The determination of seismic performance of single-story masonry building

doi:10.21203/rs.3.rs-5347299/v1

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The determination of seismic performance of single-story masonry building

https://doi.org/10.21203/rs.3.rs-5347299/v1

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Unreinforced masonry buildings are important for preserving traditional construction techniques for future generations. However, such buildings are generally inadequate against earthquake loads. In this study, a comprehensive evaluation was conducted, taking into account the building's current condition, material properties, and geometric structure. The existing condition of the single-story building and the necessary structural data were collected. In light of these data, various earthquake analyses were performed on the structure. Modern engineering methods, such as response spectrum analysis, nonlinear static pushover analysis, and kinematic analysis, were used. The results showed that high stresses and deformations occurred in certain areas of the structure. In particular, the analyses aimed at identifying weak areas and potential collapse mechanisms revealed critical points in the structure. Based on these findings, recommendations were developed for strengthening the building. Retrofitting strategies include approaches such as improving the structural system, increasing material strength, and integrating new technologies. This study serves as an important guide for assessing the seismic performance of residential buildings and provides a foundation for future research.

Civil Engineering

Seismic Performance

Masonry structures

URM

Kinematic analysis

Pushover analysis

Masonry structures are types of structures that are generally built using materials such as stone, brick or concrete and are built by placing materials on top of each other. This type of building is a construction technique dating back thousands of years and was frequently used by ancient civilisations. Masonry structures continue to exist as a construction technique that maintains its importance with various advantages and disadvantages throughout history and today.

A large number of masonry structures date back to a period when building regulations did not exist and construction rules were of empirical origin. This often makes unreinforced masonry structures highly vulnerable to some load combinations. Since the construction of these structures was carried out without considering seismic effects, most of them are unable to absorb the seismic loads caused by earthquakes [1]. Especially in earthquake zones, the evaluation of earthquake performance of masonry structures has become an important issue in recent years [2]. Turkey is a seismic region with many fault lines including three major earthquake zones. The recent earthquake of 6 February 2023 affected 11 districts [3]. In order for this type of structure to survive, earthquake performance analyses of structures located in earthquake zones should be performed.

