JOURNAL OF ASIAN ARCHITECTURE AND BUILDING ENGINEERING https://doi.org/10.1080/13467581.2023.2165402 BUILDING STRUCTURES AND MATERIALS Finite element analyses on hysteretic behavior of steel frames infilled with AAC masonry wall with circular-arc opening a b c b You-Sheng Yu , Cheng Li , Yu-Min Cui and Ya-Nan Guo Department of Civil Engineering, Qingdao University of Technology, Qingdao, Department of Civil Engineering, Qingdao University of b c Technology, China; Postgraduate Student, Department of Civil Engineering, Qingdao University of Technology, Qingdao, China; Qingdao Municipal Bureau of Housing and Urban-Rural Development, Qingdao, China ABSTRACT ARTICLE HISTORY Received 7 July 2022 The steel frame infilled with the autoclaved lightweight aerated concrete (AAC) masonry wall is Accepted 3 January 2023 widely applied in buildings. However, earthquake damage investigation has revealed that infill walls have a significant influence on the mechanical behaviors of the frame structure. In this KEYWORDS paper, a new type of AAC masonry wall with circular-arc openings at the corners was proposed Infill walls; steel frames; based on the principle that setting openings at the corners of the infill wall would weaken the interaction; circular-arc tension (compression) band, so as to reduce the unfavorable interaction between the steel openings; finite element frame and the infill walls. Additionally, the seismic performance of steel frames infilled with analysis AAC masonry walls with circular-arc openings at the corners under low cycle loading was investigated through finite element (FE) method simulations on 11 specimens. The results demonstrated that the circular-arc openings are effective in delaying the cracking of the AAC wall and weakening the additional stiffness of the AAC masonry wall for the steel frame. 1. Introduction wall was suddenly distributed to adjacent components In traditional structural design, the infill wall is com- after the masonry wall failed. Three two-story, two- monly regarded as a non-structural component span RC frames infilled with various types of infill (Sekhar 1997; Scheuer, Keoleian, and Reppe 2003; walls were tested by Fei et al. 2021). It was discovered Yagust and Yankelevsky 2007; Turgay et al. 2014; that the infill wall produced additional stiffness to the Kumar, Rai, and Jain 2015; Perrone, Leone, and Aiello frame at the initial stage of loading, which led to an 2016). Thus, the interaction between the frame struc- increase in the horizontal load-bearing capacity of the ture and the infill wall is generally ignored. However, frame structure and reduced the deformation perfor- the research on the reinforced concrete (RC) frame mance of the frame. (Ozturkoglu, Ucar, and Yesilce with masonry walls revealed that the infill wall partici- 2017) investigated the effect of masonry infill walls pated in sharing the load of the frame, and the large in- with openings on the mechanical properties of RC plane stiffness of the infill wall changed the perfor- frames by performing pushover analysis on bare, par- mance of the frame (Crisafulli 1997). Subsequently, tially and fully infilled RC frames. The results verified a series of investigations on the 1999 Turkey earth- that the position and dimensions of openings in the quake (Sezen et al. 2003), the 2008 Wenchuan earth- infill wall significantly influence the lateral stiffness of quake in China (Zhao, Taucer, and Rossetto 2009a), and the frame. (Kaya, Tekeli, and Anil 2018) examined RC the 2009 L’Aquila earthquake in Italy (Ricci, De Luca, frames infilled with masonry with rebar-reinforced and Verderame 2011) have demonstrated that the stucco, suggesting that rebar-reinforced stucco adverse effects of infill walls on the frame structure increased the load-bearing capacity of RC frames. P.G. were underestimated. Therefore, it is critical to accu- (Asteris et al. 2017) investigated earthquake damage rately assess the influence of infill walls on the mechan- and found that in-plane damaged infill walls increased ical properties of the frame system. the risk of out-of-plane damage to infill walls. In addi- The interaction between the infill wall and the tion to quasi-static test studies, shaking table tests frame has been broadly investigated by a significant were employed to simulate the failure of structures number of experimental and numerical analyses under earthquake action (Hashemi and Mosalam (Biondi, Colangelo, and Nuti 2000; Dolšek and Fajfar 2006; Centeno, Ventura, and Foo 2008; Crozet, 2005; Brodsky, Rabinovitch, and Yankelevsky 2017, Politopoulos, and Chaudat 2019). These test results 2018). (El-Dakhakhni, Elgaaly, and Hamid 2003) tested implied that the seismic performance of the frame the steel frame filled with concrete masonry, drawing was significantly changed due to the existence of the the conclusion that the seismic force borne by the infill infill wall. CONTACT You-Sheng Yu firstname.lastname@example.org Department of Civil Engineering, Qingdao University of Technology, Qingdao, 266033, China © 2023 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group on behalf of the Architectural Institute of Japan, Architectural Institute of Korea and Architectural Society of China. