Sustainable Structural System Selection Using Hybrid Fuzzy Multi-Criteria Decision Model Based on Seismic Performance

Abstract

In the rapidly evolving field of sustainable construction, this study aims to address the critical need for advancement in the building industry, focusing on vital indicators like energy efficiency and cost-effectiveness, as well as improving occupant comfort. This research introduces a novel approach to support the choice of suitable structural systems for mass housing projects, with a case study on Iran’s national housing scheme. This methodology involves a four-phase process, beginning with compiling a database from existing studies to outline primary and secondary indicators affecting structural system selection. It utilizes the fuzzy AHP method for criteria prioritization and the fuzzy TOPSIS technique for alternatives (LSF, 3DP, ICF, TRC, and RCCF). The study identified the light steel framing (LSF) system as the optimal choice for Iran’s housing needs based on various criteria. Then, in the final phase, the study evaluates the seismic performance of cold-formed steel (CFS) frames with various sheathing panel types (OSB, DFP, CSP, and GWB) under monotonic loads, examining key seismic parameters across 38 frame setups. The findings reveal that LSF structures can effectively withstand seismic events within the elastic behavior range, suggesting that this construction approach is viable for enhancing mass housing production in Iran’s construction sector.

1. Introduction

Generally, one of the critical sectors that plays a fundamental role in human societies is housing. Issues arise when housing shortages occur and the expectations and demands of the people are not met. Indeed, this is a matter that both officials and the public are fully aware of and understand [1]. Due to its unique position in socio-economic analyses, the construction industry is referred to as the engine of development in societies [2]. According to official reports from international institutions, the construction industry, employing over 100 million workers worldwide, comprises six percent of total global GDP [3], which is predicted to increase to about 15 percent by 2030 [4]. However, housing policy in Iran has experienced many ups and downs over the past four decades. Policies have sometimes led to the boom and growth of construction and have sometimes led to significant recessions. The exponential increase in the price of land and housing, periods of recession and inflation, the traditional state of construction and the absence of modern technologies, the lack of appropriate urban design and planning, etc., all indicate the lack of a macro perspective toward this sector and the inefficiency of the policies implemented for sustainable prosperity in the housing sector and the challenges thereof in Iran [5]. Meanwhile, countries in similar situations have efficiently transformed their housing sector into the driving force of their economy, leading to economic growth and prosperity [6,7].

As the construction industry progresses towards the Fourth Industrial Revolution, the emergence of Construction 4.0 has been pivotal in steering the sector towards modern technologies and industrial methods. This initiative is enhancing the industry’s efficiency and providing benefits like cost reductions, improved delivery timelines, enhanced levels of quality and safety, better reputations, and environmental sustainability [8,9].

Designing and producing buildings based on rationality and sustainable industrial production and applying structural elements are optimal solutions for industrial production in the construction sector. This concept, which can be called the modularization of building production, has been widely applied across the country with practical relevance in both modern and traditional (conventional) sectors, increasing their production efficiency and aiding in their development. Thus, built environments can be created in both sectors, contributing to the richness of architectural production in Iran and creating the basis for contemporary Iranian architecture in line with cultural, geographical, environmental, economic, social, and industrial conditions [10,11]. In addition, the construction industry is recognized as a dynamic sector that continues to respond to technological innovations and, as a result, economic conditions, environmental changes, socio-cultural developments, etc. [12].

In this context, ignoring certain parameters can be harmful; attention should be paid to housing projects that suffer delays, that lack advanced tools and machines, that do not employ an experienced expert contractor, that do not observe environmental issues during the construction phase, and that do not have an appropriate structure, design, or architecture for the climate, among other conditions. These issues not only cause irreparable material damages but can also be catastrophic for the development and growth of society [13,14].

In other words, according to the opinion of construction industry experts in Iran, the most important reasons for reducing production efficiency in construction are shortages of materials and delays in their timely delivery, the insufficient use of machines, difficulties in allocation and work, the order of workers, the waste of materials in workshops, and the effects of heat and cold in summer and winter.

Despite all the efforts of those involved, for a long time, they practically ignored one crucial aspect: new technologies in construction. Thus, adjusting to and learning new approaches to solving these problems by implementing industrialized buildings considering the economic aspects of society, such as socio-cultural and environmental issues, etc., would allow the construction industry to meet the current needs of communities and optimize the speed, quality, and price of improvements.

However, after the Industrial Revolution and the specialization of knowledge, architecture has been considered by some experts as one of the disciplines in which, due to its nature, it is not possible to separate science, art, and structure without adverse effects on building design. Therefore, paying attention to building design parameters from an architectural perspective is particularly important in the design of structures. By evaluating the results of current construction designs, it has become clear that the relationship between architecture and structure needs to be kept in mind and examined in further studies in the field of architecture.

The Mehr housing project was introduced in 2007 and later entered the execution phase in 2019 as a national housing project to balance the supply and demand of housing by eliminating land costs, providing housing for low-income groups, revitalizing housing production, increasing production volume with the entry of modern technologies and industrialization, and ultimately establishing justice in terms of access to housing. The new managers and decision makers of this national housing movement believe that constructing four million houses over four years will compensate for the backlog caused by the housing construction recession in Iran. Undertaking such a large and complex process, in addition to the integration and preparation of technical and engineering infrastructures at higher levels, requires modern technologies and industrialization in the construction sector.

This study develops a decision support system for selecting optimal structural systems for mass construction in the construction industry, specifically tailored to withstand Iran’s seismic challenges. Key factors influencing structural system selection are identified through expert opinions and research then rigorously analyzed and prioritized to choose the most suitable system. Utilizing a combination of fuzzy multi-criteria decision making approaches, this study addresses the uncertainties involved in choosing a sustainable system for the national housing project. Therefore, to select the optimal structural system, two multi-criteria decision making (MCDM) techniques are used: the fuzzy AHP and fuzzy TOPSIS. Each decision-making method has a vital task, one of which is to measure the criteria, and the other is to rank the options, which are discussed in the Section 3. Finally, in the next part of the research, by evaluating the seismic behavior of the superior structural system (as a case study) according to the geotechnical and seismic conditions of Iran and based on the existing structural and seismic standards, an attempt is made to analyze the seismic parameters. By determining the different performance levels of the superior structure system, a practical step should be taken to improve the quality level of the national housing project. In other words, the prominent focus of this research is to increase the reliability of the structures in national housing projects against seismic risks by selecting the process of the superior structural system after conducting seismic evaluations.

2. Literature Review

The significance of project management elements such as cost, time, and quality in determining and prioritizing factors that influence the choice of suitable structural systems in the construction sector cannot be overstated. However, even with extensive research in this area, persistent uncertainties and gaps remain in realizing various aspects of sustainable development within the industry, underscoring the need for continued research and deeper analyses to select the most appropriate structural systems. Yunus and Yang [15] evaluated the selection of industrial structural systems from an environmental perspective using the SWOT method. The AHP approach to structural system selection has attracted the attention of many researchers. Gudiene et al. [16] identified and analyzed the key influential parameters in Lithuanian construction projects using the AHP method. In this study, factors such as clear project objectives, planning, competence, and having project stakeholders with sufficient experience were considered the most critical indicators influencing project success. Additionally, in studies conducted by Eram and Mirseaady [17], Si et al. [18], Erdogan et al. [19], and Siadati and Shah Hosseini [20], the selection of sustainable building systems from various perspectives was examined using the AHP or fuzzy AHP techniques.

Nevertheless, many researchers have evaluated the factors influencing the selection of an appropriate structural system in the construction industry using combined MCDM methods. Abdollahzadeh et al. [1], in a study, selected an appropriate structural system among traditional and modern methods considering criteria such as dead load, energy saving, architectural constraints, lifespan, and performance facilitation using the ANP and fuzzy AHP methods. Balali et al. [21] proposed a conceptual algorithm for selecting an appropriate structural system in low-rise residential buildings in Iran using the combined methods of ELECTRE III and PROMETHEE II. In this research, sixteen criteria were used to select the most suitable structural system among the proposed options (LSF, ICF, Tronco, Wood, CFT, 3D panel, Tunnel, and D2), considering uncertainties related to the judgments of project stakeholders (the client, consultant, and contractor). The results indicated the proposed algorithm’s suitability for project management in the construction industry. Islam et al. [22] provided an approach to optimize life cycle costs and environmental impacts resulting from the design and implementation of residential buildings using single-objective optimization (SOO) and multi-objective optimization (MOO) techniques. Mathiyazhagan et al. [23], in a paper aimed at selecting an optimal strategy for choosing sustainable materials in the construction industry, identified and prioritized 23 sub-criteria using the BMW and fuzzy TOPSIS methods. The research findings indicate that the proposed conceptual model facilitates the evaluation and selection of sustainable building materials. Zumrut et al. [24] selected an industrial structural system using a combined MCDM approach in a study. In this study, using the AHP and TOPSIS methods and based on the criteria examined (cost, time, lifespan, labor, equipment, environmental impacts, performance during execution, and architectural constraints), the steel structural system was the most suitable option for selecting the industrial structural system. Aghazadeh et al. [25] proposed a method for the optimal selection of building systems with sustainable materials based on fuzzy MCDM combined methods. This paper evaluated five structural systems (LSF, PRC, ICF, 3DP, and TRC) among four main criteria and 42 sub-criteria using the fuzzy SWARA and fuzzy ARAS methods. The research findings indicate that LSF, ICF, and PRC systems have the highest priority in achieving sustainable development goals in the construction industry. Alam Bhuiyan and Hammad [26] proposed a developed decision-making model for selecting the most sustainable materials for constructing multi-story buildings, considering the opinions of all project stakeholders (the client, consultant, and contractor) using combined methods of the fuzzy AHP, fuzzy TOPSIS, and fuzzy VIKOR. The results indicate that timber is recognized as the most sustainable material, and any group of specialists can use the proposed developed model as an efficient tool for achieving sustainable construction and increasing stability in the decision-making process.

