Investigation of Seismic Performance for Low-Rise RC Buildings with Different Patterns of Inﬁll Walls

: Evaluating the structural performance of low-rise RC buildings with inﬁll walls is an essential issue in Thailand, as most inﬁll walls were not designed for lateral load resistance. The purpose of this study was to predict the structural behavior and illustrate the effects of inﬁll walls. Residential, commercial, and educational buildings were selected as representative buildings with different patterns of inﬁll walls. Based on the results, inﬁll walls contributed to considerable strength and stiffness. Most of the inﬁll walls that affected the low-rise buildings were at the ground ﬂoor level. The behavior of the buildings that had a contribution of inﬁll walls was found to be brittle until the inﬁll walls collapsed, and then the buildings became ductile. Some patterns in which inﬁll walls were placed improperly led to a torsional effect, resulting in columns in the affected areas reaching failure criteria more than those without this effect. Considering the NLRHA procedure, only inﬁll walls on the ground ﬂoor contributed to the building being subjected to a ground motion. The fully inﬁlled frame tended to reach the inﬁll crack before the other patterns. For the UMRHA procedure, only the ﬁrst vibration mode was adequate to predict seismic responses, such as roof displacement and top-story drift.


Introduction
Seismic hazards play a critical role in the field of earthquake engineering and structural engineering in which large lateral forces are induced by earthquake shaking.Earthquakes are recognized as one of the natural hazards putting any structure at risk, especially existing low-rise RC buildings with infill walls.Most of the damage to buildings during earthquakes is within a range of light to severe damage levels.Slight damage occurs to structural members, such as beams and columns, and to nonstructural members, such as façades and ceilings, which do not contribute strength or stiffness to buildings.However, buildings with façades and ceilings can survive, and operational systems such as elevators and fire protection can still be functional.For severe levels, the overall structural performance is lost, resulting in sudden member failure and building collapse.Based on lessons learned from past earthquakes, seismic performance evaluation should be performed to investigate whether such buildings will survive future earthquakes.The effects of infill walls on RC buildings should also be examined.Several studies in the past determined that RC buildings with infill walls seemed to have both positive and negative effects on buildings.
Murty and Jain [1] indicated that the negative effects of infill walls were well known as the short column effect, soft-story effect, and out-of-plane collapse due to torsion.The beneficial effects were that infill walls can contribute to strength, stiffness, ductility, and energy dissipation capacity. Lee and Woo [2] found that infill walls showed positive behavior; for instance, an increase in earthquake inertia force was less compared to a contribution of strength by infill walls.The effect of infill walls also led to the reduction in global lateral displacement.Al-Chaar et al. [3] demonstrated that an infilled frame provided higher strength and initial stiffness than a bare frame, and these properties can be increased together, yet not linearly, with an increase in the number of bays.Asteris [4] determined that the lateral stiffness of an infilled frame can be considerably reduced due to an increase in the percentage of openings and the positions of openings moving toward the compression diagonal.The shear force on the columns was found to decrease due to the presence of infill walls.However, the shear force on the columns was higher than the shear force of the bare frame in the case of a weak-story frame.Anil and Altin [5] indicated that the arrangement of the infill as a wing wall was found to be an effective strengthening method and provided higher strength compared to the bare frame.An increase in the aspect ratio of the wing walls also increased the strength and stiffness of the corresponding specimen.However, strength, stiffness, and energy dissipation appeared to be substantially decreased due to the presence of the window opening incorporated into the frame, and a substantial reduction in strength could be observed after the infill concrete was crushed.Dolšek and Fajfar [6] demonstrated that the strength and stiffness of the corresponding frame could be considerably increased by the presence of masonry infills.Hashem et al. [7] indicated that the presence of infill walls led to an increase in frame capacity whereas the presence of openings within infill walls led to an increase in the frame lateral displacement.The presence of shear connectors in infilled frames was also found to decrease lateral displacement and increase ultimate load capacity.Niyompanitpattana and Warnitchai [8] demonstrated that an infill wall with or without an opening contributes significantly to increasing its lateral strength and stiffness, and modifying the hysteretic behavior.The overall strength and stiffness of the building were increased; however, the displacement capacity was decreased due to the presence of infill walls [9,10].
Risi et al. [11] expressed that with the comparison between the results of square infill walls and rectangular infill walls, the latter seemed to sustain higher damage than the former at approximately the same drift level.Khan et al. [12] demonstrated that infill walls played an important role in RC structures, especially for the full infill wall type, since the infill walls made structures stiffer and reduced the fundamental period and the relative displacement.Furtado et al. [13] indicated that infill walls interacting with the bounding frame during an earthquake caused various failure modes due to both in-plane and out-of-plane behavior.Out-of-plane failure was regarded as one of the most crucial failure modes of infill walls subjected to seismic loading [14,15] and was noted to occur on the lower stories of a building [15].Chrysostomou and Asteris [16] reported that it was difficult to account for the behavior modes of infill walls since the walls were related to several parameters involving their nonlinearity and behavior.Additionally, the exhibition of infill walls was different between in-plane and out-of-plane behavior.The uncertainty regarding the characteristics of infill walls also has a dramatic impact on seismic response parameters [17].
A widely used tool to estimate the structural performance of a building is called a nonlinear static procedure, also known as pushover analysis.This tool is simple and time-saving yet effective.The results, i.e., capacity curves or pushover curves, are shown in terms of force versus displacement format or broadly recognized as base shear versus roof displacement format.Due to the benefit of a pushover curve, the global behavior of the building, such as strength and stiffness, can readily be investigated, as has been undertaken by many researchers [18][19][20].Girgin and Darilmaz [21] performed pushover analysis to evaluate the seismic response of infilled frame buildings.They found that infills with no irregularity in elevation have advantages for buildings and, therefore, the global lateral displacements of buildings can be reduced.Other studies that are related to pushover analysis can be found in [22][23][24].Although pushover analysis seems to provide satisfying results, this type of analysis cannot be used to simulate the actual phenomenon resulting from earthquake shaking because earthquake forces do not incrementally increase; in other words, the sign and shape of earthquake forces are randomly varied and reversed.Accordingly, nonlinear response history analysis (NLRHA) appears to be the most suitable method to compute seismic responses or seismic demands; however, NLRHA is very time-consuming and has a higher computational effort.An alternative method can be used to calculate seismic responses other than the NLRHA procedure: a simplified version of the NLRHA procedure, such as uncoupled modal response history analysis (UMRHA).This method was first developed for nonlinear systems of modal pushover analysis [25,26].Chopra and Goel [27] performed a comparison between the NLRHA and UMRHA procedures to investigate errors in terms of seismic demands and whether the procedure was acceptable.The errors in response quantity appeared to be admissible for approximation approaches for evaluating seismic demands.In addition, the computational effort of the UMRHA procedure was significantly lower than that of the NLRHA procedure [28][29][30].
The purpose of this study was to evaluate the seismic performance of low-rise RC buildings with various configurations of infill walls.The types buildings studied consisted of residential, commercial, and educational buildings, which encompass most of the existing low-rise RC building types in Thailand.The infill wall patterns are classified mainly into bare frames, fully infilled frames, original frames, open ground-story frames, and open top-story frames.These representative buildings were examined using pushover analysis to investigate the global behavior of each, shown in terms of pushover curves.Local behavior in terms of the failure mechanisms of structural members, such as beams and columns, and infill walls, were also investigated.The UMRHA procedure was also performed to estimate seismic responses.The results were compared with the results from the NLRHA procedure.

