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Engineering Structures

journal homepage: www.elsevier.com/locate/engstruct

Multi-bay and pinned connection steel infilled frames; an experimental andnumerical study

Majid Mohammadia,⁎, Sayed Mohammad Motovali Emamib

a International Institute of Earthquake Engineering and Seismology (IIEES), Dibajee, Farmanieh, P.O. Box: 19395/3913, Tehran, IranbDepartment of Civil Engineering, Najafabad Branch, Islamic Azad University, Najafabad, Iran

A R T I C L E I N F O

Keywords:Infill wallPinned connections frameEquivalent strut modelMulti-bay infilled frameFEM

A B S T R A C T

The equivalent diagonal strut is one of the most prevalent approaches to model the infill panels recommended bymany seismic guidelines. Previous studies have revealed that the rigidity of frame connections affects the be-havior of the infill frames, but this matter is not considered in the macro modeling of the infill panels. Further,use of the same equivalent struts in the multi-bay infilled frame is questionable, while, the previous researcheshave suggested that the strength and stiffness of double-bay infill panels are not twice as large as those of asingle-bay one. Here, an experimental program has been conducted to explore the effect of connection rigidityand number of bays on the behavior of infilled steel frames. Five specimens including one bare frame, twoinfilled rigid connection frames, and two infilled pinned connection frames were tested under in-plane lateralloading excitation. Considering the results of experimental tests, a series of parametric analyses have beenconducted on the finite element models. The results indicated that the strength and stiffness of the infill panel inthe pinned connection frames were less than those in the rigid connection frames. Therefore, a new equivalentstrut model was proposed to model the infills in the pinned connection frames. In addition, it was observed thatthe influence of infill panels in the multi-bay infill frames had a direct relationship with the number of bays. Inother words, the properties of equivalent struts do not vary with the increase in the bay numbers in the infilledframes.

1. Introduction

Masonry infill panels are used as interior or exterior walls inbuildings. As reported by many researchers and also observed in recentearthquakes, the infill walls change the mechanical properties ofstructures and enhance the stiffness and strength of the surroundingframe. However, the infill panels are considered as non-structuralcomponents in the analysis and design process of the structures.Ignoring the effect of the infills is not always a conservative approach,since stiffer buildings are usually associated with higher seismic loads.Furthermore, asymmetric distribution of the infill walls in the plan ofthe building may change the building into an irregular structure whichwas assumed to be regular. It has been experimentally and numericallyshown that, due to the interaction between the infill and the sur-rounded frame, the stiffness and strength of the infilled frames cannotbe directly determined by adding the behavior of the infill and frameseparately. Many modeling approaches have been proposed in the lit-erature to consider the influence of infills on structures. These modelscould be classified into two general categories: micro modeling and

macro modeling. The micro modelling approach is more precise but it iscomplicated and demands more computing cost as well as a largenumber of parameters, making this method not as popular as the macromodeling approach [1]. Among the macro models, the equivalent di-agonal strut model is the most prevalent, used by many seismicguidelines such as ASCE41-06 [2] and FEMA356 [3]. These guidelinesrecommend the Mainstone model [4] in which the strut thickness isequal to the infill and the strut width is controlled by the contact lengthof the infill to the frame. Previous researches have declared that thecontact length can be altered by changing the rigidity of the frameconnections. In other words, the strut width depends on the connectionstype of the surrounding frame; however, the proposed models do notconsider the effect of connection rigidity on the equivalent strut prop-erties.

The behavior of infill panels in non-rigid connections frames haspreviously been studied in the literature. Dawe and Seah [5] discoveredthat the infill in the pinned connection frame has less stiffness, strengthand ductility, compared with those in the rigid connection frame. Fla-nagan and Bennet [6] conducted a series of experimental tests on the

https://doi.org/10.1016/j.engstruct.2019.03.028Received 4 July 2018; Received in revised form 11 March 2019; Accepted 11 March 2019

⁎ Corresponding author.E-mail addresses: [email protected] (M. Mohammadi), [email protected] (S.M. Motovali Emami).

Engineering Structures 188 (2019) 43–59

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structural clay infilled steel frames were the beam-column connectionswere fabricated by double clip angles. It was concluded that the stiff-ness and strength of the specimens were about half of the estimatedvalues calculated by the Mainstone [4] formula. Goudarzi et al [7]found that wherever the bounding steel frame had low stiffness, addinghaunches improved the ultimate lateral strength up to 60%. Addinghaunches also improved the cracking lateral strength and lateral stiff-ness of the infilled steel frames, but it was not as significant as theimprovement in the ultimate lateral strength. The in-plane seismic be-havior of hinged steel frames was studied by Gu et al. [8]. They de-veloped a simplified model to simulate the seismic behavior of infilledhinged steel frames in which the infill walls and CFRP sheets were re-placed by diagonal struts. Motovali Emami and Mohammadi [9] ex-perimentally indicated that the stiffness and strength of infilled pinnedconnection frame were lower than those of infilled rigid connectionframes. Since the behavior of infilled frame was controlled by the re-sponse of both the infill wall and the surrounding frame, the lowerstiffness and strength of infilled pinned connection frame may be at-tributed to the reduction in the rigidity of the frame or the lowercontribution of the infill panel or both of them. Therefore, it can beinferred that the use of common equivalent strut models to estimate thebehavior of infilled frames with pinned connections may be imprecise.

Another subject that has been investigated by researchers involvesthe behavior of multi-bay infilled frames. Murthy and Hendry [10]proposed a formula to estimate the lateral stiffness of multi-bay infilledframes. They suggested a non-linear relationship between the numberof bays and the lateral stiffness of the infilled frames. A series of testswere performed by Mosalam et al. [11] on the single-bay and thedouble-bay infilled steel frames. They found that the maximum strengthand stiffness of the double-bay infilled frame were 2 and 1.7 times thoseobserved in the single-bay specimen respectively. An experimentalprogram was conducted to evaluate the behavior of five half-scale,single-story infilled reinforced concrete (RC) frames with differentnumbers of bays by Al-Chaar et al. [12]. They reported that the max-imum strength of the infill specimens did not linearly increase byadding the number of bays. Further, the response of multi-bay infilledframes was dramatically affected by the method of applying the lateralloading. Choi et al. [13] experimentally indicated that the equivalentdiagonal strut based on the strain measurements can accurately esti-mate the wall strengths for the single-bay and double-bay infill speci-mens throughout the loading cycle.

The current study examines the effect of frame connections rigidityand number of bays on the lateral behavior of infilled steel frames. Forthis purpose, firstly, experimental investigation has been conducted onhalf-scaled single-bay and double-bay infilled steel frames with twodifferent frame types; rigid connections and pinned connections frames.Parametric studies were performed to extend the experimental resultson different infilled frames with a variety of infill aspect ratios, relativestiffness of infill to frame and number of bays. For this purpose, para-metric numerical analyses were done using the finite element method inABAQUS [14] environment. The micro modeling approach was carriedout in which the zero-length element was used to model the mortar.Also, concrete damage plasticity (CDP) model was used for modelingthe masonry bricks. The efficiency of equivalent strut model to estimatethe behavior of infill panels in the pinned connection frames and themulti-bay frames was evaluated further. Finally, a modified diagonalequivalent strut model was proposed to appropriately model the infillpanels in the pinned connections frames.

