle of the actual structure and an equivalent viscous
system (Chopra 2001). This damping can be calculated as
ξeq=ED/(4 πES), where ED is the amount of energy dissipated
by the actual structure in one completed cycle which is
equal to the area enclosed by hysteresis loop. ES is the
amount of elastic strain energy stored in the peak of cycle,
defined as the half of the maximum displacement multiply
by the corresponding load. The equivalent viscous damping
of the specimens against the drift is drawn and shown in
Fig. 17(b). It can be seen that the damping ratio in the all
specimens increase as the drift is increased except in
specimen S2-PC-1B in which the damping ratio remains
constant after the drift of 3%. It is attributed to the failure of
the connections at this drift as it mentioned in previous
section. The difference between damping ratios of the
specimens with the same infill properties are not
considerable in the low drifts, however, in higher drifts,
damping ratios of the rigid connection specimens exceeds
(a) (b)
Fig. 17 Comparison of (a) envelop curves (b) equivalent viscous damping ratio
Table 2 The important values of strength and stiffness and corresponding drifts of specimens
Specimen λh Kinitial
(kN/mm)
Kpactical
(kN/mm)
K0.5Pm
(kN/mm) Pcr (kN) δcr (%) Pm (kN) δm (%)
BF - 9.5 - 9.33 - - 254 3.63
7.44 - 6.77 - - -215 -2.6
M-RC-1B 2.4 35 10.6 13.5 121.4 0.53 325 5.07
-39 -8.4 11.2 -98.6 -0.56 -218 -3.5
M-PC-1B 2.4 52 5.6 8.7 200.9 1.8 290.2 5.46
-29 -3.7 5.4 -105.2 -1.37 -185.3 -3.72
S2-RC-1B 3.4 95 80 79.1 302.5 0.27 458 0.63
-118 -53 -87 -331.7 -0.32 -405 -0.66
S2-PC-1B 3.4 112 52 98.9 196.1 0.16 292.8 0.56
-72 -32.7 -55.8 -131.9 -0.165 -247.9 -0.7
(a) (b)
Fig. 18 (a) Experimental and numerical backbone curve of specimen BF, (b) numerical behavior of bare frame with pinned
connections
-500
-400
-300
-200
-100
0
100
200
300
400
500
-8 -6 -4 -2 0 2 4 6 8
Late
ral l
oad
(kN
)
Drift (%)
BF
M-RC-1B
S2-RC-1B
M-PC-1B
S2-PC-1B0
5
10
15
20
25
0 1 2 3 4 5 6 7 8
Equ
ival
en
t vi
sco
us
dam
pin
g ra
tio
(%
)
Drift (%)
BFM-RC-1BS2-RC-1BM-PC-1BS2-PC-1B
0
50
100
150
200
250
300
0 1 2 3 4 5
Late
ral l
oad
(kN
)
Drift (%)
BF (RC) Experimental
BF (RC) Numerical
0
50
100
150
200
250
300
0 1 2 3 4 5
Late
ral l
oad
(kN
)
Drift (%)
BF (PC) Numerical
236
-
Effect of frame connection rigidity on the behavior of infilled steel frames
those of pinned connection specimens. It is mainly
attributed to the occurrence of damage in the connection
joints of pinned connection specimens. Thus, the specimens
with pinned connections dissipate lower energy in
comparison with the specimens with rigid connections.
Since the behavior of infilled frame are controlled by the
response of both infill wall and surrounding frame, the
reduction in stiffness and strength may be attributed to
lower rigidity of frame or decrease in contact length
between infill and frame or both of them. For this reason,
more accurate analysis should be carried out to evaluate the
contribution of infill panel in the specimens with rigid and
pinned connections. Therefore, it is necessary to have the
load-displacement behaviors of bare frames with rigid and
pinned connections. The capacity curve of bare frame with
rigid connections (specimen BF) was presented in previous
section and the behavior of bare frame with pinned
connections was obtained through numerical analysis.
Finite element method was utilized for the numerical
analyses. Having reliable results in finite element analysis,
the numerical analysis method was verified by the output
obtained from experimental investigation of specimen BF.
For this purpose nonlinear pushover analysis was performed
using ABAQUS (2012). All frame elements were modeled
using deformable solid element, C3D8R, available in
ABAQUS (2012). The material properties of steel for the
numerical analysis were from the steel coupon test results.