Nonlinear Modeling Approach
Frame structures were modeled using the distributed plasticity approach, also known as fiber elements [31].The fiber beam-column element, a mixed-type force-based element and displacement-based element, was regarded as the most precise and rigorous distributed plasticity beam-column formulation [32] and was used in this study.A great deal of research has been conducted involving the strut model together with the corresponding parameters and its constitutive law to represent the behavior of infill walls [33][34][35][36][37].In this study, the nonlinear response of an infill panel was captured by modeling a four-node masonry panel element proposed by Crisafulli [38].This masonry panel element consists of two eccentric struts in each diagonal direction carrying axial loads.The vertical separation between struts, i.e., the distance between internal and dummy nodes, is estimated as half of the contact length [38].A shear strut was also incorporated in the proposed masonry panel to carry shear from the top to the bottom of the panel in each diagonal direction.The masonry strut hysteresis model shown in Figure 1c was employed to represent the four struts, whereas a bilinear hysteresis rule shown in Figure 1d was employed to represent the shear strut.The schematic presentation of the four-node panel element and fiber elements related to the RC cross-section [39] are shown in Figure 1a,b.
from earthquake shaking because earthquake forces do not incrementally increase; in other words, the sign and shape of earthquake forces are randomly varied and reversed.Accordingly, nonlinear response history analysis (NLRHA) appears to be the most suitable method to compute seismic responses or seismic demands; however, NLRHA is very time-consuming and has a higher computational effort.An alternative method can be used to calculate seismic responses other than the NLRHA procedure: a simplified version of the NLRHA procedure, such as uncoupled modal response history analysis (UMRHA).This method was first developed for nonlinear systems of modal pushover analysis [25,26].Chopra and Goel [27] performed a comparison between the NLRHA and UMRHA procedures to investigate errors in terms of seismic demands and whether the procedure was acceptable.The errors in response quantity appeared to be admissible for approximation approaches for evaluating seismic demands.In addition, the computational effort of the UMRHA procedure was significantly lower than that of the NLRHA procedure [28][29][30].
The purpose of this study was to evaluate the seismic performance of low-rise RC buildings with various configurations of infill walls.The types buildings studied consisted of residential, commercial, and educational buildings, which encompass most of the existing low-rise RC building types in Thailand.The infill wall patterns are classified mainly into bare frames, fully infilled frames, original frames, open ground-story frames, and open top-story frames.These representative buildings were examined using pushover analysis to investigate the global behavior of each, shown in terms of pushover curves.Local behavior in terms of the failure mechanisms of structural members, such as beams and columns, and infill walls, were also investigated.The UMRHA procedure was also performed to estimate seismic responses.The results were compared with the results from the NLRHA procedure.