In research, Jalali et al. [27] determined and prioritized the most effective indicators in the architectural design of buildings using the AHP method. The results showed that the indicators of the exterior of the building, interior design, and safe space are considered to have the highest priorities. In a separate study, Karimi et al. [28] explored the difficulties in deploying structures for architectural design purposes. Their research aims to ascertain the barriers, challenges, and problems faced when integrating structural information into all stages of an architectural design process and, more specifically, at the building conceptual design level from various perspectives. The research findings indicate that several participants have adequate structural knowledge but struggle to participate in architectural design. The reasons for many of these problems include the participants showing a lack of maturity in their viewpoints and a lack of understanding of the relationship between architectural design and structural design. Additionally, the participants do not have the same level of geometric knowledge regarding structural systems.

3. Methods

Figure 1 outlines a detailed framework of the methodology used to meet the research objectives, divided into four primary sections: (I) Collection and validation of criteria for choosing a suitable structural system; (II) Determination of the weight importance for each criterion and sub-criterion using the fuzzy AHP method; (III) Ranking the alternatives and selecting the best structural system using the fuzzy TOPSIS method; and (IV) Conducting finite element modeling of the chosen structure and assessing its behavior and seismic performance. In other words, the studied structural systems are compared and evaluated considering the general parameters. Then, the seismic performance of the superior structure system is carefully analyzed and investigated. The methods and procedures utilized in each section are thoroughly described.

Given the objectives outlined in this research for thoroughly examining fundamental subjects, a mixed (quantitative/qualitative) research approach was chosen. Accordingly, data related to the subject were initially collected based on a qualitative approach and literature and research tools. However, in the subsequent stage, field tools were utilized to analyze the data obtained from quantitative methods and examine the research foundations. Articles, books, theses, and databases, including the Internet, were used to gather information and review the research literature. The study population for this research comprises experts in Iran’s construction industry, including 15 individuals who are contractors, academic researchers, project managers, and design and consulting engineers in the building industry. Field studies and questionnaires are utilized to determine the research topic. It is noted that MSC PATRAN-NASTRAN software (2012) is employed for the finite element analysis of the desired structure for numerical analysis in the research’s final phase.

3.1. Identification and Preparation of Required Information

In this section of the research, a database was developed that includes factors influencing the selection of suitable structural systems for mass construction projects. This resource aims to assist project stakeholders in promoting sustainability within national housing projects in Iran. A thorough review and field survey were carried out, utilizing scholarly articles, international databases, and current regulations and guidelines on mass housing construction. Extensive engagement with experts through various forms of communication, including interviews, questionnaires, and inquiries helped pinpoint critical factors.

Table 1. Introduction to the structural systems studied.

Information	Structural System
This construction system enhances quality with 90% factory production, lowers dead weight by 60%, and uses bolt–nut connections on-site. It offers 10% more space due to its thinner walls, energy efficiency, and all-weather construction, reducing time and labor without heavy machinery. It promises over 50 years of durability, easy utility installation, plan flexibility, diverse material options, and eco-friendliness with minimal waste [29].	Light Steel Frame (LSF)
This construction method offers easy transportation and setup, suitability for various building types, more space from thinner walls, versatility in facades, and impenetrability. It ensures a clean, debris-free workshop and uses a non-flammable, ozone-friendly modified polystyrene core [29].	3D Sandwich Panel (3DP)
The Insulating Concrete Form (ICF) system uses permanent EPS forms to construct reinforced concrete walls that are integral to the structure post-concrete pour.	Insulating Concrete Framework (ICF)
These forms, typically two 5-cm EPS panels linked by ties, are protected with finishes. The structural walls primarily handle and transfer loads, with uniform distribution to the foundation. This system’s high indeterminacy suggests good seismic performance [29].
The Tronco system blends traditional and modern approaches for low-rise buildings, utilizing on-site fabricated galvanized steel tubes as its core. It integrates frames for doors, windows, and utilities during construction. It has EPS panels in walls, ceilings, and hollow tube spaces, excels in energy conservation, and reduces structural weight [29].	Tronco System (TRC)
The Tunnel Formwork method, a modern construction approach, utilizes concrete for load-bearing walls and ceilings, in which reinforcement, formwork, and pouring happen simultaneously. Named for its tunnel-shaped metal forms, this method eliminates beams and columns, with walls directly handling loads. It enhances seismic behavior through a box-like structure, spreads stress more evenly, increases structural indeterminacy, and delays plastic hinge formation. This method also stands out for its fast construction pace, lower concrete use than traditional frameworks, and reduced material waste [29].	Reinforced Concrete Continuous Frame (RCCF)

systematically presents options or research objectives for selecting an appropriate structural system, while Figure 2 showcases visual representations of the structural systems under study.

In Figure 3, the hierarchy diagram of decision-making issues is displayed.

3.2. Hybrid MCDM Method

The process of multi-criteria decision making (MCDM) is crucial for selecting structural systems in substantial construction endeavors and is categorized into multi-objective and multi-attribute decision making. The analytic hierarchy process (AHP) and TOPSIS stand out in MCDM, with AHP assigning weights and values to options and TOPSIS selecting options closest to the ideal. These methods, however, struggle with vague data, prompting the incorporation of fuzzy logic to better address decision uncertainties and improve accuracy in ambiguous environments. This paper suggests refining AHP and TOPSIS with fuzzy logic to mirror real-world complexities more effectively. Specifically, fuzzy TOPSIS enhances traditional methods by incorporating fuzzy numbers in weight and decision matrices, thus providing a more detailed method for evaluating alternatives relative to ideal solutions [30,31,32,33].

3.2.1. Fuzzy AHP Method

AHP’s primary role is to assign preferential weights to each decision alternative, in which preferences are determined through natural language or numerical assessments of each attribute’s significance. According to research [34], the fuzzy AHP method, which generalizes the standard approach, is elaborated in

Table 2. Sequential description of decision making using the fuzzy AHP method.

Equations		Description	Step
(1)	${\tilde{\mathrm{A}}}^{\mathrm{k}}=\left[\begin{array}{ccc}{\tilde{\mathrm{a}}}_{11}^{\mathrm{k}}& \cdots & {\tilde{\mathrm{a}}}_{1\mathrm{n}}^{\mathrm{k}}\\ ⋮& \ddots & ⋮\\ {\tilde{\mathrm{a}}}_{\mathrm{m}1}^{\mathrm{k}}& \cdots & {\tilde{\mathrm{a}}}_{\mathrm{mn}}^{\mathrm{k}}\end{array}\right]$	Developing a hierarchical structure and executing fuzzy scale-based comparisons among criteria or alternatives to form a pairwise comparison matrix, as displayed in Equation (1);	1
(2)	${\tilde{\mathrm{a}}}_{\mathrm{ij}}=\frac{{{\displaystyle \sum }}_{\mathrm{k}=1}^{\mathrm{K}}{\mathrm{a}}_{\mathrm{ij}}^{\mathrm{k}}}{\mathrm{K}}$	Averaging the preferences of all decision makers as per Equation (2) to create a new pairwise comparison matrix shown in Equation (3);	2
(3)	$\tilde{\mathrm{A}}=\left[\begin{array}{ccc}{\tilde{\mathrm{a}}}_{11}& \cdots & {\tilde{\mathrm{a}}}_{1\mathrm{n}}\\ ⋮& \ddots & ⋮\\ {\tilde{\mathrm{a}}}_{\mathrm{m}1}& \cdots & {\tilde{\mathrm{a}}}_{\mathrm{mn}}\end{array}\right]$
(4)	${\tilde{\mathrm{z}}}_{\mathrm{i}}={\left[{\displaystyle {\displaystyle \prod }_{\mathrm{j}=1}^{\mathrm{n}}}{\tilde{\mathrm{a}}}_{\mathrm{ij}}\right]}^{1/\mathrm{n}}\mathrm{i}=1,2\dots ,\mathrm{m}$	Calculating the geometric mean for each criterion using Equation (4);	3
(5)	${\tilde{\mathrm{w}}}_{\mathrm{i}}={\tilde{\mathrm{z}}}_{\mathrm{i}}\oplus {\left({\tilde{\mathrm{z}}}_1{ \oplus \tilde{\mathrm{z}}}_2 \oplus \dots {\oplus \tilde{\mathrm{z}}}_{\mathrm{n}}\right)}^{1/\mathrm{n}}=\left({\mathrm{l}}_{\mathrm{i}}{,\mathrm{m}}_{\mathrm{i}}{,\mathrm{u}}_{\mathrm{i}}\right)$	Deriving the fuzzy weights (${\tilde{w}}_i$) and conducting a vector summation of each ${\tilde{z}}_i$, inversely scaling the sum vector, ordering it, and finally multiplying by the reciprocal vector as shown in Equation (5);	4
(6)	${\mathrm{S}}_{\mathrm{i}}=\frac{{\mathrm{l}}_{\mathrm{i}}+{\mathrm{m}}_{\mathrm{i}}+{\mathrm{u}}_{\mathrm{i}}}{3}$	Transforming fuzzy triangular numbers into precise values using the center of area de-fuzzification technique, as detailed in Equation (6);	5
(7)	${\mathrm{T}}_{\mathrm{i}}=\frac{{\mathrm{S}}_{\mathrm{i}}}{{{\displaystyle \sum }}_{\mathrm{i}=1}^{\mathrm{m}}{\mathrm{S}}_{\mathrm{i}}}$	Normalizing the crisp weights derived from the previous step using the process outlined in Equation (7).	6

. This method applies fuzzy logic to enhance the handling of decision-making complexities in situations of uncertainty. Comparisons between pairs of elements are made using a 9-point scale. Fuzzy comparison between pairs of elements is such that fuzzy numbers (membership function) $\tilde{1}$ (1, 1, 3), $\tilde{3}$ (1, 3, 5), $\tilde{5}$ (3, 5, 7), $\tilde{7}$ (5, 7, 9), and $\tilde{9}$ (7, 9, 9) are used for equally important, weakly important, essentially important, very strongly important, and absolutely important linguistic changes, respectively (data from [34]).

