Multi-Criteria Assessment of Timber-Based Structural Systems for a Grocery Store

Abstract

To reduce the negative impact on the environment, architects, designers, and construction companies need to find and apply eco-friendly and sustainable building solutions. Due to its renewable nature and numerous advantages, timber has become an attractive substitute for steel and concrete in both residential and non-residential construction projects. However, timber application in the construction of grocery stores is a relatively new concept. The purpose of this research is to propose three alternative timber-based structural systems for a grocery store in Lithuania and to select the most efficient option based on multi-criteria decision-making methods. Three alternative glued laminated timber (glulam) structural systems—the glulam column and truss system, the glulam three-hinge frame system, and the glulam column and double-tapered beam system—were designed. The systems were evaluated against ten criteria, reflecting structural properties, cost efficiency, assembling complexity, and aesthetics. Multiple-criteria assessments by the COmplex PRoportional ASsessment (COPRAS) method and simple additive weighting (SAW) method revealed that the best-performing alternative is the glulam column and double-tapered beam system due to the lower cost of load-bearing structures, the smaller quantity of required steel details and fittings, and the highest maximum utility ratio according to serviceability limit states compared to other alternatives.

1. Introduction

The construction industry is one of the biggest global consumers of natural resources and energy [1,2] and one of the major producers of greenhouse gas (GHG) emissions, carbon emissions in particular [3,4], and waste [5]; therefore, it is a significant contributor to climate change [6]. To reduce the negative impact on the environment, architects, designers, and construction companies need to find and apply eco-friendly, sustainable building solutions. Due to its renewable nature and numerous advantages in lowering carbon dioxide (CO₂) emissions [3,4,7,8], timber is becoming an attractive substitute for steel and concrete in both residential and non-residential construction projects.

The introduction of new engineered timber products based on laminating and glueing, such as glued laminated timber (glulam), cross-laminated timber (CLT), and laminated veneer lumber (LVL), among many other options, improved the structural properties of timber, such as stability, strength, stiffness, and fire safety [9,10,11]. Therefore, the number of mass timber buildings is increasing across different countries.

Along with the environmental benefits, mass timber construction has many economic advantages. Engineered timber elements are cost-effective, as they are lightweight, structurally efficient, easy, and fast to install on the construction site, especially in the case of prefabrication [12]. Faster assembly reduces the required on-site labor resources, and, subsequently, labor costs, as well as project timelines [10].

From a social perspective, mass timber structures create aesthetic value [13] and have good thermal and noise insulation properties [14]. In addition, studies reveal that timber exposed in indoor environments has a positive effect on the emotional state of building users [10,11,15] and also leads to a lower systolic blood pressure and heart rate [16].

At present, mass timber structures are mostly used in residential building projects and are also becoming more popular in the commercial sector, for instance, in the construction of office buildings and hotels. Nevertheless, the use of timber structures in grocery stores is a new concept. By using the newest mass timber technologies, architects and designers have an opportunity to create a new generation of supermarkets. A few examples of such grocery stores in Europe are the SuperHub Meerstad Market in Groningen, the Netherlands, REWE in Wiesbaden, Germany, and ADEG in Arriach, Austria [17].

Many studies worldwide investigate design solutions for modern timber buildings [18,19,20,21]. However, design solutions for grocery stores are rarely discussed and compared. The first step in the structural design process is choosing a suitable structural system. The selection of the most suitable structural system requires extensive expertise, as conflicting criteria have to be taken into consideration. To solve this problem, multi-criteria decision-making (MCDM) methods can be used [22,23,24,25,26,27,28,29,30]. Although MCDM methods have been widely applied in management and other fields, their use in design solutions, particularly for the selection of structural systems, is relatively new. To address the aforementioned gaps, this study aims to propose three alternative timber-based structural systems for a grocery store in Lithuania and to select the most efficient one using the MCDM techniques.