Nonlinear Modeling Approach
Frame structures were modeled using the distributed plasticity approach, also known as fiber elements [31].The fiber beam-column element, a mixed-type force-based element and displacement-based element, was regarded as the most precise and rigorous distributed plasticity beam-column formulation [32] and was used in this study.A great deal of research has been conducted involving the strut model together with the corresponding parameters and its constitutive law to represent the behavior of infill walls [33][34][35][36][37].In this study, the nonlinear response of an infill panel was captured by modeling a four-node masonry panel element proposed by Crisafulli [38].This masonry panel element consists of two eccentric struts in each diagonal direction carrying axial loads.The vertical separation between struts, i.e., the distance between internal and dummy nodes, is estimated as half of the contact length [38].A shear strut was also incorporated in the proposed masonry panel to carry shear from the top to the bottom of the panel in each diagonal direction.The masonry strut hysteresis model shown in Figure 1c was employed to represent the four struts, whereas a bilinear hysteresis rule shown in Figure 1d was employed to represent the shear strut.The schematic presentation of the four-node panel element and fiber elements related to the RC cross-section [39] are shown in Figure 1a
It is essential to prove that the structural model used in this study is reliable and valid, so verification of the models must first be carried out.Three cases of experimental studies were selected from the literature for comparison with analytical models.The three experimental studies were Karayannis et al. [40], Niyompanitpattana and Warnitchai [8], and Van and Lau [41].Selected specimens were used for the verification to compare between the experimental and analytical results consisting of a bare frame and an infilled frame from the three selected studies.This study aimed mainly at the effect of fully infilled walls, so partially infilled walls with openings, such as doors and windows, were not considered.The compared results in terms of global behavior, i.e., lateral force and lateral displacement, and local behavior such as the formation of plastic hinges and failure mechanisms, were investigated.
The structural details, such as the cross-section of the beams and columns of Karayannis et al. [40], are shown in Figure 2, while their corresponding material properties are depicted in Table 1.[39]; (b) fiber elements associated with RC cross-section [39]; (c) strut curve parameters [38]; and (d) shear curve parameters [38].
It is essential to prove that the structural model used in this study is reliable and valid, so verification of the models must first be carried out.Three cases of experimental studies were selected from the literature for comparison with analytical models.The three experimental studies were Karayannis et al. [40], Niyompanitpattana and Warnitchai [8], and Van and Lau [41].Selected specimens were used for the verification to compare between the experimental and analytical results consisting of a bare frame and an infilled frame from the three selected studies.This study aimed mainly at the effect of fully infilled walls, so partially infilled walls with openings, such as doors and windows, were not considered.The compared results in terms of global behavior, i.e., lateral force and lateral displacement, and local behavior such as the formation of plastic hinges and failure mechanisms, were investigated.
The structural details, such as the cross-section of the beams and columns of Karayannis et al. [40], are shown in Figure 2, while their corresponding material properties are depicted in Table 1. Figure 1.Equivalent diagonal strut model and fiber elements: (a) compression or tension struts and shear strut [39]; (b) fiber elements associated with RC cross-section [39]; (c) strut curve parameters [38]; and (d) shear curve parameters [38].
It is essential to prove that the structural model used in this study is reliable and valid, so verification of the models must first be carried out.Three cases of experimental studies were selected from the literature for comparison with analytical models.The three experimental studies were Karayannis et al. [40], Niyompanitpattana and Warnitchai [8], and Van and Lau [41].Selected specimens were used for the verification to compare between the experimental and analytical results consisting of a bare frame and an infilled frame from the three selected studies.This study aimed mainly at the effect of fully infilled walls, so partially infilled walls with openings, such as doors and windows, were not considered.The compared results in terms of global behavior, i.e., lateral force and lateral displacement, and local behavior such as the formation of plastic hinges and failure mechanisms, were investigated.
The structural details, such as the cross-section of the beams and columns of Karayannis et al. [40], are shown in Figure 2, while their corresponding material properties are depicted in Table 1.The comparison of analytical models and experimental models [40] is shown in Figure 3.For the analytical result of the bare frame, the peak force on the positive side is equal to 33.11 kN and the lateral displacement is equal to 26.88 mm.The peak force on the negative side is equal to −36.03 kN and the lateral displacement is equal to −10.27 mm.The hysteretic loop of the experimental result is small in the inelastic range but similar in the elastic range.For local behavior regarding analytical results, since the column section is smaller than the beam section, most of the failure mechanisms are implied to occur on columns before the beam.Due to the formation of plastic hinges on the structural elements, including beams and columns, the sequence of failure mechanisms can readily be investigated.Initially, reinforcing steel yielding is found at the bottom of both columns, while nothing occurs on the beam.Subsequently, the previous failure mechanism is replaced by unconfined concrete crushing at the same locations, while reinforcing steel yielding occurs at the ends of both columns and the ends of the beam.In the final stage, unconfined concrete crushing at the bottom of both columns is replaced by confined concrete crushing, while the top of both columns is found to have unconfined concrete crushing.This analytical model seems to successfully investigate local behavior, especially for the formation of plastic hinges that occur at both ends of the beam and columns.For the analytical result of the infilled frame, the peak force on the positive side is equal to 74.79 kN, and the lateral displacement is equal to 5.92 mm.The peak force on the negative side is equal to −84.21 kN, and the lateral displacement is equal to −5.76 mm.The hysteretic loop of the analytical result is similar to the hysteretic loop of the experimental result.For local behavior regarding the analytical result, reinforcing steel yielding is found at the bottom of both columns, while nothing occurs on the beam.The diagonal cracking is also found to begin.Subsequently, unconfined concrete crushing occurs at both ends of columns, whereas reinforcing steel yielding occurs on both ends of the beam.Then, diagonal cracking is completely achieved.In the final stage, confined concrete crushing is found to occur only at the bottom of both columns.This analytical model can successfully predict local behavior in terms of the development of plastic hinges on beams and columns.The model can also be used to investigate infill cracks and infill failures.
The structural details of the cross-section of the beams and columns of Niyompanitpattana and Warnitchai [8] are shown in Figure 4, while their corresponding material properties are depicted in Table 2.The structural details of the cross-section of the beams and columns of Niyompanitpattana and Warnitchai [8] are shown in Figure 4, while their corresponding material properties are depicted in Table 2.The comparison of analytical models and experimental models [8] is shown in Figure 5.For the analytical result of the bare frame, the peak force on the positive side is equal to 47.8 kN, and the percentage of drift is equal to +1.25%.The peak force on the negative side is equal to −48.8 kN, and the percentage of drift is equal to −1.31%.The hysteretic loop of the analytical result is large in the inelastic range but similar in the elastic range.For local behavior, failure mechanisms of the bare frame occur only at columns.In the first stage, unconfined concrete crushing occurs at both ends of columns.Subsequently, reinforcing steel yielding occurs at the same locations and, thus, confined concrete crushing occurs in the final stage.This analytical model can successfully predict local behavior in terms of the development of plastic hinges on columns, consistent with that shown in the experimental result.In other words, deformation predominantly occurs at both ends of columns.The analytical model cannot predict the type of deformation that occurs at columns, as opposed to the experimental model.For the analytical result of the infilled frame, the peak force on the positive side is equal to 167.5 kN, and the percentage of drift is equal to +1.00%.The peak force on the negative side is equal to −168.8 kN, and the percentage of drift is equal to −0.90%.The hysteretic loop of the analytical result is similar to the hysteretic loop of the experimental result.For local behavior regarding the analytical result, failure mechanisms of the infilled frame occur only at columns and in the failure mechanisms of the bare frame.Initially, only diagonal cracking is found at the infill wall, whereas nothing occurs at the beam and columns.Subsequently, complete diagonal cracking occurs, and unconfined concrete crushing also takes place at both ends of the columns.In the final stage, reinforcing steel yielding occurs, followed by confined concrete crushing.This analytical model can predict local behavior in terms of the development of plastic hinges on columns and cracks, ranging from the initial stage to the final stage on infill walls.This model cannot predict where the location within infill walls first starts to crack, as opposed to the experimental model.
The structural details of the cross-section of the beams and columns of Van and Lau [41] are shown in Figure 6, while their corresponding material properties are depicted in Table 3.The structural details of the cross-section of the beams and columns of Van and Lau [41] are shown in Figure 6, while their corresponding material properties are depicted in Table 3.The comparison of analytical models and experimental models [41] is shown in Figure 7.For the analytical result of the bare frame, the peak force on the positive side is equal to 14.41 kN, and the displacement is equal to 40.48 mm.The peak force on the negative side is equal to −15.18 kN, and the displacement is equal to −20.84 mm.The hysteretic loop of the analytical result is large in the inelastic range but similar in the elastic range.For local behavior regarding the analytical result, failure mechanisms of the bare frame occur at the beam before columns.Initially, reinforcing steel yielding occurs at both ends of the beam, while unconfined concrete crushing occurs at the bottom of both columns.Subsequently, the previous failure mechanism is replaced by reinforcing steel yielding at the  The structural details of the cross-section of the beams and columns of Van and Lau [41] are shown in Figure 6, while their corresponding material properties are depicted in Table 3.The comparison of analytical models and experimental models [41] is shown in Figure 7.For the analytical result of the bare frame, the peak force on the positive side is equal to 14.41 kN, and the displacement is equal to 40.48 mm.The peak force on the negative side is equal to −15.18 kN, and the displacement is equal to −20.84 mm.The hysteretic loop of the analytical result is large in the inelastic range but similar in the elastic range.For local behavior regarding the analytical result, failure mechanisms of the bare frame occur at the beam before columns.Initially, reinforcing steel yielding occurs at both ends of the beam, while unconfined concrete crushing occurs at the bottom of both columns.Subsequently, the previous failure mechanism is replaced by reinforcing steel yielding at the The comparison of analytical models and experimental models [41] is shown in Figure 7.For the analytical result of the bare frame, the peak force on the positive side is equal to 14.41 kN, and the displacement is equal to 40.48 mm.The peak force on the negative side is equal to −15.18 kN, and the displacement is equal to −20.84 mm.The hysteretic loop of the analytical result is large in the inelastic range but similar in the elastic range.For local behavior regarding the analytical result, failure mechanisms of the bare frame occur at the beam before columns.Initially, reinforcing steel yielding occurs at both ends of the beam, while unconfined concrete crushing occurs at the bottom of both columns.Subsequently, the previous failure mechanism is replaced by reinforcing steel yielding at the same locations.In the final stage, confined crushing takes place only at the right-hand column, while the right-hand end of the beam changes from reinforcing steel yielding to unconfined concrete crushing.This analytical model can predict local behavior in terms of the development of plastic hinges on beams and columns.For the analytical result of the infilled frame, the peak force on the positive side is equal to 33.05 kN, and the displacement is equal to 24.67 mm.The peak force on the negative side is equal to −37.39 kN, and the displacement is equal to −13.00 mm.The hysteretic loop of the analytical result is similar to the hysteretic loop associated with the experimental result.Regarding the analytical result, for local behavior, failure mechanisms of the infilled frame occur on the beam before columns and in the failure mechanisms of the bare frame.Initially, only diagonal cracking takes place at the infill wall, whereas nothing occurs at the beam and columns.Subsequently, reinforcing steel yielding occurs at both ends of the beam, while unconfined concrete crushing occurs at the bottom of both columns.A complete diagonal crack occurs.In the final stage, reinforcing steel yielding occurs at the bottom of both columns while nothing occurs at the top of the columns.This analytical model can predict local behavior in terms of the development of plastic hinges on beams and columns.However, this model cannot indicate which type of cracks occur on such elements, for instance, flexural or shear cracks, as opposed to the experimental model.(e) (f)