Fig. 18(a) compares the capacity curve of specimen BF
(bare frame with rigid connection which noted as BF (RC)
here), obtained from numerical analysis with envelope of
hysteresis curve of the experimental result in positive
direction. It can be seen that the behavior of specimen BF is
predicted accurately up to drift of 3.6% at which the
damage of frame connections was initiated in the
experimental test. Therefore, it can assure that the results of
finite element analysis are reliable and this method can be
used for extracting the behavior of bare frame with pinned
connections with acceptable accuracy. Fig. 18(b) shows the
pushover curve of the bare frame with pinned connections,
BF (PC), obtained by numerical analysis.
Table 3 Experimental and analytical stiffness comparison
Specimen
Strut width (mm)
Flanagan &
Bennet Mainstone
Stafford-Smith &
Carter
M-RC-1B 227 309 989
227 309 989
M-PC-1B 227 309 989
227 309 989
S2-RC-1B 143 257 622
143 257 622
S2-PC-1B 143 257 622
143 257 622
The infill contributions of the masonry infill specimens
(λh=2.4) and shotcreted masonry ones (λh=3.4) are shown in
Fig 19(a) and 19(b), respectively. According to Fig 19(a), it
can be observed that in the both specimens with rigid and
pinned connections, the major behavior of masonry infilled
frame (λh=2.4) is controlled by the surrounding frame.
Moreover, the infill contribution of specimen M-RC-1B is
approximately twice of that of specimen M-PC-1B up to a
drift of 2.2%. Afterward, the infill contribution of specimen
M-PC-1B is increased to that of specimen M-RC-1B. This
is attributed to increasing the interaction between the frame
and infill of specimen M-PC-1B by increasing the drift,
which leads to increase the contribution of infill panel.
Focusing on the contribution of infill panel in the
specimens with shotcreted masonry (λh=3.4) indicates that
the behavior of the infilled frames is mostly controlled by
infill panels, as shown in Fig. 19 (b). The curves related to
specimen S2-PC-1B are drawn up to the drift of 2.5%,
corresponding to the beam to column connections failure. It
is evident that the infill contribution of the specimen with
rigid connections (S2-RC-1B) is greater than that of
specimen with pinned connections (S2-PC-1B). It is mainly
due to early occurrence of damage in pinned connections of
specimen S2-PC-1B at the drift of 0.56% leading to
decrease in infill panel contribution. In summary, it can be
concluded that contribution of infill is reduced by changing
(a) (b)
Fig. 19 Comparison between infill contribution of infilled frames with rigid and pinned connections in (a) specimens with
masonry infill (λh=2.4); (b) specimens with masonry + shotcrete infill (λh=3.4)
0
50
100
150
200
250
300
350
400
0 1 2 3 4 5
Late
ral l
oad
(kN
)
Drift (%)
M-RC-1BBF (RC) 0Contribution of M-RC-1B infillM-PC-1BBF (PC)Contribution of M-PC-1B infill
0
50
100
150
200
250
300
350
400
450
500
0 1 2 3 4 5
Late
ral l
oad
(kN
)
Drift (%)
S2-RC-1BBF-RCContribution of S2-RC-1B infillS2-PC-1BBF (PC)Contribution of S2-PC-1B infill
237
-
Sayed Mohammad Motovali Emami and Majid Mohammadi
the connection type from rigid to pin which is more
intensive for specimen with higher λh.
8. Accuracy of analytical formulas to estimate the strength and stiffness
To examine the efficiency of proposed methods in the
literature for estimation of stiffness and strength of infilled
frames, the test results have been compared with computed
parameters by analytical equations. For this purpose,
Mainstone (1971), Flanagan and Bennet (1999), (2001),
Stafford-Smith and Carter (1969) methods are considered.