3.2.2. Fuzzy TOPSIS Method

The primary goal of the TOPSIS method is to rank the available alternatives using specific decision-making criteria. Initially, a decision matrix is created in which each alternative is evaluated based on each criterion. If the decision matrix values are derived from concrete data and existing statistics, fuzzy TOPSIS is not suitable because the values are clear and unambiguous. However, in many situations, including in this study, alternatives are assessed based on expert opinions for each criterion. Under such circumstances, fuzzy calculations tend to yield better outcomes. This segment of the research outlines the fuzzy TOPSIS analysis procedure in

Table 3. Sequential description of decision making using the fuzzy TOPSIS method.

Equations		Description	Step
(8)	$\mathrm{D}=\left[\begin{array}{ccc}{\tilde{\mathrm{x}}}_{11}& \cdots & {\tilde{\mathrm{x}}}_{1\mathrm{m}}\\ ⋮& \ddots & ⋮\\ {\tilde{\mathrm{x}}}_{\mathrm{n}1}& \cdots & {\tilde{\mathrm{x}}}_{\mathrm{nm}}\end{array}\right]$ where n denotes the number of decision alternatives and m denotes the number of decision criteria.	Build a decision matrix where n$\times$n represents the number of alternatives and m$\times$m the number of criteria;	1
(9)	$\widetilde{{\mathrm{n}}_{\mathrm{ij}}}=\left(\frac{{\mathrm{l}}_{\mathrm{ij}}}{{\mathrm{u}}_{\mathrm{j}}^{\ast }},\frac{{\mathrm{m}}_{\mathrm{ij}}}{{\mathrm{u}}_{\mathrm{j}}^{\ast }},\frac{{\mathrm{u}}_{\mathrm{ij}}}{{\mathrm{u}}_{\mathrm{j}}^{\ast }}\right){ \mathrm{u}}_{\mathrm{j}}^{\ast }={\max \mathrm{u}}_{\mathrm{ij}}$	Normalize the decision matrix, converting fuzzy expert opinions into a scaled matrix using Equation (9) for positive components and Equation (10) for negative components;	2
(10)	$\widetilde{{\mathrm{n}}_{\mathrm{ij}}}=\left(\frac{{\mathrm{l}}_{\mathrm{j}}^{-}}{{\mathrm{u}}_{\mathrm{ij}}},\frac{{\mathrm{l}}_{\mathrm{j}}^{-}}{{\mathrm{m}}_{\mathrm{ij}}},\frac{{\mathrm{l}}_{\mathrm{j}}^{-}}{{\mathrm{l}}_{\mathrm{ij}}}\right){ \mathrm{l}}_{\mathrm{j}}^{-}={\min \mathrm{l}}_{\mathrm{ij}}$
(11)	${\mathrm{v}}_{\mathrm{ij}}={\mathrm{r}}_{\mathrm{ij}}\times {\mathrm{w}}_{\mathrm{j}}$	Generate a scaled matrix v devoid of fuzzy weights, based on the vector wij as specified in Equation (11);	3
(12)	${\mathrm{A}}^{+}=\left(\widetilde{{\mathrm{v}}_1^{\ast }}, \widetilde{{\mathrm{v}}_2^{\ast }}\dots , \widetilde{{\mathrm{v}}_{\mathrm{n}}^{\ast }}\right) \mathrm{where} \widetilde{{\mathrm{v}}_{\mathrm{j}}^{\ast }}=\left(\widetilde{{\mathrm{c}}_{\mathrm{j}}^{\ast }},\widetilde{{\mathrm{c}}_{\mathrm{j}}^{\ast }},\widetilde{{\mathrm{c}}_{\mathrm{j}}^{\ast }}\right) \mathrm{and} \widetilde{{\mathrm{c}}_{\mathrm{j}}^{\ast }}=\underset{\mathrm{i}}{\max }\left\{\widetilde{{\mathrm{c}}_{\mathrm{ij}}}\right\}$	Identify the fuzzy ideal (A+) and fuzzy anti-ideal (A−) points, defined as the maximum and minimum values in each criterion column, respectively;	4
(13)	${\mathrm{A}}^{-}=\left(\widetilde{{\mathrm{v}}_1^{-}}, \widetilde{{\mathrm{v}}_2^{-}}\dots , \widetilde{{\mathrm{v}}_{\mathrm{n}}^{-}}\right) \mathrm{where} \widetilde{{\mathrm{v}}_{\mathrm{j}}^{-}}=\left(\widetilde{{\mathrm{a}}_{\mathrm{j}}^{-}},\widetilde{{\mathrm{a}}_{\mathrm{j}}^{-}},\widetilde{{\mathrm{a}}_{\mathrm{j}}^{\ast -}}\right) \mathrm{and} \widetilde{{\mathrm{a}}_{\mathrm{j}}^{-}}=\underset{\mathrm{i}}{\min }\left\{\widetilde{{\mathrm{a}}_{\mathrm{ij}}}\right\}$
(14)	${\mathrm{d}}_{\mathrm{i}}^{+}={\displaystyle {\displaystyle \sum }_{\mathrm{j}=1}^{\mathrm{n}}}\mathrm{dv} (\widetilde{{\mathrm{v}}_{\mathrm{ij}}},\widetilde{{\mathrm{v}}_{\mathrm{j}}^{\ast }}), \mathrm{i}=1,2,\dots ,\mathrm{m}$	Compute the total distances of each alternative from the fuzzy positive ideal and the fuzzy negative ideal;	5
(15)	${\mathrm{d}}_{\mathrm{i}}^{-}={\displaystyle {\displaystyle \sum }_{\mathrm{j}=1}^{\mathrm{n}}}\mathrm{dv} (\widetilde{{\mathrm{v}}_{\mathrm{ij}}},\widetilde{{\mathrm{v}}_{\mathrm{j}}^{-}}),=1,2,\dots ,\mathrm{m}$
(16)	${\mathrm{CC}}_{\mathrm{i}}=\frac{{\mathrm{d}}_{\mathrm{i}}^{-}}{{\mathrm{d}}_{\mathrm{i}}^{-}+{\mathrm{d}}_{\mathrm{i}}^{+}}$	Calculate the similarity index for each option relative to the ideal solution;	6
		The ranking of alternatives.	7

.

4. Research Findings and Discussion

4.1. Identification of Criteria, Sub-Criteria, and Alternatives (Phase I)

The names of the primary criteria, sub-criteria, and their corresponding codes are listed in

Table 4. Evaluation criteria and codes.

Reference(s)	Influence	Sub-Criteria (Evaluation Criteria) (Code)	Main Criteria (Code)
[35,36,37]	Beneficial criteria	Manufacturing and Production Technology $\left({\mathrm{C}}_{1-1}\right)$	Technical and Executive Regulations Criteria $\left({\mathrm{C}}_1\right)$
[38,39]	Beneficial criteria	Availability of Materials $\left({\mathrm{C}}_{1-2}\right)$
[29,40]	Beneficial criteria	Operational and Seismic Guidelines $\left({\mathrm{C}}_{1-3}\right)$
[41,42]	Beneficial criteria	The Required Experience of Contractors and Workers$\left({\mathrm{C}}_{1-4}\right)$
[43,44]	Cost criteria	Challenges of Project Implementation $\left({\mathrm{C}}_{1-5}\right)$
[45,46,47]	Beneficial criteria	Mechanization of Project Execution $\left({\mathrm{C}}_{1-6}\right)$
[47,48,49]	Cost criteria	The Duration of the Project $\left({\mathrm{C}}_{2-1}\right)$	Economic Criteria $\left({\mathrm{C}}_2\right)$
[47,48,50]	Cost criteria	Cost of Equipment, Machinery and Workers $\left({\mathrm{C}}_{2-2}\right)$
[51,52,53]	Cost criteria	Life Cycle Cost (Useful Life and Durability)$\left({\mathrm{C}}_{2-3}\right)$
[39,43,54,55]	Cost criteria	Energy Consumption Amount $\left({\mathrm{C}}_{2-4}\right)$
[35,39,44,49]	Cost criteria	Cost of Required Materials $\left({\mathrm{C}}_{2-5}\right)$
[56,57]	Beneficial criteria	The Interior of the Building $\left({\mathrm{C}}_{3-1}\right)$	Building Design and Architecture Criteria $\left({\mathrm{C}}_3\right)$
[58,59,60,61]	Beneficial criteria	Impact on the Facade of the Building $\left({\mathrm{C}}_{3-2}\right)$
[56,58]	Beneficial criteria	Impact on Building Layout $\left({\mathrm{C}}_{3-3}\right)$
[56,60]	Beneficial criteria	Impact on the lighting of the Building $\left({\mathrm{C}}_{3-4}\right)$
[35,50,51]	Cost criteria	Mineral Extraction $\left({\mathrm{C}}_{4-1}\right)$	Environmental Criteria $\left({\mathrm{C}}_4\right)$
[50,54,62,63]	Cost criteria	Pollution $\left({\mathrm{C}}_{4-2}\right)$
[50,64]	Beneficial criteria	Renewability and Reusability $\left({\mathrm{C}}_{4-3}\right)$
[37,64,65]	Beneficial criteria	Compliance with Sustainable Development $\left({\mathrm{C}}_{4-4}\right)$
[66,67,68]	Beneficial criteria	Safety and Health $\left({\mathrm{C}}_{5-1}\right)$	Socio-cultural Criteria $\left({\mathrm{C}}_5\right)$
[52,63,69]	Beneficial criteria	Efficiency and Effectiveness $\left({\mathrm{C}}_{5-2}\right)$
[39,70,71]	Beneficial criteria	Compatibility with Identity and Ecology $\left({\mathrm{C}}_{5-3}\right)$
[38,43,56,72,73]	Beneficial criteria	Human Satisfaction $\left({\mathrm{C}}_{5-4}\right)$

. The indices, derived from research in the literature and direct interviews with experts and authorities, are organized into five main groups (primary criteria) and 23 sub-criteria for the selection and prioritization of research objectives. To assess the importance and impact of these identified factors, a 15-item questionnaire is crafted based on insights from experts. This questionnaire was developed by professionals in the construction industry, including contractors, academic researchers, project managers, and design engineers and consultants. All participants involved in the study were considered as experts in the field of mass construction, specifically focusing on national housing projects, through comprehensive interviews and questionnaires.