Selection of Representative Buildings
Residential, commercial, and educational buildings can easily be found in most existing low-rise buildings in Thailand.Residential buildings mostly have a single story and up to two stories, but the latter is more typical for this building type.Commercial buildings have up to four stories, but most commercial buildings can be found with two or three stories, such as stores and residences.The uniqueness of this building type is that there is always an opening in the ground story.An educational building or school building mostly has two stories constructed from a standard plan provided by the Ministry of Education.These buildings are in the seismicity region near active faults.The buildings were selected as representative buildings because their structural plan is typical.In addition, they can readily be found in some regions in Thailand that have moderate earthquakes based on the information from the earthquake observation division of Thailand.Past earthquakes have occurred in that area, leading to slight to moderate damage to buildings.Some of the buildings could be repaired and still be functional, while others collapsed.Accordingly, these types of buildings are shown to be important to consider.
There are three main types of RC moment-resisting frames: ordinary, intermediate, and special moment-resisting frames.The ordinary moment-resisting frame can easily be found in Thailand.This type does not account for the ductile behavior of the building and is not designed according to earthquake-resistant design standards.The spacing of the stirrups is very high and the hook of the stirrups is 90 degrees.The intermediate and special moment-resisting frame, however, requires at least 135 degrees on the hook of the stirrups, known as the seismic hook.Additionally, the spacing of the stirrups is very low compared to the ordinary moment-resisting frame.With this assertion, the representative buildings are regarded as intermediate moment-resisting frames because of the details of the provided reinforcing bars and stirrups, as shown in Figure 8d,e.The corresponding plans of the representative buildings are shown in Figure 8a-c for the original frame.The structural properties of the representative buildings with different infill wall patterns, as

Selection of Representative Buildings
Residential, commercial, and educational buildings can easily be found in most existing low-rise buildings in Thailand.Residential buildings mostly have a single story and up to two stories, but the latter is more typical for this building type.Commercial buildings have up to four stories, but most commercial buildings can be found with two or three stories, such as stores and residences.The uniqueness of this building type is that there is always an opening in the ground story.An educational building or school building mostly has two stories constructed from a standard plan provided by the Ministry of Education.These buildings are in the seismicity region near active faults.The buildings were selected as representative buildings because their structural plan is typical.In addition, they can readily be found in some regions in Thailand that have moderate earthquakes based on the information from the earthquake observation division of Thailand.Past earthquakes have occurred in that area, leading to slight to moderate damage to buildings.Some of the buildings could be repaired and still be functional, while others collapsed.Accordingly, these types of buildings are shown to be important to consider.
There are three main types of RC moment-resisting frames: ordinary, intermediate, and special moment-resisting frames.The ordinary moment-resisting frame can easily be found in Thailand.This type does not account for the ductile behavior of the building and is not designed according to earthquake-resistant design standards.The spacing of the stirrups is very high and the hook of the stirrups is 90 degrees.The intermediate and special moment-resisting frame, however, requires at least 135 degrees on the hook of the stirrups, known as the seismic hook.Additionally, the spacing of the stirrups is very low compared to the ordinary moment-resisting frame.With this assertion, the representative buildings are regarded as intermediate moment-resisting frames because of the details of the provided reinforcing bars and stirrups, as shown in Figure 8d,e.The corresponding plans of the representative buildings are shown in Figure 8a-c for the original frame.The structural properties of the representative buildings with different infill wall patterns, as shown in Table 4, were set to be the same so that the seismic behavior of such buildings could be investigated, and the buildings could easily be compared to each other.
stirrups is very high and the hook of the stirrups is 90 degrees.The intermediate and special moment-resisting frame, however, requires at least 135 degrees on the hook of the stirrups, known as the seismic hook.Additionally, the spacing of the stirrups is very low compared to the ordinary moment-resisting frame.With this assertion, the representative buildings are regarded as intermediate moment-resisting frames because of the details of the provided reinforcing bars and stirrups, as shown in Figure 8d,e.The corresponding plans of the representative buildings are shown in Figure 8a-c for the original frame.The structural properties of the representative buildings with different infill wall patterns, as shown in Table 4, were set to be the same so that the seismic behavior of such buildings could be investigated, and the buildings could easily be compared to each other.In addition to representative building types, five infill wall configuration patterns were examined.These patterns were the bare frame, original frame, fully infilled frame, open ground-story frame, and open top-story frame.The bare frame is a frame without any infill walls.The fully infilled frame is a frame that has the presence of infill walls in the exterior parts for any story.The original frame is a frame that has infill walls based on the actual structural plan without partially infilled walls, which consist of doors and windows.Only full infill panels were considered; in other words, infill walls with openings such as doors and windows were not considered.The open ground-story frame is a frame that has infill walls in the exterior parts for any floor level, except for the ground floor level.The open top-story frame is a frame that has infill walls only on the ground floor.With different patterns of infill walls, seismic performance in terms of the strength and stiffness of the building are expected to be discriminated.Especially for the bare frame and the fully infilled frame, the bare frame should provide the lowest strength and stiffness, while the fully infilled frame should provide the highest strength and stiffness.For other infill wall patterns, a different increase in strength and stiffness should be found.For the direction of the presence of infill walls, infill walls that are placed in the considered direction will affect the building rather than infill walls in the other directions.For the behavior of buildings with various configurations of infill walls, brittle and ductile behavior, or a combination of both, might obviously be observed in such buildings.The infill wall patterns of those representative buildings are shown in Figure 9.

Seismic Performance Based on Modal Pushover Analysis
In this section, the SeismoStruct [39] fiber element-based software was implemented to simulate the representative buildings and perform analyses.As described in Section 2, frame elements, i.e., beams and columns, were modeled using the fiber beam-column el-

