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
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.
section aria should multiplied by (1/2) and (1/2), 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
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
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
Displacement(mm)
Cycle No.
(a) (b)
Fig. 2 Bracing system to prevent out of plane movement (a) side view. (b) top view
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
Lateral load (kN)
Drift (%) BF
-300 -200 -100 0 100 200 300
-6 -4 -2 0 2 4 6
Lateral load (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
Lateral load (kN)
Drift (%) M-RC-1B
-400 -300 -200 -100 0 100 200 300 400
-8 -6 -4 -2 0 2 4 6 8
Lateral load (kN)
Drift (%) Occurrence of inclined cracking
Terminate the test due to excessive out of plane movement
Occurrence of inclined cracking
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
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
Lateral load (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
Lateral load (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
Lateral load (kN)
Drift (%) M-PC-1B
-400 -300 -200 -100 0 100 200 300 400
-8 -6 -4 -2 0 2 4 6 8
Lateral load (kN)
Drift (%) Occurrence of inclined cracking
beam to column connection failure
Occurrence of inclined cracking beam to column
connection failure
Begining of damage in connection plate
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
Lateral load (kN)
Drift (%) S2-PC-1B
-400 -300 -200 -100 0 100 200 300 400
-8 -6 -4 -2 0 2 4 6 8
Lateral load (kN)
Drift (%)
beam to column connection failure
beam to column connection failure
beginning of damage on beam to column connection plate beginning of damage in
beam to column connection plate
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 col
fe m
h
h
h I E
t
E
41
inf inf
4
2 sin
(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
i i t
t E t 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
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
-8 -6 -4 -2 0 2 4 6 8
Drift (%)
S2-PC-1B
0
0 1 2 3 4 5 6 7 8
Drift (%)
0 50 100 150 200 250 300
0 1 2 3 4 5
Lateral load (kN)
Drift (%)
BF (RC) Experimental BF (RC) Numerical
0 50 100 150 200 250 300
0 1 2 3 4 5
Lateral load (kN)
Drift (%)
BF (PC) Numerical
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
Lateral load (kN)
Drift (%) M-RC-1B
BF (RC) 0
Contribution of M-RC-1B infill M-PC-1B
BF (PC)
Contribution of M-PC-1B infill
0 50 100 150 200 250 300 350 400 450 500
0 1 2 3 4 5
Lateral load (kN)
Drift (%) S2-RC-1B BF-RC
Contribution of S2-RC-1B infill S2-PC-1B
BF (PC)
Contribution of S2-PC-1B infill
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
2
a
(3)Mainstone (1971) gives the width of equivalent strut as
inf 4 .
)
0( 175 .
0 h r
a
col (4)and Flanagan and Bennet (1999) propose the following formula for calculation of strut width
cos
a C
(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
-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
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)
inf
cos
inf
m
U
a t f
H
(6)Flanagan and Bennet (1999) give the strength of infill panel as
m ult
U
K t f
H
inf
inf
(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
results of this study revealed that these methods overestimate the stiffness and strength of infilled frames with pinned connections. Therefore, the authors suggest that more experimental as well as analytical and numerical investigations are needed to propose a new macro model for infilled frames with semi-rigid and pinned connections.
Acknowledgments
This study is supported financially by International Institute of Earthquake Engineering and Seismology (IIEES), as well as Organization for Renovating, Developing and Equipping Schools of Iran under grant No.
7386 and 7387, respectively.
References
ABAQUS user manual (2012), Version 6.12. Dassault Systemes Simulia Corp, Rhode Island, U.S.A.
AISC Committee (2010), Specification for structural steel buildings (ANSI/AISC 360-10), American Institute of Steel Construction, Chicago.
ASCE/SEI Seismic Rehabilitation Standards Committee (2007),
"Seismic rehabilitation of existing buildings (ASCE/SEI 41- 06)", American Society of Civil Engineers, Reston, VA.
ASTM C109 (2002), Standard test method for compressive strength of hydraulic cement mortars (Using 2-In. or [50-Mm]
Cube Specimens), ASTM Int., West Conshohocken.
ASTM C1314-03b (2004), Standard test method for compressive strength of masonry prisms, ASTM Int.
ASTM E8/E8M (2009), “Standard test methods for tension testing of metallic materials”, ASTM Int., West Conshohocken.
Chopra, A.K. (2001), “Dynamics of structures: Theory and applications to earthquake engineering”, Prentice-Hall.
CSA S304 (2004), Design of masonry structures, Canadian Standards Association, Mississauga, Canada.
CSI SAP2000 V 14.1 (2010), “Integrated finite element analysis and design of structures basic analysis reference manual”, Comput. Struct., Berkeley, U.S.A.
Dawe, J.L. and Seah, C.K. (1989), “Behaviour of masonry infilled steel frames”, Canada. J. Civil Eng., 16, 865-876.
https://doi.org/10.1139/l89-129.
El-Dakhakhni W.W., Elgaaly, M. and Hamid, A.A. (2003), “Three- strut model for concrete mansonry-infilled steel frames”, J.
Struct. Eng., 129, 177-185.
https://doi.org/10.1061/(ASCE)0733-9445(2003)129:2(177).
Fang, Y., Gu, Q. and Shen, L. (2008), “Hysteretic behavior of simi-rigid composite steel frame with reinforced concrete infill wall in column weak axis”, J. Build. Struct., 2.