Masonry buildings display a highly nonlinear mechanical behavior, making it challenging to predict their typological characteristics numerically unless the appropriate material parameters and solution strategy are applied. In this subject, it is useful to compare the results of complex numerical analyses with simplified analyses in order to provide a practical perspective [4]. In line with this objective, various studies have been conducted in the literature. Yon et al. (2020) investigated conventionally built masonry structures damaged by earthquakes on the Eastern Anatolian Fault. As a result of the study in which the causes and mechanisms of collapse were analysed, solutions were proposed in accordance with the guidelines based on the conclusion that the biggest problem in the damage and/or collapse of masonry type structures is that they were not constructed in accordance with earthquake regulations [5]. Sayin et al. (2021) conducted an analysis of the Sivrice-Elazig earthquake, which had a moment magnitude of 6.8 and occurred along the Eastern Anatolian Fault zone. They explored the earthquake history and the current seismic characteristics of the region. The damages resulting from the earthquake were categorized into reinforced concrete, masonry houses, and non-residential structures, with the collected data subsequently discussed [6]. Sarhosis et al. (2021) studied school, residential and church type buildings in Greece. Damages caused by earthquakes with moment magnitudes of 6.3 and 6.1 were analysed in these structures. The findings show that the structures constructed in accordance with the latest seismic guidelines are less affected, while masonry structures built with traditional construction techniques are damaged [7]. Erdil et al. (2022) investigated the effects of earthquakes and environmental effects such as freeze-thaw on masonry structures in Van. 5.9 moment magnitude earthquakes, it was concluded that it was not damaged by environmental effects, but only damaged or collapsed due to the earthquake [8]. Uroš et al. (2023) considered a historical residential building located in Dubrovnik, a region with high earthquake risk. A numerical model of the structure was created in Abaqus finite element software and time history analyses were performed. Following the analyses, the critical sections of the structure were identified, and recommendations for strengthening were provided [9]. Valluzzi et al. (2022) analysed the damages to two thousand three hundred buildings in twenty villages after the earthquake in Italy in 2016. The impact of features such as geometric and architectural details, as well as horizontal and vertical structural components and their materials, was compared and assessed. As a result, they introduced new methodologies for the typological categorization and statistical analysis of construction parameters [10]. Gioffrè et al. (2022) investigated the dynamical response of two-story URM structures of the same geometry using shake table tests. The study concluded that enclosed masonry buildings perform better than unreinforced masonry buildings [11]. Misir et al. (2022) studied a historical masonry building and carried out material characterisation by non-destructive methods and mortar samples were taken. With the data obtained, large-scale wall specimens were prepared and quasi-static cyclic tests, ambient vibration tests were carried out and the stages of damage formation and the corresponding drift limits were obtained [12]. Oyguc (2022) analysed the structural damages caused by the Sivrice-Elazig earthquake that occurred due to the East Anatolian Fault. It was discovered that structures in rural areas suffered significant damage, revealing major shortcomings in both the design and construction phases of reinforced concrete and masonry structures in Elazig [13]. Vintzileou et al. (2022) took a masonry type structure and reduced it by ½ and constructed one as unreinforced masonry structure (URM) and the other as an addition with timber strips in the vertical direction. Both buildings were subjected to seismic tests up to the repairable damage level and the damages caused by these impacts were repaired. Both buildings were reinforced by grouting the wall and providing the diaphragm effect of the slab. After retrofitting, the structures were re-evaluated under seismic effects, leading to the conclusion that the applied retrofitting methods enhanced the earthquake performance of the structures. Additionally, it was found that timber ties can significantly improve the seismic resilience of historical masonry buildings [14]. Yon (2021) analysed another earthquake that occurred in Sivrice-Elazığ and investigated 65 masonry and adobe structures. As a result of this 5.2 moment magnitude earthquake, it was determined that structural damages were primarily due to deficiencies in the detailing of connections between walls or from walls to the roof, as well as the absence of beams. Strengthening methods have been proposed for undamaged structures in order to overcome these deficiencies [15]. Preciado et al. (2022) studied the impacts of 8.2 and 7.1 magnitude earthquakes on historic masonry structures in Mexico. They suggested practical methods for monitoring crack patterns in structural elements to ensure the effective strengthening of masonry buildings [16]. Duvnjak et al. (2023) focused on the recent earthquakes in Croatia, which have caused major damage to masonry structures, focussing on the interest in experimental research and structural performance assessment for reconstruction purposes. The assessment of structural conditions prior to the occurrence of seismic activities is of great importance to understand the influence on the stiffness of systems. This paper examines a damaged high school in Sisak, Croatia, through experiments like shear testing and operational modal analysis, alongside numerical modeling. The refined model, based on structural dynamics, assessed the building's pre-earthquake condition. The study highlights changes in natural frequencies and mode shapes between damaged and undamaged states, offering insights into post-earthquake dynamics [17]. Namlı and Aras (2024) analyzed and retrofitted an unreinforced masonry educational building under the Istanbul Project Coordination Unit, adding reinforced concrete layers with shotcrete to the walls. Six dynamic identification tests were conducted to monitor changes in the building's dynamic characteristics before and after retrofitting. The study shows that the retrofit effectively increased the structure's frequencies, though significant numerical differences between experimental and numerical results suggest careful consideration in seismic analysis of similar structures [18]. Kocaman and Kazaz (2023) assessed the seismic performance of four historically important masonry mosques. They performed nonlinear dynamic analyses using data from the 1992 Erzincan, 1992 Cape Mendocino, and 1995 Kobe earthquakes. The findings revealed that the mechanisms and crack patterns in domed mosques with square floor plans exhibited similarities [19]. Liguori et al. (2023) introduced a mechanistic framework for evaluating seismic vulnerability curves at a local scale, focusing on unreinforced masonry buildings in Cosenza, Italy. Using basic exposure data and an efficient finite element model, they performed static nonlinear analyses to assess structural behavior. Vulnerability curves were derived through Monte Carlo simulations, accounting for uncertainties. This method offers a framework for developing seismic vulnerability curves at the sub-municipal level [20]. Mohammad et al. examined the seismic response of masonry structures using nonlinear static analysis to develop vulnerability functions for various limit states. They evaluated the seismic performance of historic buildings in Karachi by modeling a prototype masonry structure with the 3-Muri tool and conducting pushover analyses for three material groups. The results were used to create damage matrices for different earthquake intensities, and empirical and analytical methods were compared to validate the findings [21]. Vitorino and colleagues (2024) used finite element modeling to assess the seismic response of the Cathedral of Santa Maria del Fiore in Florence. Seven natural acceleration records with recurrence periods of 50, 75, 101, 201, and 475 years were analyzed, and accelerations, tensions, and deformations were examined. As a result of the analyses, the failure zones of the structure were determined and evaluations were made [22]. Pacella et al. (2023) examined the difficulties encountered during the evaluation of the earthquake resistance of masonry structures by nonlinear finite element method and discussed how to evaluate the data obtained as a result of equivalent frame modelling method. In the case studies, linear and nonlinear analyses were performed and they emphasised that geometrical complexities in masonry structures require a special definition for each structure in the modelling phase. In line with these analyses, some solutions regarding modelling methods are proposed [23]. Uroš et al. (2024) analyzed an unreinforced historic masonry structure after the 2020 Zagreb earthquake to assess similar regional structures. They used response spectrum, static pushover, and out-of-plane collapse mechanism analyses, stressing the need to combine nonlinear static or dynamic analysis with out-of-plane analysis [24]. Romero-Sánchez et al. (2023) developed numerical models to assess earthquake impacts on complex historical structures, focusing on the Giralda Tower in Seville. Using OpenSees software, they conducted finite element and modal analyses, verifying damage assessments against previous earthquake records. The study emphasizes safeguarding historical buildings from seismic effects [25].

