Seismic Risk of Steel and Reinforced Concrete Buildings Considering Floor Accelerations: A Novel Performance-Based Assessment Approach

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This study introduces a novel approach to extracting the seismic risk of steel and reinforced concrete structures, with a specific focus on floor accelerations. By evaluating performance levels across three return periods, the paper provides a robust framework for assessing structural reliability in line with modern performance-based design philosophy.

Abstract

Seismic excitations induce floor accelerations that can damage non-structural components and, in extreme cases, contribute to global structural failure. Although floor acceleration demands have been widely studied, their integration into probabilistic seismic performance and reliability frameworks remains limited within Performance-Based Seismic Design (PBSD). This study addresses this gap by proposing a reliability-based framework that incorporates the stochastic nature of floor accelerations through their probability density functions. Five-story steel and reinforced concrete (RC) buildings, designed according to Mexican codes, were analyzed using nonlinear dynamic simulations in PERFORM 3D under 33 ground motions corresponding to immediate occupancy (IO), life safety (LS), and collapse prevention (CP) levels. Structural reliability was quantified using the probability of failure ($p_f$) and the reliability index (β). Results show that peak accelerations occur at the roof level, with higher demands in the steel structure. For the IO level, β ranged from approximately 2.29 to values above 4.0 in steel buildings, while RC structures reached up to β ≈ 4.97. At LS and CP levels, RC buildings maintained β values generally above 3.0, whereas steel structures showed values as low as β ≈ 1.32. The Kernel distribution best captured response variability, reflecting high dispersion ($C.V.$ > 30%). The proposed framework enhances PBSD by linking acceleration demands with reliability-based decision-making.

1. Introduction

Globally, the sudden impact of seismic events has resulted in a wide range of structural failures, including diagonal wall cracking, column buckling, beam failures, structural pounding, soft-story collapse, and foundation displacement [1,2]. While traditional and prescriptive building codes are mainly calibrated to prevent total collapse and guarantee life safety [3], they often fail to mitigate the broader range of the above-mentioned damages. Consequently, Performance-Based Seismic Design (PBSD) has gained significant popularity within the structural engineering community, controlling the structural damage through previously established performance levels [4,5]. Historically, PBSD philosophy focused on the seismic response in terms of inter-story drift [6,7], which is the primary cause of beam-column connection failures, structural instability, and shear wall degradation. However, evaluating seismic performance through floor acceleration is emerging as a critical research priority. High floor accelerations in buildings can provoke brittle failures such as slab-column punching. In addition, floor acceleration inflicts severe damage on acceleration-sensitive non-structural elements [8,9]. Thus, evaluating the building performance via floor acceleration is evolving into a keystone of PBSD research.

One of the most influential studies on floor accelerations in buildings with rigid diaphragms was conducted by Rodriguez et al. [10], who demonstrated that floor accelerations generate inertia forces capable of causing structural damage and, in extreme cases, collapse, with peak values typically occurring at upper stories. Building on this foundation, subsequent research has focused on developing methodologies to estimate floor acceleration demands. For instance, Miranda and Taghavi [11] proposed a practical approach to evaluate floor acceleration responses in multistory buildings, enabling the assessment of non-structural component performance across different performance levels. This methodology was later validated and extended by Taghavi and Miranda [12], confirming its computational efficiency and applicability.

In steel structures, Wieser et al. [13] investigated moment-resisting frames through incremental dynamic analyses, identifying key parameters governing acceleration demands and emphasizing the importance of bidirectional response spectra and improved code formulations. For reinforced concrete structures, parametric studies such as Petrone et al. [14] revealed that provisions in Eurocode 8 [15] may underestimate acceleration demands over a wide range of structural periods, leading to the proposal of refined approaches that incorporate higher-mode effects.

Complementary research has focused on simplified methodologies and experimental validation. Vukobratović and Fajfar [16] developed approaches based on structural dynamics and empirical relationships to generate floor acceleration spectra, while Gonzalez et al. [17] highlighted the sensitivity of acceleration demands to damping modeling. Studies involving instrumented buildings and experimental testing [18,19,20] have confirmed the amplification of floor accelerations toward upper levels and validated amplification profiles used in seismic design. More recent contributions [21,22] have demonstrated the influence of diaphragm flexibility and retrofit strategies on acceleration demands, highlighting the role of energy dissipation mechanisms in improving seismic performance.

Despite significant advances in estimating floor acceleration demands, their integration into probabilistic seismic performance and structural reliability frameworks remains relatively limited. Several studies have addressed performance-based evaluation methodologies considering multiple performance levels, ranging from immediate occupancy to collapse prevention. For example, Maffei et al. [23] validated approaches applicable to a wide range of structural systems using nonlinear dynamic analysis, while Jeong et al. [24] developed fragility-based assessments for reinforced concrete buildings, enabling the estimation of limit-state exceedance probabilities under varying seismic intensities.

Further developments have incorporated specific phenomena and sources of uncertainty into probabilistic frameworks. Tubaldi et al. [25] evaluated performance-based seismic risk considering structural pounding effects, demonstrating that viscous dampers significantly reduce interaction probabilities between adjacent structures. Similarly, Celarec and Dolšek [26] investigated the influence of modeling uncertainties on seismic response, particularly the role of plastic hinge capacity in beams and columns. These concepts were later extended to high-rise buildings by Li et al. [27], who showed that the stochastic nature of seismic input has a direct impact on collapse probability.

More recently, computationally efficient approaches have been proposed for structural reliability assessment. Mohsenian et al. [28] introduced a methodology based on endurance time analysis, enabling accurate estimation of seismic performance with a significant reduction in computational cost compared to traditional incremental dynamic analyses. However, most existing studies have primarily focused on global response parameters such as inter-story drift. The explicit incorporation of floor accelerations as an engineering demand parameter within probabilistic reliability frameworks remains limited, which motivates the present study.