4.2. Prioritizing Criteria and Sub-Criteria (Phase II)

In the second phase of this research, experts constructed a pairwise comparison matrix to determine the relative importance of various criteria using a nine-point scale. Using the fuzzy AHP method, weights for primary and sub-criteria were derived and listed in

Table 5. Determining the weight of criteria and sub-criteria.

Rank		Normalized Weight	Definitive Weight	Fuzzy Weight		Weight
General	Group				Criteria
2		0.274	0.301	(0.147, 0.273, 0.509)	Technical and Executive Regulations
3	1	0.295	0.318	(0.156, 0.297, 0.523)	Manufacturing and Production Technology
17	6	0.094	0.101	(0.053, 0.092, 0.164)	Availability of Materials
9	4	0.146	0.157	(0.083, 0.146, 0.255)	Operational and Seismic Guidelines
14	5	0.117	0.126	(0.065, 0.116, 0.204)	The Required Experience of Contractors and Workers
6	2	0.178	0.191	(0.094, 0.174, 0.323)	Challenges of Project Implementation
7	3	0.170	0.183	(0.127, 0.174, 0.257)	Mechanization of Project Execution
1		0.389	0.426	(0.210, 0.165, 0.315)	Economic
1	1	0.401	0.442	(0.219, 0.412, 0.726)	The Duration of the Project
2	2	0.218	0.240	(0.111, 0.214, 0.421)	Cost of Equipment, Machinery, and Workers
15	5	0.080	0.088	(0.048, 0.078, 0.147)	Life Cycle Cost (Useful Life and Durability)
11	4	0.100	0.110	(0.056, 0.097, 0.188)	Energy Consumption Amount
4	3	0.201	0.222	(0.099, 0.198, 0.391)	Cost of Required Materials
3		0.168	0.184	(0.091, 0.165, 0.315)	Building Design and Architecture
19	4	0.103	0.112	(0.059, 0.098, 0.193)	The Interior of the Building
5	1	0.392	0.428	(0.226, 0.404, 0.681)	Impact on the Facade of the Building
10	3	0.232	0.254	(0.129, 0.232, 0.423)	Impact on Building Layout
8	2	0.273	0.299	(0.134, 0.266, 0.529)	Impact on the Lighting of the Building
5		0.074	0.081	(0.043, 0.071, 0.138)	Environmental
23	4	0.116	0.127	(0.065, 0.112, 0.220)	Mineral Extraction
18	2	0.258	0.283	(0.133, 0.252, 0.495)	Pollution
20	3	0.221	0.243	(0.117, 0.219, 0.416)	Renewability and Reusability
16	1	0.405	0.445	(0.225, 0.416, 0.722)	Compliance with Sustainable Development
4		0.095	0.104	(0.053, 0.093, 0.177)	Cultural and Social
13	2	0.340	0.375	(0.178, 0.339, 0.645)	Safety and Health
12	1	0.392	0.431	(0.206, 0.400, 0.718)	Efficiency and Effectiveness
22	4	0.132	0.145	(0.074, 0.127, 0.252)	Compatibility with Identity and Ecology
21	3	0.136	0.150	(0.077, 0.134, 0.254)	Human Satisfaction

, revealing the normalized weights for each. It is necessary to explain that, to perform a fuzzy AHP analysis, a pairwise comparison matrix should be formed based on Equation (1), then its elements should be completed by experts through Equations (2) and (3). Then, the geometric mean of each criterion is obtained through Equation (4), and the fuzzy weight of the criteria is obtained using Equation (5). Finally, by using Equations (6) and (7), defuzzification and weight normalization are performed for each criterion.

The main criteria include technical and execution regulations, economic factors, fac-tors affecting the design and architecture of buildings, environmental factors, and cultural and social factors. Additionally, the sub-indices of each main criterion are compared pairwise, and their weights and rankings are determined and presented using the fuzzy AHP method. According to Table 4 and Figure 4, which result from the pairwise comparison of the main criteria, the economic factors criterion has the highest weight (0.389), followed by technical and execution regulations, factors affecting the design and architecture of the building, cultural and social factors, and environmental factors, with weights of 0.274, 0.168, 0.095, and 0.074, respectively. Therefore, economic factors are the most critical and influential criterion in examining parameters affecting the selection of an appropriate structural system for mass housing construction in Iran. Among the sub-indices of economic factors, the criterion of project execution duration ranks first with a weight of 0.401. This is followed by the cost of equipment, machinery, and labor (0.218) in the second rank and the criteria of material costs, energy consumption, and lifecycle costs with weights of 0.201, 0.100, and 0.080, respectively, in subsequent priorities.

Regarding the criterion of technical and execution regulations, which ranks second after economic factors as the most critical criteria in examining parameters affecting the selection of an appropriate structural system, the sub-criterion of construction and pro-duction technology is considered the most essential and effective sub-criterion with a weight of 0.295. The sub-criteria of project execution challenges (0.178), the mechanization of project execution (0.170), the existence of execution and seismic guidelines (0.146), the necessary experience of contractors and workers (0.117), and the availability of materials (0.094) rank second to sixth, respectively.

In the evaluation of the main criterion affecting the design and architecture of buildings, which ranks third among the main criteria, the sub-criteria of impact on building facade (0.392), impact on building lighting (0.273), impact on space planning (0.232), and impact on interior spaces (0.102) are among the most effective sub-indices affecting the design and architecture of buildings in examining the parameters affecting the selection of an appropriate structural system.

Regarding the main criterion of cultural and social factors, the sub-criterion of productivity and efficiency ranks first with a weight of 0.392. Additionally, the sub-criteria of safety and health, human satisfaction, and compatibility with identity and ecology weigh 0.341, 0.136, and 0.132, respectively, ranking second to fourth.

Finally, the criterion of environmental factors, which is the last adequate criterion in prioritizing the main criteria, includes sub-criteria such as mineral resource extraction, pollution, renewability, reusability, and compliance with sustainable development. The comparative analysis results of these sub-criteria, derived from their pairwise comparisons, showed that compliance with sustainable development, pollution, renewability, reusability, and mineral resource extraction are ranked first to fourth with weights of 0.405, 0.258, 0.221, and 0.116, respectively, as the most critical and practical sub-indices of the environmental factors criterion.

Additionally, this study ensured the validity and reliability of the evaluations by maintaining an acceptable inconsistency rate, as suggested by Gogus and Boucher [74]. The fuzzy AHP method helped keep inconsistency rates below 10%, ensuring robust and reliable decision making, as depicted in Figure 5.

4.3. Prioritizing Structural Systems (Phase III)

In this segment of the research, alternatives are ranked using the fuzzy TOPSIS method, which employs a fuzzy decision matrix and the final weights derived from the fuzzy AHP method in the previous phase (Table 3). Initially, each option is evaluated against each criterion using an appropriate linguistic scale (described in Section 3.2.1).

After assessing the impact of each criterion as beneficial or costly, the user input table is converted into a fuzzy decision matrix via a triangular membership function. The matrix is normalized according to whether the criterion is beneficial or costly (using Equations (9) and (10)). For the beneficial criteria, the membership function values are divided by the maximum value in the set, while the cost criteria are divided by the minimum values. Following this, the fuzzy positive ideal solution (FPIS) and fuzzy negative ideal solution (FNIS) are derived from the weighted normalized fuzzy decision matrix (refer to

Table 6. Distance from FPIS.

$C_{3-2}$	$C_{3-1}$	$C_{2-5}$	$C_{2-4}$	$C_{2-3}$	$C_{2-2}$	$C_{2-1}$	$C_{1-6}$	$C_{1-5}$	$C_{1-4}$	$C_{1-3}$	$C_{1-2}$	$C_{1-1}$	Criteria	Alternative
0.012	0.006	0.047	0.023	0.019	0.051	0.094	0.009	0.029	0.012	0.015	0.005	0.005	LSF
0.047	0.010	0.061	0.030	0.026	0.072	0.133	0.025	0.042	0.020	0.025	0.018	0.043	3DP
0.023	0.010	0.047	0.023	0.024	0.066	0.121	0.016	0.038	0.020	0.025	0.009	0.015	ICF
0.035	0.010	0.047	0.023	0.024	0.072	0.133	0.016	0.042	0.020	0.025	0.014	0.028	TRC
0.047	0.010	0.069	0.034	0.027	0.075	0.138	0.025	0.043	0.020	0.025	0.018	0.043	RCCF
SUM (di+)			$C_{5-4}$	$C_{5-3}$	$C_{5-2}$	$C_{5-1}$	$C_{4-4}$	$C_{4-3}$	$C_{4-2}$	$C_{4-1}$	$C_{3-4}$	$C_{3-3}$	Criteria	Alternative
0.397			0.002	0.002	0.007	0.009	0.005	0.003	0.011	0.005	0.013	0.011	LSF
0.711			0.009	0.009	0.019	0.015	0.016	0.008	0.015	0.008	0.032	0.027	3DP
0.550			0.004	0.004	0.013	0.015	0.010	0.005	0.011	0.007	0.022	0.019	ICF
0.619			0.007	0.007	0.019	0.009	0.016	0.005	0.011	0.005	0.032	0.019	TRC
0.758			0.009	0.009	0.027	0.022	0.022	0.012	0.017	0.008	0.032	0.027	RCCF

and

Table 7. Distance from FNIS.