These methods are recommended by FEMA 356 (2000),
Masonry Standards Joint Committee (MSJC) (2012) and
Canadian masonry design standard, CSA S304 (2004),
respectively. In these methods, it is assumed that the infill
panel is replaced with an equivalent compression strut. The
equivalent strut has the same thickness and module of
elasticity of the infill panel and the strut width is calculated
by proposed formula in each method. Stafford-Smith &
Carter (1969) give the strut width as
2a (3)
Mainstone (1971) gives the width of equivalent strut as
inf
4.0)(175.0 rha col (4)
and Flanagan and Bennet (1999) propose the following
formula for calculation of strut width
cosCa (5)
Where, rinf is the diagonal length of infill panel and C is
an empirical constant which is proposed as 10.47 cm by
Masonry Standards Joint Committee (2012). To estimate the
Table 4 Experimental and analytical stiffness comparison
Specimen
Stiffness (kN/mm)
K1/Kp K2/Kp K3/Kp Kp
Flanagan &
Bennet (K1)
Mainstone
(K2)
Stafford-
Smith &
Carter (K3)
M-RC-1B
10.64 18.91 22.24 48.85 1.78 2.09 4.59
-8.4 -16.59 -19.92 -45.62 1.98 2.37 5.43
M-PC-1B
5.6 16.68 20.07 46.79 2.98 3.58 8.36
-3.59 -14.44 -17.78 -43.57 4.02 4.95 12.14
S2-RC-1B
80.3 46.04 71.58 136.05 0.57 0.89 1.69
-52.63 -42.99 -67.52 -128.70 0.82 1.28 2.45
S2-PC-1B
52 43.98 69.64 134.41 0.85 1.34 2.58
-32.76 -40.93 -65.53 -126.90 1.25 2.00 3.87
Avg. of RC 1.29 1.66 3.54
Std 0.60 0.60 1.52
COV(%) 46.7 36.0 43.0
Avg. of PC 2.27 2.97 6.74
Std 1.29 1.41 3.78
COV(%) 56.7 47.4 56.1
Table 5 Experimental and analytical strength comparison
Specimen
Ultimate strength (kN)
P1/Pm P2/Pm
Pm
P3/Pm
Flanagan & Bennet
(P1) Pm
Flanagan &
Bennet (P1)
Mainstone
(P2)
Stafford-
Smith &
Carter (P3)
M-RC-1B
325 370.5 467 990 1.14 1.44 3.05
-218 -320.5 -417 -940 1.47 1.91 4.31
M-PC-1B
290.2 340.5 437 960 1.17 1.51 3.31
-185.3 -270.5 -367 -890 1.46 1.98 4.80
S2-RC-1B
458 482.6 583 1087 1.05 1.27 2.37
-405 -447.6 -548 -1052 1.11 1.35 2.60
S2-PC-1B
292.8 328.6 429 933 1.12 1.47 3.19
-247.9 -302.6 -403 -907 1.22 1.63 3.66
Avg. of RC 1.19 1.49 3.08
Std 0.16 0.25 0.75
COV(%) 13.7 16.6 24.3
Avg. of PC 1.24 1.64 3.74
Std 0.13 0.20 0.64
COV(%) 10.4 12.3 17.1
238
-
Effect of frame connection rigidity on the behavior of infilled steel frames
lateral stiffness of infilled frame, the equivalent strut with
two-end-pinned connections is added to the bare frame and
then an analysis was carried out using commercial software
SAP2000 (2010). Moreover, the calculated strut widths
based on the above formulas are shown in Table 3. It should
be noted that the strut thickness in both M-RC-1B and M-
PC-1B specimens was 95 mm and in S2-RC-1B and S2-PC-
1B specimens was 145 mm.
For the ultimate strength of the infill panel, the
following equations can be applied regarding the methods
of Mainstone (1971) as well as Stafford-Smith and Cater
(1969)
cosinfinf mU ftaH (6)
Flanagan and Bennet (1999) give the strength of infill
panel as
multU ftKH infinf (7)
In which, Kult is an empirical constant that is proposed to
be 15.24 cm by Masonry Standards Joint Committee
(2012). As it was mentioned earlier the values obtained
from abovementioned formula are related to the strength of
infill panel and must be added to the strength of bare frame
to calculate total capacity of infilled frame.
The comparison between the experimental and
analytical stiffness and strength values of the infill
specimens are shown in Table 4 and Table 5, respectively.