This study examines a single-story masonry building located in Istanbul, Turkey. The research includes linear earthquake performance analysis, nonlinear static pushover analysis, and kinematic analysis. The structural analyses of the residential building were conducted using the Turkish Earthquake Codes [26, 27]. The guidelines were applied collectively, and the analyses were repeated for three different earthquake levels. The linear performance analyses show the horizontal displacements of the structure and shear forces on the walls, while the nonlinear analyses provide a comparison with the linear results in terms of horizontal displacements. In the third stage, kinematic analyses were performed to examine the mechanisms that may occur locally in the walls of the structure. Based on the earthquake analyses and in-situ investigation findings, the structure's performance was evaluated under the impact of three different earthquake levels.

2.1 Finite element method

The earthquake performance analyses of the masonry structure for DD-3, DD-2 and DD-1 earthquake levels were performed by considering TBEC-2018 [26] and SRMGHS-2017 [27] guidelines together. The masonry structure was analyzed for earthquake levels DD-3, DD-2, and DD-1. For a DD-3 earthquake, the recurrence interval is 72 years with a 50% chance of occurrence in half a century. A DD-2 earthquake has a recurrence interval of 475 years with a 10% chance of occurring in the same period. For a DD-1 earthquake, the recurrence interval is 2475 years with a 2% probability of happening over 50 years [26]. Linear analyses were based on the equivalent earthquake load method. The base shear forces applied to the historic masonry structure in both the x and y directions were increased to exceed 80% of the equivalent earthquake load as specified by the earthquake code [26]. Dead and live loads were applied to the structure as vertical loads. Figure 5 presents the elastic spectrum derived from the Earthquake Hazard Map [28], based on the location and soil class of the masonry structure under examination. The spectrum is plotted for earthquake levels DD-3, DD-2, and DD-1, with the earthquake load reduction coefficient (Ra) set to 1 (Fig. 1). Table 1 provides detailed information on the soil class of the building's location and the earthquake parameters used in the linear analyses. Eq. 1 illustrates the derivation of the design spectral acceleration coefficients for the building, assuming a ZD soil class, using the DD-2 earthquake level for instance. The masonry walls are modeled as shell elements with a mesh size of 50 cm. The finite element model of the single-story structure, modeled using Midas Gen [29] software, with a story height of 2.7 m, a length of 9.9 m in the x-direction, and a length of 8.5 m in the y-direction, is shown in Fig. 3 according to the floor plan given in Fig. 2. The brick masonry walls are modeled as shell elements. Table 2 shows the material properties used in the finite element model of the structure.