Seismic Performance Based on Modal Pushover Analysis
In this section, the SeismoStruct [39] fiber element-based software was implemented to simulate the representative buildings and perform analyses.As described in Section 2, frame elements, i.e., beams and columns, were modeled using the fiber beam-column element, while infill walls were modeled using the proposed four-node masonry panel element [38].A slab was modeled using a rigid diaphragm.For constitutive laws of materials, the concrete model of Mander et al. [45] was employed as a concrete material model, whereas the steel model of Menegotto and Pinto's [46] was employed as a steel material model.The former consists of a stress-strain relationship together with a simplified uniaxial concrete model, and the latter provides nonlinear behavior, which ranges from elastic to plastic behavior and is a uniaxial material with optional isotropic hardening.However, only flexural failure on RC frames, which accounts for shear failure and the P-Delta effect, was not considered in this study.Modal pushover analysis was carried out in both the x-and y-directions for all representative buildings.The displacement-controlled lateral load method was employed.In other words, such buildings were laterally pushed until reaching a predefined target displacement.The results of modal pushover analysis are known as pushover curves.These curves can be in several formats.However, the most widely used is in the base shear versus roof displacement relationship.Due to the benefits of this relationship, the global behavior of buildings can easily be investigated in terms of strength and stiffness, in addition to the local behavior of structural and nonstructural elements regarding failure mechanisms.Three types of representative buildings with various configurations of infill walls were examined.
The observed structural elements and the pushover curve of residential (RES) buildings are shown in Figure 10.According to global behavior, for the pushover curve in the x-direction, the fully infilled frame and the open top-story frame seemed to equally provide strength and stiffness.Both strength and stiffness may be implied to be largely contributed by the presence of infill walls on frame structures.Nevertheless, initially, the behavior of these frames expressed brittle behavior, and they became ductile after the collapse of infill walls.The original frame appeared to have lower strength and stiffness.In addition, this original frame behaved in the same way as the fully infilled frame and the open top-story frame.The open ground-story frame and the bare frame expressed lower strength and stiffness than others, whereas their behavior seemed to be ductile.For local behavior, in terms of structural elements, the failure mechanism of Column C1 started from unconfined concrete crushing, reinforcing steel yielding, confined concrete crushing, and reinforcing steel fracturing.However, no failure mechanism occurred on the beams.In terms of nonstructural elements for the fully infilled frame, only infill walls placed parallel to the x-direction at the ground floor were found to have both infill cracks and infill failures, while the y-direction was found to have only infill cracks.For the original frame, only infill walls placed parallel to the x-direction were found to have both infill cracks and infill failures only on the ground floor and this pattern appeared to have a torsional effect.For the open ground-story frame, there was no failure mechanism related to infill walls.For the open top-story frame, the phenomenon that occurred in this type was the same as in the fully infilled frame.
infill cracks and infill failures, while some belonging to the x-direction had only infill cracks.For the original frame, only infill walls placed parallel to the y-direction on the ground floor had both infill cracks and infill failures, while some in the other direction had only infill cracks.This type was also found to have a torsional effect.For the open ground-story frame, no failure mechanism was found related to infill walls.For the open top-story frame, infill walls placed parallel to the y-direction had infill cracks only on the ground floor.The observed elements and the pushover curve of commercial (COM) buildings are shown in Figure 11.According to global behavior, for the pushover curve in the x-direction, the fully infilled frame provided the highest strength and stiffness.Initially, this frame exhibited brittle behavior, and became ductile later, after the collapse of infill walls.For other frame patterns, the sequence of strength and stiffness were as follows: the open top-story frame, the open ground-story frame, the original frame, and the bare frame.In addition, while the fully infilled frame made a large contribution due to the presence of infill walls, other types of configurations appeared to make no contributions.The other four frame patterns exhibited brittle behavior, as opposed to the fully infilled frame.For local behavior, in terms of structural elements, Columns C1 and C2 represented columns related to the ground and second floors.Only two columns were selected because no failure mechanism was found related to the beams.For Column C1, failure mechanisms started from unconfined concrete crushing, reinforcing steel yielding, and confined concrete crushing.In addition, the failure mechanism of Column C1 occurred on all frame patterns, except for the open top-story frame.However, only Column C2 had failure mechanisms including unconfined concrete crushing and reinforcing steel yielding.In terms of nonstructural elements, for the fully infilled frame, only infill walls placed parallel to the x-direction at the ground floor had both infill cracks and infill failures.According to global behavior, for the pushover curve in the y-direction, the fully infilled frame was found to provide the highest strength and stiffness, whereas lower strength and stiffness were provided by the open top-story frame.The original frame seemed to provide slightly higher strength and stiffness compared to the open groundstory frame and the bare frame.In addition, the behavior of the fully infilled frame in the y-direction was similar to the fully infilled frame in the x-direction, while the open top-story frame and the original frame in the y-direction seemed to be different from the x-direction because of ductile behavior.However, the bare frame and the open ground-story frame appeared to be the same as in the x-direction.The sequence of failure mechanisms regarding structural elements was similar to the sequence of failure mechanisms of the x-direction, except for Column C2.Only the case of the open top-story frame was found to have failure mechanisms of Column C2, including unconfined concrete crushing and reinforcing steel yielding.In terms of nonstructural elements, for fully infilled frames, only infill walls placed parallel to this direction at the ground floor were found to have both infill cracks and infill failures, while some belonging to the x-direction had only infill cracks.For the original frame, only infill walls placed parallel to the y-direction on the ground floor had both infill cracks and infill failures, while some in the other direction had only infill cracks.This type was also found to have a torsional effect.For the open ground-story frame, no failure mechanism was found related to infill walls.For the open top-story frame, infill walls placed parallel to the y-direction had infill cracks only on the ground floor.
The observed elements and the pushover curve of commercial (COM) buildings are shown in Figure 11.According to global behavior, for the pushover curve in the x-direction, the fully infilled frame provided the highest strength and stiffness.Initially, this frame exhibited brittle behavior, and became ductile later, after the collapse of infill walls.For other frame patterns, the sequence of strength and stiffness were as follows: the open top-story frame, the open ground-story frame, the original frame, and the bare frame.In addition, while the fully infilled frame made a large contribution due to the presence of infill walls, other types of configurations appeared to make no contributions.The other four frame patterns exhibited brittle behavior, as opposed to the fully infilled frame.For local behavior, in terms of structural elements, Columns C1 and C2 represented columns related to the ground and second floors.Only two columns were selected because no failure mechanism was found related to the beams.For Column C1, failure mechanisms started from unconfined concrete crushing, reinforcing steel yielding, and confined concrete crushing.In addition, the failure mechanism of Column C1 occurred on all frame patterns, except for the open top-story frame.However, only Column C2 had failure mechanisms including unconfined concrete crushing and reinforcing steel yielding.In terms of nonstructural elements, for the fully infilled frame, only infill walls placed parallel to the x-direction at the ground floor had both infill cracks and infill failures.For the original frame, the open ground-story frame, and the open top-story frame, no failure mechanism was found related to infill walls.However, in the case of the open ground-story frame, it seemed to have a torsional effect.
According to global behavior, for the pushover curve in the y-direction, the original frame provided the highest strength and stiffness.The reason for this was that the original frame provided more infill walls in the y-direction than other frame patterns.The fully infilled frame provided lower strength and stiffness, whereas the open ground-story frame, the open top-story frame, and the bare frame seemed to provide equal strength and stiffness.However, the failure mechanisms in terms of structural elements were similar to the frame patterns of the x-direction.For the fully infilled frame, only infill walls placed parallel to this direction on the ground floor were found to have both infill cracks and infill failures.For the original frame, infill walls placed parallel to the y-direction on the ground floor had both infill cracks and infill failures, and this pattern appeared to have a torsional effect.For the open ground-story frame, no failure mechanism was found related to infill walls.However, this pattern appeared to have a torsional effect.For the open top-story frame, this pattern had failure mechanisms related to infill walls similar to failure mechanisms of the open ground-story frame, except for the torsional effect.
The observed elements and pushover curve of educational (EDU) buildings are shown in Figure 12.According to global behavior, for the pushover curve in the x-direction, the fully infilled frame and the open top-story frame seemed equal to provide higher strength and stiffness than other frame patterns.Initially, the behavior of this frame exhibited brittle behavior and became ductile after the collapse of infill walls.The open ground-story frame, the original frame, and the bare frame expressed strength and stiffness at the same level.In addition, the behavior of these was ductile, as opposed to the fully infilled frame and the open top-story frame.For local behavior in terms of structural elements, Column C1 had failure mechanisms that started from unconfined concrete crushing, reinforcing steel yielding, confined concrete crushing, and reinforcing steel fracturing.In terms of nonstructural elements, for the fully infilled frame, infill walls placed parallel to this direction at the ground floor had both infill cracks and infill failures, while some of the infill walls regarding the y-direction had only infill cracks.In addition, some of the infill walls placed parallel to the x-direction on the second floor had infill cracks.For the original frame, only infill walls placed parallel to the x-direction had infill cracks.For the open ground-story frame, no failure mechanism was found related to infill walls.For the open top-story frame, the phenomenon that occurred on this type was similar to the fully infilled frame, regardless of the failure mechanism on the second floor.The observed elements and pushover curve of educational (EDU) buildings are shown in Figure 12.According to global behavior, for the pushover curve in the x-direction, the fully infilled frame and the open top-story frame seemed equal to provide higher strength and stiffness than other frame patterns.Initially, the behavior of this frame exhibited brittle behavior and became ductile after the collapse of infill walls.The open ground-story frame, the original frame, and the bare frame expressed strength and stiffness at the same level.In addition, the behavior of these was ductile, as opposed to the fully infilled frame and the open top-story frame.For local behavior in terms of structural elements, Column C1 had failure mechanisms that started from unconfined concrete while failure mechanisms occurred on Beam B1, consisting of unconfined concrete crushing, reinforcing steel yielding, confined concrete crushing, and reinforcing steel fracture.For the fully infilled frame, only infill walls placed parallel to the y-direction on either the ground floor or the second floor had both infill crack and infill failures.For the original frame, infill walls placed parallel to the y-direction had both infill cracks and infill failures.For the open ground-story frame and the open top-story frame, only infill walls placed parallel to the y-direction had both infill cracks and infill failures.According to global behavior, for the pushover curve in the y-direction, the original frame provided higher strength and stiffness than other frame patterns, followed by the fully infilled frame, the open ground-story frame, the open top-story frame, and the bare frame.For local behavior in terms of structural elements of all frame patterns, regarding Column C1, only unconfined concrete crushing and reinforcing steel yielding occurred, while failure mechanisms occurred on Beam B1, consisting of unconfined concrete crushing, reinforcing steel yielding, confined concrete crushing, and reinforcing steel fracture.For the fully infilled frame, only infill walls placed parallel to the y-direction on either the ground floor or the second floor had both infill crack and infill failures.For the original frame, infill walls placed parallel to the y-direction had both infill cracks and infill failures.For the open ground-story frame and the open top-story frame, only infill walls placed parallel to the y-direction had both infill cracks and infill failures.
In conclusion, the comparison of three types of representative buildings resulted in some findings.For bare frames and open ground-story frames, the behavior was similar for most of the aforementioned building types, as they showed ductility.This phenomenon occurred as bare frames had a soft story effect.In addition, for open ground-story frames, there was no contribution of infill walls.For fully infilled frames, buildings behaved in a brittle manner first; after the collapse of infill walls, the buildings became ductile again.For the original frames and open top-story frames, buildings behaved differently for some building types because some buildings had infill walls while some did not.This result indicates that the shape of buildings and the direction of the presence of infill walls were the major factors producing their effects on buildings.The advantages and disadvantages of each infill wall pattern are summarized in Table 5.
Table 5.The advantages and disadvantages of different infill wall patterns.