2. Experimental work

2.1. Test specimens

A four story, three-bay, moment-resisting steel frame was designedin accordance with the third edition of Iranian seismic code [15] andAISC-ASD01 [16] steel code of practice. The bay length and the story

height of the prototype were 4500mm and 3000mm, respectively(length-to-height ratio was 1.5) and the wall thickness was 190mm.Note that the service live load was taken to be 2 kN/m2, and dead loadwas estimated to be 6 kN/m2. As a result, the frame columns and beamssections at the first story were determined 2IPE 400 and IPE 330, re-spectively. The single- and double-bay specimens were chosen from thefirst story of exterior frame of the prototype building. Due to limitationof research facilities and equipment of the laboratory, the specimenswere scaled to 1:2. The scaling process of the steel frames and themasonry walls was employed in accordance with Harris and Sabnis[17]; the height and length of the single-bay specimen was reduced to1500mm and 2250mm, respectively. Further, sections area (A) andmoment of inertia (Ixx) should be multiplied by ( )1

22 and ( )1

24. The beams

and columns of the specimens were chosen from the available sectionsin the market with closest values to obtained A and Ixx.

The characteristics of the specimens are summarized in Table 1where all specimens are infilled frames except the first one, which is abare frame. The bare frame as well as two infill specimens had rigidconnections, while the two others had pinned connections. In addition,each infill specimen was considered for both single-bay and double-bayframes. The names of the infill specimens in Table 1 start by letter Mindicate the material of infill panel (Masonry). The second part of thespecimens name denotes the type of beam to column connections; RCand PC represent the Rigid Connections and Pinned Connections, re-spectively. The last part, 1 or 2 followed by letter of B shows thenumber of bays of the specimens.

2.2. Test setup

The experimental layouts including the lateral loading system andthe dimensions for the double-bay and single-bay specimens are shownin Fig. 1(a) and (b), respectively. The infill panels were constructed byclay masonry brick with thickness of 95mm. In-plane cyclic lateral loadwas applied to the specimen by a hydraulic actuator through a loadingbeam as illustrated in Fig. 1. The loading beam was connected to theframe through the shear keys welded to the top beam and columns ofthe frame specimen. The detail of shear keys is shown in Fig. 1(e). Thelateral loading setup approximately led to a realistic distribution oflateral loading along the top beam of frame as it is done practicallyduring a seismic excitation. Note that this novel lateral loading setup ismore notable for the multi-bay infilled frames as reported in previousstudies such as [12]. The maximum capacities of actuators for single-bay and double-bay specimens were 500 kN and 1000 kN, respectively,with the same stroke of± 150mm. The rigid connections were made bymeans of two cover plates at the top and bottom faces of the beams. Thedimension of cover plates were 180×100×8mm. The cover plateswere connected to the column faces and beam flanges by full-penetra-tion and fillet welding, respectively. Further, two 120×80×6mmplates were used to connect the beam web to the column face by thefillet welding with a 6mm throat size. The pinned connections weremanufactured by connecting the beams webs to the columns faces usingtwo web plates. The details of the rigid and pinned connections areillustrated in Fig. 1(c) and (d), respectively. The lateral loading direc-tions are shown in Fig. 1(a) and (b). Note that the directions of loadingwere named “positive” and “negative” in this paper whenever the

Table 1Summary of specimens.

Specimen Bays Height(mm)

Length(mm)

Column Beam Beam to columnconnection

BF 1 1500 2250 IPBL 180 IPBL 120 rigidM-RC-1B 1 1500 2250 IPBL 180 IPBL 120 rigidM-PC-1B 1 1500 2250 IPBL 180 IPBL 120 PinnedM-RC-2B 2 1500 4500 IPBL 180 IPBL 120 rigidM-PC-2B 2 1500 4500 IPBL 180 IPBL 120 Pinned

M. Mohammadi and S.M. Motovali Emami Engineering Structures 188 (2019) 43–59

44

actuator pulled and pushed the specimen, respectively. Due to theavailable group of holes on the strong floor of the laboratory and fixeddistances between them, the columns base plates were tied to the strongfloor in such a way that its behavior was dissimilar in the each directionof loading. Note that the base plates were rigid whenever the specimenwas loaded in the positive direction but they could rotate while thelateral loading was applied in the negative direction, as shown sche-matically in Fig. 1(f) and (g). The specimens were constructed andtested in the structural laboratory of International Institute of Earth-quake Engineering and Seismology (IIEES). Relative lateral displace-ment of the specimens was measured by two LVDTs installed along thetop and bottom beams of the frames, as shown in Fig. 1(a) and (b). The

specimens were laterally braced to ignore undesirable out-of-planemovements during the test.

2.3. Loading pattern

The cyclic lateral displacement pattern recommended by FEMA461[18] was applied to the specimens. The amplitude of the loading historystarted from 1.7 mm displacement and gradually increased by 1.4 timesof previous amplitude. Each cycle repeated twice and the last cycleamplitude reached 135mm as illustrated in Fig. 2. The test was con-tinued up to the occurrence of severe damage in the specimen, testsetup or instruments.

Fig. 1. Experimental setup for (a) double-bay specimens, (b) single-bay specimens; (c) rigid connection; (d) pinned connection. (e) detail of shear key in the lateralloading setup; (f) column base plate in the positive direction; (g) rotation of column base plate in the negative direction. (all dimensions in mm).


45

2.4. Material properties

Material tests were conducted on the masonry prism, mortar andsteel coupons. The masonry prisms consisted of three brick unit and twolayers of mortar which were made in the same time of infill wall con-structing. Note that all of the infill walls were built by an experiencedmason to minimize workmanship effects. The average dimensions of 10solid brick units were measured as 195×95×55mm and the heightto thickness of the masonry prisms was 2. The brick units were pre-soakbefore using in the infill construction to reduce the water absorption ofmortar, recommended by Iranian National Building code-part 8 [19].Twelve Standard masonry prisms were tested as per ASTM C1314 [20]and the mean compressive strength, ′fm and the modulus of elasticity Emof the prisms were measured as 9.9MPa and 1892MPa, respectively.The mortar mixture composed of six part sand to one part Portlandcement type II and enough water to produce a workable mix. The meancompressive of twelve 50mm standard cube of mortar was calculated8.3 MPa with a standard deviation of 1.2MPa in accordance with ASTMC-109 [21]. Six masonry specimens consisted of two brick units and themortar joint between them were tested to calculate shear strength bondas well as friction coefficient of the mortar to the brick units as perASTM C952 [22]. The average shear bond strength was 0.30MPa andthe coefficient of friction was calculated µ=0.75. Further, six steelcoupon specimens were tested to determine steel properties of theframes in accordance with ASTM E8/E8M [23]. These coupon speci-mens were provided from both the beam and column sections. Table 2shows the results of the steel tests including modulus of elasticity (Es),yield stress ( fy), ultimate stress ( fu) as well as their correspondingstrains (εy& εu). The illustrations of material testing are shown in Fig. 3.

3. Experimental results

3.1. Testing description

3.1.1. Specimen BFThe hysteresis load-drift ratio diagram of specimen BF is shown in

Fig. 4(a). The initial stiffness of the specimen was obtained 9.5 and7.45 kN/mm in the positive and negative directions, respectively. Thelinear behavior of specimen BF was continued up to the drift of 1.25%.Then, the nonlinear response of the bare frame was initiated and sub-sequently the plastic hinges were formed at the both ends of beams.Afterward, at the drift of 3.5%, the rigid connections at the one side ofthe specimen were initially damaged and finally they were collapsed atthe drift of 5.3%. The schematic view of specimen BF and its failedconnections are shown in Fig. 4(b). According to Fig. 4(a), the as-cending branch of the hysteresis curve stopped at the drift% of 3.5% inwhich while the damage was initiated at the connection. The maximumstrengths of the specimen were measured 254 kN and 215 kN in thepositive and negative directions, respectively.