During the last five years (2021–2026), the shift toward performance-based seismic design (PBSD) has intensified, moving beyond prescriptive code requirements to address specific performance objectives such as building functionality and loss mitigation. Padalu and Surana [29] provide a comprehensive framework for this transition, highlighting that PBSD allows designers to meet targeted criteria that exceed standard code prescriptions, which is particularly vital for lifeline structures like hospitals. Building on this framework, recent research has focused heavily on the seismic demand of acceleration-sensitive non-structural components. Muho et al. [30] and Merino et al. [31,32] emphasize that accurate prediction of peak floor acceleration and floor response spectra is essential for a holistic resilience strategy. Specifically, Muho et al. [30] established empirical expressions correlating peak floor acceleration with inter-story drift ratios, while Merino et al. [31] expanded these methodologies to include the influence of masonry infills on RC frame response, ensuring consistency between absolute acceleration and relative displacement demands. Furthermore, the focus has shifted toward practical, analytical tools that reduce the computational burden of nonlinear time-history analyses. Merino et al. [32] introduced an analytical approach to estimate floor response spectra without the need for preliminary numerical modeling, achieving mean relative errors below 20% across various structural performances. This need for simplified yet accurate assessment is echoed by Khedikar et al. [33], who developed damage indices to quantify structural resilience in RC frames of varying heights, facilitating the achievement of Immediate Occupancy (IO) and Life Safety (LS) targets. Finally, the validation of these numerical and analytical models using real-world data remains a priority; Anajafi et al. [34] utilized recorded responses from instrumented buildings to evaluate the influence of lateral force-resisting systems and inelastic behavior on nonstructural components demands. Collectively, these studies underscore a clear research trend (2021–2026) toward integrating acceleration-sensitive demands into displacement-based design frameworks to ensure building functionality and minimize economic losses.

While the reviewed literature provides a robust foundation for studying floor accelerations in buildings subjected to ground motions, several critical gaps remain. From a scientific perspective, there is still limited theoretical understanding of how floor acceleration demands influence the probabilistic seismic risk of different structural systems, particularly when comparing steel and reinforced concrete buildings. In addition, from an applied perspective, the lack of reliability-based metrics linked to floor accelerations restricts the ability to improve performance-based design strategies for reducing seismic damage in both structural and non-structural components. Specifically, comparative studies between the seismic acceleration demands of steel and reinforced concrete structures are scarce, and there is a lack of probabilistic research explicitly quantifying seismic risk in terms of reliability index across different performance levels. Consequently, the characterization of structural reliability under varying seismic intensities remains insufficiently explored. To address these gaps, this study proposes a novel performance-based assessment framework to evaluate floor accelerations induced by earthquakes. The methodology is applied to both steel and reinforced concrete buildings under three performance levels: immediate occupancy (IO), life safety (LS), and collapse prevention (CP), associated with return periods of 72, 475, and 2475 years, respectively. The inherent uncertainty of seismic floor accelerations is incorporated through the evaluation of their probability density functions (PDFs), enabling a probabilistic representation of seismic demand. As a result, the seismic risk of each structural system is quantified in terms of a reliability index, providing a consistent basis for performance-based comparison and design-oriented decision-making. The remainder of this paper presents the material and methods, followed by the proposed framework, results, discussion, and concluding remarks.

2. Materials and Methods

This section details the materials and methods employed to evaluate the seismic performance of the study buildings. First, the site locations and structural configurations are defined. Next, we establish the structural performance levels necessary for assessing varied seismic responses. Finally, the selection of representative ground motions is outlined, alongside the finite element modeling strategy and the PDF-based reliability analysis used to quantify structural safety.

2.1. Location of Designed Buildings

The steel and RC buildings analyzed in this study are located in Mexicali, Mexico. This site was selected due to its classification as a high-seismicity region, making the evaluation of structural performance in this area critical for advancing seismic engineering practices. Furthermore, both steel and RC structures represent the predominant construction typologies in this region. Figure 1 illustrates the geographical location of Mexicali within the northwestern region of Mexico.

2.2. Steel and Reinfornced Concrete Buildings

Figure 2 illustrates the geometric configuration of the analyzed structural systems, which was intentionally designed to ensure structural regularity and enable a controlled comparison of seismic response between steel and RC buildings.

Figure 2a presents the plan layout, consisting of a symmetric arrangement with three bays in both orthogonal directions and uniform 8 m spans. This regular configuration provides a balanced distribution of mass and stiffness, which is essential to minimize torsional irregularities and ensure that the global seismic response is primarily governed by translational modes. Such regularity allows isolating the influence of the structural system on floor acceleration demands and reliability indices, while avoiding the effects associated with plan eccentricities.

Figure 2b shows the elevation of the structures, where a 5.5 m first story is followed by uniform 3.5 m story heights. This vertical configuration represents a typical mid-rise building and introduces a slight stiffness discontinuity at the ground level, which is relevant for capturing dynamic amplification effects associated with the first vibration mode. The selected geometry is consistent with performance-based seismic design assumptions and enables a consistent comparison of inter-story demand distribution and roof acceleration amplification between both structural systems.

Overall, the regularity in both plan and elevation was deliberately adopted to reduce geometric uncertainty and to focus the analysis on system-dependent dynamic behavior under seismic loading.

Table 1. Cross-section shapes for steel building.

Building	Columns	Main Beam	Secondary Beam	Braces	Stories
Steel building *	W27 × 146	W18 × 60	W18 × 60	HSS10 × 10 × 5/8	0–1
	W27 × 146	W18 × 60	W18 × 60	HSS10 × 10 × 5/8	1–2
	W27 × 84	W18 × 60	W18 × 60	HSS8 × 8 × 5/8	2–3
	W27 × 84	W18 × 60	W18 × 60	HSS8 × 8 × 5/8	3–4
	W27 × 84	W18 × 60	W18 × 60	HSS8 × 8 × 5/8	4–5

* Section properties and dimensions for all structural steel members are based on the American Institute of Steel Construction (AISC) Steel Construction Manual [35].

summarizes the structural cross-sections specified for the steel building under consideration. Within context, W27 wide-flange shapes were assigned to all column members, while W18 sections were utilized for both primary and secondary beams. To resist lateral loading, the structure incorporates a bracing system with Hollow Structural Sections (HSS) ranging from HSS10 to HSS8.

Figure 3 provides a 3D isometric view of the steel building, clearly detailing the arrangement of columns, beams, and the lateral bracing system.

Table 2. Cross-sectional dimensions and reinforcement for RC building.

