Effect of frame connection rigidity on the behavior of infilled steel …research.iaun.ac.ir/pd/sm.emami/pdfs/PaperM_1726.pdf · 2020. 11. 4. · direction of loading. Noted that,

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

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

228


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

229


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

-150

-100

-50

0

50

100

150

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30

Dis

pla

cem

ent

(mm

)

Cycle No.

(a) (b)

Fig. 2 Bracing system to prevent out of plane movement (a) side view. (b) top view

230


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

-300

-200

-100

0

100

200

300

-6 -4 -2 0 2 4 6

Late

ral l

oad

(kN

)

Drift (%)

BF

-300

-200

-100

0

100

200

300

-6 -4 -2 0 2 4 6

Late

ral l

oad

(kN

)

Drift (%)

Begining of beam to column connection

damage

Beam to column connection failure

Beam to column connection failure

-400

-300

-200

-100

0

100

200

300

400

-8 -6 -4 -2 0 2 4 6 8

Late

ral l

oad

(kN

)

Drift (%)

M-RC-1B

-400

-300

-200

-100

0

100

200

300

400

-8 -6 -4 -2 0 2 4 6 8

Late

ral l

oad

(kN

)

Drift (%)

Occurrence of inclined cracking

Terminate the test due to excessive out of plane movement


231


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

232


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

-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 (%)

S2-RC-1B

-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 (%)

Occurrence of corner crushing

Occurrence of corner crushing

-400

-300

-200

-100

0

100

200

300

400

-8 -6 -4 -2 0 2 4 6 8

Late

ral l

oad

(kN

)

Drift (%)

M-PC-1B

-400

-300

-200

-100

0

100

200

300

400

-8 -6 -4 -2 0 2 4 6 8

Late

ral l

oad

(kN

)

Drift (%)


beam to column connection failure



Begining of damage in connection plate

233


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

-400

-300

-200

-100

0

100

200

300

400

-8 -6 -4 -2 0 2 4 6 8

Late

ral l

oad

(kN

)

Drift (%)

S2-PC-1B

-400

-300

-200

-100

0

100

200

300

400

-8 -6 -4 -2 0 2 4 6 8

Late

ral l

oad

(kN

)

Drift (%)



beginning of damage on beam to column

connection plate

beginning of damage in beam to column connection plate

234


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


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


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


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


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


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.

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