This study is structured as follows: after Introduction, Section 2 provides a literature review on the application of MCDM techniques for the selection of structural systems. Section 3 describes a multi-criterion assessment methodology based on the COmplex PRoportional ASsessment (COPRAS) method and the simple additive weighting (SAW) method. Section 4 demonstrates a practical application of the proposed methodology: three alternative timber-based structural systems are designed and described, criteria for their comparison are selected, the significance of the criteria is determined, and multi-criterion evaluation is performed to find the most efficient system option. The results are discussed in Section 5. The last section concludes the paper.

2. Literature Review

MCDM methods and tools help to select the best option among various alternatives based on the criteria from multiple sources that may be contradictory. Reviews reveal an increasing number of articles and the suitability of the MCDM techniques for solving real-world construction problems. For instance, Jato-Espino et al. [31] reviewed 88 papers on the MCDM techniques used in the construction industry published from 1992 to 2013. They concluded that MCDM approaches can significantly improve decision making, especially in cases of conflicting decision criteria. Stojčić et al. [32] reviewed the use of MCDM methods in sustainability engineering. They analyzed 108 papers published from 2008 to 2018 and distinguished five MCDM application areas, namely, civil engineering and infrastructure, supply chain management, transport and logistics, energy, and other engineering disciplines. Emovon and Oghenenyerovwho [33] reviewed 55 papers on the selection of building materials published from 1994 to 2019. Their study revealed that cost is the most common criterion for construction material selection.

A more extensive review was published by Zhu et al. [34]. They studied 530 articles on construction published from 2000 to 2019 and categorized the papers according to seven major MCDM application areas, namely, (1) contractor (subcontractor)/staff/supplier selection, (2) cost/time/quality performance assessment, (3) design/system/method/project/portfolio selection, (4) layout/location selection, (5) material/equipment selection, (6) risk/safety management, and (7) sustainability/environment assessment. On the other hand, Klumbytė et al. [35], based on a review of 66 papers published from 2016 to 2020, concluded that the number of articles on using MCDM methods for sustainable construction increased; however, it is still low compared to that of the papers on using MCDM in other research areas.

There is a growing interest in the MCDM approach in the building design process [36]. User-centered design has gained more attention lately since the designs developed by architects and designers have to satisfy the needs of clients and end users, and, at the same time, have to be favorable to building contractors. The introduction of new structural systems into the construction industry has created new tasks for structural engineers, whereas the selection of the most appropriate structural system has become increasingly complicated [22]. Therefore, some studies used MCDM techniques to select structural systems for different projects. A summary of MCDM applications is provided in

Table 1. MCDM applications in selecting structural systems.