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 2 Y.-S. YU ET AL. In summary, the infill wall has an unfavorable effect on the frame under the action of an earthquake, such as the torsion effect and soft layer effect caused by irregularities in the plane and the short-column effects (Negro and Colombo 1997). In addition, the in-plane damage to the infill wall significantly reduced the out- of-plane bearing capacity (Angel, Abrams, and Shapiro et al. 1994). Based on the aforementioned issues, researchers verified that infill walls with slits can sig- nificantly improve the energy consumption and ducti- lity of the frame structure (Li, Li, and Rong 2011). Therefore, the current research focuses on weakening Figure 1. Schematic diagram of the tension (compression) the role of infill walls in the frame to ensure that the band of the infill wall. infill walls do not significantly change the failure mode of the frame (Huang, Guo, and Kuang 2016). Ruey Shyang et al. 2012) conducted a push-over experiment significantly reduced the deformation capacity of RC on multistory frame models with soft first story config - frames infilled with AAC walls. The literature review urations, revealing that the infill wall with vertical slits emphasizes the interaction between the frame and on the edge addressed the soft layer problem caused the AAC masonry wall. However, there is little research by the vertical irregular structure. (Jiang, Liu, and Mao exploring the methods to improve the seismic perfor- 2015) performed tests on the RC frame infilled with mance of steel frames with AAC infill walls. masonry walls. As suggested by the analytical results, Notably, little attention was paid to the steel frames the stiffness, strength, and energy dissipation capacity infilled with autoclaved lightweight aerated concrete of the specimen decreased significantly, while the dis- (AAC) masonry wall, and the openings are mostly ver- placement ductility ratio of the frame increased. (Sun tical slits and horizontal slits to the infill wall. et al. 2011) conducted the horizontal cyclic load experi- Considering the masonry infilled steel frame generates ments on the partially-restrained RC with RC infill walls, tension (compression) bands under the low cyclic load, validating that setting hidden vertical slits in the RC the circular-arc openings were adopted on the corners infill wall contributed to the lesser lateral resistance of the infill wall. The schematic diagram of the tension but higher ductility of the structure. Subsequently, (compression) band of the infill wall is illustrated in the steel frames with the prescribed concealed vertical Figure 1. Furthermore, 11 finite element method mod- slit RC walls were examined under horizontal cyclic els were established to investigate the seismic perfor- loading by (Sun et al. 2017c). It was found that the mance of specimens subjected to low cyclic loads. The vertical slits reduced the degradation of peak strength influence of the AAC masonry wall with circular-arc and achieved the desired ductile failure mode. openings on the hysteretic performance, load-bearing Additionally, You-Sheng, Ya-Nan, and Mei 2021) per- capacity, ductility, stiffness degradation, strength formed both experimental and FE studies on the steel degradation, and energy dissipation capacity of the frames infilled with cellulose fiber cement sheets auto- steel frame was also explored. Additionally, the opti- claved (CCA) wall with preset vertical slits. The results mal value range of the size of the circular-arc openings verified that the preset vertical slits were effective in was determined. The diagram of a steel frame infilled weakening the restraint effect of the steel frame on the with AAC masonry wall with circular-arc openings is CCA wall and delaying the cracking of the CCA wall. exhibited in Figure 2. In recent years, more and more studies have demonstrated that the interaction between frame and infilled walls using high-strength masonry units 2. Finite element analysis is more significant (Asteris et al. 