Building	Columns (m)	Column Reinforcement	Beams (m)	Beam Reinforcement	Stories
Reinforced concrete building *	0.80 × 0.80	Longitudinal reinforcement: 10 ø25.4 (face 1) + 10 ø25.4 (face 2); Ties: ø9.5 @ 0.15 m (center) and ø9.5 @ 0.10 m (ends)	0.50 × 0.70	Longitudinal reinforcement: 4 ø25.4 (top) + 6 ø25.4 (bottom); Stirrups: ø9.5 @ 0.20 m (center) and ø9.5 @ 0.10 m (ends)	0–1
	0.80 × 0.80	Longitudinal reinforcement: 10 ø25.4 (face 1) + 10 ø25.4 (face 2); Ties: ø9.5 @ 0.15 m (center) and ø9.5 @ 0.10 m (ends)	0.50 × 0.70	Longitudinal reinforcement: 4 ø25.4 (top) + 6 ø25.4 (bottom); Stirrups: ø9.5 @ 0.20 m (center) and ø9.5 @ 0.10 m (ends)	1–2
	0.80 × 0.80	Longitudinal reinforcement: 7 ø25.4 (face 1) + 7 ø25.4 (face 2); Ties: ø9.5 @ 0.15 m (center) and ø9.5 @ 0.10 m (ends)	0.50 × 0.70	Longitudinal reinforcement: 4 ø25.4 (top) + 6 ø25.4 (bottom); Stirrups: ø9.5 @ 0.20 m (center) and ø9.5 @ 0.10 m (ends)	2–3
	0.80 × 0.80	Longitudinal reinforcement: 7 ø25.4 (face 1) + 7 ø25.4 (face 2); Ties: ø9.5 @ 0.15 m (center) and ø9.5 @ 0.10 m (ends)	0.50 × 0.70	Longitudinal reinforcement: 4 ø25.4 (top) + 6 ø25.4 (bottom); Stirrups: ø9.5 @ 0.20 m (center) and ø9.5 @ 0.10 m (ends)	3–4
	0.80 × 0.80	Longitudinal reinforcement: 7 ø25.4 (face 1) + 7 ø25.4 (face 2); Ties: ø9.5 @ 0.15 m (center) and ø9.5 @ 0.10 m (ends)	0.50 × 0.70	Longitudinal reinforcement: 4 ø25.4 (top) + 6 ø25.4 (bottom); Stirrups: ø9.5 @ 0.20 m (center) and ø9.5 @ 0.10 m (ends)	4–5

* Reinforcement: Bar diameters are indicated by “ø” followed by the nominal diameter in millimeters. Longitudinal reinforcement is reported as quantity and bar diameter (e.g., “3ø15.9 (top)”) and transverse reinforcement as bar diameter @ spacing in meters (e.g., “ø9.5 @ 0.20 m”).

summarizes the cross-sectional dimensions and reinforcement details for the RC building’s structural members. All columns feature a uniform square profile of 0.80 × 0.80 m. In contrast, the beams consist of a rectangular cross-section with a 0.50 m base and a 0.70 m depth.

Figure 4 provides a three-dimensional rendering of the RC building, illustrating the spatial distribution and relative proportions of the beam and column members.

2.3. Structural Performance Levels

Table 3. Performance level, description and limits for floor acceleration [36].

Performance Level	Probability of Exceedance	Return Period (Years)	Performance Description	Floor Acceleration Limit Value
IO	50% in 50 years	72	The building maintains almost its full pre-earthquake structural integrity. Damage to structural elements is negligible, and non-structural components remain largely functional with only minor, cosmetic repairs required. The building is safe for immediate re-entry and continued operation.	±0.80 g
LS	10% in 50 years	475	The structure sustains significant damage to both structural and non-structural components, resulting in a reduction in its original stiffness and strength. While the risk of life-threatening injury is low and the building remains stable, extensive repairs are likely required before it can be safely re-occupied.	±1.20 g
CP	2% in 50 years	2475	The structure has reached a state of imminent failure, characterized by severe damage and a significant loss of lateral-force-resisting capacity. Although the building remains standing to prevent total collapse and protect occupants during egress, it possesses little to no residual strength and may be irreparable.	±2.00 g

summarizes the seismic performance levels evaluated for both the steel and RC buildings, correlating each level of expected performance with its probability of exceedance, return period, description and corresponding floor acceleration limit. As shown, the performance objectives range from IO to CP. The floor acceleration limits range from ±0.80 g for the IO level to ±2.00 g for the CP level.

2.4. Selection of Representative Earthquakes

The selection of representative ground motions is based on target response spectra developed for each performance level. These spectra are defined by their specific probabilities of exceedance and corresponding return periods, as summarized in Table 3. Consequently, three distinct target spectra were generated to guide the ground motion selection process.

The ground motion selection process for each performance level is conducted as follows. Once the target response spectra are established, eleven ground motion records are selected for every performance level from a database of 20,000 candidates which is hosted by the Engineering Institute of the National Autonomous University of Mexico. The raw acceleration time histories are converted into acceleration response spectra ($S{a}_c$) to ensure compatibility with the target spectra ($S{a}_t$). Subsequently, scale factors ($SF$) are applied to the spectral acceleration of each record ($S{a}_c$) to match the target spectral acceleration ($S{a}_t$) at the fundamental period of vibration ($T_1$) of the structure under consideration. Within this context, $SF$ for every ground motion is calculated as:

$$SF={\displaystyle \frac{S{a}_t\left(T_1\right)}{S{a}_c\left(T_1\right)}}$$

(1)

Based on the above and following the initial anchoring at the fundamental period ($T_1$), a subset of eleven ground motions is selected based on their spectral shape compatibility. Specifically, the records demonstrating the closest fit to the target response spectrum within the period range of 0.20$T_1$ to 1.50$T_1$ are retained [37]. The main objective of selecting within such a range of periods is to capture higher mode effects (0.20$T_1$) and period elongation (1.50$T_1$). Section 3.1 and Section 3.2 detail these selections for both the steel and RC buildings across the IO, LS, and CP performance levels, respectively. Figures within these sections illustrate the individual response spectra of the eleven records alongside their corresponding target spectra. Detailed information about the selected ground motions is summarized in

Table 4. Peak roof accelerations for the steel structure.

