For the specific external elevator project in an existing RC building in Shanghai City, the external elevator well is designed as a height of 19.6 m and a width of 2 m, as illustrated in Figure 2 . According to Figure 3 , the cross-section of the elevator well is square, measuring 2 m × 2 m. The RC pit and footing are both designed with a thickness of 250 mm, while the square steel of the external elevator well is designed as 200 mm × 200 mm.

As illustrated in Figure 2 , the design for the external elevator pit has a height of 1.5 m. Based on the same external elevator structural design, five different RC footing cases are designed. These concrete footings are designed at varying heights of 300 mm, 600 mm, 900 mm, 1200 mm, and 1500 mm. This range of designs allows for a comparative analysis of the structural implications at different RC footing heights, ensuring comprehensive findings of the influences on the overall stability and performance of the external elevator well.

For the external elevator project in an existing RC building in Shanghai City, the design specifies that the concrete pit and RC footing are to be 250 mm thick. This dimension is slightly larger than the square steel sections (200 mm × 200 mm) that form the main structural framework of the external elevator well as Figure 3 shows. This design ensures that the concrete components adequately accommodate and support the square steel installations, providing enhanced stability and structural integrity for the external elevator well.

The research of Mohammad T. Alkhamis et al. [18] underscores the critical role that cement properties play in affecting the stresses and strains within concrete components. This insight is particularly relevant when selecting materials for the concrete footing of external elevators, where the performance of concrete under seismic load is crucial. Especially, the research of Mohammad T. Alkhamis et al. [18] underscores the critical role that cement properties play in affecting the stresses and strains within concrete components.

In this research, the concrete selected is C30, according to the Chinese standards GB 50010-2010 (Code for Design of Concrete Structures) and GB 50011-2010 (Code for Seismic Design of Buildings), as shown in Table 1 . The code specifies the concrete compressive strength and the expected concrete compressive strength is 20.1 MPa. The C30 concrete is specifically used in constructing the external elevator pit and the RC footing parts of the project.

According to the Chinese standards GB 50010-2010 (Code for Design of Concrete Structures) and GB 50011-2010 (Code for Seismic Design of Buildings), the rebar selected is HRB400 as illustrated in Table 2 . The code specifies that the rebar has a minimum yield stress of 400 MPa and a minimum tensile stress of 540 MPa. The HRB400 rebar is used in conjunction with C30 concrete in constructing the external elevator pit and the RC footing parts.

The design for the external elevator pit and RC footing includes a total section thickness of 250 mm. According to the specific design of the external elevator project, this includes a concrete cover of 36.35 mm. The rebar is arranged in a grid pattern with two layers at 0˚ and 90˚ on both the top and bottom of the section.

The primary structure of the external elevator well, as depicted in Figure 4 , is constructed using square steel. The section of the square steel measures 200 mm × 200 mm, with a thickness of 8 mm. The design of the primary structure of the external elevator well is based on the specific requirements of this project, ensuring that the structural framework is both robust and capable of supporting the external elevator system effectively.

For the square steel members used in the external elevator well, the selected steel is Q235, in accordance with Chinese standards GB/T 700-2006 (Carbon Structural Steels) and GB 50011-2010 (Code for Seismic Design of Buildings). As illustrated in Table 3 , the code of GB/T 700-2006 specifies that Q235 steel has a minimum yield stress of 235 MPa and a minimum tensile stress of 370 MPa.

In this research, three main materials are utilized for constructing the external elevator well: Q235 square steel, HRB400 rebar, and C30 concrete, and these materials form the structure of the external elevator well. This research incorporates five different design variations of the elevator well, as illustrated in Figure 2 . The primary objective of this research is to analyze how the RC footing influences the overall structural integrity and performance of the external elevator well. By examining these different designs, the research aims to provide insights into optimizing the structural components for enhanced stability and durability.

Based on the specific design of the external elevator well for this project and in accordance with GB/T 7588-2020 (Safety Rules for the Construction and Installation of Lifts), the passenger load capacity of the elevator is set at 630 kg. Additionally, using the scale coefficient, the self-weight of the elevator cabin is calculated to be 787.5 kg, as detailed in Table 4 .

Furthermore, in accordance with the Chinese standard GB 50011-2010 (Code for Seismic Design of Buildings), the Dead Load and Live Load for the structure can be determined using specific equations as below:

${\omega }_D=\frac{P_D}{L}$ (1)

${\omega }_L=\frac{P_L}{L}$ (2)

where $P_D$ is the force from the Dead Load and ${\omega }_D$ is the uniform load from the Dead Load. On the other hand, $P_L$ is the force from the Live Load and ${\omega }_L$ is the uniform load from the Live Load. Through the calculation above, the value of Dead Load is given in 1.93 kN/m, and the value of Live Load is given in 1.54 kN/m as Table 4 illustrates.