3.1.2. Specimen M-RC-1BThe hysteresis behavior of specimen M-RC-1B is shown in Fig. 5.

The stiffness values in the positive and negative directions were 10.64and 8.4 kN/mm, respectively. The reported stiffness of the infill spe-cimens in the present study was measured as the slopes of a line fromthe origin to a point where the major cracking of the infill was started.The maximum strengths were calculated 325 and 218 kN in the positiveand negative directions which were corresponding to the drift of 5.1%and 3.5%, respectively. The infill wall major cracking was initiated atthe drift of 1.1% and were formed approximately 65 degrees to thehorizontal in both directions of loading. The cracks were propagatedthrough the infill panel that led to formation of two compressive strutsin each direction of loading as schematically depicted in Fig. 6. It can beseen the cracks are shown with the darker color by increasing the driftof the specimen. The struts were initiated at the top of windwardcolumn and the bottom of leeward column and continued to the op-posite beam. The struts width was calculated approximately 330mm.The test was terminated at the drift of 7.4%, due to the out of planemovement of the specimen in the negative direction of loading. Thepredominant failure mode of the specimen caused to forming twocompressive struts is illustrated Fig. 7.

3.1.3. Specimen M-PC-1BThe hysteresis behavior of specimen M-PC-1B is illustrated in Fig. 8.

The stiffness values were measured as 5.6 and 3.6 kN/mm in the po-sitive and negative directions, respectively, which were 57% smallerthan those of specimen M-RC-1B. The peak loads of the specimen were290 kN in the positive direction and 185 kN in the negative direction atthe drifts of 5.5%, 3.7%, respectively. The major cracks of the infillwere initiated at the drift of 0.57%. Afterward, damage in the webplates of the pinned connections was started at the drift of 3.5%.Consequently, the pinned connections of both sides of the top beam

-150

-100

-50

0

50

100

150

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

Dis

plac

emen

t(m

m)

Cycle No.

Fig. 2. Displacement pattern applied.

Table 2Mechanical properties of steel specimens.

Test No. Es (GPa) fy (MPa) fu (MPa) εy εu

1 186450 286.5 494.1 0.00153 0.1302 185340 291.0 490.3 0.00157 0.1403 186135 287.7 490.9 0.00154 0.1314 183870 303.4 480.3 0.00163 0.1485 184640 299.4 487.4 0.00162 0.1516 183830 296.4 485.8 0.00161 0.145


46

were completely failed (as shown in Fig. 9) at the drift of 5.5% andtherefore, the test was terminated. Cracking patterns of the infill paneland their corresponding drifts at both directions are shown in Fig. 10.Similar to specimen M-RC-1B, two compressive struts at 65 degreeswith respect to the horizontal were formed in the infill panel, but ob-served width of the struts was smaller than that in specimen M-RC-1Band measured about 255mm.

3.1.4. Specimen M-RC-2BThe load-drift relationship of specimen M-2B-RC is shown in Fig. 11.

The stiffness values were 17.2 kN/mm and 16 kN/mm in the positiveand negative directions, respectively. The maximum strengths of thespecimen were 623 kN at the drift of 3.56% and 580 kN at the drift of

4.6% in the positive and negative directions, respectively. The firstmajor cracking in the infill panels was observed at the drift of 1.7%.Afterwards, the cracks were propagated in the both infill panels causedformation of two compressive struts in each infill.

As it can be seen in Fig. 11, the ascending branch of the curve isstopped at the drift of 3.5%. It is due to the failure of the weld con-nected the bottom cover plate to the beam flange as shown in Fig. 12.Hence, the lateral strength of the specimen was decreased. The majorfailure mode of the infill panels was similar to the others and twocompressive struts with 65 degrees to the horizontal could be observedin each infill wall. The illustration of specimen M-RC-2B at the end ofthe test (drift of 7.1%) is depicted in Fig. 13 in which two struts arehighlighted in each infill panel.

Fig. 3. Experimental setup for (a) masonry prism compression test; (b) mortar compression test; (c) masonry shear test; (d) steel coupon test.

)b()a(

-300

-200

-100

0

100

200

300

-6 -4 -2 0 2 4 6

Late

ral l

oad

(kN

)

Drift (%)

BF

Fig. 4. (a) Hysteresis behavior (b) failure mode; of specimen BF.


47

3.1.5. Specimen M-PC-2BThe hysteresis behavior of specimen M-PC-2B is shown in Fig. 14.

The stiffness values were 13.9 kN/mm and 9.9 kN/mm in the positiveand negative directions, respectively. In this specimen the pinnedconnections of the surrounding frame were failed at the drift of 1.7%and subsequently the test was terminated. The maximum strengthswere obtained 288 kN and 245 kN in the positive and negative direc-tions, respectively. The recorded strength values were simultaneouswith the failure of the frame connections. One can conclude that themaximum strength could be continued up to higher values if the pinnedconnections were not failed. Focusing on the infill panels, the shearcracks in the middle of infill panels and the mortar joints were observedat the many low drift. By increasing the lateral drift, the inclinedcracking was developed in the both infill panels. Due to termination ofthe test at the drift of 1.7%, the observed cracks in the infill panels werefewer than those in the other specimens. Fig. 15 shows two compressivestruts formed in the infill panels.

3.2. Comparison of experimental results

The important behavioral characteristics of the specimens are pre-sented in Table 3. In this table the + and – signs refer to the calculatedvalues in the positive and negative directions, respectively. Comparingspecimen BF to specimen M-RC-1B, the infill panel caused an increase

in the stiffness and strength of the frame. Note that the presence of infillwall in specimen M-RC-1B caused an increasing of strength by 28%compared to that of specimen BF, in the positive direction (from 254 kNto 325 kN). Further, the initial stiffness of specimen BF, 9.48 kN/mm, isincreased to 10.46 kN/mm in specimen M-RC-1B. Note that the stiffnessof the bare frame in Table 3 is related to the initial stiffness, while thereported stiffness of the infill specimens is attributed to the slopes of a

-400

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0

100

200

300

400

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

Late

ral l

oad

(kN

)

Drift (%)

M-RC-1B

Fig. 5. Hysteresis behavior of specimen M-RC-1B.

(a) Left loading (b) Right loadingFig. 6. Cracking pattern and formation of compressive strut in specimen M-RC-1B.

Fig. 7. Cracking pattern and failure mode at the end of the test of specimen M-RC-1B.

-400

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-100

0

100

200

300

400

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

Late

ral l

oad

(kN

)

Drift (%)

M-PC-1B

Fig. 8. Hysteresis behavior of specimen M-PC-1B.


48

line from the origin to the point corresponding to the major infillcracking. In other words, due to the interface cracking of the infill at thevery low drift and subsequently immediate decrease of the stiffness, theinitial stiffness values of the infill specimens are not reported. One canconclude that the increasing of initial stiffness due to presence of theinfill panel was more than the reported values.

3.2.1. Effect of connection rigidityThe backbone curves of the specimens are shown in Fig. 16(a).

According to these curves and Table 3, the stiffness of infilled pinnedconnection frames are averagely decreased by about 50% in compar-ison to those of the rigid connection specimens. Note that the stiffnessof specimen M-PC-2B is 15% less than that of specimen M-RC-2B inpositive direction, while the difference was 43% in the negative di-rection. In the single-bay infilled frames, the decrease of stiffness due tothe reduction in rigidity of the frame connections were 48% and 57% inthe positive and negative directions, respectively. Moreover, the max-imum strength of specimen M-PC-1B is 90% of that of specimen M-RC-1B. Meanwhile the maximum strength of M-PC-2B was 65% of that ofspecimen M-RC-2B. Note that the strength comparison of double-bayspecimens is done for the drift of 1.7% in which the test of specimen M-PC-2B was terminated, as reported previously. The difference betweenthe behavior of the infilled pinned connection and rigid connectionframes is mainly attributed to the change in the connections rigidity ofsurrounding frames and also decrease in contact length of infill-to-frame. In other words, the connection rigidity of frame affected the

interaction between the infill wall and the frame and consequentlychanged the contribution of infill in the infilled frames. The effect ofconnection rigidity on the infill-frame interaction is numerically in-vestigated in the following section. Moreover, as reported previously,the crack propagation in the infill panels was affected by the connectionrigidity of the surrounding frame. The approximated crack width in theinfill of specimen M-RC-1B was 330mm while, it decreased to 225mmin specimen M-PC-1B. The effect of connection rigidity on the crackwidth in the infill panel is numerically and analytically studied in the

Fig. 9. Failure of pinned connection in specimen M-PC-1B.

gnidaolthgiR)b(gnidaoltfeL)a(

Fig. 10. Crack pattern and formation of compressive strut in specimen M-PC-1B.