For earthquake level DD-2:

$$\:{S}_{DS}={S}_{S}\:{F}_{S}=0.858\:\text{x}\:1.157=0.993{S}_{D1}={S}_{1}\:{F}_{1}=0.242\:\text{x}\:2.116=0.512$$

Table 1

Soil and earthquake parameters
Parameters	Value / Class
Local soil class	ZD*
Earthquake ground motion level	DD-3, DD-2, DD-1
Earthquake map spectral acceleration coefficients	DD-3, Ss = 0.351, S₁ = 0.100 DD-2, Ss = 0.858, S₁ = 0.242 DD-1, Ss = 1.541, S₁ = 0.430
Peak ground acceleration	DD-3, PGA = 0.149g DD-2, PGA = 0.357g DD-1, PGA = 0.627g
Local soil effect coefficients	DD-3, Fs = 1.519, F₁ = 2.400 DD-2, Fs = 1.157, F₁ = 2.116 DD-1, Fs = 1.000, F₁ = 1.870
Spectral acceleration coefficients	DD-3, S_DS = 0.533, S_D1 = 0.240 DD-2, S_DS = 0.993, S_D1 = 0.512 DD-1, S_DS = 1.541, S_D1 = 0.804
Live load participation coefficient (n)	0.30
*Medium-firm - compact layers of sand, gravel or very solid clay

Table 2

Mechanical properties of masonry walls
Definition	Value/Class
Masonry unit type	Brick
Material type	Isotropic
Masonry unit group	Group 1
Unit Volume Weight, kN/m³	18
Masonry unit compressive strength, f_b MPa	5.0
Mortar compressive strength, f_m MPa	1.0
Characteristic wall compressive strength, f_k MPa	1.8
Wall initial shear strength, f_vko MPa	0.1
Poisson ratio	0.25
Wall modulus of elasticity, E_wall MPa	1350

2.2 Kinematic analysis approach

Masonry structures have exhibited various collapse mechanisms during past earthquakes, and building codes now require the evaluation of these typical mechanisms [24]. Due to the differing geometries of these structures, assessing the overturning of rigid blocks becomes increasingly complex. Although traditional or modern techniques may be used to ensure the correct distribution of seismic forces, if global box-like behavior is not achieved, masonry walls remain vulnerable to overturning under seismic loads. As a result of these earthquake effects, damage and collapses can occur in masonry walls [26]. Kinematic limit analysis is an effective technique for evaluating the stability and load-bearing capacity of masonry structures. This method is based on calculating critical load and displacement values by identifying the possible collapse mechanisms of the structure. Numerous studies in the literature have demonstrated the application of kinematic limit analysis to both historical and modern masonry structures. These studies make important contributions, particularly to the preservation of historical buildings and the assessment of their earthquake performance. Figure 4 illustrates some of the mechanisms that can occur in masonry walls.

2.3 Nonlinear analysis approach

Pushover analysis is a crucial method for assessing the nonlinear static behavior of masonry structures. This technique aims to determine the structure's response to a specified lateral load and identify potential collapse mechanisms. Numerous studies in the literature demonstrate the use of pushover analysis for evaluating the seismic performance of masonry structures. Nonlinear static analysis enables the determination of the correlation between base shear force and horizontal displacement, taking into account plastic dissipation [31]. This method is particularly valuable for the preservation, retrofitting, and seismic performance assessment of historic buildings. In the evaluation of the masonry structure, a pushover curve was created according to the SRMGHS guideline and limit values were determined according to this curve (Fig. 5). According to this curve, 0.3%, 0.7% and 1.0% limit values indicate Limited Damage, Controlled Damage and Pre-Collapse performance levels, respectively.

3.1 Linear Analysis

The linear performance analyses of the historic masonry building under study were conducted in accordance with the guidelines of TBEC 2018 [26] and SRMGHS-2017 [27]. The masonry walls and slabs of the building were modeled as shell elements using Midas Gen [29] finite element software. Due to the limited information available, the information level coefficient was set to 0.75. Modal analyses were conducted on this structure, and the mode shapes were identified. Figure 6 presents these mode shapes, while Table 3 provides the corresponding period and mass participation values.