FEMA 356 (2000), Commentary for the seismic rehabilitation of buildings, Federal Emergency Management Agency, Washington, D.C.
Harris, H.G. and Sabnis, G. (1999), “Structural modeling and experimental techniques”, CRC Press.
Hashemi, S.J., Razzaghi, J., Moghadam, A.S. and Lourenço, P.B.
(2018), “Cyclic testing of steel frames infilled with concrete sandwich panels”, Archive. Civil Mech. Eng., 18(2), 557-572.
Holmes, M. (1961), “Steel frames with brickwork and concrete infilling”, In ICE Proceedings. Thomas Telford, 19, 473-478.
https://doi.org/10.1680/iicep.1961.11305.
https://doi.org/10.1016/j.acme.2017.10.007.
INBC-Part 8 (2005), Design and construction of masonry buildings, Iranian national building code, part 8. IR (Iran), Ministry of Housing and Urban Development.
Kaltakcı, M.Y., Köken, A. and Korkmaz, H.H. (2006), “Analytical solutions using the equivalent strut tie method of infilled steel frames and experimental verification”, Canada. J. Civil Eng., 33, 632-638. https://doi.org/10.1139/l06-004.
Liu, Y. and Manesh, P. (2013), “Concrete masonry infilled steel frames subjected to combined in-plane lateral and axial loading-an experimental study”, Eng. Struct., 52, 331-339.
https://doi.org/10.1016/j.engstruct.2013.02.038.
Mainstone, R.J. (1971), “On the stiffness and strengths of infilled frames”, In ICE Proceedings. Thomas Telford, 49, 230.
Mander, J.B. and Nair, B., Wojtkowski, K. and Ma, J. (1993), “An experimental study on the seismic performance of brick- infilled steel frames with and without retrofit”, In Technical Report. National Center for Earthquake Engineering Research (NCEER).
Masonry Standard Joint Committee (2012), Building code requirements for masonry structures, ACI S30/ASCE 5/TMS 402, American Concrete Institute, the American Society of Civil Engineers and The Masonry Society, U.S.A.
Moghadam, H., Mohammadi, M.G. and Ghaemian, M. (2006),
“Experimental and analytical investigation in to crack strength determination of infilled steel frames”, J. Construct. Steel Res., 62, 1341-1352. https://doi.org/10.1016/j.jcsr.2006.01.002.
Moghaddam, H. (2004), “Lateral load behavior of masonry infilled steel frames with repair and retrofit”, J. Struct. Eng., 130, 56-63. https://doi.org/10.1061/(ASCE)0733- 9445(2004)130:1(56).
Moghaddam, H.A. and Dowling, P.J. (1987), “The state of the art in infilled frames”, London: Imperial College of Science and Technology, Civil Engineering Department.
Mohamed, H.M. and Romao, X. (2018), “Performance analysis of a detailed FE modelling strategy to simulate the behaviour of masonry-infilled RC frames under cyclic loading”, Earthq.
Struct., 14(6), 551-565.
https://doi.org/10.12989/eas.2018.14.6.551.
Mohammadi, M. (2007), “Stiffness and damping of infilled steel frames”, Proceedings of the ICE-Structures and Buildings, 160, 105-118. https://doi.org/10.1680/stbu.2007.160.2.105.
Mohammadi, M. and Motovali Emami, S.M. (2019), “Multi-bay and pinned connection steel infilled frames; An experimental and numerical study”, Eng. Struct., 188, 43-59.
https://doi.org/10.1016/j.engstruct.2019.03.028.
Motovali Emami, S.M. and Mohammadi, M. (2016), “Influence of
vertical load on in-plane behavior of masonry infilled steel frames”, Earthq. Struct., 11(4), 609-627.
http://dx.doi.org/10.12989/eas.2016.11.4.609
Peng, X., Gu, Q. and Lin, C. (2008), “Experimental study on steel frame reinforced concrete infill wall structures with semi-rigid joints”, China Civ. Eng. J., 41(1), 64-69.
Polyakov, S.V. (1960), “On the interaction between masonry filler walls and enclosing frame when loaded in the plane of the wall”, Translations Earthq. Eng., 2(3), 36-42.
Sakr, M.A., Eladly, M.M., Khalifa, T. and El-Khoriby, S. (2019),
“Cyclic behaviour of infilled steel frames with different beam- to-column connection types”, Steel Composite Struct., 30(5), 443-456. https://doi.org/10.12989/scs.2019.30.5.443.
Stafford-Smith, B. and Carter, C. (1969), “A method of analysis for infilled frames”, In ICE Proceedings Thomas Telford, 44, 31-48.
Standard No 2800 (2005), “Iranian code of practice for seismic resistant design of buildings”, Third Revision, Building and Housing Research Center, Iran.
Sun, G., He, R., Qiang, G. and Fang, Y. (2011), “Cyclic behavior of partially-restrained steel frame with RC infill walls”, J.
Construct. Steel Res., 67(12), 1821-1834.
https://doi.org/10.1016/j.jcsr.2011.06.002
Yan, P. (2006), Hysteretic Behavior and Design Criterion of Composite Steel Frame Reinforce Concrete Infill Wall Structural System with FR Connections, Ph. D. Dissertation, Xi’an University of Architecture and Technology.
Yekrangnia, M. and Mohammadi, M. (2017), “A new strut model for solid masonry infills in steel frames”, Eng. Struct., 135, 222-235. https://doi.org/10.1016/j.engstruct.2016.10.048.
CC