Reference	Application	Alternatives	Methods *	Criteria
Invidiata et al. [1]	Selecting the design strategies for a multi-family social building	X-Lam; Reinforced concrete frame; Steel frame	AHP and COPRAS	Number of hours in which there is internal thermal comfort, primary energy demand over the life cycle, carbon dioxide emissions over the life cycle, and cost over the life cycle
Balali et al. [22]	Selecting the structural system for low-rise multi-housing project	3D panel with light walls in building frames; LSF; ICF; Tunnel formwork system; Tronco	AHP and PROMETHEE	Cost, ease of construction, energy saving, dead load, number of stories, life cycle time
Tamosaitiene and Gaudutis [23]	Assessing structural systems for 24-storey administrative building	Semi-rigid frame (sectional monolithic concrete); Semi-rigid frame (monolithic concrete); Semi-rigid frame (steel beams and columns, concrete span); Rigid frame (monolithic concrete); Rigid frame without beams (monolithic concrete)	COPRAS-G	Effective height of the structural system (storeys), typical floor-to-floor height, lengthwise step of a column, transverse step of a column, length of a slab span, price for the design of the structural system, terms of performance, price for the construction of the building, embodied energy, embodied carbon, price for the demolition of the building
Balali et al. [24]	Selecting the structural system for multi-housing project	LSF (light steel frame); 3D panel; ICF (insulated concrete formwork); Tunnel formwork system; Tronco; Timber; D2; CFT (concrete-filled steel tube)	ELECTRE III and PROMETHEE II	Cost, ease of construction, energy saving, maximum dead load, number of stories, age, durability
Teracciano et al. [25]	Selecting vertical reinforcement and energy retrofitting systems for existing masonry constructions	Reinforced concrete; Masonry; Steel; Glued laminated timber; Cold-formed thin-walled steel	TOPSIS	Structural, economic, environmental, and energy criteria
Turskis et al. [26]	Assessing structural elements of frames	Three cases of steel frames; Precast reinforced concrete columns and beam; Precast reinforced concrete columns and steel beam	AHP, ARAS-F, and MULT-F	Costs, impact on the environment, instalment time, weight, consumption of steel, consumption of concrete
Tupenaite et al. [27]	Selecting structural system for wooden public building	Double-tapered glulam beams and columns; Laminated veneer lumber (LVL) trusses and columns; Single-tapered glulam beam and type I steel column	SAW	Achieved useful height of the building, partial factor for material, eco-friendliness of materials, massiveness of structure, structural aesthetics, assembling complexity, simplicity of foundation design solution, simplicity of structural system production
Sánchez-Garrido and Yepes [28]	Comparing alternative sustainable structures for single-family home	Reinforced concrete; Autoclave-cured and aerated concrete; Elesdopa double-wall structural elements	MIVES	Energy consumption, improving environmental impact, cost, certainty of the final cost, period of construction, responsiveness, added value, user comfort
Sánchez-Garrido et al. [29]	Comparing alternatives for the structure of single-family homes	Reinforced concrete structure and brick walls; Prefabricated option with semi-dry assembly (Ytong material); Elesdopa double-wall structural elements	NAHP-G and VIKOR	43 indicators considering all stages of the life cycle
Zumrut et al. [30]	Selecting a structural system for industrial facility	Prefabricated reinforced concrete system; On-site reinforced concrete system; Steel structural system	AHP and TOPSIS	Project cost, project duration, project lifetime, labor and equipment requirement, recycling opportunities, resistance to environmental effects, suitability for installation and natural lighting needs

* Note: AHP—analytic hierarchy process; ARAS-F—fuzzy additive ratio assessment; COPRAS—COmplex PRoportional ASsessment; ELECTRE—Elimination and Choice Translating Reality; MIVES—Spanish Integrated Value Model for Sustainability Assessment; MULT-F—fuzzy multiplicative utility function; NAHP-G—neutrosophic group analytical hierarchy process; PROMETHEE—preference ranking organization method; SAW—simple additive weighting; TOPSIS—technique for order preference by similarity to ideal solutions; VIKOR—license agreement VlseKriterijumska Optimizacija I Kompromisno Resenje.

.

The literature review revealed that MCDM methods have been used in the selection of different structural systems for multi-housing projects, single-family homes, public buildings, and industrial facilities. Different MCDM methods, such as COPRAS, ELECTRE, PROMETHEE, AHP, TOPSIS, SAW, and VIKOR, were used for the selection of structures. Most of the researchers applied technical, economic, environmental, and social criteria.

It was observed that the literature on MCDM application for the selection of structural systems is very limited. Moreover, the practice of selecting timber-based structures is relatively recent. Balali et al. [24] analyzed timber-based structural systems as an alternative to steel-based and reinforced concrete systems for a multi-housing project. Teracciano et al. [25] evaluated a glued laminated timber system as one of the possible solutions for a vertical addition in the retrofitting of masonry buildings. Invidiata et al. [1] compared CLT, reinforced concrete frame, and steel frame structures for designing a multi-family social building. Only one previous study by the researchers [27] described the application of the SAW multi-criterion assessment method to select a timber-based structural system for the shopping centre. Therefore, more studies on the selection of timber-based structures are required. These findings are in line with the findings of Invidiata et al. [1], who highlighted the need for the use of MCDM methods for the selection of design solutions to construct more sustainable buildings.