The values with the sign of + and – correspond to the
positive and negative directions, respectively. Table 4 shows
that all methods estimate better the stiffness of infilled
frame with rigid connections, since the pinned connections
reduce the stiffness of the system. It is evident that Stafford-
Smith and Carter (1969) method significantly overestimates
the stiffness of all specimens especially those with pinned
connections showing an overall analytical-to-test mean of
6.74 with a COV of 56.1%. Although, Mainstone (1971)
formula estimates better the stiffness values compared to
Stafford-Smith and Carter (1969), the most precise
estimation of the stiffness is produced by Flanagan and
Bennet (1999) for both infilled frames with rigid and pinned
connections. Liu and Menesh (2013), also, showed that
Flanagan and Bennet (1999) method calculates better the
stiffness of infilled steel frames. In case of Flanagan &
Bennet (1999), the overall analytical-to-test mean stiffness
of rigid connections specimen is 1.29 with a COV of
46.7%, while, it increases to 2.27 with a COV of 56.7% for
specimens with pinned connections.
In case of strength, all methods overestimate the
capacity of the specimens, especially, Stafford-Smith and
Carter (1969). Similar to estimation of stiffness, Flanagan
and Bennet (1999) method shows the best precision in
estimation of strength. The overall analytical-to-test means
are 1.19 with COV of 13.7% and 1.24 with COV of 10.4%
in the specimen with rigid and pinned connections,
respectively. Generally, it is shown that Flanagan and
Bennet (1999) approach provides an improved estimate on
both stiffness and strength of masonry infilled steel frames
compared to the other methods. It shows that, contrary to
stiffness estimation, the strength is calculated with an
approximately same analytical-to-test ratio in both
specimens with rigid and pinned connections. One can
conclude that the proposed equations in the literature
overestimate the stiffness of infilled frame with pinned
connections, but, can appropriately provide the strength of
this type of infilled frames. On the other hand, based on the
results in this study, a reduction factor is needed in the
calculation of strut width to consider the effect of pinned
connections. However, the estimated strength by these
formulas is reliable for infill specimen with pinned
connections by comparing corresponding values of infill
specimen with rigid connections.
It, also, should be pointed out that these conclusions are
obtained by the results of testing 4 infill specimens. On the
other hand, more experimental and analytical investigations
should be done to provide more generalized conclusions.
9. Conclusions
An experimental program was carried out to investigate
the effect of beam to column connection rigidity on the in-
plane behavior of infilled steel frames. For this purpose,
five half-scaled specimens including four masonry infilled
frames as well as one bare frame were tested under in-plane
lateral loading. The bare frame and two infill specimens
were fabricated with rigid beam to column connections,
while the others have pinned connections. To consider the
effect of relative stiffness of infill to the frame (λh), the infill
panels of two specimens were masonry (λh=2.4) and two
others were masonry with two shotcrete layers applied on
each side (λh=3.4). The strength and stiffness of the infill
specimens were estimated by some proposed conventional
formulas in the literature to check their validity for both
infilled frames with rigid and pinned connections. The
important observations as well as conclusions based on
experimental and analytical investigations can be
summarized as following:
The predominant failure mode of the masonry infill
specimen was observed like inclined cracking in which two
inclined compression struts were formed in the infill panel.
These cracking were initiated from the top of the windward
column and the bottom of the leeward column. The
connection plates of the infilled frames having pinned
connections were failed during the testing. It was observed
that by increasing the λh, the connections failure occurred at
lower drifts, so that the failure of connections in specimen
M-PC-1B and S2-PC-1B were observed at the drifts of
2.5% and 5%, respectively. The presence of pinned
connections instead of rigid connections in the surrounding
frames results in reduction of stiffness and strength of
infilled frames which depends on the λh. It can be said that
by increasing the λh the effects of connection rigidity
become more significant. Moreover, by reduction of beam
to column rigidity, the equivalent viscous damping was also
decreased. The infill contribution in the specimens with
pinned connections was less than that of in the infilled
frames with rigid connections. The mentioned difference
was more significant by increasing the λh. Comparison of
experimental values with analytical ones shows that
239
-
Sayed Mohammad Motovali Emami and Majid Mohammadi
Flanagan and Bennet method provides an accurate estimate
on stiffness of masonry infilled steel frame compared to
other methods, while the Mainstone formula is more
reliable in case of strength. Also, it was concluded that
Flanagan and Bennet method estimates the strength and
stiffness of infilled frame with an acceptable precision
comparing to the other considered methods.
Consequently, the conventional analytical methods
proposed in seismic codes can only be used for modeling of
infill panels in the frames with rigid connections. The
results of this study revealed that these methods
overestimate the stiffness and strength of infilled frames
with pinned connections. Therefore, the authors suggest that
more experimental as well as analytical and numerical
investigations are needed to propose a new macro model for
infilled frames with semi-rigid and pinned connections.