$C_{3-2}$	$C_{3-1}$	$C_{2-5}$	$C_{2-4}$	$C_{2-3}$	$C_{2-2}$	$C_{2-1}$	$C_{1-6}$	$C_{1-5}$	$C_{1-4}$	$C_{1-3}$	$C_{1-2}$	$C_{1-1}$	Criteria	Alternative
0.051	0.011	0.042	0.021	0.017	0.046	0.084	0.027	0.026	0.019	0.024	0.020	0.054	LSF
0.017	0.007	0.011	0.006	0.002	0.005	0.010	0.012	0.003	0.011	0.015	0.006	0.021	3DP
0.041	0.007	0.042	0.021	0.005	0.012	0.023	0.020	0.007	0.011	0.015	0.016	0.047	ICF
0.028	0.007	0.042	0.021	0.005	0.005	0.010	0.020	0.003	0.011	0.015	0.011	0.035	TRC
0.017	0.007	0.002	0.001	0.001	0.002	0.004	0.012	0.001	0.011	0.015	0.009	0.021	RCCF
SUM (di+)			$C_{5-4}$	$C_{5-3}$	$C_{5-2}$	$C_{5-1}$	$C_{4-4}$	$C_{4-3}$	$C_{4-2}$	$C_{4-1}$	$C_{3-4}$	$C_{3-3}$	Criteria	Alternative
0.623			0.010	0.010	0.028	0.022	0.023	0.012	0.010	0.005	0.032	0.027	LSF
0.211			0.004	0.004	0.016	0.015	0.013	0.007	0.003	0.000	0.013	0.011	3DP
0.402			0.008	0.008	0.023	0.015	0.019	0.010	0.010	0.001	0.022	0.019	ICF
0.331			0.006	0.006	0.016	0.022	0.013	0.010	0.010	0.005	0.013	0.019	TRC
0.164			0.004	0.004	0.009	0.009	0.008	0.004	0.000	0.000	0.013	0.011	RCCF

). The Euclidean distance between each criterion and each option relative to both the fuzzy positive and negative ideals is calculated (using Equations (14) and (15)). Subsequently, the similarity index (CCi) for each option is computed using Equation (16), leading to the prioritization of the alternatives.

The prioritization and similarity indices of the evaluated systems are detailed in

Table 8. Ranking of the alternatives.

Rank	CC	di-	di+	Alternative
1	0.611	0.623	0.397	LSF
4	0.229	0.211	0.711	3DP
2	0.422	0.402	0.550	ICF
3	0.349	0.331	0.619	TRC
5	0.178	0.164	0.758	RCCF

. The results indicate that the LSF structural system ranks higher than the other systems analyzed.

The research findings indicate that the LSF, ICF, TRC, 3DP, and RCCF structural systems are prioritized based on the studied criteria, respectively. The LSF and ICF systems, in particular, are highly preferred over the other alternatives according to the criteria under examination, including execution and seismic regulations, economic factors, factors affecting design and architectural structure, environmental factors, and sociocultural factors. Additionally, the findings suggest that the 3DP and RCCF structural systems approximately share the same level of importance in terms of their execution and seismic guidelines, contractors and workers having the necessary breath of experience, level of compatibility with identity and ecology, and human satisfaction.

Ultimately, the prioritization of the evaluated alternatives revealed that the LSF, ICF, and TRC systems are the top three choices, with similarity indices of 0.611, 0.422, and 0.349, respectively. Following these, the 3DP and RCCF systems, with similarity indices of 0.229 and 0.178, respectively, ranked lower based on the criteria established for selecting suitable structural systems for the national housing construction project in Iran (refer to Table 8).

Figure 6 displays the impact level and prioritization of structural systems based on each of the studied criteria. For example, in the LSF structural system, the influences of technical and executive criteria, economic factors, building design, architectural factors, environmental factors, and socio-cultural factors are 19.16%, 26.02%, 19.21%, 17.93%, and 17.68%, respectively.

4.4. Case Study: Numerical Modeling and Seismic Performance Evaluation (Phase IV)

This phase focused on evaluating the seismic performance of light steel framing (LSF) systems, chosen for their precision, lightness, and ease of installation, which offer advantages over traditional materials like wood. Using a conventional finite element analysis (CFEA), this study assessed the lateral stiffness and resistance of these systems, highlighting the importance of vertical studs and screw-connected cover plates for structural support.

Several research efforts have further explored the seismic capabilities of cold-formed steel (CFS) constructions (Figure 7). Martinez [75] developed a simplified finite element analysis (SFEA) to reduce computation time without compromising accuracy, efficiently assessing shear wall panels compared to the more time-intensive CFEA. Research by Javaheri et al. [76] tested various stud and screw configurations under cyclic loading, revealing that tighter stud spacing could significantly enhance shear resistance. Their findings indicated a strong seismic performance, with response modification factors generally above seven. Zeynalian and Ronagh [77] evaluated the seismic resilience of CFS frames with fiber cement board panels, noting a subpar performance under cyclic loads but proposing modifications that significantly improved their reliability and seismic resistance. In the study of Gerami and Lotfi [78,79,80], the nonlinear behavior of 112 cold-formed steel frames with different bracing arrangements and aspect ratios was investigated. Seismic parameters were investigated, including the strength reduction factor, ductility, and force reduction factor due to ductility, for all samples. Additionally, the seismic response correction factor was calculated for these systems. The findings indicate that the highest response correction factor in bracing systems was obtained for sample B (with X bracing), with a bilateral cross-bracing system with a value of 3.14. Ayatollahi et al.’s study [81] on CFS frames with gypsum panels under combined loads pointed out the impact of load conditions on shear capacity, stiffness, and energy absorption, highlighting that two-sided sheathing increased their shear resistance but reduced their ductility. Yilmaz et al. [82] assessed CFS frames with OSB sheeting, observing that adjustments in screw spacing and OSB thickness could enhance lateral capacity and energy dissipation, although higher vertical loads adversely affected these properties.

Further research has supported the development of non-linear modeling approaches for CFS constructions, which are essential for performance-based designs (PBDs) that aim to achieve specific seismic performance levels. This approach categorizes performance into four levels: usability, immediate operation, life safety, and collapse prevention, each designed to cope with increasing seismic impacts while ensuring structural integrity [83,84,85,86,87,88,89,90,91].

Figure 7. (a) View of the components of a CFS frame. (b) CFS frame with sheeting [92].

Figure 7. (a) View of the components of a CFS frame. (b) CFS frame with sheeting [92].

Performance-based design protocols, such as those outlined by FEMA 273 [93], are crucial for ensuring that buildings meet established seismic performance criteria, particularly in managing lateral drift and enhancing the resilience of shear wall panels (Figure 8).

4.4.1. Fundamental Principles

Examining the parameters of nonlinear behavior and ductility is crucial. These aspects are covered under the concept of the response modification factor.

Stiffness

In evaluating the structural systems, particularly walls, this study considers nominal and predicted lateral yield strengths (S_yn and S_yp) and shear stiffness. These values are derived considering the material properties and the geometric configuration of the braces. The nominal yield strength, S_yn, relates to the tension yield of the wall, calculated using the brace’s area and minimum yield stress, and adjusted for the brace’s angle. The nominal lateral shear stiffness, k_n, is calculated based on the axial stiffness of the braces, adjusted according to their orientation. The measured yield strength S_y indicates the maximum load the wall can endure under testing conditions, while the initial elastic shear stiffness K_e is defined as the stiffness up to 40% of the maximum load according to ASTM E2126 standards [94] (Figure 9).

Ductility

Ductility, a crucial factor for seismic resilience, refers to a structure’s capacity to undergo significant nonlinear displacements without collapsing. It is quantified by comparing the system’s elastic stiffness and lateral yield resistance to its displacement at 80% of the ultimate resistance, showcasing the structure’s ability to withstand forces beyond its yielding point [94].

$$\mathsf{\mu }=\frac{{\mathsf{\Delta }}_{0.8}}{\mathsf{\Delta }}$$

(17)

Response Modification Factor

This factor indicates a structure’s capacity to absorb seismic energy and delay failure by providing additional resistance and ductility. Earthquake regulations often permit designs with less strength in favor of greater displacement capabilities. The additional resistance factor (R₀) and the force reduction factor due to ductility (R_d) are major components of this modification factor, with R_d values calculated for the structures with fundamental periods between 0.1 and 0.5 s using the reference equation [95].

$$\mathrm{R}={ \mathrm{R}}_{\mathrm{o}}\times {\mathrm{R}}_{\mathrm{d}}$$

(18)

$${\mathrm{R}}_0=\frac{{\mathrm{s}}_{\mathrm{y}}}{{\mathrm{s}}_{\mathrm{yn}}}$$

(19)

$${\mathrm{R}}_{\mathrm{d}}=\sqrt{2\mathsf{\mu }-1}$$

(20)

Performance Level

As defined in FEMA 273 [93], performance levels dictate the acceptable deformations for structures under seismic stress. For steel-framed structures, specific deformations are associated with operational performance (OP) levels, with submission elements calculated at the outset. For shear wall panels (SWP), the drift ratio, a critical performance indicator, is determined by the height of the SWP and the deformations at different performance levels (IO, LS, and CP). Branston et al. [96] provided drift ratios for various performance targets, which are essential for understanding structural limits under seismic loading. The capacity spectrum method, used in seismic performance evaluations, involves plotting structural capacity against seismic demand to determine if a structure can withstand specific seismic events, illustrated by the capacity–need curves on the acceleration displacement response spectrum (ADRS) (Table 9).

$$\mathrm{d}=\frac{{\mathsf{\Delta }}_{\mathrm{cp}}}{{\mathsf{\Delta }}_{\mathrm{y}}}$$

(21)

$$\frac{{\Delta }_{LS}}{{\Delta }_y}=1.0+0.8\left(d-1\right)$$

(22)

$$\frac{{\Delta }_{IO}}{{\Delta }_y}=1.0+0.2\left(d-1\right)$$

(23)

$$LDR\left(\%\right)=\left(\frac{{\Delta }_{PL}}{{\Delta }_y}\right)\frac{{\Delta }_y}{h}\times 100$$

(24)

In Equation (24), “LDR” refers to the limiting drift ratio for the performance level, which is presented as a percentage. Here, “h” denotes the height of the SWP, while “Δ_PL” is the deformation of the SWP at a chosen performance level, such as IO, LS, or CP. “Δ_y” represents the deformation of the SWP in its submission state, and the ratio “Δ_pl/Δ_y” indicates the normalized deformation.

Table 9. Detailed steps of the capacity–need curve within the ADRS unit set.