IO		LS		CP
Earthquake	Roof Maximum Acceleration (g)	Earthquake	Roof Maximum Acceleration (g)	Earthquake	Roof Maximum Acceleration (g)
1	0.2872	12	0.5590	23	0.9890
2	0.5437	13	2.1678	24	3.9414
3	0.5799	14	1.3176	25	2.5709
4	0.4207	15	1.7512	26	2.3311
5	0.8459	16	1.1212	27	2.1014
6	0.7146	17	3.0382	28	1.9365
7	0.2887	18	1.6162	29	2.9091
8	0.4181	19	1.3971	30	2.4717
9	1.3313	20	1.0572	31	1.6739
10	0.3206	21	1.3521	32	1.9758
11	0.4764	22	0.3743	33	0.7146
$\mathit{\mu }=$	0.5661	$\mathit{\mu }=$	1.4320	$\mathit{\mu }=$	2.1469
$\mathit{\sigma }=$	0.3087	$\mathit{\sigma }=$	0.7346	$\mathit{\sigma }=$	0.8839
$\mathit{C}.\mathit{V}.\left(\mathit{\%}\right)=$	54.5225	$\mathit{C}.\mathit{V}.\left(\mathit{\%}\right)=$	51.2961	$\mathit{C}.\mathit{V}.\left(\mathit{\%}\right)=$	41.1696

and

Table 5. Peak roof accelerations for the RC structure.

IO		LS		CP
Earthquake	Roof Maximum Acceleration (g)	Earthquake	Roof Maximum Acceleration (g)	Earthquake	Roof Maximum Acceleration (g)
34	0.1742	45	0.4727	56	0.8554
35	0.2519	46	1.2553	57	2.2835
36	0.2689	47	0.7927	58	2.0239
37	0.2649	48	1.0749	59	1.2354
38	0.4423	49	1.1867	60	1.5820
39	0.2706	50	0.5225	61	0.9654
40	0.2369	51	1.0436	62	1.6944
41	0.3558	52	0.7282	63	1.4134
42	0.3099	53	0.6171	64	1.0773
43	0.5705	54	1.0039	65	1.6507
44	0.4823	55	0.2607	66	0.4617
$\mathit{\mu }=$	0.3298	$\mathit{\mu }=$	0.8144	$\mathit{\mu }=$	1.3857
$\mathit{\sigma }=$	0.1205	$\mathit{\sigma }=$	0.3232	$\mathit{\sigma }=$	0.5336
$\mathit{C}.\mathit{V}.\left(\mathit{\%}\right)=$	36.5401	$\mathit{C}.\mathit{V}.\left(\mathit{\%}\right)=$	39.6880	$\mathit{C}.\mathit{V}.\left(\mathit{\%}\right)=$	38.5081

; in total, 66 seismic records were selected for the analysis presented in this paper.

2.5. Finite Element Software to Extract Seismic Performance

The nonlinear seismic response of both steel and RC buildings was evaluated using PERFORM-3D (Version 9) [38], a specialized finite element package developed by Computers and Structures, Inc. (CSI) for performance-based design. The software was selected for its robust ability to model inelastic component behavior, as well as its sophisticated solver for nonlinear dynamic analysis. This allowed for a precise assessment of structural response for every performance level in terms of floor accelerations provoked by the selected ground motions.

2.6. Reliability Analysis Implementing PDFs

Using the aforementioned finite element software, the seismic response of both the steel and RC buildings is quantified in terms of floor accelerations. To account for the inherent stochasticity of the structural response, the optimal PDF for the floor acceleration data is determined for each ground motion. The PDF fitting utilized an effective sample of response history associated with the maximum response. This ensures that the high temporal dependency of the ground motion does not artificially bias the PDF estimation or the subsequent reliability index. The selection process evaluates twelve PDFs candidates: Lognormal, Log-logistic, Logistic, Normal, Generalized Extreme Value (GEV), Extreme Value (EV), Kernel, Stable, Birnbaum-Saunders, Weibull, Gamma, and t-Location Scale (tLS) [39]. The optimal PDF is identified using the Chi-squared goodness-of-fit test, defined as follows [40]:

$${\chi }^2={\displaystyle \sum _{i=1}^k}{\displaystyle \frac{{(O_i-E_i)}^2}{E_i}}$$

(2)

where $E_i$ represents the expected frequency; $O_i$ is the observed frequency; ${\chi }^2$ is the computed test statistic for the random variable; $k$ denotes the total number of intervals. In accordance with probability theory, the PDF that yields the minimum ${\chi }^2$ value is selected as the best-fit PDF.

Based on the fundamental concepts of structural reliability, the probability of failure ($p_f$) and the corresponding probability of survival ($p_s$) are established by evaluating the probability that the structural response falls within specified performance limits. For a given distribution, $p_f$ is defined as follows [40]:

$$p_f=1-P(a<x\le b)$$

(3)

where $x$ represents the floor acceleration, while $a$ and $b$ denote the lower and upper performance limits defined in Table 3. Within this frame of reference, the term $P(a<x\le b)$ represents the area under the optimal PDF, $f_x\left(x\right)$, within the interval [$a$, $b$], calculated via integration [40]:

$$P\left(a<X\le b\right)={\int }_a^b{f}_x\left(x\right)dx$$

(4)

Then, with the help of Equations (3) and (4) the reliability index ($\beta$) can be calculated by the evaluation of Equation (5) as [40]:

$$\beta =-{\Phi }^{-1}\left(p_f\right)$$

(5)

where ${\Phi }^{-1}$ denotes the inverse value of the Cumulative Density Function (CDF).

In this study, this probabilistic framework is implemented to quantify $\beta$ for the floor accelerations of both the steel and RC buildings. This index serves as a robust safety indicator, characterizing the likelihood of structural damage under seismic loading. The following section provides a comprehensive report of the results obtained through this methodology.

Finally, a methodological framework is presented to summarize the sequential procedure adopted in this study, from structural modeling to seismic performance evaluation and reliability assessment, as illustrated in Figure 5.

3. Results

This section presents a comprehensive evaluation of the results derived from the methodology detailed in Section 2. The findings are structured as follows: First, the selected ground motion suites and their corresponding response spectra are presented for the IO, LS, and CP performance levels for both the steel and RC buildings. Second, the peak roof accelerations for each structure are summarized and compared. Finally, the seismic reliability of each building is quantified and reported in terms of $\beta$.

3.1. Ground Motion Suite Selection for Steel Structure

Table A1. Suite selection of ground motions for the steel building.