3. Materials and Methods

The literature review revealed that MCDM methods can be successfully used for the analysis and selection of the most preferred structural system. In the present study, two MCDM methods were applied to assess alternative timber-based structural systems for a grocery store. The flowchart of the research methodology is presented in Figure 1.

The problem of the research is to select the most suitable timber-based structural system for a grocery store in Vilnius district, Lithuania. The snow and wind loading values assumed in the design are characteristic of the major part of Lithuania. The research was performed in the following steps.

Step 1. Designing three alternative structural systems. Three alternative timber-based structural systems were designed for a grocery store with approximately 1000 m² of floor area. An engineered timber product—glued laminated timber (glulam)—was selected for the load-bearing structures due to its distinctive technical properties and availability in the engineered timber market.

Glulam is composed of multiple layers of dimensional solid timber joined together with durable, moisture-resistant structural adhesives so that the grain of timber layers runs parallel to the longitudinal axis. This mass timber product can be manufactured in large sizes and complex shapes. It has advanced strength and stiffness properties and a very high strength-to-weight ratio; by weight, it can be even stronger than structural steel [37]. In addition, glulam is stronger and more reliable compared to solid timber.

Step 2. Selecting evaluation criteria. A set of ten criteria was selected to evaluate the efficiency of the proposed alternative timber-based structural systems based on the literature review [22,23,24,25,26,27,28,29,30], Eurocode 5 [38], and practical experience of the authors. Evaluation criteria are in line with general requirements for building load-bearing structures and cover strength, stability, serviceability, cost efficiency, assembling complexity, and architectural aesthetics.

Step 3. Determining the significance of the criteria. The significance of the criteria was assessed using the expert judgment method. A questionnaire was designed to collect experts’ opinions. The experts had to rank the criteria on a 10-point scale, where 1 = least significant criterion, 10 = most significant criterion.

The experts were selected based on the following requirements:

• Experts are representatives of design/construction or similar companies;
• Experts are acquainted with the commonly used timber-based structural systems;
• Experts have a technical background in civil engineering;
• Experts have experience of more than five years.

Initially, a questionnaire was distributed to 12 selected experts; however, only 7 experts filled it out correctly. Therefore, the opinion of seven experts was considered to determine the significance of the criteria.

Equation (1) was used to calculate the aggregated significance of each criterion:

$$q_i=\frac{\overline{c_i}}{\sum _{i=1}^m\overline{c_i}}; i=\overline{1,m.}$$

(1)

In addition, it was important to evaluate the consistency of experts’ opinions. Kendall’s coefficient of concordance (W) was calculated for this purpose [39]:

$$W=\frac{12S}{r^{2}m\left(m^2-1\right)};W∊\left[0;1\right].$$

(2)

The significance of the concordance coefficient (${\chi }^2$) was calculated by Equation (3):

$${\chi }^2=Wr\left(m-1\right)$$

(3)

and compared with the tabular value ${\chi }_{\propto ,\upsilon }^2$. If ${\chi }^2>{\chi }_{\propto ,\upsilon }^2,$ the experts’ opinion is consistent and the calculated significance of the criteria can be used in further calculations.

Step 4. Composing the decision-making matrix. The initial decision-making matrix M has the following expression:

$$\mathrm{M} {\left[x_{ij}\right]}_{\left[m\times n\right]}; i=\overline{1,m}; j=\overline{1,n}.$$

(4)

The attribute values for each alternative structural system were calculated using the commercial finite element software Dlubal Rfem 5 according to Eurocode 5 [38], outlining fundamental design principles for timber structures, including the current Lithuanian national annexes. All three alternative systems were designed with full detailing of connections between elements. Mathcad 14 software was used for the structural connection design.

The total cost of load-bearing structures was determined by a survey of three glulam manufacturers, which took place in January 2022. The surveyed manufacturing companies were located in Lithuania and Latvia, as there is only one glulam manufacturer in Lithuania. The companies provided total price proposals for selected structures, including manufacturing and transportation costs. The lowest available price was used for calculations.