-800

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-400

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0

200

400

600

800

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

Late

ral l

oad

(kN

)

Drift (%)

M-RC-2B


Fig. 12. Damage in rigid connection of specimen M-RC-2B.


49

following of the paper. The experimental results indicated that theangle of major infill cracking with respect to the horizontal was notaffected by the connection rigidity and it remained constant 65°.

The potential of infilled frames to dissipate energy in the structurescan be determined using damping definition. In this study the equiva-lent viscous damping recommended by Chopra [24] was used to showthe damping ratio. This damping can be calculated as =ξ E πE/(4 )eq D S ,where ED is the amount of energy dissipated by the actual structure in

one completed cycle which is equal to the area enclosed by the hys-teresis loop. ES is the amount of elastic strain energy stored in the peakof the cycle, defined as the half of the maximum displacement multiplyby the corresponding load. The equivalent viscous damping of the infillspecimens versus lateral drifts are shown in Fig. 16b. It can be seen thatspecimen BF has the minimum damping ratio at the beginning, howeverit is higher than that of the infill specimens after the drift of 1.8% andremains constant after the drift of 3.5%. The latter may be attributed tothe failure of beam-column connection at specimen BF after the drift of

Fig. 13. Cracking pattern and final failure mode of specimen M-RC-1B.

-500

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0

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500

-3 -2 -1 0 1 2 3

Late

ral l

oad

(kN

)

Drift (%)

M-PC-2B


Fig. 15. Cracking pattern in the infill specimen M-RC-1B at the drift of 1.7%

Table 3Important values of strength and stiffness and corresponding drifts of speci-mens.

Specimen Stiffness Major infill cracking Maximum strength

(kN/mm) Load (kN) Drift (%) Load (kN) Drift (%)

BF 9.48* – – 254 3.63−7.44* – – −218 −3.59

M-RC-1B 10.64 197 1.07 325 5.1−8.40 −125 −0.79 −218 −3.5

M-PC-1B 5.60 200 1.8 290 5.5−3.59 −130 −1.9 −185 −3.7

M-RC-2B 16.20 444 1.76 623 3.56−17.20 −307 −1.16 −580 4.6

M-PC-2B 13.86 317 1.24 288 1.7−9.93 198 −0.83 −245 −1.8

* initial stiffness


50

3.5%. For specimen M-PC-2B, the equivalent viscous damping is drawnup to the drift of 1.7% in which the test was terminated due to con-nection failure. The damping ratios of the infilled rigid connectionframes are more than those of infilled pinned connection frames. This isdue to the occurrence of more cracks and sliding in the bricks of ma-sonry infill as well as more nonlinearity in the surrounding frame ofrigid connection specimens.

3.2.2. Effect of number of baysAccording to Table 3 and Fig. 16a, the maximum strength of spe-

cimen M-RC-2B has been 1.9 times of specimen M-RC-1B in the positivedirection. Further, the maximum strength of specimen M-PC-2B hasbeen 1.95 times that of specimen M-PC-1B at the drift of 1.8%. Com-paring the stiffness of the infilled rigid connection frames, the stiffnessof specimen M- RC-2B is about twice as large as the stiffness of spe-cimen M-RC-1B, while in the pinned connection specimens, the stiffnessof specimen M-PC-2B is 2.5 times the specimen M-PC-1B stiffness. Dueto the existence of more beams and columns as well as infill panels inthe double-bay specimens, enhanced strength and stiffness in thesespecimens in comparison with the single-bay ones was completelypredictable. However, the separate influence of the infill panels and thesurrounding frames in the global behavior of double-bay infilled framesis not clear. To determine the exact contribution of the infill walls onthe behavior of multi-bay infilled frame, a series of finite elementanalyses will be done further. In addition, according to Fig. 16b, thedamping ratios of specimens M-RC-1B and M-RC-2B were approxi-mately identical during the test. In other words, the number of bays didnot significantly affect the equivalent viscous damping ratio of infilledsteel frames

4. Numerical investigation

In this section, numerical investigations have been performed toachieve more comprehensive and accurate results on the effect of theconnection rigidity and the number of bays on the behavior of infilledsteel frames. For this purpose, nonlinear static analyses were conductedon the infilled steel frames. The variable parameters of the infilled steelframes included the aspect ratios (length-to-height), the connectiontypes and the relative stiffness of infill to frame (λh). The latter will bedescribed in the following section.

4.1. Theoretical background for modeling

The infilled steel frames were modeled using finite element method(FEM) by ABAQUS [14]. Then, the global behavior of the infilled framemodels were obtained through nonlinear static analysis using ABAQUS/Explicit. Ensuring quasi static behavior, energy balance checking andmass scaling were applied while using dynamic explicit analysis. Thematerial models of masonry units and mortar interface have been ex-plained subsequently.

4.1.1. Concrete damage plasticityTo simulate the nonlinear behavior of the masonry units, concrete

damage plasticity (CDP) model was used. The CDP model has beendeveloped to predict the behavior of concrete and other quasi-brittlematerials such as masonry and mortar under cyclic loading. The modelis based on primary models proposed by Lubliner et al. [25] and Leeand Fenves [26]. The CDP model assumes that the uniaxial compressiveand the tensile response of material are characterized by damagedplasticity as shown in Fig. 17.

)b()a(

-700

-500

-300

-100

100

300

500

700

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

Late

ral l

oad

(kN

)

Drift (%)

BFM-RC-1BM-RC-2BM-PC-1BM-PC-2B

0

2

4

6

8

10

12

14

16

18

20

0 1 2 3 4 5 6

Equi

vale

nt v

isco

us d

ampi

ng ra

tio

(%)

Drift (%)

BF

M-RC-1B

M-RC-2B

M-PC-1B

M-PC-2B

Fig. 16. Comparison of (a) envelop curves; (b) equivalent viscous damping ratio.

(a) )b(noisneT Compression

Fig. 17. Response of CDP model to uniaxial loading [14].


51

4.1.2. Cohesive surface-base elementGenerally, cohesive interactions are a function of displacement se-

paration between the edges of potential cracks. The concept of cohesivezone was firstly employed by Dugdale [27]. Needleman [28] recognizedthat the cohesive elements are partially useful when interface strengthare relatively weak compared to the adjoining materials. Mortar jointbetween brick units is an example for modeling with the adhesivebonded interfaces. Adhesive bonded interface is appropriate to modelthe separation between two initially bonded surfaces. Three methodscan be drawn for the mechanical constitutive behavior of cohesiveelements: (1) uniaxial stress-based, (2) continuum based and (3) trac-tion–separation constitutive model. Where two units are connected by athird part material like mortar, the continuum based modeling is ap-propriate for the adhesive. In this case, the mortar should be consideredwith a finite thickness. Where cracks are anticipated to propagate, thecohesive elements can be used. In this model, cracks are limited todevelop along the head and bed joints of the mortar layers.