2013; Basha and 2.1. Design of specimens Kaushik 2016; Zovkic, Sigmund, and Guljas 2013). Given the aforementioned issues, AAC is widely used One bare steel frame (KJ-1), one steel frame infilled in infilled wall frames owing to its lightweight and high with AAC masonry wall (KJ-2), and 9 steel frames durability. Meanwhile, researchers have paid special infilled with AAC masonry wall with circular-arc open- attention to the seismic performance of RC frames ings of different sizes (KJ-3-1~ KJ-3-9) were designed. infilled with AAC walls (Schwarz, Hanaor, and The columns and the beams of the models are Yankelevsky 2015; Siddiqui, Sucuoglu, and Yakut H-shaped H200 × 200 × 8 × 12 and H-shaped 2015). The out-of-plane pressure tests of six single- H300 × 200 × 6.5 × 9, respectively. The web of the bay single-story half-scaled RC frames with AAC infill beam was connected with the column by fillet welds, walls were performed (Binici et al. 2019), and the and the flange was connected by butt welds. Stiffeners results suggested that the out-of-plane pressure were welded to the steel column of the beam-column JOURNAL OF ASIAN ARCHITECTURE AND BUILDING ENGINEERING 3 problem, and the large displacement of the compo- nent is the geometric nonlinear problem. For the con- venience of calculation, the problem is transformed from nonlinear to equivalent linear, generally involving three methods of the incremental method, Newton- Raphson, and hybrid method (Yin 2007). In this paper, the Newton-Raphson method was applied to perform FE analysis on the steel frames infilled with AAC masonry walls. The calculation diagram of the Newton- Raphson method is displayed in Figure 4. The nonlinear equations solved by the Newton- Raphson method (Eq.1–3): � � � 1 1 i i i i Δδ ¼ K φ ¼ K R F (1) T T � � � � i i @ φ @ F K ¼ ¼ (2) @ δ @ δ iþ1 i i δ ¼ δ þ Δδ (3) Figure 2. Diagram of steel frame infilled with AAC masonry Where δ represents the displacement of the structure wall with circular-arc openings. iþ1 in the i state; δ denotes the displacement of the structure in the i + 1 state; Δδ indicates the displace- connection. The steel was grade Q355B (f = 355MPa), i ment correction value; K indicates the stiffness corre- following the Chinese national standard GB 50017– sponding to the structure in the i state; R represents 2017 (2017). The span of each specimen was the load applied to the structure; F represents the 4400 mm, the height was 3000 mm, and the thickness internal force of the structure in the i state; φ indicates of all infill walls was 200 mm. Table 1 lists the para- the iterative force residual value. meters of specimens. The location and dimension of the circular-arc openings in the infill wall were taken as the variables of the steel frames infilled with the AAC 3. Construction of FE models masonry wall. The dimension of the specimens was 3.1. Model establishment determined by l and l . Among them, l denotes the 1 2 1 distance from the arc endpoint to the corner of the The software ABAQUS was applied to establish the FE infill wall, and l represents the distance from the mid- models. The model is composed of steel beams, steel point of the arc to the corner of the infill wall. The columns, stiffeners, and AAC masonry walls. The FE details of the specimens are provided in Figure 3. models are illustrated in Figure 5. In FE analysis, each element type was adopted to different analysis meth- ods. Besides, C3D8R (8-node hexahedral reduced inte- 2.2. Calculation of FE models gral entity element) was employed to simulate steel In the calculation of FE models, the plastic develop- beams, steel columns, stiffeners, and AAC masonry ment of the material belongs to the material nonlinear walls. Structured mesh division technology was Table 1. Parameters of specimens. Parameters of the circular-arc openings Number of Characteristics of l/ Opening Fig. specimens specimens Quantity Location l/H mm S/mm rate /% number KJ-1 Bare steel frame - - - - - - - 2-(a) KJ-2 Steel frames infilled with AAC masonry wall 0 - - - - - - 2-(b) KJ-3 KJ-3-1 Steel frames infilled with AAC masonry wall with 4 Four corners of AAC 1/ 225 353.43 1.40 2-(c) circular-arc openings masonry wall 12 245 KJ-3-2 1/ 270 384.85 1.66 11 300 KJ-3-3 1/ 337 424.12 2.02 10 386 KJ-3-4 1/9 450 471.24 2.49 KJ-3-5 1/8 540 529.36 3.15 KJ-3-6 1/7 675 606.33 4.13 KJ-3-7 1/6 706.86 5.61 KJ-3-8 1/5 848.23 8.08 KJ-3-9 1/4 1060.29 12.62 4 Y.