The calculation is crucial for accurately assessing the loads that the structure will need to support. This ensures that the design meets the required seismic performance criteria, which is vital for the safety and stability of the structure. Additionally, these calculations are integral to the structural analysis conducted in this research, specifically under the pushover analysis method. This analysis helps evaluate how the structure responds to seismic forces, further ensuring its resilience and reliability.

To satisfy the simulation requirements for nonlinear pushover analysis, it is essential to assign plastic hinge properties to each structural component. This involves defining specific characteristics for these plastic hinges to accurately simulate how the components will behave under nonlinear pushover analysis. The criteria for determining these properties are outlined in ASCE 41-13 and this code is endorsed and supported by SAP 2000, ensuring that the analysis is both accurate and consistent with industry practices. These measures are crucial for a thorough and reliable structural analysis.

The plastic hinges for the column section are established by ASCE 41-13 standards. This modeling process specifically follows the parameters and criteria outlined in Tab. 9-6, which focuses on steel columns in nonlinear procedures. The degree of freedom for the column is set as P-M2-M3, which represents the axial force and moments in two directions. This approach ensures that the modeling accurately reflects the column’s behavior under various loads and stresses, providing a reliable basis for the nonlinear analysis.

The beam section of the external elevator structure uses the same square steel as the column section and follows Tab. 9-6 in ASCE 41-13 guidelines for the plastic hinge design, however, unlike the column section, which has a degree of freedom set as P-M2-M3, the degree of freedom is established as M3 for beam section, reflecting the specific characteristics of beam. This differentiation ensures that the plastic hinge modeling accurately represents the behaviors and mechanic responses of both beams and columns within the structural analysis.

Regarding the nonlinear pushover analysis in this research, considering load combinations is a critical aspect that significantly influences the structural assessment. The Chinese standard GB 50011-2010 (Code for Seismic Design of Buildings) emphasizes the pivotal role of load combinations in structural analyses and offers a calculated method to determine the appropriate combinations of loads as below:

$LC=1.0\cdot DL+0.5\cdot LL$ (3)

where $LC$ is load combinations, $DL$ and $LL$ are Dead Load and Live Load separately.

The nonlinear pushover analysis is designed to use a displacement control system, where control is maintained through conjugate displacement. The analysis is structured to include 50 steps, each systematically accounting for different displacements. This comprehensive range of data points allows for a detailed exploration of the structure’s response to progressively increasing lateral loads. By varying the displacement levels, the analysis thoroughly examines the behavior of the structure, capturing the evolution of deformations and identifying critical points in the load-displacement relationship. This 50-step design is expected to ensure a meticulous and thorough assessment of the structure’s performance under seismic conditions.

The analysis includes results presented in Tables 5 - 6 , providing a comprehensive overview of the performance points for CASE-1 to CASE-5. These performance points are assessed under the guidelines of ACT-40 and FEMA 440, which inform the evaluation of structural performance under seismic conditions. By following these guidelines, the analysis ensures a detailed and accurate assessment of how the structure responds to seismic forces. This thorough presentation of results across different cases enables an understanding of the structural behavior and performance under varying RC footing in this research.

For the external elevator project located on Jinzhong Rd in Shanghai City, the performance points of the external elevator well are defined according to Tables 5.1.4-1 and 5.1.4-2 of the Chinese standard GB 50011-2010 (Code for Seismic Design of Buildings). The seismic intensity in this area is classified as 7, with a seismic acceleration of 0.1 g. Additionally, the maximum influence factor is set at 0.12, the characteristic ground period is determined to be 0.4, and the period time discount factor is 1. These parameters ensure that the structural performance evaluation aligns with the specific seismic conditions and requirements of the project location, providing a thorough and accurate assessment of the seismic resilience of the external elevator well in this research.

Referring to the results of the performance point under ACT-40, as illustrated in Table 5 , it is evident that the height of the RC footing significantly influences the structural performance. Specifically, increasing the height of the RC footing decreases both the base shear and the structural lateral displacement. In terms of S_a (Spectral acceleration) and S_d (Spectral displacement), the results indicate that a higher footing height leads to an increase in S_a but a decrease in S_d. Furthermore, the structural period, a critical evaluation criterion for seismic performance, also decreases as the height of the RC footing increases. These findings highlight the pivotal role of the RC footing height in enhancing the overall seismic resilience of the structure.

Similar to the results in Table 5 , the results of the performance point under FEMA 440, as illustrated in Table 6 , also confirm that the height of the RC footing significantly influences structural performance, specifically, increasing the height of the RC footing results in a decrease in both the base shear and the structural lateral displacement. Additionally, a higher footing height leads to an increase in S_a and a decrease in S_d. Furthermore, the structural period also decreases as the height of the RC footing increases.