Gound Motions	Performance Level	Station Name	Magnitude (Mw)	Scale Factor
Earthquake 1	IO	Aeropuerto Zihuatanejo	6.3	0.89
Earthquake 2	IO	Caleta de Campos	6.1	1.40
Earthquake 3	IO	Caleta de Campos	6.8	0.71
Earthquake 4	IO	Copala	6.2	1.20
Earthquake 5	IO	Las Negras	6.5	0.83
Earthquake 6	IO	Nuxco 2	7.2	1.60
Earthquake 7	IO	Raboso	6.4	0.75
Earthquake 8	IO	San Marcos	6.3	1.10
Earthquake 9	IO	Tamazulapan	6.5	1.40
Earthquake 10	IO	La Union	6.8	0.65
Earthquake 11	IO	Zacatula	6.8	1.40
Earthquake 12	LS	Acapulco Centro Cultural	5.7	1.30
Earthquake 13	LS	Acapulco Centro Cultural	6.0	2.20
Earthquake 14	LS	Acapulco la Zanja	6.0	1.30
Earthquake 15	LS	Caleta de Campos	6.5	1.30
Earthquake 16	LS	Las Negras	6.5	1.10
Earthquake 17	LS	Oaxaca Fac. de Medicina	6.5	2.60
Earthquake 18	LS	Rio Grande	6.5	2.00
Earthquake 19	LS	Sicartsa Caseta Testigo	7.0	1.30
Earthquake 20	LS	Sicartsa Caseta Testigo	6.1	1.10
Earthquake 21	LS	Sicartsa Caseta Maestro	7.0	1.10
Earthquake 22	LS	Zacatula	6.8	1.10
Earthquake 23	CP	Acapulco Centro Cultural	5.7	2.30
Earthquake 24	CP	Acapulco Centro Cultural	6.0	4.00
Earthquake 25	CP	Acapulco SOP	5.5	2.00
Earthquake 26	CP	Oaxaca Fac. Medicina	6.5	1.70
Earthquake 27	CP	Caleta de Campos	6.5	2.40
Earthquake 28	CP	Acapulco Escuela Diana	6.0	2.30
Earthquake 29	CP	Sicartsa Caseta Testigo	7.0	1.80
Earthquake 30	CP	Sicartsa Caseta Testigo	6.1	1.90
Earthquake 31	CP	Las Negras	6.3	2.40
Earthquake 32	CP	Sicartsa Caseta Maestro	7.0	2.20
Earthquake 33	CP	Zacatula	6.8	2.10

summarizes the results of the ground motion selection process for the steel building, which yielded a total of 33 seismic records (See Appendix A). For the IO performance level, the suite primarily comprises events with magnitudes exceeding M_w 6.0. Conversely, for the LS and CP levels of performance, the selection incorporates larger magnitude events, reaching up to M_w 7.0. The calculated scale factors range from 0.65 to 4.00. This range is considered acceptable within literature [41], as it preserves the inherent frequency content and non-stationary characteristics of the original acceleration time histories.

Figure 6 illustrates the response spectra for the 33 ground motions selected for the IO, LS, and CP performance levels, which correspond to return periods of 72, 475, and 2475 years, respectively. All spectra are anchored to the target spectral acceleration at the steel building’s fundamental period ($T_1=0.575 \mathrm{s}$). Furthermore, spectral compatibility was maintained within the period range of 0.115 to 0.863 s (corresponding to $0.2T_1 \mathrm{t}\mathrm{o} 1.5T_1$). As expected, a progressive increase in spectral acceleration is observed across the IO, LS, and CP levels. Given their close adherence to the target spectral shapes, the selected ground motions are considered suitable for the nonlinear dynamic analyses presented in the following sections.

3.2. Ground Motion Suite Selection for RC Structure

Table A2. Suite selection of ground motions for the RC building.

Gound Motions	Performance Level	Station Name	Magnitude (Mw)	Scale Factor
Earthquake 34	IO	Acapulco Cent. Cultural	6.3	1.50
Earthquake 35	IO	Aeropuerto Zihuatanejo	6.8	1.50
Earthquake 36	IO	Caleta de Campos	6.8	1.90
Earthquake 37	IO	Chila de las Flores	6.4	1.30
Earthquake 38	IO	Las Negras	6.5	0.82
Earthquake 39	IO	Raboso	6.4	0.71
Earthquake 40	IO	Sicartsa Aceracion	6.1	0.63
Earthquake 41	IO	San Luis de la Loma 2	7.2	0.88
Earthquake 42	IO	San Marcos	6.3	1.00
Earthquake 43	IO	Tamazulapan	6.5	1.60
Earthquake 44	IO	La Union	6.8	0.99
Earthquake 45	LS	Acapulco Cent. Cultural	5.7	2.10
Earthquake 46	LS	Acapulco Cent. Cultural	6.0	1.70
Earthquake 47	LS	Acapulco la Zanja	6.0	1.90
Earthquake 48	LS	Caleta de Campos	6.5	1.90
Earthquake 49	LS	Las Negras	6.5	2.20
Earthquake 50	LS	Parque la Habana	6.4	0.76
Earthquake 51	LS	Rio Grande	6.5	1.50
Earthquake 52	LS	Sicartsa Caseta Testigo	7.0	1.10
Earthquake 53	LS	Sicartsa Caseta Testigo	6.1	1.20
Earthquake 54	LS	Sicartsa Caseta Maestro	7.0	1.20
Earthquake 55	LS	Zacatula	6.8	0.96
Earthquake 56	CP	Acapulco Cent. Cultural	5.7	3.80
Earthquake 57	CP	Acapulco Cent. Cultural	6.0	3.10
Earthquake 58	CP	Acapulco Escuela Diana	6.1	3.40
Earthquake 59	CP	Caleta de Campos	6.5	3.60
Earthquake 60	CP	Las Negras	6.5	4.00
Earthquake 61	CP	Parque la Habana	6.4	1.40
Earthquake 62	CP	Rio Grande	6.5	2.70
Earthquake 63	CP	Sicartsa Caseta Testigo	7.0	2.00
Earthquake 64	CP	Sicartsa Caseta Testigo	6.10	2.30
Earthquake 65	CP	Sicartsa Caseta Maestro	7.0	2.10
Earthquake 66	CP	Zacatula	6.8	1.70

details the seismic data for the records selected for the RC building, including the ground motion identifier, performance level, station name, magnitude (M_w), and applied scale factor (See Appendix A). This suite comprises 33 ground motions distributed across the IO, LS, and CP performance levels. Notably, the magnitudes range from M_w 5.7 to 7.2, providing a diverse representation of seismic demands consistent with the three performance objectives. The calculated scale factors range from 0.71 to 4.00, a bracket that ensures the fundamental spectral characteristics and non-stationary properties of the original records are preserved without significant numerical distortion.