-S. YU ET AL. Figure 3. Dimensions of specimens (Unit: mm). Figure 5. FE model. Figure 4. Schematic diagram of the Newton-Raphson method. should be divided more finely. The contact surface of the steel beam and the steel column was defined as “ master surface”, and the infill wall was defined as the selected to mesh the FE models (Qi Wei 2016). “slave surface”. In the FE models, the number of meshes Structured mesh division technology is to apply stan- near the arc opening of the infill wall was increased, the dard mesh patterns to simple-shaped geometric areas. mesh size of the infill wall in the arc opening area was Additionally, the number and quality of mesh division 20 mm, and the other parts was 50 mm. The number of exerted a significant influence on the calculation of FE meshes near the beam-column connection area was models, which was related to the calculation efficiency increased, the mesh size of the beam-column connec- and the accuracy of the results. The “slave surface” tion area was 60 mm, and the other parts of the steel mesh nodes cannot invade any part of the “master beam and the steel column was 80 mm. Figure 6 pre- surface” mesh, the number of “slave surface” meshes sents the meshing of the FE models. JOURNAL OF ASIAN ARCHITECTURE AND BUILDING ENGINEERING 5 the load-bearing capacity and initial stiffness of the specimens. The smaller the friction coefficient, the better the ductility of the specimen (Zhang Tao 2011). In practical engineering, flexible materials can be filled between the infill wall and the steel frame to reduce friction. In this paper, the friction coefficient was 0.4. The nodes of the loading end were coupled, and a low-cycle repeated load in the Y-direction was applied at the coupling point. The material parameters of steel were determined following literature : the elastic modulus (E) was 2.06 × 10 MPa, and the Poisson’s ratio (ν) was 0.3. The stress-strain curve of steel beams and columns adopted a three-linear model considering the strengthening phase and the descending phase, as illustrated in Figure 7a. The constitutive relationship of AAC masonry was obtained by the masonry stress- strain test conducted by Tongji University in 1998 (ZHU Bo-long 1998), as exhibited in Figure 7b. The elastic modulus and Poisson’s ratio of AAC masonry were Figure 6. The meshing of the FE model. 1745 MPa and 0.2, respectively. 3.2. Boundary conditions and material 3.3. Loading system of specimens constitutive parameters According to the American AISC Seismic Code (ANSI/ Appropriate constraints were adopted to define the AISC 341-10), the loading was controlled by displace- interaction between parts. The degrees of freedom of ment. The loading process is detailed as follows: the the frame in the x-direction was limited to ensure the inter-story drift angle (θ) of 0.225% was taken as the out-of-plane stability of the specimens. In order to loading displacement, and three displacement cycles simulate the fixed connection of the column base, were performed at each stage of displacement load- the degrees of freedom in all directions of the column ing. After the inter-story drift ratio reached 1/200 base was restricted. “Tie” was used to simulate the (θ > 1/200), each specimen underwent two displace- connection of steel column, steel beam, stiffener, and ment cycles at each loading stage. The loading ended AAC masonry wall. Meanwhile, the contact relationship when the model’s bearing capacity was lower than between the steel beam and the AAC masonry wall 85% of its peak load. The loading system of the speci- was established, and the penetration between the mens is exhibited in Figure 8. contact parts was restricted by using “hard contact” in the normal direction. Tangential contact was 3.4. Verification of FEM defined as penalized friction contact (Yiping and Yurong 2006). The friction coefficient between the The FE models were established based on the data of steel frame and the infill wall has a great influence on the KJ-2 specimen in the literature . The Figure 7. Material constitutive relationship curves. 6 Y.-S. YU ET AL. was not as significant as in the experiment. The devel- opment of infill wall cracks in the test aggravated the shrinkage of the hysteresis curve, the effect of the infill wall cracking was neglected in the FE simulation. Compared with the test, the boundary conditions, material properties, constraints, and other factors of the FE simulation were much more ideal, which led to differences between the FEM and the test model. In the FE simulation, the bottom of the column was the completely ideal rigid connection. The steel beam and the steel column of the test specimen were connected by butt welds. In the test, the mechanical properties of the specimen was affected by the weld defects. Additionally, in the elastic stage, the results obtained by the FE simulation were basically consistent