The total assembly cost, including the lifting equipment rent, manpower, and all other costs related to the assembly of load-bearing structures, was determined by a survey of five timber construction companies located in Lithuania in February 2022. The lowest proposed price was used for calculations.

Step 5. Multi-criterion evaluation of the alternatives. Initially, the COPRAS method was used to evaluate the efficiency of proposed timber-based structural systems. The COPRAS method was developed by Zavadskas and Kaklauskas [40]. The method selects the most suitable alternative based on the best and worst solutions. It was previously used by other researchers for the assessment of structural systems (e.g., [1,23]).

Based on the COPRAS method, the attribute values of the decision-making matrix M were normalized according to Equation (5):

$${\tilde{x}}_{ij}=\frac{x_{ij}}{\sum _{j=1}^n{x}_{ij}}.$$

(5)

In the next step, the weighted normalized decision matrix was calculated using Equation (6):

$${\widehat{x}}_{ij}={\tilde{x}}_{ij}·q_i; i=\overline{1,m}; j=\overline{1,n}.$$

(6)

Finally, the efficiency index E_j was obtained from Equation (7):

$$E_j=S_{+j}+\frac{S_{-\mathrm{m}\mathrm{i}\mathrm{n}} · \sum _{j=1}^n{S}_{-j}}{S_{-j} · \sum _{j=1}^n\frac{S_{-\mathrm{m}\mathrm{i}\mathrm{n}}}{S_{-j}}}; j=\overline{1,n},$$

(7)

where $S_{+j}$ denotes the sums of the weighted normalized values for the beneficial criteria and $S_{-j}$ the sums of the weighted normalized values for the non-beneficial criteria.

The higher the E_j value, the higher the priority of the alternative.

As calculations by the COPRAS method did not reveal very clear priorities of the alternative structural systems, another MCDM method, namely SAW [41], was used for the verification of results. The SAW method is one of the simplest, most widely known, and most frequently used methods [42].

Following the algorithm of the SAW method, the attribute values of the decision-making matrix M were normalized according to Equation (8) for beneficial criteria and Equation (9) for non-beneficial criteria:

$${\tilde{x}}_{ij}=\frac{x_{ij}}{x_j^{\mathrm{m}\mathrm{a}\mathrm{x}}};$$

(8)

$${\tilde{x}}_{ij}=\frac{x_{j }^{\mathrm{m}\mathrm{i}\mathrm{n}}}{x_{ij}}.$$

(9)

After normalization, the weighted normalized decision matrix was calculated using Equation (6) (the same as in COPRAS method). Consequently, the efficiency index E_j was calculated by Equation (10):

$$E_j={\sum }_{i=1}^n{\widehat{x}}_{ij}.$$

(10)

Finally, a clear ranking of alternative structural systems was obtained.

The nomenclature for Section 3 is provided in the back matter of the manuscript.

4. Case Study

4.1. Description of the Alternative Structural Systems

Three alternative timber-based structural systems were designed for a grocery store with approximately 1000 m² of floor area. The provided building schemes are the most practically used structural systems for a glued laminated timber building with a flat roof. The building plan dimensions are 42 m × 25 m in between the column axes, with a clear span of 25 m. All presented structural systems are designed using glued laminated timber Glulam GL28h strength class elements according to EN 14080 [43] with the following material properties:

• Bending strength f_m,k = 28.0 MPa;
• Tensile strength f_t,0,k = 22.3 MPa/f_t,90,k = 0.5 MPa;
• Compression strength f_c,0,k = 28.0 MPa/f_c,90,k = 2.5 MPa;
• Shear strength f_v,k = 3.5 MPa;
• Modulus of elasticity E_0,mean = 12.6 GPa/E_0.05 = 10.5 GPa;
• Density ρ_k = 425 kg/m³/ρ_mean = 460 kg/m³.

The analyzed building is located in Vilnius district, Lithuania, with snow and wind load values that are the most common in Europe, including some regions in northern Scandinavian countries.

A static analysis of the provided three alternative options was performed, assuming the following characteristic loads:

• Permanent load: 0.60 kPa for the roof and 0.25 kPa for the walls;
• Snow load: 1.60 kPa;
• Basic wind velocity: 24.0 m/s with a terrain category of II.