Figure 7 presents the response spectra for the 33 ground motion records selected for the RC building, corresponding to the IO, LS, and CP performance level with return periods of 72, 475, and 2475 years, respectively. In this case, the records were anchored to the target spectra at the RC building’s fundamental period of $T_1=0.830 \mathrm{s}$. To ensure spectral compatibility across higher modes and period elongation, the selection was optimized within a period range of $0.2T_1 \mathrm{t}\mathrm{o} 1.5T_1$ (specifically, from 0.166 to 1.245 s). Consistent with the seismic hazard levels, the spectral demand increases significantly at higher return periods. These suites demonstrate strong adherence to the target spectral shapes, ensuring their validity for the subsequent nonlinear response history analyses.

3.3. Comparison of Mean Peak Floor Acceleration for Steel and RC Buildings

Figure 8 compares the mean peak floor accelerations across all levels for both the steel and RC structures. For each performance level, the maximum acceleration recorded at each floor was extracted for all eleven ground motions, and the resulting mean was plotted to provide a clear profile of the maximum seismic demand in terms of acceleration. Consistent with established structural dynamics literature, the peak response consistently occurs at the roof level (5th floor) for all cases. Notably, the steel building exhibits higher floor accelerations compared to the RC building across the IO, LS, and CP performance levels, suggesting that the RC system is less sensitive to the acceleration demands of the selected records. Because the roof level represents the critical location for peak acceleration, it serves as the focal point for the subsequent parametric and reliability analyses. The following sections provide a detailed parametric and probabilistic evaluation of these roof accelerations to quantify the structural safety and seismic reliability of each building.

3.4. Maximum Floor Accelerations at Roof for Steel Structure

To evaluate the seismic performance of the steel structure more precisely, the peak floor accelerations at the roof level were analyzed using the ground motion suites detailed in Table A1. The roof was selected as the primary monitoring floor because it represents the location of maximum acceleration response, as established in the previous section. Table 4 summarizes the statistical response, including the mean ($\mu$), standard deviation ($\sigma$), and coefficient of variation ($C.V.$), across the three performance levels. As expected, the mean peak floor accelerations increases progressively from IO to LS and CP, directly reflecting the increased spectral demand of the target hazard levels. Similarly, the standard deviation increases at higher intensity levels, indicating that the structural response to the CP suite exhibits significantly greater dispersion; this is primarily attributed to the high intensity and inherent variability of the ground motions selected for this performance level. Notably, the $C.V.$ exceeds 30% across all performance levels, highlighting the substantial aleatory uncertainty associated with seismic loading and its impact on structural response.

3.5. Maximum Floor Accelerations at Roof for Reinforced Concrete Structure

Table 5 summarizes the peak floor accelerations recorded at the roof level for the RC building across the three analyzed performance levels. To derive these results, the structural model was subjected to the 33 ground motion records corresponding to the IO, LS, and CP performance levels. Within this frame of reference, Table 5 provides a statistical breakdown of the response, detailing the $\mu$, $\sigma$, and $C.V.$ for each suite of ground motions, respectively. Consistent with the steel building’s response, both $\mu$ and $\sigma$ for the RC structure increase progressively from IO to LS and CP. The growth in the $\mu$ is a direct consequence of the increasing seismic intensity associated with higher return periods. Similarly, the rise in $\sigma$ reflects the heightened sensitivity and dispersion of structural response when subjected to large-magnitude seismic events. Across all performance levels under consideration, the $C.V.$ remains above 30%, indicating a significant degree of aleatory uncertainty inherent in the seismic demand.

A comparative evaluation of the data in Table 4 and Table 5 reveals that the steel structure consistently experiences higher acceleration demands than the RC building. Furthermore, the steel building exhibits greater statistical dispersion and a higher overall variation in roof accelerations. This increased sensitivity in the steel frame, driven by its specific mass, stiffness, and damping characteristics, will be addressed in detail in the Discussion section.

3.6. Seimic Risk of Steel and RC Buildings

Following the methodology detailed in Section 2.6, the seismic risk for both the steel and RC structures was quantified using the $p_f$ and $\beta$. These metrics were calculated for each ground motion suite across the IO, LS, and CP performance levels.

Table 6. Structural reliability of steel building.

Earthquake	Performance Level	Distribution	${\mathit{p}}_{\mathit{f}}$	$\mathit{\beta }$
1	IO	Kernel	2.03 × 10−14	4.2285
2	IO	Kernel	1.51 × 10−14	4.0174
3	IO	Kernel	5.22 × 10−14	3.8341
4	IO	Kernel	1.57 × 10−14	5.8929
5	IO	Kernel	0.0043	2.9875
6	IO	Kernel	5.46 × 10−13	4.7892
7	IO	Kernel	2.11 × 10−14	3.6876
8	IO	Kernel	3.44 × 10−15	3.9477
9	IO	Kernel	0.0175	2.2878
10	IO	Kernel	0	∞
11	IO	Kernel	0	∞
12	LS	Kernel	1.68 × 10−14	4.3226
13	LS	Kernel	0.0470	1.6870
14	LS	Kernel	0.0227	2.0160
15	LS	Kernel	0.0506	1.7259
16	LS	Kernel	0.0002	3.4892
17	LS	Kernel	0.1744	0.9043
18	LS	Kernel	0.0096	2.5069
19	LS	Kernel	0.0316	2.0242
20	LS	Kernel	0.0001	3.0935
21	LS	Kernel	0.0226	2.1499
22	LS	Kernel	0	∞
23	CP	Kernel	1.68 × 10−14	4.3226
24	CP	Kernel	0.0690	1.4822
25	CP	Kernel	0.1177	1.3216
26	CP	Kernel	0.0365	1.8599
27	CP	Kernel	0.0048	2.5253
28	CP	Kernel	0.0007	3.3468
29	CP	Kernel	0.0150	2.2718
30	CP	Kernel	0.0437	1.8719
31	CP	Kernel	1.43 × 10−5	3.2743
32	CP	Kernel	0.0062	2.6729
33	CP	Kernel	0	∞

summarizes the resulting structural reliability for the steel building. Notably, for all three performance levels, the peak roof acceleration response was best characterized by a Kernel distribution. This indicates that the stochastic behavior of the floor accelerations is non-parametric in nature, requiring the flexible smoothing of a Kernel PDF estimate to accurately capture the response distribution. Furthermore, the results in Table 6 show that $\beta$ values range from 0.9043 to $\infty$. The occurrence of infinite reliability values, indicating zero exceedance of the performance threshold within the analytical sample, will be addressed in detail within the Discussion section.