with the test results. When the specimens was in the yield state, the peak load obtained by the FE simulation was Figure 8. Loading system of specimens. slightly higher than the test result. In the skeleton curve, the load obtained by the FE simulation was comparison of the hysteresis curve and the skeleton almost the same as the test results when θ < 3.0%; curve between the FE simulation results and the test the load obtained by the FE simulation is 4%, 4.5%, and results in the literature  is presented in Figures 9a 1.7% higher than the test results when θ = 3.5%, 4.0%, and b, respectively. It can be observed that the FE 4.5%, respectively. Figures 9c and d exhibits the failure simulation results were consistent with the test results. mode of the test and the FE models, respectively. The The area enclosed by the hysteresis curve of the FE failure mode of the CCA infill wall obtained by FE simulation was larger, and the cracking phenomenon models was consistent with the test results. As Figure 9. Verification of FEM. JOURNAL OF ASIAN ARCHITECTURE AND BUILDING ENGINEERING 7 revealed in the figure, the damage of the CCA infill wall flange of the upper steel beam at the non-loaded end in the test was mainly manifested in the diagonal area began to buckle when θ = 4.5%, and then the upper of the CCA infill wall and the junction area between the flange of the steel beam also buckled; the Mises stress CCA infill wall and the keel. In the test, the CCA infill of beam-column connection of the KJ-1 specimen wall consists of three parts, resulting the damage of reached the steel tensile strength of 554Mpa when the CCA infill wall in the test manifested in the splicing θ = 6% and the flanges of the upper steel beam at of the CCA infill wall. The correctness of the FE analysis the non-loaded end severely buckled. has been verified. 10 steel frames infilled with AAC masonry wall spe- cimens (KJ-2, KJ-3-1~ KJ-3-9) were simulated. It was discovered that the failure modes of the specimens were similar. The failure process was divided into 4. Analysis of FEM results three stages: the constant friction stage, the shear 4.1. Failure characteristics friction stage, and the plastic failure stage. When the KJ-2 specimen was in the constant friction stage, fric- The failure modes of the KJ-1 specimen are provided in tion occurred between the four corners of the AAC Figure 10a. The Mises stress of the KJ-1 specimen was masonry wall and the beam-column connections of less than the yield stress of 360Mpa when θ < 1.5% and the steel frame. Meanwhile, the stress in the corner of the KJ-1 specimen was in the elastic stage; the 4 node the infill wall increased. For the KJ-3-1~ KJ-3-9, the AAC domains severely deformed when θ = 4%; the lower Figure 10. Mises stress distribution of the specimens. 8 Y.-S. YU ET AL. masonry wall had no contact with the beam-column delayed the stiffness degradation of the steel frames connections of the steel frame owing to the existence infilled with AAC masonry wall. of the initial circular-arc openings. In the shear friction stage, the AAC masonry wall produced the tension 4.3. Skeleton curve and ductility (compression) band along the diagonal direction ascribed to the steel frame restrains the AAC masonry The skeleton curve of each specimen is presented in wall. Furthermore, the contribution of the AAC Figure 12. The positive ultimate bearing capacity of KJ- masonry wall to the load-bearing capacity of the steel 2, KJ-3-1~ KJ-3-9 was 83.2%, 68.9%, 70.3%, 62.7%, frame increased gradually. 62.1%, 60.3%, 52.3%, 51.2%, 43.9%, and 24.8% higher In the plastic failure stage, the contribution of the than KJ-1, respectively. The skeleton curve suggested AAC masonry wall to the load-bearing capacity of the that the AAC masonry walls significantly improved the steel frame was reduced, and the AAC masonry wall load-bearing capacity of the steel frame. The circular- was gradually out of work ascribed to severe damage. arc opening structure reduced the participation of the The Mises stress of the beam-column connection of infill wall to the load-bearing capacity of the steel the KJ-2 specimen exceeded 440Mpa when θ = 5% frame. The skeleton curve of KJ-2, KJ-3-1~ KJ-3-6 exhib- and the bottom of the steel column buckled locally. ited a descending section when the inter-story drift The load of the KJ-2 specimen was lower than 85% of angle was greater than 4.5%, which is caused by the its peak load when θ = 5%, suggesting that the speci- failure of the infill wall. The ductility coefficient (µ ) was men was damaged. For the AAC masonry wall, the obtained by the Eq. μ = Δu/Δy, which reflected the Mises