Table 3

Modal analysis results.
Mode	Period (s)	Mass-Participation Direction	Mass-Participation Ratios (%)
1	0.0790	x	81.3
2	0.0743	y	83.3
3	0.0578	y	5.5

Linear analyses were performed for DD-3, DD-2 and DD-1 earthquake levels with recurrence periods of 72 and 475 years, respectively. In these analyses, the horizontal displacements of the building were assessed based on relative story drifts. Window edges, which are the critical zones of the masonry walls of the building, were assigned as critical sections for the analysis and shear force checks were performed on these sections. Critical sections are marked in pink in Fig. 7. Given the historical significance of the analyzed structure, performance evaluations were conducted for DD-3, DD-2, and DD-1 earthquake levels following the SRMGHS-2017 [27] guidelines. The guideline requires Limited Damage, Controlled Damage and Pre-Collapse performance levels to be met for these earthquake levels, respectively. Table 4 details the limit values for these earthquake levels.

Table 4

Parameters of linear performance analysis of the structure [27].
Parameters	Value / Class
Examined earthquake ground motion levels and performance targets	Limited Damage for DD-3 Controlled Damage for DD-2 Pre-Collapse for DD-1
Performance analysis method	Linear
Story drift limit values	0.3% for limited damage 0.7% for controlled damage 1.0% for pre-collapse
Earthquake load reduction coefficient, Ra	Ra = 1 for DD-3 Ra = 3 for DD-2 Ra = 3 for DD-1

Figure 8 illustrates the horizontal displacements resulting from the earthquake forces applied in the positive x and y directions. In Table 5, the relative story drifts of the building are calculated separately for three earthquake levels and compared with the limit values specified in the regulation. As a result of these comparisons, it was determined that the structure meets the performance levels of ‘Limited Damage’ for DD-3 earthquake level, ‘Controlled Damage’ for DD-2 earthquake level, and ‘Pre-Collapse’ for DD-1 earthquake level.

Table 5

Inter-story drift checks
Earthquake level	Displacement ∆D, (mm)		Drift Oranı, ∆D/H		Limit Değer	Result
Earthquake level	x	y	%	%	%	√ / ⋅
DD-3	6.62	5.21	0.11	0.09	0.3 (LD)	√
DD-2	12.54	10.02	0.21	0.17	0.7 (CD)	√
DD-1	19.58	15.70	0.33	0.26	1.0 (PC)	√

The wall fragments (critical sections) selected from the window edges, identified as critical zones of the masonry structure, were assessed for both DD-3 and DD-2 earthquake levels. In addition, the shear forces occurring in these critical sections are shown in Fig. 9. Table 6 presents the performance analysis details, while Table 7 summarizes the analysis results. In Table 6, the shear force checks of the structure are calculated separately for both earthquake scenarios and compared against the allowable limits. As a result of the comparisons, it is concluded that the structure fails to provide the required performance levels for all earthquake scenarios, including ‘Limited Damage’ for DD-3, ‘Controlled Damage’ for DD-2, and ‘Pre-Collapse’ for DD-1 earthquake levels

Table 6

Performance levels and corresponding shear forces
Ground Motion	Combination	Story shear force (kN)	Shear force on critical sections (kN)	Ratio* (%)	Target performance level**	Performance Level
DD-3	D + L + Exp	231.00	41.20	17.84	LD	CR
	D + L + Exn	-230.70	-18.90	8.19		CR
	D + L + Eyp	226.60	-59.40	26.21		CR
	D + L + Eyn	-226.20	-9394.5	9.15		CR
DD-2	D + L + Exp	403.80	350.70	86.85	CD	CR
	D + L + Exn	-404.20	-365.70	90.48		CR
	D + L + Eyp	396.60	282.10	71.13		CR
	D + L + Eyn	-396.80	-361.60	91.13		CR
DD-1	D + L + Exp	624.10	613.8	98.35	PC	CR
	D + L + Exn	-624.00	-614.6	98.49		CR
	D + L + Eyp	612.70	604.90	98.73		CR
	D + L + Eyn	-612.70	-594.10	96.96		CR
* Ratio = Story shear force/Shear force on critical sections; Exp, Eyp: Earthquake forces in the positive direction; Exn, Eyn: Earthquake forces in the negative direction; LD: Limited damage; CR: Collapse Region