Table 7. Structural reliability of RC building.

Earthquake	Performance Level	Distribution	${\mathit{p}}_{\mathit{f}}$	$\mathit{\beta }$
34	IO	Kernel	2.39 × 10−14	4.9713
35	IO	Kernel	3.04 × 10−14	3.7485
36	IO	Kernel	1.69 × 10−14	4.2142
37	IO	Kernel	3.24 × 10−14	4.3754
38	IO	Kernel	0	∞
39	IO	Kernel	2.11 × 10−14	3.9946
40	IO	Kernel	1.69 × 10−14	4.3021
41	IO	Kernel	0	∞
42	IO	Kernel	3.44 × 10−15	4.4677
43	IO	Kernel	9.77 × 10−15	3.5014
44	IO	Kernel	0	∞
45	LS	Kernel	1.68 × 10−14	4.7864
46	LS	Kernel	0.0055	2.6809
47	LS	Kernel	1.45 × 10−14	4.0598
48	LS	Kernel	0.0002	3.1310
49	LS	Kernel	0.0004	3.8174
50	LS	Kernel	8.34 × 10−14	3.4763
51	LS	Kernel	1.17 × 10−5	4.1452
52	LS	Kernel	0	∞
53	LS	Kernel	0	∞
54	LS	Kernel	2.45 × 10−5	4.1052
55	LS	Kernel	6.99 × 10−14	4.1683
56	CP	Kernel	1.68 × 10−14	4.7864
57	CP	Kernel	7.95 × 10−3	3.1826
58	CP	Kernel	1.33 × 10−3	2.8918
59	CP	Kernel	0	∞
60	CP	Kernel	6.05 × 10−7	3.8535
61	CP	Kernel	8.34 × 10−14	3.5528
62	CP	Kernel	6.33 × 10−6	4.0474
63	CP	Kernel	6.21 × 10−10	3.9411
64	CP	Kernel	0	∞
65	CP	Kernel	2.56 × 10−5	4.0768
66	CP	Kernel	6.99 × 10−14	4.1683

presents the seismic reliability of the RC building, specifically focusing on the peak roof accelerations, the critical location for acceleration demand as identified previously. The findings are categorized by earthquake identifier, performance level, probability distribution type, $p_f$, and $\beta$. Consistent with the steel structure, the reliability analysis for the RC building is dominated by the Kernel distribution. The selection of a non-parametric Kernel density estimate is particularly advantageous here, as it effectively captures the high aleatory uncertainty and irregular dispersion inherent in the seismic record suites. Regarding $\beta$ values, they range from 2.6809 to $\infty$. Notably, the RC building demonstrates significantly higher reliability compared to the steel building. This superior performance correlates directly with the lower acceleration sensitivities reported in Section 3.4 and Section 3.5. A comprehensive interpretation of these results is provided in the Discussion section.

Figure 9 presents a comparative analysis of the average $\beta$ values for both the steel and RC structures across the three performance levels: IO, LS, and CP, respectively. To ensure statistical consistency and prevent numerical bias, $\infty$ values were excluded from the mean calculations for this specific comparison. Results indicate that the RC building consistently exhibits a higher safety margin than the steel structure when subjected to floor acceleration demands. This performance gap is directly attributable to the higher acceleration sensitivity observed in the steel frame. Notably, at the IO performance level, typically associated with lower-magnitude seismic events, the reliability of both structures is relatively comparable. However, as the seismic demand increases to the LS and CP performance levels, the RC structure demonstrates significantly greater reliability than the steel counterpart. Figure 9 also includes a horizontal dashed line representing the minimum target $\beta$ of 1.250, as specified in contemporary building codes [32]. While both structural systems maintain reliability indices above the code-specified threshold of 1.250 [37], a significant quantitative divergence in safety margins is observed. At the Immediate Occupancy (IO) level, the RC building demonstrates a mean reliability index that is approximately 5% higher than that of the steel building, indicating a relatively comparable performance under low-intensity shaking. However, the safety gap widens substantially at higher hazard levels. For the Life Safety (LS) and Collapse Prevention (CP) limit states, the RC structure exhibits $\beta$ values that are 1.6 and 1.5 times greater, respectively, than those of the steel frame. Specifically, while the steel building’s reliability approaches the marginal limit at $\beta =0.9043$ for certain records, the RC building maintains a robust minimum of $\beta =2.6809$. This represents a reduction in the $P_f$ by several orders of magnitude, quantitatively confirming that the RC system provides a significantly more stable environment for acceleration-sensitive non-structural components under extreme seismic demands.

4. Discussion

The comparative analysis of the steel and RC structures reveals distinct behavioral patterns in both seismic demand and structural reliability. In this section, a comprehensive interpretation of the findings is documented through structural dynamics philosophy and probabilistic theory.

As reported in the previous section, the steel building consistently exhibited higher peak floor accelerations and greater statistical dispersion compared to the RC building. This sensitivity may be primarily driven by three physical factors. First, the mass-inertia effects are affecting the steel structure. In this sense, the steel frame possesses a significantly higher strength-to-weight ratio, resulting in lower total mass. Thus, the steel building requires less force to reach high acceleration peaks, whereas the heavy RC building benefits from greater inertial resistance. Second, the damping mechanisms can also affect floor accelerations. The steel building operates with lower inherent damping (2%), allowing high-frequency energy to propagate with minimal dissipation. In contrast, the RC building (5% damping) utilizes micro-cracking and material non-homogeneity to dampen acceleration spikes before they reach the upper floor levels. The third critical physical factors affecting the structural response in terms of floor acceleration is the Whipping Effect. The relative flexibility of the steel moment frame facilitates the propagation of higher-mode vibrations. This creates a whipping effect at the roof level, which was identified in Figure 8 as the critical floor for both structures.