Prior to the damage, a linear traction–separation law is seen bycohesive behavior and after that the bond failure is occurred by pro-gressive degradation of the bond stiffness. When the damage is initiatedin the interface element, it will take place based on a factor defined byuser. Fig. 18(a) shows a typical traction–separation response. In theFig. 18(a) normal, tn and two shear traction components ts; tt are shownthe traction stress vector in elastic part. Fracture modes I, II, III re-presented by these components is shown in Fig. 18(b). Moreover, theinitial separations due to net normal, in-plane and out-of-plane shearstresses are respectively indicated by δn

0, δs0 and δt

0 in this model.Among different ways available in ABAQUS [14], the maximum

nominal stress (MAXS) was chosen to consider damage propagation inthe bonding zone. In this case, the damage is initiated once the max-imum nominal stress ratio reaches a value of one. In this model, theevolution of damage is defined based on the degradation of the cohesivestiffness and fully damage is occurred when the separation reach itsmaximum value (i.e. δn

f , δsf and δt

f in Fig. 18(a)).After the degradation of cohesion, a contact is occurred between

two elements and consequently coulomb frictional contact behavior isdominated in the current model. A coefficient of friction, μ, is used tocharacterize the frictional behavior in the coulomb friction model.Components penetration must be avoided after forming the contact,especially for the normal behavior of the contact. For the presentedstudy, general contact (Hard contact) available in ABAQUS was used toavoid penetration of the bricks as well as infill-frame together.Tangential movement between two surfaces is zero prior to the criticalsurface traction. The critical shear stress can be calculated by the fol-lowing Equation:

=τ μpc

where μ is the friction coefficient and p is the contact pressure betweenthe two surfaces. This equation introduces the limiting frictional shearstress for the contacting surfaces. The slip does not be occurred in thecontacting surfaces until the shear stress reaches the critical frictionshear stress.

4.2. Numerical verification

The capability of the finite element model to capture the behavior ofthe infilled steel frames was validated with the experimental data of thespecimens discussed in the previous section. The average mechanicalproperties of the surrounding steel frame as well as the masonry prismare available in Table 4 and 5 which were obtained from the experi-mental tests reported in Section 2.4.

4.2.1. Concrete damage plasticity parametersThe elastic and plastic properties of masonry units used to model

with the CDP concept are shown in Table 6. A series of experimentaltests are needed to measure the plasticity characteristics of materialwhich are beyond the scope of the present study. In the absence of suchdata, the plasticity parameters were indirectly estimated by trial anderror in the verification process as well as use of the common valuesrecommended in the literature. Modulus of elasticity and the com-pressive behavior of the CDP model were extracted from the result ofthe masonry prism tests described in previous section. Table 7 showsthe yield stress versus the inelastic strain and cracking strain obtainedfrom the prism test.

4.2.2. Joints cohesive behavior parametersCohesive behavior of the mortar was defined based on the in-

formation presented in Table 8. Mortar is the only source of the bondresistance against shear forces along the bed joints of the bricks as wellas the infill-frame. The mechanical properties of adhesive material werecalculated from the experimental shear strength test as well as try anderror to achieve the best results. The average shear bond strength be-tween the brick masonry units and the mortar were used for mode II offracture which is named shear I in the Table 8. Since there is no dif-ferent between the shear strength of in-plane and out-of-plane of themasonry wall, the shear II value (mode III) was taken equal to the shearI (mode II). The plastic displacement and exponential parameter values,which were employed in the strength degradation of the mortars, werecalculated based on try and error to obtain reasonable results. ABAQUSuses the following equation to calculate cohesive degradation:

= − ⎧⎨⎩

⎫⎬⎭

⎧

⎨⎪

⎩⎪−

− −

− −

⎫

⎬⎪

⎭⎪

−

−Dδ

δ

α

α1 1

1 exp( ( ))

1 exp( )m

m

δ δ

δ δ0

max

m m

mf

m

max 0

0

where δm0 , δm

max and δmf are the displacements imposed to the mortar at

the beginning of the test, during the test and while the mortar is fully

(a) )b(esnopsernoitarapes-noitcarT Fracture modes Fig. 18. Typical traction-separation behavior and fracture modes [29].

Table 4Mechanical properties of steel.

Modulus of elasticity(MPa)

Yield stress (σy)(MPa)

Ultimate stress (σu)(MPa)

εh εu

185000 294 488 0.0016 0.141


52

degraded, respectively. α is exponential parameter of the degradationfunction. Fig. 19 shows the schematic traction–separation behavior ofthe mortar in the model used in ABAQUS.

Since the traction–separation graph is linear, the slope of each linewhich called the stiffness coefficient was taken to be 11 MN/m.Theoretically this stiffness in the normal direction is modulus of elas-ticity of the mortar divided by thickness of the mortar which can becalculated based on the following equation [30]:

=−

K E Eh E E( )nn

u m

m u m

where, Em and Eu are modulus of elasticity of mortar and unit, re-spectively. Also, hm is actual thickness of mortar joint. For simplicity, anidentical stiffness in the normal and shear directions were assumed forthe traction–separation model, similar to Bolhassani et al. [29].

Zero thickness contact was assumed and therefore hard contact wasassigned for normal behavior of the contacts. No softening was con-sidered in the “Hard” contact interaction and as a result the surfacescannot penetrate to each other in the model. Also, the friction coeffi-cient of brick to brick was taken to be 0.75 as obtained from experi-mental shear test and brick to steel is chosen 0.57 in which the bestresults were captured.

4.3. Model outputs

Four specimens were modeled in ABAQUS to verify the ability of thenumerical model in capture the behavior of infilled steel frames. Forthis purpose, one bare frame specimen, BF, as well as three infill spe-cimens consisted of M-RC-1B, M-PC-1B and M-RC-2B were selected.C3D8R element, an 8-node linear brick reduced integration solid ele-ment was used to model both the surrounding frames and the masonryunits. The total numbers of elements used for modeling of frame andinfill wall in the single-bay specimen were 1838 and 1680, respectively.The results of finite element modeling of infilled frames were acceptedbased on two policies. (1) Acquire the best fit of numerical pushovercurve to the backbone of experimental hysteresis curve; (2) Obtain thesame failure modes of the numerical models with the experimentalones. Fig. 20 shows the comparison between the capacity curves of fi-nite element models and backbone curves of the experimental speci-mens. It can be seen that the numerical modeling of steel bare framecan properly capture the experimental behavior of specimen BF.Therefore, in the next step the infill specimens were modeled inABAQUS and their numerical results compared to those of experimentalones. Fig. 20(b-c) shows the pushover curves of single-bay infill speci-mens M-RC-1B, M-PC-1B for the both experimental and numericalanalyses. One can see that the strength and stiffness of the numerical

Table 5Mechanical properties of masonry prism.

Modulus of elasticity (MPa) Poisson’s ratio Compressive strength (MPa) Tensile strength (MPa) Shear strength (MPa) Coefficient of friction

1892 0.15 9.9 0.69 0.3 0.75

Table 6Material properties of masonry for CDP model.

Mass Elasticity PlasticityDensity (N/m3) Modulus of elasticity (MPa) Poisson’s ratio υ Dilation angle ψ Eccentricity f f/b c0 0 K Viscosity parameter18120 1892 0.15 20 0.1 1.16 0.66 0

Table 7Compressive and tensile behavior of the masonry for CDP model.

Concrete damage plasticity

Compressive behavior Tensile behavior

Yield stress (MPa) Inelastic strain Yield stress (MPa) Cracking strain

6.92 0 0.69 08.0 0.00033 0.54 0.000119.68 0.00177 0.36 0.000299.90 0.00287 0.25 0.000429.68 0.00418 0.17 0.000558.63 0.00644 0.12 0.000677.28 0.00842 0.09 0.000784.28 0.01193 0.07 0.00088

Table 8Cohesive behavior of brick to brick and infill to frame joints.