Patterns of Infill Walls Advantages Disadvantages
Original frame -If infill walls are placed in the considered direction, strength and stiffness are higher than that of the bare frame, yet brittle then ductile again.
-If infill walls are not placed in the considered direction, strength and stiffness are equal to that of the bare frame, yet ductile throughout.
-A torsional effect makes columns in an affected area undergo more failure mechanisms than columns where the position has less effect of torsion, including reinforcing steel yielding, unconfined concrete crushing, and confined concrete crushing.
-Only infill walls on the ground floor affect the buildings.
Fully infilled frame -The highest strength and stiffness.Infill walls placed in both x-and y-directions affect the buildings.
-Brittle behavior and then ductile behavior.
Open ground-story frame -Ductile behavior throughout.
-There is no contribution from infill walls.The lowest strength and stiffness.
-A torsional effect makes columns in an affected area undergo more failure mechanisms than columns where the position has less effect of torsion, including reinforcing steel yielding, unconfined concrete crushing, and confined concrete crushing.
Open top-story frame -Strength and stiffness are as high as the fully infilled frame or higher than the bare frame.
-Infill walls placed in the x-direction and some placed in the y-direction affect the buildings.
-Columns on the ground floor do not undergo any failure mechanisms.
-Brittle behavior and then ductile behavior.
-Columns on floors other than the ground floor undergo failure mechanisms, including reinforcing steel yielding, unconfined concrete crushing, and confined concrete crushing.