stress of the four corners reached 2.9Mpa. The plastic deformation performance of each specimen. four corners were severely damaged, and the The performance point values are listed in Table 2. As masonry wall suffered out-of-plane damage observed in the table, the ductility coefficient of each (Figure 10b). Figure 10c exhibits the Mises stress dis- specimen ranged from 8 to 10, which reflected that tribution of the KJ-3-5 under θ = 5.5%. The existence each specimen presented good ductility and deforma- of the circular-arc openings at the corner weakened tion properties. Figure 13 displays the definitions of the stress concentration phenomenon of the AAC performance points, such as yield load (P ), yield dis- masonry wall and reduced the risk of out-of-plane placement (θ ), ultimate load (P ), and ultimate displa- y u damage to infill walls. cement (θ ). 4.4. Stiffness degradation 4.2. Hysteresis curve To analyze the additional stiffness of AAC masonry Figure 11 illustrates the lateral load-displacement hys- walls and AAC masonry walls with circular circular-arc teresis curve of each specimen. The hysteresis curve of openings of different sizes to the steel frame, the stiff - each specimen was full, implying that each specimen ness degradation law of the specimens subjected to possessed good energy dissipation capacity. Among the action of low-cycle repeated loads were obtained. them, the hysteresis curves of KJ-1, KJ-3-7~ KJ-3-9 were The stiffness of the specimens was compared, and the fully shuttle-shaped, while the hysteresis curves of KJ- stiffness degradation expression was expressed as: 2, KJ-3-1~ KJ3-6 developed from a fusiform to an arched. There was a “pinching” phenomenon in the k k X X K ¼ P θ (4) hysteresis curve of KJ-2, KJ-3-1~ KJ3-6, reflecting the j i;j i;j i¼1 i¼1 influence of the slippage of the AAC masonry wall after cracking. Compared with KJ-1, the peak load of the where P denotes the load value at the peak value of i,j steel frame with the AAC masonry wall was signifi - the i-th cyclic under the loading level j; θ represents i,j cantly increased, revealing that the load-bearing capa- the displacement value at the peak value of the i-th city of the frame was significantly enhanced by the cyclic under the j loading level; k = 3 and k = 2 exist in AAC masonry wall. the first loading stage and the subsequent loading Compared with the steel frame infilled with AAC stages, respectively. masonry wall with circular-arc openings, the in-plane The KJ-1 specimen reached the yield state when lateral stiffness of KJ-2 was greater. Under the same θ = 1.5%, the yield stiffness (K ) only accounted for lateral displacement, the notchless AAC masonry wall 56.14% of the initial stiffness (K ), and the stiffness dramatically contributed to the load-bearing capacity corresponding to the ultimate load (K ) decreased to of the structure, but the wall cracking occurred earlier. 19.6% of the initial stiffness (K ). The yield stiffness (K ) 0 y Additionally, the decline rate of the curve slope of the of the KJ-2 specimen accounted for 74.76% of the steel frames infilled with AAC masonry wall with circu- initial stiffness (K ), and the stiffness corresponding to lar-arc openings was significantly lower than that of KJ- the ultimate load (K ) decreased to 14.5% of the initial 2, reflecting that the circular-arc opening effectively stiffness (K ). Compared with the KJ-1 and KJ-2 0 JOURNAL OF ASIAN ARCHITECTURE AND BUILDING ENGINEERING 9 Figure 11. Hysteresis curves of specimens. specimens, the yield stiffness (K ) accounted for gradually increased, which was caused by the circular- a higher proportion of the initial stiffness (K ) when arc opening weakened the interaction between the the KJ-1~ KJ-9 specimens reached the yield state, AAC masonry infill wall and the steel frame. about 75.1%~85.7% of the initial stiffness(K ). The ulti- Table 3 provides the main properties such as the mate stiffness (K ) accounted for 16.2%~18.7% of the initial stiffness (K ), the stiffness corresponding to the u 0 initial stiffness (K ) when the KJ-1~ KJ-9 specimens yield load (K ), the stiffness corresponding to the 0 y reached the ultimate load. With the increase of the ultimate load (K ), and the stiffness ratio (η ) of speci- u i opening area of the KJ-1~ KJ-9 specimens, the propor- mens. Among them, η is calculated according to tion of the yield stiffness (K ) to the initial stiffness (K ) Eq. (5). y 0 10 Y.