Surface Contact

Tangential behavior Normal behavior Cohesive behavior

Traction–separation behavior Damage

Stiffness coefficients MN/m Initiation (MPa) Evolution

Knn Kss Ktt Normal Shear I Shear II Plastic displacement (mm) Exponential parameter

Brick-Brick 0.75 Hard contact 11 11 11 0.15 0.30 0.30 1.5 2Infill-frame 0.57 Hard contact 11 11 11 0.1 0.15 0.15 1 10

Fig. 19. schematic view of mortar degradation function [14].


53

single-bay specimens acceptably similar to those of experimental onesfor both the rigid and pinned connection infill specimens. Finally, theability of finite element modeling to capture the behavior of double-bayinfilled frame was assessed. The comparison between the numerical andexperimental pushover curves of specimen M-RC-2B is illustrated inFig. 20(d). One can conclude that the FEM model was appropriatelycapable to predict the stiffness and strength of the masonry infilled steelframes regardless of their connection types or the number of bays. Notethat the same materials and interactions properties were used in allnumerical models.

For instance, the observed crack patterns in the infill panels ofspecimens M-RC-1B and M-PC-1B for the experimental and FEM modelsare compared in Fig. 21. The numerical results in the figure show thetension damage formed in the masonry bricks. The tension damage inthe CDP model is initiated from the strains more than strain corre-sponding to maximum tension stress (σtu in Fig. 17(a)), for more in-formation one can refer to ABAQUS theory manual [14]. In otherwords, the initiation of tension damage is simultaneous with formationof cracks in the masonry bricks. Therefore the crack patterns can beindicated with the cantor of tension damage. According to the Fig. 21, itis obvious that the failure mode of the infill panels in the numericalmodels was approximately similar to that of experimental ones. Thepropagation of cracks in the infill panel of finite element models formedtwo compressive struts which were similar to the observed cracks in theexperimental specimens. As a result, one can confirm that, the finiteelement numerical models used in this study can capture the nonlinearbehavior of masonry infilled steel frame with high accuracy.

5. Parametric analysis

A series of sensitivity analyses were conducted to investigate moreaccurately the effects of connection rigidity and number of bays on thebehavior of masonry infilled frames. The analyses were done based onthe abovementioned finite element modeling. For this purpose, 40models included 20 masonry infilled steel frames as well as their cor-responding surrounding bare frames were modeled. The characteristicsof infilled frames are listed in Table 9. The thickness of all masonryinfill walls was 95mm. Note that, the variable parameters were theframe connections (rigid and pinned), the infill aspect ratios (L/H), therelative stiffness of infill to frame (λh) and the number of bays. Therelative stiffness of infill to frame is a non-dimensional parameter thatcan be calculated based on the formula proposed by Mainstone [4]:

= ⎡⎣⎢

⎤⎦⎥λh h E t θ

E I hsin 2

4colme

fe col

inf

inf

14

where, hcol is the height of column, Eme is the modulus of elasticity ofinfill panel, tinf is the thickness of infill, θ is the angle whose tangent isthe infill height-to-length aspect ratio, Efe and Icol are the modulus ofelasticity and the moment of inertia of column section, respectively andhinf is the height of infill panel. One can conclude from the formula thatthe stronger surrounding frame results in the lower λ h.

Nonlinear static pushover analyses were conducted on the all nu-merical models up to the drift of 4%. Then, the initial stiffness andstrength of the infilled frames and their bare frames were calculatedand compared. Moreover, the infill contributions of the infill panels

)b()a(

(c) (d)

0

50

100

150

200

250

300

0 1 2 3 4 5

Late

ral l

oad

(kN

)

Drift (%)

Numerical (BF)

Experimental (BF)

0

50

100

150

200

250

300

350

0 1 2 3 4 5 6 7 8

Late

ral l

oad

(kN

)

Drift (%)

Numerical (M-RC-1B)

Experimental (M-RC-1B)

0

50

100

150

200

250

300

350

0 1 2 3 4 5 6 7

Late

ral l

oad

(kN

)

Drift (%)

Numerical (M-PC-1B)

Experimental (M-PC-1B)

0

100

200

300

400

500

600

700

0 1 2 3 4 5 6

Base

she

ar (k

N)

Drift (%)

Numerical (M-RC-2B)

Experimental (M-RC-2B)

Fig. 20. Comparison between experimental and numerical capacity curves.


54

were determined by subtracting the pushover curve of the infilled framefrom its bare frame.

5.1. Effect of connection rigidity

The initial stiffness ratios of the pinned connections (PC) to the rigidconnections (RC) models for the infilled frames, the bare frames and theinfill contributions with different aspect ratios and λh are listed inTable 10. The mean value of PC-to-RC stiffness ratio for the infilledframes is 0.86 with a COV (Coefficient of Variation) of 6.06%. One caninfer that the decrease in the initial stiffness of the infilled frames due tothe reduction of connection rigidity is attributed to reduction of theboth frame rigidity and the infill contribution. The mean value of PC-to-RC stiffness ratio for the bare frame is 0.81 with COV of 8.16% while itis 0.91 with COV of 5.61% for the infill contribution. The latter means

that the infill panel stiffness is reduced by decrease in the rigidity offrame connections. It can be attributed to the reduction of the infill-frame interaction due to the decrease in the rigidity of frame connec-tion. Changing the frame connections type from rigid to pin, led to thereduction in the stiffness of infill panel (infill contribution) averagely by10% which is ignored in the prevalent modeling of the infill using theequivalent compressive strut.

The strength ratio of PC-to-RC models for the infilled frames, bareframes and infill contributions are listed in Tables 11,12 and 13, re-spectively. The strength values were extracted from the pushovercurves in the drifts of 1.35%, 1.67%, 2% and 2.5% to cover the im-mediate occupancy (IO) to life safety (LS) performance levels. Ac-cording to Iranian seismic code [15] the drifts of 2% and 2.5% arecorresponding to the LS limit state depended on the predominant periodof the structures. Moreover, the drift corresponding to the immediateoccupancy IO limit state can be considered as 67% of the LS drift as perASCE 41–13 [31]. Table 11 shows that the strengths of infilled pinnedconnection frames are lower than those of infilled rigid connectionframes with an overall mean PC-to-RC ratio of 0.87 with a COV of3.35%. According to Table 12 the strengths of pinned connection to therigid connection frames are averagely reduced by 13% (the mean PC-to-

Specimen M-RC-1B

Specimen M-PC-1B(Numerical) (Experimental)

Fig. 21. Infill failure modes of experimental and numerical models.

Table 9Infilled frames model and their parameters.

ID beam column Connection type Aspect ratio (L/H) λh Bay No.

1 IPBL 120 IPBL180 Rigid 0.5 2.4 12 IPBL 120 IPBL180 Pinned 0.5 2.4 13 IPBL 120 IPBL180 Rigid 1 2.4 14 IPBL 120 IPBL180 Pinned 1 2.4 15 IPBL 120 IPBL180 Rigid 1.5 2.4 16 IPBL 120 IPBL180 Pinned 1.5 2.4 17 IPBL 120 IPBL180 Rigid 2 2.4 18 IPBL 120 IPBL180 Pinned 2 2.4 19 IPBL 100 IPBL 120 Rigid 0.5 3.4 110 IPBL 100 IPBL 120 Pinned 0.5 3.4 111 IPBL 100 IPBL 120 Rigid 1 3.4 112 IPBL 100 IPBL 120 Pinned 1 3.4 113 IPBL 100 IPBL 120 Rigid 1.5 3.4 114 IPBL 100 IPBL 120 Pinned 1.5 3.4 115 IPBL 100 IPBL 120 Rigid 2 3.4 116 IPBL 100 IPBL 120 Pinned 2 3.4 117 IPBL 120 IPBL180 Rigid 1.5 2.4 218 IPBL 120 IPBL180 Pinned 1.5 2.4 219 IPBL 120 IPBL180 Rigid 1.5 2.4 320 IPBL 120 IPBL180 Pinned 1.5 2.4 3

Table 10Effect of frame connection types on initial stiffness.