Comparison of Seismic Responses between UMRHA and NLRHA
For the UMRHA procedure, only RES buildings with various configurations of infill walls were selected because residential buildings can easily be found in Thailand.The RES building is characterized as 6.50 m × 10.70 m in plan and 6.05 m in elevation, including 1.00 m of ground column height, and 3.15 and 2.9 m of columns on the first and second floors, respectively.This procedure uses the concept of a sum of inelastic SDOF systems in each vibration mode, as shown in Figure 13.The first two vibration modes in the x-direction of the RES bare frame are shown in Figure 14A and the vibration periods are 0.44 s and 0.15 s In other words, only the first and second vibration modes in the x-direction were accounted for.In this study, the properties of RES buildings, such as masses and mode shapes, were obtained from a 3D full model together with eigenvalue analysis.The mass on each floor was computed by a sum of nodal masses on the considered floor.Mode shapes were first obtained for all nodes, and then a single value of mode shape on each floor was selected as the representative value because of the symmetrical shape of the buildings.The UM-RHA procedure regarding RES buildings accounted for 2 degrees of freedom (DOFs) where the level of ground beams was considered at the base, neglecting the DOF on this floor.Only the second floor and roof floor were considered, so the DOFs were reduced from 3 DOFs to 2 DOFs, as shown in Figure 14b.Due to the reduction in DOFs, damage to the ground columns was neglected.The masses and mode shapes used in the UMRHA procedure were the values that were converted from the 3D model to the 2D model by means of the previous explanation.Figure 15a to Figure 15c show the comparison between the modal coordinates of the hysteretic curves and the response of idealized inelastic systems to three ground motions, i.e., Imperial Valley, Kobe, and Landers.The first mode response was the inelastic response and was higher than the second mode response.The latter seemed to be lower or in the linear range compared to the first mode.Seismic responses, regardless of their types, were contributed largely by the first mode to the total response because the second mode contributed slight responses or had no contribution to the total response.Since the building RES is a low-rise building, the effects from the higher modes to the response appeared to be insignificant, as opposed to high-rise buildings or tall buildings.With this assertion, the hysteretic model was only used in the first vibration mode, while the linear model was used in the second vibration mode instead.This was found to be the simplified method.Concurrent with the UMRHA procedure, 3D full models of building RES were used to implement the NLRHA procedure.The following is a brief explanation of the UMRHA procedure.Figure 16 expresses the idealized curves that were transformed into the Fsi/Li − Di relationship to obtain the nonlinear force deformation function so that a standard governing equation of motion regarding the UMRHA procedure could be solved.The properties of the modal inelastic SDOF systems of building RES used as input parameters to perform the UMRHA procedure are shown in Table 6.In this study, the properties of RES buildings, such as masses and mode shapes, were obtained from a 3D full model together with eigenvalue analysis.The mass on each floor was computed by a sum of nodal masses on the considered floor.Mode shapes were first obtained for all nodes, and then a single value of mode shape on each floor was selected as the representative value because of the symmetrical shape of the buildings.The UMRHA procedure regarding RES buildings accounted for 2 degrees of freedom (DOFs) where the level of ground beams was considered at the base, neglecting the DOF on this floor.Only the second floor and roof floor were considered, so the DOFs were reduced from 3 DOFs to 2 DOFs, as shown in Figure 14b.Due to the reduction in DOFs, damage to the ground columns was neglected.The masses and mode shapes used in the UMRHA procedure were the values that were converted from the 3D model to the 2D model by means of the previous explanation.Figure 15a to Figure 15c show the comparison between the modal coordinates of the hysteretic curves and the response of idealized inelastic systems to three ground motions, i.e., Imperial Valley, Kobe, and Landers.The first mode response was the inelastic response and was higher than the second mode response.The latter seemed to be lower or in the linear range compared to the first mode.Seismic responses, regardless of their types, were contributed largely by the first mode to the total response because the second mode contributed slight responses or had no contribution to the total response.Since the building RES is a low-rise building, the effects from the higher modes to the response appeared to be insignificant, as opposed to high-rise buildings or tall buildings.With this assertion, the hysteretic model was only used in the first vibration mode, while the linear model was used in the second vibration mode instead.This was found to be the simplified method.Concurrent with the UMRHA procedure, 3D full models of building RES were used to implement the NLRHA procedure.The following is a brief explanation of the UMRHA procedure.Figure 16 expresses the idealized curves that were transformed into the F si /L i − D i relationship to obtain the nonlinear force deformation function so that a standard governing equation of motion regarding the UMRHA procedure could be solved.The properties of the modal inelastic SDOF systems of building RES used as input parameters to perform the UMRHA procedure are shown in Table 6.Ground motions were conveniently selected from the Pacific Earthquake Engineering Research Center (PEER) ground motion database [47].The ten ground motions were selected as representative ground motions with a moment magnitude from 5.6 to 7.51, while the peak ground acceleration of the selected ground motions ranged from 0.059 to 0.28 g.The distance from the recording site to the epicenter of the selected ground motions was less than 50 km to represent the possible earthquake event near an active fault that will probably occur in northern Thailand.Most of the earthquakes were regarded as having strong ground motion.The earthquakes were also one component of ground motion and were performed in the x-direction for both UMRHA and NLRHA procedures.Figure 17 and Table 7 show the response spectrum and the details of the selected ground motions.With the Ruaumoko-2D computer program [48], the standard governing equation of motion for inelastic SDOF systems can be solved conveniently.When the force-based response or displacement-based response is obtained, the seismic responses, for instance, roof displacement, story drift, base shear, and base moment, can be computed.The total response can be achieved through a sum of individual responses in each vibration mode.Finally, the comparison between the seismic responses of the NLRHA procedure and the UMRHA procedure must be examined to investigate the results from the UMRHA procedure and determine whether the responses were accurate and valid.Ground motions were conveniently selected from the Pacific Earthquake Engineering Research Center (PEER) ground motion database [44].The ten ground motions were selected as representative ground motions with a moment magnitude from 5.6 to 7.51, while the peak ground acceleration of the selected ground motions ranged from 0.059 to 0.28 g.The distance from the recording site to the epicenter of the selected ground motions was less than 50 km to represent the possible earthquake event near an active fault that will probably occur in northern Thailand.Most of the earthquakes were regarded as having strong ground motion.The earthquakes were also one component of ground motion and were performed in the x-direction for both UMRHA and NLRHA procedures.Figure 17 and Table 7 show the response spectrum and the details of the selected ground motions.With the Ruaumoko-2D computer program [45], the standard governing equation of motion for inelastic SDOF systems can be solved conveniently.When the force-based response or displacement-based response is obtained, the seismic responses, for instance, roof displacement, story drift, base shear, and base moment, can be computed.The total response can be achieved through a sum of individual responses in each vibration mode.Finally, the comparison between the seismic responses of the NLRHA procedure and the UMRHA procedure must be examined to investigate the results from the UMRHA procedure and determine whether the responses were accurate and valid.show peak values regarding roof displacement and top-story drift regarding RES buildings to the ten selected ground motions.The seismic responses include the time history of roof displacement and top-story drift.These responses were compared between the UMRHA procedure and the NLRHA procedure.Based on the results, the presence of infill walls in buildings can significantly reduce floor displacement and story drift.With the UMRHA procedure together with the proposed assumption, seismic responses appeared to be underestimated.The seismic responses in terms of time history did not match well between the UMRHA and NLRHA procedures, possibly because of a lack of consistency regarding tuning hysteretic models.As shown in Figures 15 and 16, the tuning idealized curve matched well in the large deformation range, whereas the curve did not match well in the small deformation range.Due to the previous statement, seismic responses cannot be accurately predicted and can lead to underestimated results.For failure mechanisms in terms of infill walls, infill cracks were first found on the fully infilled frame, whereas infill failure was finally found to occur on the original frame.This result indicated that the configuration of infill walls as the original frame expressed more durability than other patterns when they were subjected to strong ground motion.In conclusion, only one vibration mode seems to be adequate to estimate seismic responses such as floor displacement and story drift.A slight discrepancy in responses between the two procedures can be observed in the framed building affected by infill walls, as opposed to the framed buildings without the effects of infill walls.Other hysteretic models should be considered, especially for buildings that have contributions from infill walls, which may lead to more accurate results in terms of evaluating seismic responses.

Conclusions
For the buildings affected by infill walls, the behavior of buildings is first brittle; then, after the collapse of infill walls occurs, the behavior will become ductile again.However, for buildings without the effect of infill walls, the behavior is ductile.For bare frames and open ground-story frames, the behavior is similar for most of the aforementioned building types, as they behaved in a ductile manner.This phenomenon takes place as bare frames have a soft story effect.The presence of infill walls in some patterns significantly contributes strength and stiffness to buildings as high as the fully infilled frame or even more.However, some may have no contribution from infill walls and lead to a torsional effect.Due to the torsional effect on buildings, columns in an affected area undergo more failure mechanisms than columns where the position has less effect of torsion, including reinforcing steel yielding, unconfined concrete crushing, and confined concrete crushing.Some infill wall patterns, such as the open top-story frame, lead columns on the ground floor to have no failure mechanisms, whereas those on the other floors have failure mechanisms, including reinforcing steel yielding, unconfined concrete crushing, and confined concrete crushing.Considering the position of infill walls on a framed building, most of the infill walls that affect the framed buildings are found on the ground floor level.Nevertheless, a few walls on floors other than the ground floor level are also found to affect the framed buildings.In terms of directions, infill walls in both the x-and y-directions affect the buildings when the infill walls of the considered direction all collapsed before those in the other direction.For infill walls, only those on the ground floor contribute to the building when they are subjected to a ground motion in the NLRHA procedure.The fully infilled frame tends to experience infill cracking before the other patterns.The original frame, however, is the last type to experience infill failure, implying that the original frame is more durable than other patterns when it is subject to earthquake shaking.
In the UMRHA procedure, the reduction from 3 to 2 DOFs is used, considering the ground beam level as the support level, and the first and second DOFs are regarded as the second floor and roof floor, respectively.In contrast, the 3D full model is carried out according to the structural plan for the NLRHA procedure.Based on the results, only the first vibration mode is found to be adequate to estimate seismic responses.The use of a linear model in the second vibration mode is found to be an alternative to evaluating seismic responses, provided that the response contributed from the second vibration mode is less than or in the elastic range.