-S. YU ET AL. Figure 13. Definition of main performance points. Figure 12. Skeleton curves of specimens. the elastoplastic stage. Figure 14 suggested that the slope of the stiffness degradation curve of KJ- K þ K þi;j i;j η ¼ (5) 3-1~ KJ-3-9 was significantly smaller than that of K þ K þi;1 i;1 KJ-2. Thus, the circular-arc openings effectively delayed the stiffness degradation rate of the steel where K (i = 0, y, u) denotes K , K , and K of KJ-1, i,1 0 y u frames infilled with AAC masonry walls. The slope respectively; K (i = 0, y, u) represents K , K , and K of i,j 0 y u of the stiffness degradation curve of KJ-2, KJ- steel frames infilled with AAC masonry wall, 3-1~ KJ-3-9 was higher than that of KJ-1 since the respectively. cracking of the AAC masonry wall weakened its addi- The stiffness degradation curve of each specimen tional stiffness on the steel frame. is presented in Figure 14. Owing to the additional stiffness of the infill wall to the steel frame, the initial stiffness of KJ-2, KJ-3-1~ KJ-3-9 was 3.27, 2.66, 2.60, 2.49, 2.40, 2.28, 2.11, 1.92, 1.66, and 1.30 times that 4.5. Strength degradation of KJ-1, respectively. The stiffness of each specimen significantly decreased with the increase in the inter- The strength degradation coefficient (λ) of the speci- story drift angle, revealing that the specimen was in men was calculated according to Eq. (6). Table 2. P ,θ ,P ,θ and µ. y y u u P /kN θ /% P /kN θ /% y y u u Number of specimens Positive Negative Positive Negative Positive Negative Positive Negative µ KJ-1 325.05 −324.67 1.5 −1.5 450.85 −453.87 6 −6 4 KJ-2 435.71 −505.87 0.5 −0.5 826.11 −835.79 4.5 −4.5 9 KJ-3-1 360.13 −407.19 0.5 −0.5 761.91 −764.56 4.5 −4.5 9 KJ-3-2 353.97 −398.60 0.5 −0.5 767.99 −781.48 4.5 −4.5 9 KJ-3-3 342.27 −382.49 0.5 −0.5 733.83 −746.20 4.5 −4.5 9 KJ-3-4 332.28 −369.22 0.5 −0.5 731.16 −742.49 4.5 −4.5 9 KJ-3-5 319.58 −352.88 0.5 −0.5 722.97 −736.83 4.5 −4.5 9 KJ-3-6 300.07 −327.90 0.5 −0.5 686.57 −703.72 4.5 −4.5 9 KJ-3-7 277.02 −299.63 0.5 −0.5 682.03 −694.39 5.5 −5 11 KJ-3-8 244.71 −262.08 0.5 −0.5 648.90 −662.84 6 −5.5 12 KJ-3-9 211.01 −219.27 0.5 −0.5 562.81 −574.68 6.5 −5.5 13 Table 3. K ,K ,K and η. 0 y u −1 −1 −1 K /(kN·mm ) K /(kN·mm ) K /(kN·mm ) 0 y u Number of specimens Positive Negative Positive Negative Positive Negative η η η 0 y u KJ-1 12.86 12.90 7.22 7.21 2.50 2.52 1 1 1 KJ-2 42.00 43.38 31.40 33.76 6.09 5.59 3.27 4.35 2.44 KJ-3-1 34.17 34.68 25.60 27.22 5.55 5.10 2.66 3.55 2.22 KJ-3-2 33.41 33.93 25.13 26.64 5.69 5.77 2.60 3.48 2.28 KJ-3-3 32.05 32.50 24.21 25.57 5.44 5.51 2.49 3.35 2.18 KJ-3-4 30.84 31.33 23.43 24.68 5.39 5.44 2.40 3.25 2.16 KJ-3-5 29.34 29.88 22.46 23.58 5.33 5.35 2.28 3.11 2.13 KJ-3-6 27.14 27.64 21.00 21.92 5.09 5.17 2.11 2.91 2.04 KJ-3-7 24.63 25.13 19.30 20.04 4.04 4.61 1.92 2.67 1.62 KJ-3-8 21.31 21.82 16.96 17.53 3.49 3.99 1.66 2.35 1.40 KJ-3-9 16.66 17.08 14.29 14.67 2.76 3.46 1.30 1.98 1.10 JOURNAL OF ASIAN ARCHITECTURE AND BUILDING ENGINEERING 11 Figure 15. Strength degradation curves of specimens. Figure 14. Stiffness degradation curves of specimens. infilled with AAC masonry wall were in the inelastic i;j λ ¼ (6) i stage (P> P ), the strength degradation coefficient of i 1;j KJ-2 was significantly smaller than that of the steel frames infilled with AAC masonry wall with circular- Where P denotes the load value at the peak value of i,j arc openings. This implied that the circular-arc open- the i-th cyclic under the loading level j; P indicates i-1, j ings delayed the strength degradation of the steel the load value at the peak value of the i-1th cyclic frames infilled with AAC masonry walls. The strength under the loading level j. degradation curves of specimens are illustrated in Table 4 exhibits the strength degradation coeffi - Figure 15. The λ of each specimen was between 1.00 cient of each specimen during the loading process. It and 1.02 when θ ranged from 1.0% to 4.0%. The λ of KJ- can be revealed that the strength degradation coeffi - 2, KJ-3-1~ KJ-3-6 was between 0.81 and 1.01 when cient of each specimen generally decreased with the θ > 4%, suggesting that the AAC masonry walls of KJ- increase in the inter-story drift angle. Besides, the 2, KJ-3-1~ KJ-3-6 failed gradually. The strength degra- strength of KJ-1 had almost no degradation, and the dation was not significant when the specimens were in λ ranged from 0.97 to 1.03. Compared with the KJ- the elastic state (P≤ P ). The strength degradation 3-2~ KJ-3-9 specimens, the strength of KJ-2 and KJ- curve fluctuated greatly when the specimens reached 3-1 specimens degraded significantly in the inelastic the peak load. stage (P> P ). At the loading level of θ = 3.5%, the strength degradation proportion of KJ-2 and KJ-3-1 specimens was 19%. The strength degradation of KJ- 4.6. Energy dissipation 3-2~ KJ-3-9 specimens was not significant under the