Acknowledgments
This study is supported financially by International
Institute of Earthquake Engineering and Seismology
(IIEES), as well as Organization for Renovating,
Developing and Equipping Schools of Iran under grant No.
7386 and 7387, respectively.
References
ABAQUS user manual (2012), Version 6.12. Dassault Systemes
Simulia Corp, Rhode Island, U.S.A.
AISC Committee (2010), Specification for structural steel
buildings (ANSI/AISC 360-10), American Institute of Steel
Construction, Chicago.
ASCE/SEI Seismic Rehabilitation Standards Committee (2007),
"Seismic rehabilitation of existing buildings (ASCE/SEI 41-
06)", American Society of Civil Engineers, Reston, VA.
ASTM C109 (2002), Standard test method for compressive
strength of hydraulic cement mortars (Using 2-In. or [50-Mm]
Cube Specimens), ASTM Int., West Conshohocken.
ASTM C1314-03b (2004), Standard test method for compressive
strength of masonry prisms, ASTM Int.
ASTM E8/E8M (2009), “Standard test methods for tension testing
of metallic materials”, ASTM Int., West Conshohocken.
Chopra, A.K. (2001), “Dynamics of structures: Theory and
applications to earthquake engineering”, Prentice-Hall.
CSA S304 (2004), Design of masonry structures, Canadian
Standards Association, Mississauga, Canada.
CSI SAP2000 V 14.1 (2010), “Integrated finite element analysis
and design of structures basic analysis reference manual”,
Comput. Struct., Berkeley, U.S.A.
Dawe, J.L. and Seah, C.K. (1989), “Behaviour of masonry infilled
steel frames”, Canada. J. Civil Eng., 16, 865-876.
https://doi.org/10.1139/l89-129.
El-Dakhakhni W.W., Elgaaly, M. and Hamid, A.A. (2003), “Three-
strut model for concrete mansonry-infilled steel frames”, J.
Struct. Eng., 129, 177-185.
https://doi.org/10.1061/(ASCE)0733-9445(2003)129:2(177).
Fang, Y., Gu, Q. and Shen, L. (2008), “Hysteretic behavior of
simi-rigid composite steel frame with reinforced concrete infill
wall in column weak axis”, J. Build. Struct., 2.
FEMA 356 (2000), Commentary for the seismic rehabilitation of
buildings, Federal Emergency Management Agency,
Washington, D.C.
FEMA 461 (2007), Interim testing protocols for determining the
seismic performance characteristics of structural and
nonstructural components”, Federal Emergency Management
Agency.
Flanagan, R.D. and Bennett, R.M. (1999), “In-plane behavior of
structural clay tile infilled frames”, J. Struct. Eng., 125, 590-
599. https://doi.org/10.1061/(ASCE)0733-
9445(1999)125:6(590).
Flanagan, R.D. and Bennett, R.M. (2001), “In-plane analysis of
masonry infill materials”, Practice Periodical Struct. Des.
Construct., 6, 176-182. https://doi.org/10.1061/(ASCE)1084-
0680(2001)6:4(176).
Harris, H.G. and Sabnis, G. (1999), “Structural modeling and
experimental techniques”, CRC Press.
Hashemi, S.J., Razzaghi, J., Moghadam, A.S. and Lourenço, P.B.
(2018), “Cyclic testing of steel frames infilled with concrete
sandwich panels”, Archive. Civil Mech. Eng., 18(2), 557-572.
Holmes, M. (1961), “Steel frames with brickwork and concrete
infilling”, In ICE Proceedings. Thomas Telford, 19, 473-478.
https://doi.org/10.1680/iicep.1961.11305.
https://doi.org/10.1016/j.acme.2017.10.007.
INBC-Part 8 (2005), Design and construction of masonry
buildings, Iranian national building code, part 8. IR (Iran),
Ministry of Housing and Urban Development.
Kaltakcı, M.Y., Köken, A. and Korkmaz, H.H. (2006), “Analytical
solutions using the equivalent strut tie method of infilled steel
frames and experimental verification”, Canada. J. Civil Eng.,
33, 632-638. https://doi.org/10.1139/l06-004.
Liu, Y. and Manesh, P. (2013), “Concrete masonry infilled steel
frames subjected to combined in-plane lateral and axial
loading-an experimental study”, Eng. Struct., 52, 331-339.
https://doi.org/10.1016/j.engstruct.2013.02.038.