Three selected alternative timber-based structural systems are described below.

Option I comprises glulam columns and trusses, which can be prefabricated entirely in a factory. The stability of the in-plane main frame is ensured by column supports fixed to the foundation. Glulam trusses are flexibly supported on the columns. The out-of-plane stability of the entire building is ensured by a vertical and horizontal bracing element system, as shown in Figure 2. Glulam trusses are designed to use slotted-in steel plates, which create efficient multiple shear plane connections. Self-tapping dowels 7 mm in diameter are used to avoid any predrilling in timber elements and steel details. The support connections of columns, trusses, and end-wall frames are assembled using custom-made welded steel details.

The load-bearing system in Option II is a three-hinge glulam frame in which out-of-plane stability is ensured by horizontal and vertical bracing elements, as shown in Figure 3. Flexible attachment of columns to the foundation simplifies the construction of the foundation as there are no bending moments at the support. The glulam columns are composed of two elements, with a beam element in between. In this way, a double-shear timber-to-timber moment is created to resist knee connection. Separate half-frame elements are assembled on site due to the transportation restrictions for non-standard elements.

Option III consists of frames with glulam columns and double-tapered beams (see Figure 4). This structural system requires a minimum number of connections to be assembled on site. The beams are flexibly supported on the columns, and the lateral stability of the frame is ensured by rigid column-to-foundation connections. The horizontal and vertical bracing element system stabilizes the entire building in the out-of-plane direction.

The overall material quantities of glued laminated timber, welded steel details, and fittings are summarized in

Table 2. Total material quantities for glulam, steel, and fittings.

Option	Total Quantity of Glulam GL28h, m3	Welded Steel Details, kg	Fittings, kg
Option I: Glulam column and truss system	50.10	3260.00	1550.00
Option II: Glulam 3-hinge frame system	82.49	1440.00	1810.00
Option III: Glulam column and double-tapered beam system	68.41	2060.00	1030.00

. The total material quantities were calculated assuming the actual quantities of glulam elements as per static design. The total quantities of steel details and fittings were determined from the depicted connection details of each static structural system, as shown in Figure 2, Figure 3 and Figure 4. The figures show the main connection details; the quantities of other connection details were determined assuming the same principle of technical solutions.

4.2. Evaluation Criteria and Their Significance

A set of ten evaluation criteria for alternative structural systems, covering strength, stability, serviceability, economic efficiency, assembling complexity, and aesthetics, is provided in

Table 3. Evaluation criteria.