λh Aspect ratio (L/H) PC-to-RC stiffness ratio

Infilled frame Bare frame Infill contribution

2.4 0.5 0.80 0.80 0.831 0.94 0.90 0.941.5 0.86 0.85 0.872 0.93 0.90 0.97

3.4 0.5 0.85 0.78 0.961 0.83 0.73 0.921.5 0.80 0.76 0.852 0.85 0.74 0.91

Avg. 0.86 0.81 0.91Std. 0.05 0.07 0.05COV (%) 6.06 8.16 5.61


55

RC ratio is 0.87 with a COV of 2.32%). As it mentioned before the infillcontribution is calculated by subtracting the pushover curve of infilledframe from its bare frame. Table 13 shows that the infill panels in thepinned connection frame have less strength than the infills surroundedby the rigid connection frame. The overall mean PC-to-RC strength ratio

is 0.82 with COV of 11.26%. It can be suggested that the estimatedstrength of the infill wall in the pinned connection frames calculated bythe equivalent strut model should be multiply by 0.8. The hypothesishas been evaluated and proved in the following of the paper.

5.2. Effect of number of bays

To investigate the effect of number of bays on the behavior of in-filled steel frame, the behaviors of infill panels in the multi-bay infilledframes were evaluated. For this purpose the lateral responses of infillwalls in the finite element models were determined by calculating theinteraction forces created between the infills and frames. Table 14shows the stiffness and strength of infill contributions for the single-,double- and triple-bay infilled frames with rigid and pinned connec-tions. In this table, 2B/1B and 3B/1B indicate the behavioral ratios ofdouble-bay to single-bay and triple-bay to single-bay specimens, re-spectively. One can see that the stiffness and the average strength ofinfill walls in the triple-bay and double-bay infill specimens were re-spectively twice and three times as large as those in the single-bay in-filled frames. The result was similar for the both rigid connection andpinned connections models. Thus, one can conclude that for modelingthe infill panels in the multi-bay infilled frame by equivalent strutmethod, the same strut as single-bay infilled frame can be used.

6. Utilizing equivalent strut model

Previous studies [9,10] have indicated that the strength and stiff-ness of multi-bay infilled frame cannot be directly estimated by sum-ming the behavior of single-bay infilled frame. Kaltakcı et al. [32] ex-amined the ability of equivalent strut model to estimate the maximumstrength of infilled frames. They concluded that, although the equiva-lent strut model gives rather a good estimation of failure load for thesingle-bay infilled frame, there was 40% difference between the ratiosof analytical to experimental failure loads for the double-bay infilledframes.

Here, the ability of equivalent strut method to estimate the behaviorof infill panels in multi-bay infilled frames as well as infilled pinnedconnection frames was evaluated. For this purpose, nonlinear pushoveranalyses were conducted on infilled frames modeled by the diagonalcompressive strut. In the first step the characteristics of equivalent strutin a rigid frame was calibrated by the result of FEM presented in theprevious section. Then, the calibrated strut was separately evaluated inthe infilled pinned connection frame and multi-bay infilled frames. TheMainstone strut model [4] recommended by FEMA356 [3] and ASCE41-06 [2] was utilized to evaluate the behavior of infilled frames. In thismodel the infill panel is replaced by a diagonal compressive strut inwhich the strut width is calculated by:

Table 11Effect of frame connection types on the strength of infilled frame.

Infilled frame

λh Aspect ratio (L/H) PC-to-RC strength ratio Avg. Std. COV (%)

Drift (%)

1.35 1.67 2 2.5

2.4 0.5 0.88 0.90 0.91 0.91 0.90 0.02 1.781 0.85 0.86 0.85 0.89 0.86 0.02 2.391.5 0.86 0.86 0.86 0.85 0.86 0.00 0.342 0.90 0.88 0.84 0.85 0.87 0.03 2.98

3.4 0.5 0.86 0.88 0.91 0.91 0.89 0.03 2.931 0.80 0.81 0.83 0.84 0.82 0.02 2.481.5 0.84 0.84 0.86 0.85 0.85 0.01 1.282 0.88 0.89 0.90 0.85 0.88 0.02 2.46

Avg. 0.86 0.86 0.87 0.87 0.87Std. 0.03 0.03 0.03 0.03 0.03COV (%) 3.36 3.44 3.57 3.46 3.35

Table 12Effect of frame connection rigidity on the strength of bare frame.

Bare frame


Drift (%)

1.35 1.67 2 2.5

2.4 0.5 0.86 0.88 0.89 0.91 0.89 0.02 2.411 0.86 0.87 0.86 0.88 0.87 0.01 0.731.5 0.83 0.86 0.86 0.86 0.85 0.02 1.772 0.90 0.89 0.88 0.89 0.89 0.00 0.51

3.4 0.5 0.87 0.87 0.87 0.91 0.88 0.02 2.281 0.82 0.86 0.86 0.87 0.85 0.02 2.331.5 0.88 0.85 0.89 0.91 0.88 0.02 2.742 0.89 0.88 0.89 0.89 0.89 0.00 0.49

Avg. 0.86 0.87 0.88 0.89 0.87Std. 0.03 0.01 0.02 0.02 0.02COV (%) 2.97 1.61 1.74 2.15 2.32

Table 13Effect of frame connection types on the strength of infill contribution.

Infill contribution


Drift (%)

1.35 1.67 2 2.5

2.4 0.5 0.99 1.0 1.0 0.95 0.99 0.03 3.411 0.81 0.84 0.84 0.96 0.86 0.07 7.631.5 0.94 0.86 0.86 0.83 0.87 0.05 5.372 0.91 0.81 0.66 0.73 0.78 0.11 13.82

3.4 0.5 0.83 0.91 1.0 0.92 0.93 0.09 9.411 0.78 0.74 0.79 0.82 0.78 0.03 4.141.5 0.79 0.82 0.81 0.74 0.79 0.03 4.272 0.85 0.89 0.90 0.75 0.85 0.07 8.17

Avg. 0.84 0.83 0.81 0.80 0.82Std. 0.08 0.08 0.12 0.10 0.09COV (%) 9.0 10.11 15.38 11.82 11.26

Table 14Effect of number of bays on the stiffness and strength of infill contribution.

FrameConnection

Bay No. Stiffness (kN/mm)

Strength (kN)

Drift (%)

1.35 1.67 2 2.5

Rigid 1 2.0 44.4 54.6 59.5 63.8Rigid 2 4.09 95.5 108.9 118.3 137.6Rigid 3 6.11 139.8 163.6 177.8 201.7Pinned 1 1.49 32.1 41.3 50.05 59.4Pinned 2 3.05 69.7 87.7 98.3 108.2Pinned 3 4.54 101.8 129 148.3 168

Avg.Rigid 2B/1B 2.05 2.15 1.99 1.99 2.16 2.07Rigid 3B/1B 3.06 3.15 3.00 2.99 3.16 3.07Pinned 2B/1B 2.05 2.17 2.12 1.96 1.82 2.02Pinned 3B/1B 3.05 3.17 3.12 2.96 2.83 3.02


56

= −w λh r0.175( ) 0.4inf

where, rinf is diagonal length of infill panel and λh is relative stiffness ofinfill to frame previously defined. The backbone behavior of theequivalent strut model recommended by ASCE41-06 [2] was utilized toperform nonlinear analysis as shown in Fig. 22. The amounts of c, d ande parameters were determined using the suggested values in ASCE41-06[2]. Moreover, Qy is the infill shear strength V( )inf , shall be calculated inaccordance with the following equation [2]:

= =Q V A fy ni vieinf

where, Ani is the area of net mortared section across infill and fvie isthe shear strength of masonry infill.