same load level in the inelastic stage (P> P ), and the The ratio of the area of the hysteresis loop to the total proportion of maximum strength degradation was deformation energy is defined as the energy dissipa- about 9%. When the steel frames infilled with AAC tion coefficient (E), as shown in Eq. (7). The energy masonry wall were in the elastic stage (P≤ P ), the dissipation coefficient (E) is one of the important eva- strength degradation coefficient of KJ-2 was higher luation indicators of the energy dissipation capacity of than that of the steel frames infilled with AAC masonry the structure. In addition, the equivalent viscous wall with circular-arc openings. When the steel frames damping coefficient (h ) can also be used to evaluate Table 4. Strength degradation coefficient. Strength degradation coefficient (λ) Number of specimens P ≤ P P < P ≤ P P > P y y u u KJ-1 1.00–1.01 0.99–1.03 0.97–0.99 KJ-2 1.00–1.16 0.81–1.01 0.81–0.99 KJ-3-1 1.00–1.13 0.81–1.02 0.81–0.99 KJ-3-2 1.00–1.13 0.99–1.02 0.81–1.00 KJ-3-3 1.01–1.12 0.99–1.02 0.91–1.00 KJ-3-4 1.01–1.12 0.98–1.02 0.87–0.99 KJ-3-5 1.00–1.11 0.96–1.02 0.91–0.99 KJ-3-6 1.00–1.10 0.98–1.02 0.94–1.00 KJ-3-7 1.00–1.09 0.96–1.02 0.94–0.99 KJ-3-8 1.00–1.08 0.94–1.02 0.90–1.00 KJ-3-9 1.00–1.07 0.91–1.02 0.99–1.00 12 Y.-S. YU ET AL. angle. Concerning the steel frames infilled with AAC masonry wall, the h of each specimen increased with the increase in the inter-story drift angle when θ < 4%. When θ > 4%, the h of KJ-2, KJ-3-2, KJ-3-3, and KJ-3-7 decreased with the increase in the inter-story angle. This suggested that the infill walls of KJ-2, KJ-3-2, KJ- 3-3, and KJ-3-7 were gradually withdrawn from work due to severe damage. The energy dissipation capacity of the steel frames infilled with AAC masonry walls was higher than that of KJ-1 when θ < 3%. The energy dissipation capacity of the steel frames infilled with AAC masonry wall was less than that of KJ-1 when θ > 5%, revealing that the existence of the infill wall improved the energy dissipation capacity of the steel frame structure. However, the infill wall steel frame was Figure 16. Calculating diagram of the equivalent viscous destroyed before the bare steel frame because of the damping coefficient. poor deformation capacity of the infill wall. Furthermore, the growth rate of the equivalent viscous damping coefficient of KJ-2 was significantly higher than that of KJ-3-1~ KJ-3-9 when θ < 3.0%. The growth rate of the equivalent viscous damping coefficient of the steel frames infilled with AAC masonry wall gradu- ally decreased with the increase in the inter-story drift angle. When θ ranged from 3.0% to 4.5%, the equiva- lent viscous damping coefficient curves of the steel frames infilled with AAC masonry wall tended to flat. 5. Conclusions The FE models of the bare steel frame, the steel frames infilled with AAC masonry wall, and the steel frames infilled with AAC masonry wall with circular-arc open- ings of different sizes were established by using the Figure 17. Equivalent viscous damping coefficient curves of software ABAQUS. The effects of the AAC masonry wall specimens. with circular-arc openings on the hysteretic perfor- mance, load-bearing capacity, ductility, stiffness degra- the energy dissipation capacity of the structure dation, strength degradation, and energy (Chenghua et al. 2013). The larger the equivalent vis- consumption of the steel frame were investigated. cous damping coefficient (h ), the greater the energy The main conclusions of the research are drawn as dissipation capacity of the structure under earthquake. follows. S þ S EBF FDE E ¼ (7) (1) Compared with the bare steel frame, the load- S þ S ΔABO ΔCDO bearing capacity, ductility, initial stiffness, and According to Eq. (8), the equivalent viscous damping energy dissipation capacity of the steel frames coefficient (h ) was calculated to measure the energy infilled with AAC masonry wall were significantly dissipation capacity of the specimen. improved. (2) The failure mode of the AAC masonry wall S þ S EBF FDE h ¼ (8) e was changed by the circular-arc opening 2πðS þ S Þ ΔABO ΔCDO structure. Under the considerable restraint Where S +S indicates the area of the hysteresis effect of the steel frame on the infill wall, EBF FDE curve in a loading cycle; S +S represents the the infill wall produced tension (compression) ΔABO ΔCDO sum of the area of the triangle ABO and CDO. 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Journal of Asian Architecture and Building Engineering
– Taylor & Francis
Published: Sep 3, 2023
Keywords: Infill walls; steel frames; interaction; circular-arc openings; finite element analysis