Table 7

The results of performance analysis
Earthquake level	Shear force	*% r	Target performance level*	Check
DD-3	×	26.21	LD	×
DD-2	×	91.13	CD	×
DD-1	×	96.96	PC	×
*Story shear force/Shear force on critical sections

3.2 Nonlinear Analysis

A pushover analysis was conducted on the three-dimensional model created using Midas Gen [29] finite element software, applying a load of 1 kN to each node. The analyses were repeated in the positive x and y directions, and the displacements of the structure under horizontal loads were observed. According to SRMGHS 2017 [27] guideline, limit values for earthquake levels were determined. According to this guideline, when loads of 1 kN are applied up to 1% of the height of the structure, the structure will reach the collapse position. In this study, for the structure with a height of 2700 mm, a force up to 30 mm was applied, slightly beyond 27 mm, which is 1% of this value. Table 8 presents the plastic material properties utilized for the masonry material, while Fig. 10 illustrates the control points applied to the structure in the x and y directions, along with the results obtained for the Pre-Collapse performance level. As a result of the static thrust forces corresponding to the DD-3, DD-2, and DD-1 earthquake levels, displacement values of 0.3%, 0.7%, and 1% of the building height, respectively, were obtained.

Table 8

Material properties for the masonry walls.
Material	Young's modulus (MPa)	Poisson's ratio	Tensile strength (MPa)	Stiffness reduction factor
Brick	2000	0.25	0.20	0.00001
Bed joint	1250	0.25	0.15	0.00001
Head joint	1250	0.25	0.15	0.00001

Figure 11 displays the Base Shear Force versus Displacement change graph, which illustrates the results of the static pushover analysis conducted on the structure. The structure's horizontal load capacities are 91.21 kN in the + x direction and 74.23 kN in the + y direction. The vertical dashed lines on the graph represent the limit values for the DD-3, DD-2, and DD-1 earthquake levels respectively and 0.3% value indicates limited damage, 0.7% indicates controlled damage and 1.0% indicates pre-collapse performance level.

Figure 12 shows the horizontal displacements resulting from the static thrust forces applied in the positive x and y directions. Table 9 presents the relative displacements of selected control points on each story of the building, compared to the lower story. These displacements are calculated separately for each earthquake scenario and are then compared with the allowable limits. The comparison results indicate that the structure meets the performance criteria for the following levels: ‘Limited Damage’ under the DD-3 earthquake scenario, ‘Controlled Damage’ under the DD-2 earthquake scenario, and ‘Pre-Collapse” under the DD-1 scenario.

Table 9

Displacement controls for control points.
Earthquake Level	Base shear (kN)		Performance point (mm)		Drift ratio		Limit ratio
Earthquake Level	x	y	xp	yp	%	%	%	√ / ⋅
DD-3	77.84	561.74	6.99	7.02	0.259	0.260	0.30 (LD)	√
DD-2	88.03	70.78	17.99	18.02	0.666	0.667	0.70 (CD)	√
DD-1	91.21	74.24	25.99	26.02	0.963	0.964	1.0 (PC)	√

Figures 13 and 14 illustrate the principal and shear stresses, respectively, occurring in the masonry elements for the earthquake levels examined in the pushover analyses conducted in the positive x and y directions.

3.3 Kinematic Analysis

The kinematic analyses to observe the local behaviour of the masonry structure were performed by PRO_CINEm [32]. The analyses were repeated for DD-3, DD-2 and DD-1 earthquake levels considering overturning, lateral bending and vertical bending mechanism cases. Table 10 contains the earthquake data used for the kinematic analysis. The evaluation of the analysis indicates that the mechanism occurs when the a_c/a₀^* ratio is less than 1, while the mechanism does not occur when it is greater than 1. Figure 15 shows the right and rear facade mechanisms, while Table 11 and Table 12 contain the kinematic analysis results of these facades, respectively. Table 13 shows the overall kinematic analysis evaluations as a result of these analyses.