Another important part of the discussion is the relative to the probabilistic interpretation of the results of the previous section. A key finding of this study is the dominance of the Kernel PDF in characterizing the acceleration response for both buildings. Unlike parametric PDF (e.g., Normal or Lognormal), the Kernel PDF estimate does not assume a specific shape, allowing it to capture the irregular dispersion and tails inherent in seismic data. The high $C.V.$ (>30%) across all performance levels confirms the substantial aleatory uncertainty associated with ground motion records. This variability suggests that structural safety cannot be viewed through a deterministic mode; the specific frequency content of an individual earthquake can produce outliers that parametric models might under-represent.

One more discussion must be stated about the obtained $\beta$ values and the implication of $\beta =\infty$. This is discussed as follows. The reliability analysis summarized in Table 6 and Table 7 presented $\beta$ values ranging from 0.9043 to $\infty$. The occurrence of $\beta =\infty$ deserves specific technical clarification. $\beta =\infty$ occurs when the structural response remains below the performance limit for every ground motion in the suite. $\beta =\infty$ is equivalent to $p_f=0$. In these instances, the demand is so significantly lower than the capacity that the probability of exceedance cannot be quantified within the discrete sample size of the selected records. While $\beta =\infty$ suggests a high safety margin, it is most prevalent in the RC building at the IO performance level. This indicates that for low-intensity seismic events (72-year return period), the RC building’s mass and stiffness act as a natural buffer, making it nearly immune to acceleration-sensitive damage at that hazard level.

In terms of design standards, the following can be documented. Figure 9 demonstrates that despite the steel building’s higher sensitivity, both structures maintain a mean reliability index above the code-specified threshold of 1.250 [37]. At IO performance level, the reliability of both systems is comparable, as the ground motion intensities are insufficient to trigger the steel building’s higher-mode sensitivity. At LS and CP performance levels, the gap widens significantly. The RC building demonstrates superior robustness, maintaining high $\beta$ values even as seismic demand increases. The steel building, while still safe, approaches the code limit more closely, highlighting its vulnerability to non-structural damage induced by high-frequency accelerations.

Finally, from a performance-based engineering perspective, the divergence in reliability indices ($\beta$) carries significant implications for the post-event functionality of the two buildings. While both structures achieve the fundamental objective of life safety, the RC building demonstrates superior performance in terms of damage limitation and serviceability. The lower peak floor accelerations recorded in the RC structure across all limit states translate to a higher protection level for acceleration-sensitive non-structural components, such as suspended ceilings, heating, ventilation, and air conditioning systems, and sensitive electronic equipment. Quantitatively, the higher $\beta$ values for the RC building at the IO performance level suggest that it is significantly more likely to remain fully operational following a moderate seismic event. Conversely, the steel structure, despite its adequate structural capacity, faces a higher risk. The elevated acceleration demands and lower reliability margins at the roof level indicate that the steel building may require extensive non-structural repairs and experience longer downtime even when the primary structural frame remains elastic. Consequently, when evaluated through a performance-based framework, the RC building offers a more resilient solution for facilities where business continuity and the protection of internal assets are as critical as structural integrity.

5. Conclusions

This study provided a comprehensive reliability assessment of peak floor accelerations for five-story steel and RC buildings under multiple seismic hazard levels. The main findings are summarized as follows:

Scientific findings

• The steel building consistently exhibited higher peak floor accelerations and greater statistical dispersion across all performance levels. This behavior is primarily attributed to the steel frame’s lower mass and inherent damping (2%), which facilitate higher-mode amplification effects, particularly at the roof level.
• The RC building demonstrated significantly higher reliability indices ($\beta$), especially at the LS and CP performance levels. The monolithic nature, higher self-weight, and increased internal damping (5%) of the RC structure contribute to filtering high-frequency seismic energy, resulting in a more stable and predictable response.
• The observed differences in seismic response between steel and RC systems highlight the strong influence of structural properties such as mass, stiffness, and damping on floor acceleration demands and their variability.
• The dominance of the Kernel PDF in the reliability analysis reveals a high level of aleatory uncertainty ($C.V. >30\%$) in seismic demand. This finding indicates that non-parametric approaches are more suitable for capturing the irregular dispersion of floor accelerations compared to traditional parametric models (e.g., Normal or Lognormal distributions).

Applied findings

• Despite the higher acceleration demands observed in the steel structure, both buildings maintained mean reliability indices above the code-recommended threshold of $\beta =1.25$, confirming adequate safety for non-structural components under the considered seismic hazard levels.
• The steel building exhibited a smaller safety margin compared to the RC structure, indicating a higher vulnerability to acceleration-sensitive damage and suggesting the need for enhanced design considerations within PBSD.
• The proposed reliability-based framework provides a practical tool for integrating floor acceleration demands into seismic risk assessment, enabling more informed decision-making in the design and evaluation of building performance.

Limitations

• The findings are based on regular, symmetric five-story buildings. The presence of plan or vertical irregularities (e.g., soft stories or torsional eccentricity) would likely alter the acceleration profiles and increase statistical dispersion.
• The reliability indices were derived from suites of 11 ground motions per performance level. While statistically significant, the occurrence of $\beta =\infty$ suggests that larger record suites or alternative selection criteria may be required to capture low-probability failure events.
• The performance limits were defined based on literature-reported acceleration thresholds. The physical interaction between the structure and specific non-structural components (e.g., ceiling systems, sensitive equipment, or piping) was not explicitly modeled.

Based on the findings of the study, several directions for future research and practical applications can be identified. This study focuses on floor accelerations as the primary seismic performance parameter for mid-rise buildings within a reliability-based risk assessment framework. Future developments may explore complementary probabilistic approaches for seismic risk estimation that more explicitly incorporate the correlation between floor accelerations, structural demand, and damage in non-structural components, as well as the representation of uncertainties associated with dynamic response under different ground motion records. In this context, the use of alternative risk assessment methodologies would enable direct comparisons with the proposed framework, facilitating a clearer evaluation of its consistency, applicability, and effectiveness. From an applied perspective, the methodology can be extended to different structural systems, building heights, and seismic retrofitting scenarios, as well as adapted to other high-seismicity regions worldwide through appropriate calibration of seismic hazard levels and local design provisions. In addition, seismic intensity plays a key role in the magnitude and dispersion of floor accelerations, directly influencing risk estimates; therefore, its consideration across multiple hazard levels is essential for a more comprehensive assessment of structural performance.