The evaluation of structural performance under nonlinear pushover analysis relies significantly on the results derived from the capacity curve. This curve is a fundamental component in understanding how the structure responds to incremental lateral loads, offering valuable insights into its overall seismic performance. The capacity curve identifies critical points where the structure may experience significant deformations or failures. Figure 5 provides a visual representation of the capacity curves for each specific external elevator well structure in this research, illustrating how the different height of the RC footing responds to seismic forces.

Referring to the results of the capacity curves in Figure 5 , it is evident that increasing the height of the RC footing raises the base shear value for the entire structure of the external elevator well. Additionally, the results of the capacity curves also show that lower heights of the RC footing result in longer lateral displacements for the same base shear value. Furthermore, based on the results of capacity curves, Table 7 shows that the height of the RC footing influences the slope of the elastic zone. As the height increases, so does the slope value in the elastic zone under nonlinear pushover analysis. Notably, the most significant increase occurs between CASE-3 and CASE-4, representing footing heights of 900 mm to 1200 mm, while a lower increase ratio is observed between CASE-4 and CASE-5, representing heights of 1200 mm to 1500 mm. These findings highlight the critical role of RC footing height in enhancing the structural performance and stability of the external elevator well under seismic conditions.

In evaluating the seismic performance of a building, the capacity spectrum method is instrumental in determining the building’s performance level. This method involves establishing a target displacement and conducting a graphical comparison between the structure’s capacity and the seismic demand. A key feature of the capacity spectrum method is its ability to visually represent the structure’s capacity and response to seismic forces.

Referring to Riza Ainul Hakim et al. [10] , the process of converting the capacity curve to the capacity spectrum involves calculating the modal participation factor ( $MP{F}_1$) and the modal mass coefficient ( $a$) through the specific equations below:

$MP{F}_1=\frac{{\displaystyle \sum m_i{\varphi }_{i1}}}{{\displaystyle \sum m_i{\varphi }_{i1}^2}}$ (4)

$a=\frac{{\left[{\displaystyle \sum m_i{\varphi }_{i1}}\right]}^2}{\left[{\displaystyle \underset{i=1}{\overset{N}{\sum }}\frac{w_i}{g}}\right]\cdot \left[{\displaystyle \underset{i=1}{\overset{N}{\sum }}{m}_i{\varphi }_{i1}^2}\right]}$ (5)

where $\frac{w_i}{g}$ is mass assigned to level i, ${\varphi }_{i1}$ is the amplitude of model 1 at level i, and N is level N.

Based on the values of $MP{F}_1$ and $a$ are calculated, the values of S_a (spectral acceleration) and S_d (spectral displacement) are computed for each point along the capacity curve using the equations below:

$\frac{S_a}{g}=\frac{V_b}{w}\cdot \frac{1}{a}$ (6)

$S_d=\frac{{\Delta }_{roof}}{MP{F}_1\cdot {\varphi }_{roo{f}_1}}$ (7)

where $V_b$ is base shear force, $w$ is building load weight, and ${\Delta }_{roof}$ is roof displacement.

To transform a demand spectrum from S_a (spectral acceleration) and T (period) format to ADRS (Acceleration Displacement Response Spectrum) format, it is necessary to compute the value of S_d (spectral displacement) for each point on the curve using the equation below:

$S_d=\frac{T^2{S}_a}{4{\pi }^2}$ (8)

The performance point is determined by overlaying the demand spectrum onto the capacity curve in spectral coordinates or ADRS format, and this process is facilitated by the built-in capacity spectrum method within the SAP 2000.

Referring to Figure 6 , the specific response spectrum of GB 50011-2010 (Code for Seismic Design of Buildings) is provided for evaluating the performance points of the external elevator project for an existing RC building in Jinzhong Rd, Shanghai City (121˚36'69''E, 31˚21'99''N). The results indicate that all five

different designs of the external elevator satisfy the GB 50011-2010 code. However, a comparison of the five different capacity spectrums reveals that the height of the RC footing significantly influences the overall structure of the external elevator well. Higher RC footings result in faster S_a (Spectrum acceleration) and shorter S_d (Spectrum displacement). This analysis underscores the critical influence of footing height on the seismic performance and stability of the external elevator structure, aligning with the findings from the capacity curve.

The states of plastic hinges are crucial in evaluating the performance of structures under nonlinear pushover analysis. The research of Van Long Hoang et al. [19] emphasizes the importance of analyzing plastic hinge states in steel frames under static loads, highlighting how the plastic hinge states influence structural performance. Furthermore, the research of Yi Zhou et al. [20] underscores the significance of plastic hinge analysis in welded high-strength steel frames, analyzing various steel frame designs through the plastic hinge states. Both studies demonstrate that understanding the behavior of plastic hinges is essential for assessing the resilience and integrity of steel frame structures under different loading conditions.