Mainstone, R.J. (1971), “On the stiffness and strengths of infilled
frames”, In ICE Proceedings. Thomas Telford, 49, 230.
Mander, J.B. and Nair, B., Wojtkowski, K. and Ma, J. (1993), “An
experimental study on the seismic performance of brick-
infilled steel frames with and without retrofit”, In Technical
Report. National Center for Earthquake Engineering Research
(NCEER).
Masonry Standard Joint Committee (2012), Building code
requirements for masonry structures, ACI S30/ASCE 5/TMS
402, American Concrete Institute, the American Society of
Civil Engineers and The Masonry Society, U.S.A.
Moghadam, H., Mohammadi, M.G. and Ghaemian, M. (2006),
“Experimental and analytical investigation in to crack strength
determination of infilled steel frames”, J. Construct. Steel Res.,
62, 1341-1352. https://doi.org/10.1016/j.jcsr.2006.01.002.
Moghaddam, H. (2004), “Lateral load behavior of masonry
infilled steel frames with repair and retrofit”, J. Struct. Eng.,
130, 56-63. https://doi.org/10.1061/(ASCE)0733-
9445(2004)130:1(56).
Moghaddam, H.A. and Dowling, P.J. (1987), “The state of the art
in infilled frames”, London: Imperial College of Science and
Technology, Civil Engineering Department.
Mohamed, H.M. and Romao, X. (2018), “Performance analysis of
a detailed FE modelling strategy to simulate the behaviour of
masonry-infilled RC frames under cyclic loading”, Earthq.
Struct., 14(6), 551-565.
https://doi.org/10.12989/eas.2018.14.6.551.
Mohammadi, M. (2007), “Stiffness and damping of infilled steel
frames”, Proceedings of the ICE-Structures and Buildings, 160,
105-118. https://doi.org/10.1680/stbu.2007.160.2.105.
Mohammadi, M. and Motovali Emami, S.M. (2019), “Multi-bay
and pinned connection steel infilled frames; An experimental
and numerical study”, Eng. Struct., 188, 43-59.
https://doi.org/10.1016/j.engstruct.2019.03.028.
Motovali Emami, S.M. and Mohammadi, M. (2016), “Influence of
240
-
Effect of frame connection rigidity on the behavior of infilled steel frames
vertical load on in-plane behavior of masonry infilled steel
frames”, Earthq. Struct., 11(4), 609-627.
http://dx.doi.org/10.12989/eas.2016.11.4.609
Peng, X., Gu, Q. and Lin, C. (2008), “Experimental study on steel
frame reinforced concrete infill wall structures with semi-rigid
joints”, China Civ. Eng. J., 41(1), 64-69.
Polyakov, S.V. (1960), “On the interaction between masonry filler
walls and enclosing frame when loaded in the plane of the
wall”, Translations Earthq. Eng., 2(3), 36-42.
Sakr, M.A., Eladly, M.M., Khalifa, T. and El-Khoriby, S. (2019),
“Cyclic behaviour of infilled steel frames with different beam-
to-column connection types”, Steel Composite Struct., 30(5),
443-456. https://doi.org/10.12989/scs.2019.30.5.443.
Stafford-Smith, B. and Carter, C. (1969), “A method of analysis
for infilled frames”, In ICE Proceedings Thomas Telford, 44,
31-48.
Standard No 2800 (2005), “Iranian code of practice for seismic
resistant design of buildings”, Third Revision, Building and
Housing Research Center, Iran.
Sun, G., He, R., Qiang, G. and Fang, Y. (2011), “Cyclic behavior
of partially-restrained steel frame with RC infill walls”, J.
Construct. Steel Res., 67(12), 1821-1834.
https://doi.org/10.1016/j.jcsr.2011.06.002
Yan, P. (2006), Hysteretic Behavior and Design Criterion of
Composite Steel Frame Reinforce Concrete Infill Wall
Structural System with FR Connections, Ph. D. Dissertation,
Xi’an University of Architecture and Technology.
Yekrangnia, M. and Mohammadi, M. (2017), “A new strut model
for solid masonry infills in steel frames”, Eng. Struct., 135,
222-235. https://doi.org/10.1016/j.engstruct.2016.10.048.
CC
241