Figure 2 .
Figure 2. Cross-sections of the beam and column of Karayannis et al. [40].

Figure 2 .
Figure 2. Cross-sections of the beam and column of Karayannis et al. [40].

Figure 2 .
Figure 2. Cross-sections of the beam and column of Karayannis et al. [40].

Figure 3 .
Figure 3.Comparison of analytical models in this study with experimental models [40]: (a) analytical and experimental results of the bare frame; (b) failure mechanisms of the bare frame based on the analytical model; (c) failure mechanisms of the bare frame based on the experimental model; (d) analytical and experimental results of the infilled frame; (e) failure mechanisms of the infilled frame based on the analytical model; (f) failure mechanisms of the infilled frame based on the experimental model.

Figure 3 .
Figure 3.Comparison of analytical models in this study with experimental models [40]: (a) analytical and experimental results of the bare frame; (b) failure mechanisms of the bare frame based on the analytical model; (c) failure mechanisms of the bare frame based on the experimental model; (d) analytical and experimental results of the infilled frame; (e) failure mechanisms of the infilled frame based on the analytical model; (f) failure mechanisms of the infilled frame based on the experimental model.Buildings 2022, 12, x FOR PEER REVIEW 7 of 29

Figure 4 .
Figure 4. Cross-sections of the beam and column of Niyompanitpattana and Warnitchai [8].

Figure 4 .
Figure 4. Cross-sections of the beam and column of Niyompanitpattana and Warnitchai [8].

Figure 6 .
Figure 6.Cross-sections of the beam and column of Van and Lau [41].

Figure 5 .
Figure 5.Comparison of analytical models in this study with experimental models [8]: (a) analytical and experimental results of the bare frame; (b) failure mechanisms of the bare frame based on the analytical model; (c) failure mechanisms of the bare frame based on the experimental model; (d) analytical and experimental results of the infilled frame; (e) failure mechanisms of the infilled frame based on the analytical model; (f) failure mechanisms of the infilled frame based on the experimental model.

Figure 5 .
Figure 5.Comparison of analytical models in this study with experimental models [8]: (a) analytical and experimental results of the bare frame; (b) failure mechanisms of the bare frame based on the analytical model; (c) failure mechanisms of the bare frame based on the experimental model; (d) analytical and experimental results of the infilled frame; (e) failure mechanisms of the infilled frame based on the analytical model; (f) failure mechanisms of the infilled frame based on the experimental model.

Figure 6 .
Figure 6.Cross-sections of the beam and column of Van and Lau [41].

Figure 6 .
Figure 6.Cross-sections of the beam and column of Van and Lau [41].

Figure 7 .
Figure 7.Comparison of analytical models in this study with experimental models [41]: (a) analytical and experimental results of the bare frame; (b) failure mechanisms of bare frame based on the analytical model; (c) failure mechanisms of the bare frame based on the experimental model; (d) analytical and experimental results of the infilled frame; (e) failure mechanisms of the infilled frame based on the analytical model; (f) failure mechanisms of the infilled frame based on the experimental model.

Figure 7 .
Figure 7.Comparison of analytical models in this study with experimental models [41]: (a) analytical and experimental results of the bare frame; (b) failure mechanisms of bare frame based on the analytical model; (c) failure mechanisms of the bare frame based on the experimental model; (d) analytical and experimental results of the infilled frame; (e) failure mechanisms of the infilled frame based on the analytical model; (f) failure mechanisms of the infilled frame based on the experimental model.

Figure 8 .
Figure 8. Structural drawing and cross-section of beams and columns for representative buildings: (a) residential building (RES); (b) commercial building (COM); (c) educational building (EDU); (d) RES and COM buildings; (e) EDU building.
For the original frame, the open ground-story frame, and the open top-story frame, no failure

Figure 14 .
Figure 14.Mode shape and simplified concept of building RES: (a) first two vibration modes in the x-direction of the RES bare frame; and (b) 2 DOFs of RES.

Figure 14 .Figure 15 .Figure 15 .Figure 14 .Figure 15 .Figure 16 .
Figure 14.Mode shape and simplified concept of building RES: (a) first two vibration modes in the x-direction of the RES bare frame; and (b) 2 DOFs of RES.

Figure 17 .
Figure 17.The response spectrum of the selected ground motions.Figure17.The response spectrum of the selected ground motions.

Figure 17 .
Figure 17.The response spectrum of the selected ground motions.Figure17.The response spectrum of the selected ground motions.

Figures 18 and 19
Figures 18 and 19 show the time history of the seismic responses of the RES open ground-story frame and the RES open top-story frame to the three selected ground motions, while Tables8-12show peak values regarding roof displacement and top-story drift regarding RES buildings to the ten selected ground motions.The seismic responses include the time history of roof displacement and top-story drift.These responses were compared between the UMRHA procedure and the NLRHA procedure.Based on the results, the presence of infill walls in buildings can significantly reduce floor displacement and story drift.With the UMRHA procedure together with the proposed assumption, seismic responses appeared to be underestimated.The seismic responses in terms of time history did not match well between the UMRHA and NLRHA procedures, possibly because of a lack of consistency regarding tuning hysteretic models.As shown in Figures15 and 16, the tuning idealized curve matched well in the large deformation range, whereas the curve did not match well in the small deformation range.Due to the previous statement, seismic responses cannot be accurately predicted and can lead to underestimated results.For failure

Figure 18 .
Figure 18.Comparison of roof displacement and top-story drift of RES open ground-story frame subjected to the selected ground motions: (a) Imperial Valley; (b) Kobe; (c) Landers.

Figure 18 .Figure 19 .
Figure 18.Comparison of roof displacement and top-story drift of RES open ground-story frame subjected to the selected ground motions: (a) Imperial Valley; (b) Kobe; (c) Landers.

Figure 19 .
Figure 19.Comparison of roof displacement and top-story drift of RES open top-story frame subjected to the selected ground motions: (a) Imperial Valley; (b) Kobe; (c) Landers.

Table 4 .
Structural properties of representative buildings.

Table 4 .
Structural properties of representative buildings.

Table 6 .
Properties of the first modal inelastic SDOF systems of RES.

Table 6 .
Properties of the first modal inelastic SDOF systems of RES.

Table 6 .
Properties of the first modal inelastic SDOF systems of RES.

Table 7 .
List of the selected ground motions.

Table 8 .
Peak values regarding roof displacement and top-story drift of RES bare frame.

Table 9 .
Peak values regarding roof displacement and top-story drift of RES original frame to the selected ground motions.Buildings 2022, 12, x FOR PEER REVIEW 24 of 29

Table 10 .
Peak values regarding roof displacement and top-story drift of RES fully infilled frame to the selected ground motions.

Table 11 .
Peak values regarding roof displacement and top-story drift of RES open ground-story frame to the selected ground motions.

Table 12 .
Peak values regarding roof displacement and top-story drift of RES open top-story frame to the selected ground motions.