Equations		Description	Step
(25)	${\mathrm{S}}_{\mathrm{a}}=\frac{\left(\raisebox{1ex}{${\mathrm{V}}_{\mathrm{i}}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{W}$}\right.\right)}{{\mathsf{\alpha }}_1}$	These equations link structural displacements to base shear, utilizing the effective mass index, participation factor, base shear, total construction weight, and roof form shape. The capacity curve is created using the pushover method, plotting base shear against roof displacement.	1
(26)	${\mathrm{S}}_{\mathrm{di}}=\frac{{\mathsf{\Delta }}_{\mathrm{roof}}}{{\mathrm{PF}}_1\times {\mathsf{\Phi }}_{1,\mathrm{roof}}}$
where α1, PF1, V, W, and φ1,roof represent the effective mass index in the first mode, the participation factor in the first mode, base shear, total construction weight (including a percentage of live load), and the first mode form shape in the roof floor, respectively.
		The seismic demand curve is derived from the elastic design spectrum with 5% damping, adjusted using structural behavior reduction coefficients.	2
(27)	${\mathsf{\beta }}_{\mathrm{eff}}=\frac{63.7{\mathrm{k}}_{\mathrm{h}}\left({\mathrm{a}}_{\mathrm{y}}{\mathrm{d}}_{\mathrm{p}}-{\mathrm{a}}_{\mathrm{p}}{\mathrm{d}}_{\mathrm{y}}\right)}{{\mathrm{a}}_{\mathrm{p}}{\mathrm{d}}_{\mathrm{p}}}+5.0$	Using this equation, the equivalent damping, period, and yield points are calculated from the capacity curve, allowing for the estimation of energy absorption by the structure. Parameters for converting ideal hysteresis diagrams to a parallelogram and other specifics are shown in Figure 10 (data from [97]).	3
The coefficient of kh was utilized to transform the ideal Hysteresis diagram into a parallelogram, with other parameters detailed in Figure 10.
(28)	${\mathrm{SR}}_{\mathrm{A}}=\frac{3.21-0.68 \times \ln ({\mathsf{\beta }}_{\mathrm{eff}})}{2.12}$	These equations are used to plot the reduced acceleration displacement response spectrum (ADRS), calculating effective damping and spectrum reduction coefficients.	4
(29)	${\mathrm{SR}}_{\mathrm{V}}=\frac{2.31-0.41 \times \ln ({\mathsf{\beta }}_{\mathrm{eff}})}{1.65}$
		Target displacement (dpi) is determined, where the capacity curve intersects the reduced Sa − Sd spectrum. The corresponding forces are assessed through non-linear static analysis (refer to [97]).	5
		An iterative process ensures accuracy by comparing dpi with initial assumptions and repeating the previous steps until convergence is achieved.	6

Table 9. Detailed steps of the capacity–need curve within the ADRS unit set.

Equations		Description	Step
(25)	${\mathrm{S}}_{\mathrm{a}}=\frac{\left(\raisebox{1ex}{${\mathrm{V}}_{\mathrm{i}}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{W}$}\right.\right)}{{\mathsf{\alpha }}_1}$	These equations link structural displacements to base shear, utilizing the effective mass index, participation factor, base shear, total construction weight, and roof form shape. The capacity curve is created using the pushover method, plotting base shear against roof displacement.	1
(26)	${\mathrm{S}}_{\mathrm{di}}=\frac{{\mathsf{\Delta }}_{\mathrm{roof}}}{{\mathrm{PF}}_1\times {\mathsf{\Phi }}_{1,\mathrm{roof}}}$
where α1, PF1, V, W, and φ1,roof represent the effective mass index in the first mode, the participation factor in the first mode, base shear, total construction weight (including a percentage of live load), and the first mode form shape in the roof floor, respectively.
		The seismic demand curve is derived from the elastic design spectrum with 5% damping, adjusted using structural behavior reduction coefficients.	2
(27)	${\mathsf{\beta }}_{\mathrm{eff}}=\frac{63.7{\mathrm{k}}_{\mathrm{h}}\left({\mathrm{a}}_{\mathrm{y}}{\mathrm{d}}_{\mathrm{p}}-{\mathrm{a}}_{\mathrm{p}}{\mathrm{d}}_{\mathrm{y}}\right)}{{\mathrm{a}}_{\mathrm{p}}{\mathrm{d}}_{\mathrm{p}}}+5.0$	Using this equation, the equivalent damping, period, and yield points are calculated from the capacity curve, allowing for the estimation of energy absorption by the structure. Parameters for converting ideal hysteresis diagrams to a parallelogram and other specifics are shown in Figure 10 (data from [97]).	3
The coefficient of kh was utilized to transform the ideal Hysteresis diagram into a parallelogram, with other parameters detailed in Figure 10.
(28)	${\mathrm{SR}}_{\mathrm{A}}=\frac{3.21-0.68 \times \ln ({\mathsf{\beta }}_{\mathrm{eff}})}{2.12}$	These equations are used to plot the reduced acceleration displacement response spectrum (ADRS), calculating effective damping and spectrum reduction coefficients.	4
(29)	${\mathrm{SR}}_{\mathrm{V}}=\frac{2.31-0.41 \times \ln ({\mathsf{\beta }}_{\mathrm{eff}})}{1.65}$
		Target displacement (dpi) is determined, where the capacity curve intersects the reduced Sa − Sd spectrum. The corresponding forces are assessed through non-linear static analysis (refer to [97]).	5
		An iterative process ensures accuracy by comparing dpi with initial assumptions and repeating the previous steps until convergence is achieved.	6

Figure 10. Depicts the capacity and bilinear curves (data from [97]).

Figure 10. Depicts the capacity and bilinear curves (data from [97]).

4.4.2. Finite Element Modeling

The current study employs the finite element method to model frames, a technique fundamental to addressing various engineering challenges through the discretization of complex geometries into simpler, smaller elements. This method facilitates an easier analysis by breaking down the frame’s geometry into numerous triangular and rectangular surfaces composed of standard four-node elements (CQUAD 4). To ensure the analysis converged effectively, the number of elements was carefully selected to balance the analysis time with the result accuracy. This study focuses on a nonlinear pushover analysis for the lateral behavior of walls, incorporating a nonlinear stress–strain relationship and considering the second derivative of ductility in the strain calculations, thereby allowing for a more precise evaluation of structural behavior and ductility.

Verification of Analytical Model by Laboratory Model

To enhance the level of confidence in its numerical models, this study compares the numerical results with laboratory findings [84,85], ensuring the finite element model accurately reflects real-world conditions and can simulate the complexities involved, including potential failures of components and connections under various loading conditions. Specifically, the behavior of cold-formed steel frames is analyzed using a laboratory model of an LSF frame, modeled with MSC PATRAN-NASTRAN software (2012) [98]. This analysis is then meticulously compared with actual laboratory results [84] to validate the model and minimize errors.

Table 10. Size specifications and material characteristics [99,100].

Nominal Grade Fy (MPa)	Dimensions (mm)	Thickness (mm)	Member
345	152 × 41 × 12.7	1.91	Chord studs
230	152 × 41 × 12.7	1.22	Interior studs
345	152 × 31.8	1. 91	Tracks
230	300 × 300	1.91	Connection plate

outlines the dimensions and material properties of various structural members. Chord and interior studs have different yield strengths and dimensions, while tracks and connection plates are specified to have a consistent thickness but vary in dimensions and material strength (data from [99,100]).

The initial elasticity coefficients of the OSB, CSP, DFP, and GWB sheathing materials are 9917 MPa, 7376 MPa, 10,445 MPa, and 1290 MPa, respectively. In addition, the Poisson’s ratios of the OSB, CSP, DFP, and GWB sheathing materials are 0.3, 0.25, 0.3, and 0.2, respectively (data from [101]).

The ultimate stresses (yield stress) and nominal thicknesses for chord studs, internal studs, and tracks are 489 MPa (352 MPa) and 1.91 mm, 398 MPa (356 MPa) and 1.23 mm, and 474 MPa (348 MPa) and 1.94 mm, respectively, which are critical for determining the structural performance under loads (data from [100]).

Modeling Accuracy and Experimental Comparison

The experimental [84] and numerical results of shear wall panels are compared, and there is a high correlation between the lateral resistance and drift parameters. The numerical analysis showed that the shear strength and drift are 74.93 kN and 0.184%, respectively. In comparison, these values are reported in the reference article [84] as 78.76 kN and 0.175%, respectively (a difference of about 5%). In other words, the verification that was performed shows the reliability of the finite element models used in this study.

Parameter Analysis

The study further investigates the impact of various sheathing types and thicknesses on the seismic performance of shear walls. Using finite element software, the shear walls were modeled with different covers (OSB, DFP, CSP and GWB) at varying thicknesses (10 mm to 20 mm) and aspect ratios to understand the influence of the cover type and wall geometry on the structural response under seismic conditions. The analysis considered different loading conditions and thicknesses, particularly focusing on the seismic response based on the demand spectrum plotted on the S_a − S_d diagram (Figure 11). This research aims to optimize load growth considerations specific to cold-formed steel constructions, with adjustments made based on the type of structure and expected loads.

Figure 11. Demand spectrum.

Figure 11. Demand spectrum.

4.4.3. Findings and Discussions

Table 11. A summary of the results of one-sided sheathed specimens.