According to the code of ASCE 41 - 13, which is used for plastic hinge analysis in SAP 2000, the different stages of plastic hinge formation are illustrated in Figure 7 . The linear response occurs between point A (unloaded element) and the effective yield point B. The slope from point B to point C is typically a small percentage (0% to 10%) of the elastic slope, representing phenomena such as strain hardening. Point C represents the strength of the element, with an abscissa value indicating the deformation where significant strength degradation begins, leading from point C to point D. Beyond point D, the element’s strength substantially reduces until point E, where the seismic strength is essentially zero.

In the plastic range, acceptance criteria for deformation or deformation ratios for P (Primary components) and S (Secondary components) are defined corresponding to the target structure performance levels: IO (Immediate Occupancy), LS (Life Safety), and CP (Collapse Prevention), as shown in Figure 7 . Referring to Mircea D. Botez et al. [21] , IO indicates a structural performance level where only very limited structural damage has occurred, allowing the building to remain usable post-earthquake. LS represents a performance level where significant damage has occurred, but there is still some margin against partial or total structural collapse, ensuring occupant safety. CP signifies a performance level where the building is on the verge of partial or total collapse, indicating a severe damage state.

Previous research emphasizes that layer displacement and layer drift ratio are critical analytical results for evaluating structural seismic behavior [22] - [25] . In line with the characteristics of nonlinear pushover analysis, this research examines these metrics for the external elevator structure. Referring to Figures 8 - 12 , the analysis is conducted under plastic hinge conditions at the effective yield point B and the collapse prevention point CP. This approach provides a comprehensive understanding of how the external elevator structure responds to seismic forces, offering insights into its performance at different stages of deformation.

Referring to Figures 8 - 12 , the structural displacement at plastic hinge B (Effective Yield) point increases as the height of the RC footing increases, a trend also evident in graph (a) of Figure 13 . Additionally, when plastic hinges are at the CP (Collapse Prevention) point, despite some inconsistent displacement results in CASE-3, the results still show that higher RC footings generally lead to longer displacements, as depicted in graph (b) of Figure 13 . However, the analysis also reveals that lower heights of the RC footing cause significant damage to the column section on the first floor. This is indicated by the increased number of plastic hinges appearing at the bottom of the entire external elevator structure. Moreover, this phenomenon is further discussed in the layer drift ratio results, as illustrated in both graphs of Figure 14 .

Based on the results of layer displacement, the findings indicate that higher RC footings lead to longer overall structural lateral displacement, as illustrated in graph (a) of Figure 13 . However, when examining the lower floors of the external elevator well, longer lateral displacements occur with lower RC footings. This trend is less clear when plastic hinges reach the CP (Collapse Prevention) point compared to the B (Effective Yield) point. Nonetheless, higher RC footings consistently result in longer overall displacement, while lower floors experience greater displacement with lower RC footings, as depicted in graph (b) of Figure 13 . These findings highlight the complex impact of footing height on structural lateral displacement across different floors of the external elevator well during seismic events.

The layer drift ratio for each distinct story in the external elevator well is determined by calculating the ratio of the structural lateral displacement to the story height. This involves using the equations to accurately assess how much each story displaces laterally relative to its height as below:

$\Delta ={\delta }_x-{\delta }_{x-1}$ (9)

${\Delta }_{ratio}=\frac{\Delta }{h}$ (10)

where ${\delta }_x$ is the displacement at the x floor, ${\delta }_{x-1}$ is the displacement at the x − 1 floor, $\Delta$ is the drift between the x floor and the x − 1 floor, $h$ is the height of the story, and ${\Delta }_{ratio}$ is the drift ratio.

Based on the results of layer displacement in Figure 13 , the layer drift ratio can be calculated through equations (9) and (10), with the results illustrated in Figure 14 . The findings emphasize that higher RC footings in the external elevator well lead to larger overall layer drift ratios. However, when focusing on the lower floors, larger drift ratios occur with lower RC footings. These trends are observed at both the B (Effective Yield) and CP (Collapse Prevention) points, as shown in graphs (a) and (b) of Figure 14 , highlighting the influences of the RC footing height on the drift ratio across different stories of the structure.

The discussion delves into how the height of RC footings influences the performance of the external elevator structure as a whole. It underscores that higher RC footings enhance the ability of the structure to withstand seismic forces, resulting in improved performance during nonlinear pushover analysis. Essentially, higher RC footings enhance the resistance of the structure to seismic events, indicating a more robust design.

Moreover, due to the taller first-floor height (4200 mm) than other floors (2800 mm), the taller first-floor height reveals a mechanical separation effect due to the longer columns. This mechanical separation effect has a detrimental impact on overall structural performance during nonlinear pushover analysis. However, the research findings indicate that higher RC footings counteract this effect. By avoiding the stress concentration on first-floor columns, higher footings mitigate the mechanical separation due to the long column, leading to enhanced overall structural performance.