The used parameters to model infill wall via the equivalent strut inthe rigid connection frame are shown in Table 15. It should be notedthat fvie was determined based on the experimental shear test of ma-sonry reported in the previous section.

Based on the abovementioned parameter, the infilled rigid con-nection steel frame was modeled. The nonlinear static analysis(Pushover) was conducted using commercial software SAP2000 [33].Fig. 23 compared the capacity curves of the infilled frame obtained bySAP2000 [33] (equivalent compressive strut) and ABAQUS [14] (finiteelement analysis). It can be seen that the calibrated compressive strutmodel can appropriately capture the behavior of infilled rigid connec-tion frame.

In the next step, the ability of calibrated strut model to estimate thebehavior infilled pinned connection frame was examined. Therefore,the capacity curve of infilled pinned connection frame modeled by thecalibrated equivalent strut was compared with that of the finite elementmodel (Fig. 24(a)). It shows that the strut model calibrated by rigidconnection model, overestimates the stiffness and strength of infilledpinned connection frame. It was concluded from the parametric ana-lyses that the stiffness and strength of infill wall in the pinned con-nection steel frame were respectively 0.9 and 0.8 times of those in therigid connection frame. Therefore, the calibrated equivalent strut wasmodified using the mentioned values for using in the pinned connectionframe. In other words, the strut width and infill shear strength wereconsidered w=309×0.9=278mm and Vvie=60×0.8= 48 kN,respectively. Fig. 24(b) illustrates the capacity curve of the infilledpinned connection frame modeled with modified equivalent strut. It isevident that the modified diagonal strut can accurately estimate thestiffness and strength of infilled pinned connection frame. As a result, tomodel the infill walls by equivalent diagonal strut in pinned connectionframes. the following equations are proposed:

= × =− −w λh r λh r0.9 0.175( ) 0.157( )0.4inf

0.4inf

= =Q V A f0.8y ni vieinf

The behaviors of multi-bay infilled frames modeled by equivalentdiagonal struts were also assessed. For this purpose, as discussed andproofed in Section 5, the same struts were utilized for the modeling ofinfill panels in each frame of multi-bay infilled frames. Then, thepushover curves of the analytical models in SAP and the numericalmodels in ABAQUS were compared with each other. Two- and three-bay infilled frames for both rigid and pinned connections specimens (M-RC-2B, M-RC-3B, M-PC-2B and M-PC-3B) were analytically and nu-merically modeled in SAP2000 [33] and ABAQUS [14] software, re-spectively. Note that the three-bay infilled frames were numericallymodeled based on verified finite element modeling discussed earlier.Further, the characteristics of the equivalent struts were identical tothose of the calibrated struts used previously in the single-bay infilledrigid and pinned connection frames. Nonlinear static analyses werecarried out on the macro infilled frame models. The results werecompared with those of finite element analysis in ABAQUS as illustratedin Fig. 25. It shows that use of the same equivalent diagonal strut ineach bay can appropriately capture the behavior of multi-bay infilledframes. The result is valid for both infilled rigid and pinned connectionframes.

7. Conclusion

An experimental program was performed to investigate the effect ofbeam to column connection rigidity and number of bays on the in-planebehavior of infilled steel frames. Five half-scaled specimens includingone bare steel rigid connection frame and four infill specimens withdifferent numbers of bays and frame connection types were tested.Experimental results revealed that the stiffness and strength of masonryinfilled pinned connection frames were 50% and 90% those of infillspecimens with rigid connections respectively. Further, the maximumstrength and stiffness of double-bay infilled frames specimens were 1.9and 2 times those of single-bay infilled frame, respectively. This result ismainly due to the use of a new lateral loading setup in which the lateralload was uniformly distributed along the top beam of the specimens.The experimental observations indicated that two major inclinedcracking patterns were formed in the infill panels. Note that the angle ofinclined cracking with respect to the horizontal was not affected by theconnection rigidity and number of bays of the surrounding frames and

Fig. 22. Generalized Force-Deformation Relation for infill wall [2].

Table 15Characteristics of equivalent strut model in RC frame.

Modulus of elasticity Eme (MPa) Strut width w (mm) Strut thickness t (mm) Ani (mm2) fvie (MPa) Vvie (kN)

1892 309 95 197600 0.3 60

0

50

100

150

200

250

300

350

0 2 4 6 8

Base

she

ar (k

N)

Drift (%)

ABAQUS (M-RC-1B)

SAP2000 (M-RC-1B)

Fig. 23. Capacity curves of masonry infilled steel frame with rigid connections(M-RC-1B) modeled with calibrated strut and finite element methods.


57

remained constant at 65°.In addition, the parametric finite element study showed that the

stiffness and strength of infill panel in the pinned connection frameswere 0.9 and 0.8 times as large as those in the rigid connection frame,respectively. Further, the response of infill walls in the multi-bay frameshad a direct relationship with the number of bays. The results of nu-merical modeling were used to evaluate the capability of the equivalentdiagonal strut method in the modeling infill walls in the pinned con-nection and multi-bay infilled steel frames. It was observed that theequivalent strut can appropriately capture the behavior of the infillwalls in the multi-bay frames. Nevertheless, it was found that it must bemodified to model infill panels in the pinned connection frames.Therefore, a new equivalent strut was proposed for modeling the infillpanel in the pinned connection steel frames. In this model, the strength

and strut width of Mainstone model were modified by the factors of 0.8and 0.9, respectively.

Acknowledgments

This study was supported financially by International Institute ofEarthquake Engineering and Seismology (IIEES), as well asOrganization for Development, Renovation and Equipping Schools ofI.R. Iran, under grant No. 7386 and 7387.

References

[1] Asteris P, Antoniou S, Sophianopoulos D, Chrysostomou CZ. Mathematical macro-modeling of infilled frames: state of the art. J Struct Eng 2011;137:1508–17.

)b()a(

0

50

100

150

200

250

300

350

0 1 2 3 4 5 6

Base

she

ar (k

N)

Drift (%)

ABQUS (M-PC-1B)

SAP2000 calibrated strut model

0

50

100

150

200

250

300

0 1 2 3 4 5 6

Base

she

ar (k

N)

Drift (%)

ABAQUS (M-PC-1B)

SAP2000 propoed model

Fig. 24. Comparison between capacity curves of infilled steel frame with pinned connections (M-PC-1B) (a) Mainstone strut and finite element method; (b) proposedstrut and finite element method.

)b()a(

(c) (d)

0

100

200

300

400

500

600

0 1 2 3 4 5 6

Base

she

ar (k

N)

Drift (%)

M-RC-2B ABAQUS

M-RC-2B SAP

0

100

200

300

400

500

600

700

800

900

0 1 2 3 4 5 6

Base

she

ar (k

N)

Drift (%)

M-RC-3B ABAQUS

M-RC-3B SAP

0

100

200

300

400

500

0 1 2 3 4 5

Base

she

ar (k

N)

Drift (%)

M-PC-2B ABAQUS

M-PC-2B SAP

0

100

200

300

400

500

600

700

0 1 2 3 4 5

Base

she

ar (k

N)

Drift (%)

M-PC-3B ABAQUS

M-PC-3B SAP

Fig. 25. Comparison between capacity curves of ABAQUS and SAP for (a) double-bay rigid connections; (b) three-bay rigid connections; (c) double-bay pinnedconnections; (b) three-bay pinned connections; infilled frames.


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