Specimen	Thickness mm	Sy kN	Syp kN	Ke kN/mm	μ	Energy kN.mm	Kp kN/mm	$\frac{{\mathbf{S}}_{\mathbf{y}}}{{\mathbf{S}}_{\mathbf{y}\mathbf{p}}}$ (%)	$\frac{{\mathbf{S}}_{\mathbf{y}}}{{\mathbf{S}}_{\mathbf{y}\mathbf{n}}}$ (%)	$\frac{{\mathbf{K}}_{\mathbf{e}}}{{\mathbf{K}}_{\mathbf{p}}}$ (%)	$\frac{{\mathbf{K}}_{\mathbf{e}}}{{\mathbf{K}}_{\mathbf{n}}}$ (%)
DFP	12.5	214.06	255.76	9.78	2.41	16,785	38.26	83.70	203.87	25.56	55.89
	15	235.13	280.63	11.08	2.06	18,761	50.47	83.79	223.93	21.95	63.31
	17.5	235.70	302.85	13.92	1.83	19,938	50.08	83.77	241.62	27.80	79.54
	20	273.35	322.52	16.93	1.49	21,228	60.03	84.75	260.33	28.20	96.73
OSB	10	189.26	225.75	8.29	3.06	14,803	29.55	83.84	180.25	28.05	47.36
	12.5	203.94	244.66	9.11	2.67	15,912	36.54	83.36	194.23	24.93	52.06
	15	229.47	271.48	10.74	2.38	18,228	45.02	84.53	218.54	23.86	61.37
	17.5	246.15	293.37	13.08	2.08	19,033	47.48	83.90	234.43	27.55	74.74
	20	265.59	315.96	16.01	1.70	20,633	56.91	84.06	252.94	28.14	91.50
CSP	10	176.11	217.58	7.71	3.52	14,632	27.06	80.94	167.72	28.48	44.04
	12.5	198.26	234.21	8.76	3.088	15,084	34.36	84.65	188.82	25.49	50.06
	15	219.82	265.61	9.93	2.64	17,971	41.63	82.76	209.35	23.85	56.74
	17.5	235.01	287.51	12.36	2.31	18,113	45.08	81.74	223.82	27.42	70.63
	20	257.03	307.58	15.50	1.88	19,146	54.04	83.57	244.79	28.68	88.57
GWB	10	161.72	213.06	7.21	4.06	11,143	24.69	75.90	154.02	29.19	41.19
	12.5	181.69	224.62	8.19	3.55	12,436	31.30	80.89	173.04	26.17	46.80
	15	212.44	258.68	9.31	2.86	14,555	32.99	82.12	202.32	28.22	53.20
	17.5	226.94	279.92	11.67	2.48	15,199	44.15	81.07	216.13	26.43	66.69
	20	241.16	296.45	14.63	2.02	15,811	52.92	81.35	229.68	27.65	83.62

and

Table 12. A summary of the results of two-sided sheathed specimens.

Specimen	Thickness mm	Sy kN	Syp kN	Ke kN/mm	μ	Energy kN.mm	Kp kN/mm	$\frac{{\mathbf{S}}_{\mathbf{y}}}{{\mathbf{S}}_{\mathbf{y}\mathbf{p}}}$ (%)	$\frac{{\mathbf{S}}_{\mathbf{y}}}{{\mathbf{S}}_{\mathbf{y}\mathbf{n}}}$ (%)	$\frac{{\mathbf{K}}_{\mathbf{e}}}{{\mathbf{K}}_{\mathbf{p}}}$ (%)	$\frac{{\mathbf{K}}_{\mathbf{e}}}{{\mathbf{K}}_{\mathbf{n}}}$ (%)
DFP	12.5	247.54	307.69	15.32	1.62	2.445	45.26	80.45	235.75	33.85	87.54
	15	278.18	326.49	16.41	1.54	22,025	63.27	85.20	264.93	25.94	93.77
	17.5	296.08	346.68	18.96	1.42	23,516	60.89	85.40	281.98	31.14	108.36
	20	319.12	371.34	22.85	1.31	26,045	72.59	85.94	303.92	31.05	130.57
OSB	10	207.22	269.84	12.56	1.97	18,063	36.86	76.79	197.35	34.08	71.79
	12.5	245.51	298.94	13.41	1.83	19,367	41.31	82.13	233.82	32.46	76.63
	15	269.02	318.36	15.23	1.72	21,448	56.15	84.50	256.21	27.12	87.03
	17.5	287.62	337.69	18.01	1.61	22,469	58.47	85.17	273.92	30.81	102.93
	20	306.96	358.98	21.61	1.49	25,239	69.78	85.51	292.34	30.97	123.50
CSP	10	201.50	259.85	11.62	2.18	17,349	32.60	77.54	191.90	35.64	66.41
	12.5	245.51	298.43	12.35	2.04	16,982	38.11	81.93	232.85	32.41	70.57
	15	256.34	309.76	13.89	1.86	20,784	51.46	82.75	244.13	26.99	79.37
	17.5	279.47	329.79	17.11	1.79	21,902	56.12	84.74	166.16	30.48	97.75
	20	291.83	341.67	20.09	1.65	23,863	66.24	85.41	277.93	30.32	114.77
GWB	10	176.79	239.54	9.84	2.57	13,884	28.05	73.80	168.37	35.09	56.24
	12.5	211.26	254.26	10.51	2.28	15,370	35.43	83.09	201.20	29.66	60.06
	15	239.77	287.81	12.67	2.09	17,396	44.76	83.31	288.35	28.31	72.40
	17.5	263.43	311.24	16.15	1.92	18,040	53.86	84.64	250.89	29.99	92.29
	20	278.54	328.27	19.22	1.77	18,969	64.88	84.85	265.28	29.62	109.82

present the results obtained in regards to the lateral load. The performance of shear wall panels was assessed, and it was found that while these panels did not meet the expected quotas, they effectively resisted the nominal design shear forces. The stiffness value (K_e) recorded was significantly lower than expected (K_p). An analysis showed that the aspect ratios of the frames did not significantly influence the behavior of shear walls with wooden covers, allowing these ratios to be used reliably in further calculations.

Among the sheathing materials tested, the DFP sheathings demonstrated the highest strength and rigidity. Following DFP, the other materials can be ranked in decreasing order of strength and rigidity as follows: OSB, CSP, and GWB. Using two-sided sheathings significantly improved both the rigidity and strength of the shear walls compared to those when one-sided sheathings were used (Table 11 and Table 12). However, as the thickness increased, the rigidity gains from using two-sided sheathings diminished; for instance, there was an 18% increase in rigidity for 12.5 mm thick sheathings and a 12% increase for 20 mm thick sheathings in DFP, OSB, and CSP. The GWB sheathings showed a consistent rigidity increase of about 10% across all thicknesses (Figure 12; data from [78,80]).

The response modification factors, which measure how wall sheathing behaves under stress, were detailed in

Table 13. Evaluated seismic parameters for sheathing walls (H/L = 1).

Specimen	Thickness (mm)	One-Side				Two-Side
		$\mathbf{\mu }$	${\mathbf{R}}_{\mathbf{d}}$	${\mathbf{R}}_{\mathit{o}}$	R	$\mathbf{\mu }$	${\mathbf{R}}_{\mathbf{d}}$	${\mathbf{R}}_{\mathit{o}}$	R
DFP	12.5	2.41	1.95	2.04	3.99	1.62	1.50	2.36	3.53
	15	2.06	1.77	2.24	3.96	1.54	1.44	2.65	3.82
	17.5	1.83	1.63	2.42	3.95	1.42	1.36	2.82	3.83
	20	1.49	1.41	2.60	3.66	1.31	1.27	3.04	3.87
OSB	10	3.06	2.26	1.80	4.07	1.97	1.71	1.97	3.38
	12.5	2.67	2.08	1.94	4.04	1.83	1.63	2.24	3.65
	15	2.38	1.94	2.18	4.23	1.72	1.56	2.56	4.00
	17.5	2.08	1.78	2.34	4.16	1.61	1.49	2.74	4.08
	20	1.70	1.55	2.53	3.92	1.49	1.41	2.92	4.11
CSP	10	3.52	2.46	1.68	4.13	2.18	1.83	1.92	3.52
	12.5	3.08	2.27	1.89	4.29	2.04	1.75	2.33	4.09
	15	2.64	2.07	2.09	4.32	1.86	1.65	2.44	4.02
	17.5	2.31	1.90	2.24	4.26	1.79	1.61	2.66	4.27
	20	1.88	1.66	2.45	4.07	1.65	1.52	2.78	4.22
GWB	10	4.06	2.67	1.54	4.11	2.57	2.03	1.68	3.42
	12.5	3.55	2.47	1.73	4.27	2.28	1.89	2.01	3.79
	15	2.86	2.17	2.02	4.39	2.09	1.78	2.88	5.14
	17.5	2.48	1.99	2.16	4.30	1.92	1.69	2.51	4.23
	20	2.02	1.74	2.30	4.01	1.77	1.59	2.65	4.22

, and a quality diagram of these factors is shown in Figure 13 (data from [78,80]). The highest response modification factor was noted in the GWB sheathing at a 15 mm thickness with a value of 5.14. Generally, thicker sheathings decreased wall plasticity but increased stiffness and resistance. For the DFP sheathing, the highest response modification factor was 3.99 at a 12.5 mm thickness in a one-sided application. OSB reached its peak at 4.23 with a 15 mm thickness, and CSP at 4.29 with a 12.5 mm thickness. These findings suggest that while thicker sheathings typically enhance stiffness and resistance, their effect on the response modification factor varies due to differing impacts on wall plasticity (Table 13).

Figure 14 and Figure 15 present a comparative analysis of maximum resistance and drift across various shear wall panels (data from [78,80]). Among the panels tested, the DFP sheathing with double-sided covers and a 20 mm thickness exhibited the highest resistance at 371.34 kN. Conversely, the DSP sheathing of the same thickness showed the least amount of drift, recording values at 0.92 and 0.72, indicating robust structural stability.

This study’s findings align closely with prior laboratory research conducted by Branston et al. [87,96], confirming the numerical analysis’s accuracy when compared with empirical data. This study introduces new variables, such as sheathing thickness, material types, and the configuration of lateral braces (one-sided vs. two-sided covers), expanding on previous research.

Table 14. One-sided frame cover.