No	Criterion	Max/Min *	Measuring Unit	Description
C1	Total cost of load-bearing structures	k€	Min	The total cost of glued laminated timber elements, welded steel details, and fittings. The production and transportation from the factory to the building site are also included. Determined by a survey of glulam manufacturers located at >1500 km from the factory to the building site.
C2	Total quantity of glulam	m3	Min	The criterion takes into account all load-bearing glulam elements. The provided quantity of glulam is the actual sum of the volumes of separate elements (see Table 2).
C3	Total quantity of steel details and fittings	kg	Min	The total quantity of welded steel details necessary for the assembling of separate glulam elements, connections, and support details. All glued laminated timber elements are assembled using custom-made welded steel details and bolts, dowels, and screws (see Table 2).
C4	Maximum utility ratio according to ultimate limit states (ULSs)	%	Max	According to the Eurocodes, it is allowed to design structures up to a 100% utility ratio. The utility ratio is determined by both element design and connection design. In the structural design of timber elements, it is usually hard to reach high utility ratios when the determining factor is connection design. The parameter defines the structural efficiency of the analyzed system. Calculated using Dlubal Rfem 5 and Mathcad 14 software.
C5	Maximum utility ratio according to serviceability limit states (SLSs)	%	Max	The utility ratio for serviceability defines the efficiency of the structural system in terms of vertical and horizontal deformations. High utility ratios for serviceability limit states could be easier to reach for structural systems with a relatively low number of connections, as systems with connections are more sensitive to deformations. Calculated using Dlubal Rfem 5 and Mathcad 14 software.
C6	The total available height of the building	m	Max	The total height of the building is defined as the sum of the internal effective height of the building below the roof structure and the height of the roof structure. The height directly influences the total costs of the entire construction and maintenance of the building. Determined in design process.
C7	Total assembly cost	k€	Min	The total assembly cost includes the lifting equipment rent, manpower, and all other costs related to the assembling of load-bearing structures. Determined by a survey of timber construction companies.
C8	Complexity of assembly	Points	Min	The complexity of assembly takes into account the speed of assembling separate structural elements. This criterion also evaluates the need for lifting equipment for the heaviest structural elements. It is a qualitative criterion evaluated on a 3-point scale: 1 = the simplest assembly, 2 = the moderately complex assembly, and 3 = the most complex assembly. Determined based on the knowledge and practical experience of the authors.
C9	Architectural aesthetics	Points	Max	The architectural aesthetics are evaluated by the biophilic design concept of the building load-bearing structures. Glued laminated timber structures are exposed and, therefore, the natural appearance of the structures is significant. It is a qualitative criterion evaluated on a 3-point scale: 1 = the worst appeal, 2 = the moderate appeal, and 3 = the best appeal. Determined by the authors.
C10	Simplicity of the foundation design solution	Points	Min	The simplicity of foundation-laying solution to bear the load of timber superstructure. It is a qualitative criterion evaluated on a 3-point scale: 1 = the simplest foundation design solution, 2 = the moderately simple foundation design solution, and 3 = the most complex foundation design solution. Determined based on the knowledge and practical experience of the authors.

* Note: Max—higher value of criterion is preferred; Min—lower value of criterion is preferred.

below.

The significance of the criteria was evaluated based on the opinions of seven experts. Expert profiles provided in

Table 4. The profiles of experts.

Expert	Profile of a Company	Years of Experience
E1	Structural design of timber structures	11–15
E2	Construction of timber buildings	11–15
E3	Structural design of timber structures	5–10
E4	Construction (different structures)	21–25
E5	Construction (different structures)	>26
E6	Construction (different structures)	>26
E7	Inspection of the buildings	11–15

show that the survey involved seasoned experts, 75% of them having up to 20 years of experience. All invited experts had a technical background in civil engineering and were acquainted with the commonly used timber-based structural systems.

The significance of the criteria was calculated using Equation (1) (see Section 3). The calculated results are provided in

Table 5. Determination of the significance of criteria.

Criterion	E1	E2	E3	E4	E5	E6	E7	Sum	Significance
Total cost of load-bearing structures	10	10	10	10	9	10	10	69	0.1774
Total quantity of glulam	9	9	9	8	9	7	7	58	0.1491
Total quantity of steel details and fittings	8	8	7	9	6	8	8	54	0.1388
Maximum utility ratio according to ULSs	7	7	8	7	8	9	9	55	0.1414
Maximum utility ratio according to SLSs	3	6	6	5	7	6	6	39	0.1003
Total available height of the building	4	3	3	3	3	3	1	20	0.0514
Total assembly cost	6	5	4	4	4	4	5	32	0.0823
Complexity of assembly	5	4	2	2	2	5	2	22	0.0566
Architectural aesthetics	2	2	5	6	10	2	3	30	0.0771
Simplicity of the foundation design solution	1	1	1	1	1	1	4	10	0.0257
Total								386	1

.

The results reveal that experts had different opinions on the ranking of criteria due to their professional profiles. Therefore, it was necessary to determine the consistency of their opinions. The calculated Kendall’s coefficient of concordance (W) was 0.832. The significance of the concordance ratio was χ² = 52.41. χ² > ${\chi }_{\propto ,\upsilon }^2$ = 37.44 > 16.92 (where ∝ = 0.05; υ = 9). It can be concluded that expert opinion is consistent, and the determined significance of criteria can be used in further research.