Table 10

Kinematic analysis data.
Earthquake Level	PGA	S_DS	R_a	a_g
DD-3	0.149	0.533	1	0.079g
DD-2	0.357	0.993	2	0.177g
DD-1	0.627	1.541	2	0.483g

Table 11

Results of kinematic analysis on the front facede.
Mechanism	Earthquake level	$\:{\alpha\:}_{0}$	a₀^* _(g)	a_{c (g)}	a_c/a₀^*	Check (a_c/a₀^*)
Overturning	DD-3	0.045	0.036	0.079	2.194	√
	DD-2	0.045	0.036	0.177	4.917	√
	DD-1	0.045	0.036	0.255	7.083	√
Vertical bending	DD-3	0.282	0.209	0.037	0.177	×
	DD-2	0.282	0.209	0.079	0.378	×
	DD-1	0.282	0.209	0.255	1.220	√
Lateral bending	DD-3	1.952	1.475	0.021	0.014	×
	DD-2	1.952	1.475	0.142	0.096	×
	DD-1	1.952	1.475	0.292	0.198	×

Table 12

Results of kinematic analysis on the right facede.
Mechanism	Earthquake level	$\:{\alpha\:}_{0}$	a₀^* _(g)	a_{c (g)}	a_c/a₀^*	Check (a_c/a₀^*)
Overturning	DD-3	0.042	0.031	0.079	2.548	√
	DD-2	0.042	0.031	0.177	5.709	√
	DD-1	0.042	0.031	0.255	8.226	√
Vertical bending	DD-3	0.116	0.086	0.037	0.430	×
	DD-2	0.116	0.086	0.079	0.919	×
	DD-1	0.116	0.086	0.255	2.965	√
Lateral bending	DD-3	7.331	5.515	0.019	0.003	×
	DD-2	7.331	5.515	0.142	0.026	×
	DD-1	7.331	5.515	0.292	0.053	×

Table 13

Kinematic analysis results for all facades.
	Mechanism check (a_c/a₀^*)
Earthquake level	Overturning	Vertical bending	Lateral bending
DD-3	√	×	×
DD-2	√	×	×
DD-1	√	√	×

The seismic performance of the evaluated structure was assessed using numerical analysis methods. To assess the building's performance under DD-3, DD-2, and DD-1 earthquake levels, linear, nonlinear, and kinematic limit analyses were utilized. Linear analyses of the residentialbuilding under dead and live loads indicated that its strength was adequate for compressive stresses. The results of the linear performance analyses revealed the following:

The relative story drifts of the masonry walls achieved the performance target of ‘Limited Damage’ for the DD-3 earthquake level, ‘Controlled Damage’ for the DD-2 earthquake level, and ‘Pre-Collapse’ for the DD-1 earthquake level.
However, the shear forces met the 'Controlled Damage' performance level for the DD-2 earthquake level, but they do not satisfy the 'Limited Damage' performance level for the DD-3 earthquake level or the 'Pre-Collapse' performance level for the DD-1 earthquake level.

It was concluded that the structure can safely accommodate displacements for all three earthquake levels. However, it can only meet the shear force requirements for the DD-2 earthquake level and falls short for the other two levels.

Kinematic limit analyses revealed that yielding, vertical bending, and lateral bending mechanisms were activated across all earthquake levels. As a result of the kinematic limit analyses, while the overturning mechanism did not occur, the vertical bending mechanism was not activated only for the DD-1 earthquake level but did occur for the other two earthquake levels. The lateral bending mechanism occurred for all earthquake levels.Based on the findings from the response spectrum, static pushover, and kinematic analyses, it was determined that the structure requires strengthening. The next study will focus on the strengthening of the residential masonry structure.

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The authors declare no competing interests.

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The determination of seismic performance of single-story masonry building

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Abstract

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1. Introduction

2. The numerical methods

2.1 Finite element method

2.2 Kinematic analysis approach

2.3 Nonlinear analysis approach

3. Analysis Results

3.1 Linear Analysis

3.2 Nonlinear Analysis

3.3 Kinematic Analysis

4. Conclusions

References

Additional Declarations

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