Sheathing	Thickness (mm)	Δtarget (mm)	Δy (mm)	d $\left(\frac{{\mathbf{\Delta }}_{\mathit{f}\mathit{a}\mathit{l}\mathit{i}\mathit{u}\mathit{e}\mathit{r}}}{{\mathbf{\Delta }}_{\mathit{y}}}\right)$	Normalized Displacement (mm)				Drift Ratio (%)
					CP	LS	IO	OP	CP	LS	IO	OP
GWB	10	5.18	29.27	4.70	120.15	101.98	47.24	11.17	4.92	4.29	1.94	0.48
	12.5	4.07	26.76	4.62	120.01	101.86	46.10	10.70	4.92	4.27	1.89	0.44
	15	2.91	13.74	4.50	71.73	60.13	25.34	5.50	2.94	2.46	1.04	0.23
	17.5	2.70	12.72	4.10	57.29	48.37	21.63	5.09	2.35	1.98	0.89	0.21
	20	2.52	12.04	3.54	42.64	36.52	18.16	4.82	1.75	1.50	0.74	0.20
CSP	10	1.19	14.91	6.82	99.78	82.98	31.80	5.96	4.07	3.39	1.30	0.24
	12.5	1.05	13.63	6.79	99.30	82.48	31.35	5.45	4.07	3.38	1.28	0.22
	15	0.99	9.39	6.66	63.70	52.88	20.26	3.76	2.61	2.17	0.83	0.15
	17.5	0.94	8.93	5.75	51.38	42.89	17.42	3.57	2.11	1.76	0.71	0.15
	20	0.87	8.51	4.49	38.24	32.30	14.46	3.40	1.57	1.32	0.59	0.14
OSB	10	1.13	12.86	6.52	83.37	69.26	26.96	5.14	3.42	2.84	1.10	0.21
	12.5	0.98	11.76	6.48	83.35	69.26	26.56	4.70	3.42	2.84	1.09	0.19
	15	0.86	8.19	6.24	56.81	47.09	17.91	3.28	2.33	1.93	0.73	0.13
	17.5	0.84	7.64	5.99	45.73	38.11	15.26	3.06	1.87	1.56	0.63	0.13
	20	0.80	7.44	4.57	34.04	28.72	12.76	2.98	1.39	1.18	0.52	0.12
DFP	12.5	0.97	10.81	7.10	76.80	63.60	24.01	4.32	3.15	2.61	0.98	0.18
	15	0.85	7.64	6.24	47.71	39.70	15.65	3.06	1.96	1.63	0.64	0.13
	17.5	0.83	7.31	5.34	39.04	32.69	13.66	2.92	1.60	1.34	0.56	0.12
	20	0.82	7.15	4.06	29.05	24.67	11.53	2.86	1.19	1.01	0.47	0.12

and

Table 15. Two-sided frame cover.

Sheathing	Thickness (mm)	Δtarget (mm)	Δy (mm)	d $\left(\frac{{\mathbf{\Delta }}_{\mathit{f}\mathit{a}\mathit{l}\mathit{i}\mathit{u}\mathit{e}\mathit{r}}}{{\mathbf{\Delta }}_{\mathit{y}}}\right)$	Normalized Displacement (mm)				Drift Ratio (%)
					CP	LS	IO	OP	CP	LS	IO	OP
GWB	10	5.18	29.27	4.70	120.15	101.98	47.24	11.17	4.92	4.29	1.94	0.48
	12.5	4.07	26.76	4.62	120.01	101.86	46.10	10.70	4.92	4.27	1.89	0.44
	15	2.91	13.74	4.50	71.73	60.13	25.34	5.50	2.94	2.46	1.04	0.23
	17.5	2.70	12.72	4.10	57.29	48.37	21.63	5.09	2.35	1.98	0.89	0.21
	20	2.52	12.04	3.54	42.64	36.52	18.16	4.82	1.75	1.50	0.74	0.20
CSP	10	1.19	14.91	6.82	99.78	82.98	31.80	5.96	4.07	3.39	1.30	0.24
	12.5	1.05	13.63	6.79	99.30	82.48	31.35	5.45	4.07	3.38	1.28	0.22
	15	0.99	9.39	6.66	63.70	52.88	20.26	3.76	2.61	2.17	0.83	0.15
	17.5	0.94	8.93	5.75	51.38	42.89	17.42	3.57	2.11	1.76	0.71	0.15
	20	0.87	8.51	4.49	38.24	32.30	14.46	3.40	1.57	1.32	0.59	0.14
OSB	10	1.13	12.86	6.52	83.37	69.26	26.96	5.14	3.42	2.84	1.10	0.21
	12.5	0.98	11.76	6.48	83.35	69.26	26.56	4.70	3.42	2.84	1.09	0.19
	15	0.86	8.19	6.24	56.81	47.09	17.91	3.28	2.33	1.93	0.73	0.13
	17.5	0.84	7.64	5.99	45.73	38.11	15.26	3.06	1.87	1.56	0.63	0.13
	20	0.80	7.44	4.57	34.04	28.72	12.76	2.98	1.39	1.18	0.52	0.12
DFP	12.5	0.97	10.81	7.10	76.80	63.60	24.01	4.32	3.15	2.61	0.98	0.18
	15	0.85	7.64	6.24	47.71	39.70	15.65	3.06	1.96	1.63	0.64	0.13
	17.5	0.83	7.31	5.34	39.04	32.69	13.66	2.92	1.60	1.34	0.56	0.12
	20	0.82	7.15	4.06	29.05	24.67	11.53	2.86	1.19	1.01	0.47	0.12

present the drift limitations for various sheathing materials and thicknesses. The highest and lowest drift percentages were noted in the GWB models with a 10 mm cover sheet and the DFP models with a 20 mm thickness, respectively. These results are supported by specific parameters such as Δ_target and Δ_y, which are crucial for evaluating the structural performance of these models.

An essential finding from the study is the negligible difference (less than 3%) in the limiting drift ratio between one-sided and two-sided cover sheets. This suggests that opting for one-sided sheathing does not compromise seismic performance significantly. Moreover, using one-sided cover sheets can lead to considerable economic benefits without sacrificing structural integrity (Figure 16).

5. Conclusions

Based on the Islamic Consultative Assembly of Iran’s resolutions, the government must produce and offer an average of one million residential units annually over four years as part of the national housing production and supply plan (National Housing). According to statistics announced by various sources, this plan comes at a time when approximately 500,000 residential units are being built annually by various public and private sectors, some of which lack sustainable conditions against seismic hazards and other natural and unnatural incidents. Therefore, utilizing the experiences of other countries in industrialized building production to achieve predefined quantitative and qualitative goals requires policymaking, planning, regulation drafting, and extensive research by decision makers and project stakeholders. Thus, the current study aims to present a decision support system for identifying and prioritizing parameters influencing the selection of an appropriate structural system for the national housing scheme and evaluating the seismic performance of the preferred structural system among the studied systems based on Iran’s seismic activity. Accordingly, this article consists of four continuous study phases: Phase I: The collection and validation of the considered criteria to select the appropriate structural system approach; Phase II: The calculation of the importance weight for each criterion and sub-criterion using the fuzzy AHP method; Phase III: Prioritizing the studied alternatives and selecting the superior structural system using the fuzzy TOPSIS method; and Phase IV: The finite element modeling of the chosen structure and evaluating its behavior and seismic performance level. In the first phase of this research, a deep and comprehensive evaluation was conducted to identify and extract the most significant parameters affecting the selection of an appropriate structural system in national housing construction projects. The identified factors were assigned to groups, including primary and secondary indices, and their content validity was determined based on expert opinions. In the second phase, structured questionnaires based on the fuzzy AHP analysis method were designed to determine the relative importance of factors and the weight of each criterion and sub-criterion, along with the extraction of the opinions of the statistical population. The primary criteria selected in the second phase were determined using the fuzzy AHP analysis method. Economic factors had the highest weight (0.389), followed by technical and execution regulations, building design and architecture factors, cultural and social factors, and environmental factors, with weights of 0.274, 0.168, 0.095, and 0.074, respectively. Thus, economic factors are the most critical and influential criterion in examining parameters affecting the selection of an appropriate structural system for mass housing construction in Iran.

In the third phase of the research, the introduced structural systems were prioritized using the fuzzy TOPSIS method. According to the results of this phase, the LSF, ICF, TRC, 3DP, and RCCF structural systems, in that order, are prioritized based on the studied criteria. The LSF and ICF systems are highly preferential to the other alternatives in terms of execution and seismic regulations, as well as economic, design and architectural, environmental, and cultural and social factors.

Finally, in the fourth phase of this research, after selecting the LSF structural system as the optimal system for housing construction in the national housing project, this phase evaluated the seismic performance. It determined the performance level of LSF building frames. The nonlinear behavior of cold-formed steel frames and their seismic performance levels with four types of shear walls (OSB, DFP, CSP, and GWB) under monotonic loading were evaluated using the nonlinear finite element analysis method. In total, 38 CFS frames with various types of sheathing plates, different aspect ratios, and thicknesses of sheathing plates were examined. Seismic parameters were evaluated for all samples, including the strength reduction factor, ductility, and force reduction factor due to ductility. Additionally, these systems’ seismic response modification factor was calculated, along with target displacement values and limit drift ratios for different performance levels.

Between the braced specimens, the sheathing DFP had the maximum mean value of yield strength S_y, the maximum mean value of rigidity, and the maximum energy absorption capability. The highest mean ratio S_y/S_yp between the shear wall panels and the sheathings is related to the DFP specimens with a sheathing thickness of 20 mm.

Generally, the shear wall panels with the sheathing plates could not achieve their anticipated quota. The response modification factors in the shear wall models were better than those in the braced wall models. The highest amount was 5.14, related to the shear wall GWB specimen with two-sided sheathing and a thickness of 15 mm. With the increase in the resistance of the shear wall panels with the sheathings with a lower thickness, the effect of the two-sided sheathing was more than that of the one-sided sheathing. As for the walls of the DFP, OSB, and CSP specimens with sheathing, there was an 18% increase at a thickness of 12.5 mm and a 12% increase at a thickness of 20 mm in the one-sided sheathing resistance (compared to the two-sided sheathing resistance). In the GWB specimen with sheathing, the increase in all thicknesses was about 10%.

Performance design methods are an attempt to find methods of analysis and more accurate designs for the actual performance of structures under earthquakes with various levels. In these methods, by defining various performance levels for structural behavior, applying different seismic levels of a plan, and performing nonlinear analyses, the actual behavior of constructions against earthquakes can be predicted.

According to all of the walls studied in this study, the structure responds to an earthquake in a linear state, and the performance point is at the elastic stage of structural behavior. Generally, due to having low freedom degrees and small periods, low-height structures can respond to an earthquake by increasing their stiffness linearly.

Furthermore, these studies indicate that the light steel framing (LSF) construction system is appropriate for withstanding earthquakes. Therefore, given the system’s suitable performance against earthquakes, this construction method can be considered a suitable approach for the national housing production and supply plan (National Housing) in the construction industry in Iran.

Moreover, one reason for choosing the LSF structural system, along with other studied structural systems, is its ability to access a significant amount of habitable land in different cities for housing construction. The LSF structural system is not recommended for the construction of high-density housing and is usually used for the construction of buildings with a limited height.