According to experts’ estimates, the most significant criteria are the total cost of load-bearing structures, with a significance of 0.1774, the total quantity of glulam (0.1491), and the maximum utility ratio according to ULSs (0.11414). The least significant criteria are the simplicity of the foundation design solution (0.0257), the maximum total height of the building (0.0514), and the complexity of assembly (0.0566). This selection suggests that the experts gave priority to the economic and structural properties of timber-based structural systems.

4.3. Multiple-Criteria Assessment

Three alternative timber-based structural systems were evaluated by the COPRAS method (see description in Section 3). At first, an initial decision-making matrix with the values of each criterion for each alternative (further—attribute values) was prepared (see

Table 6. Decision-making matrix.

Criteria	Min/Max	Significance	Alternative Structural Systems
			Option I	Option II	Option III
C1	Min	0.1774	87.059	83.664	66.875
C2	Min	0.1491	50.1	82.49	68.41
C3	Min	0.1388	4310	3250	3090
C4	Max	0.1414	89	97	93
C5	Max	0.1003	64	85	99
C6	Max	0.0514	6.78	6.2	5.8
C7	Min	0.0823	30.564	45.372	34.546
C8	Min	0.0566	3	1	2
C9	Max	0.0771	3	2	1
C10	Min	0.0257	2	1	3

). The attribute values were determined as explained in Section 3 and Table 3.

In the next step, the attribute values of the decision-making matrix were normalized and weighted by Equations (5) and (6), and the final efficiency indexes of alternatives were calculated by Equation (7) (see

Table 7. Weighted decision-making matrix and final calculation results by the COPRAS method.

Criteria	Weighted Normalized Criteria Values
	Option I	Option II	Option III
C1	0.0650	0.0625	0.0499
C2	0.0372	0.0612	0.0507
C3	0.0562	0.0424	0.0403
C4	0.0451	0.0492	0.0471
C5	0.0259	0.0344	0.0400
C6	0.0186	0.0170	0.0159
C7	0.0228	0.0338	0.0257
C8	0.0283	0.0094	0.0189
C9	0.0386	0.0257	0.0129
C10	0.0086	0.0043	0.0129
The sums of weighted normalized maximizing indices S+j	0.1281	0.1262	0.1159
The sums of weighted normalized minimizing indices S−j	0.2179	0.2135	0.1984
$E_j$	0.3300	0.3323	0.3377
Rank	3	2	1

).

It can be observed that, according to the COPRAS method, the least preferred alternative is Option I—Glulam column and truss system (efficiency index 0.3300). The best-performing alternative is Option III—Glulam column and double-tapered beam system, with a significance of 0.3377, followed by Option II—Glulam three-hinge frame system, with a significance of 0.3323. However, the difference between Option II and Option I regarding the efficiency criterion is relatively low. Therefore, another MCDM method, SAW, was used to verify the results.

The attribute values of the decision-making matrix (Table 6) were normalized and weighted by Equations (6), (8) and (9), and the final efficiency indexes were calculated by Equation (10) (see

Table 8. Weighted decision-making matrix and final calculation results by the SAW method.

Criteria	Weighted Normalized Criteria Values
	Option I	Option II	Option III
C1	0.1363	0.1418	0.1774
C2	0.1491	0.0906	0.1092
C3	0.0995	0.1320	0.1388
C4	0.1297	0.1414	0.1356
C5	0.0648	0.0861	0.1003
C6	0.0514	0.0470	0.0440
C7	0.0823	0.0554	0.0728
C8	0.0189	0.0566	0.0283
C9	0.0771	0.0514	0.0257
C10	0.0129	0.0257	0.0086
$E_j$	0.8219	0.8279	0.8405
Rank	3	2	1

).

The multiple-criterion evaluation results revealed that the least preferred structural system is Option I—Glulam column and truss system (efficiency index 0.8219). The best-performing alternative is Option III—Glulam column and double-tapered beam system, with an efficiency index of 0.8405, followed by Option II—Glulam three-hinge frame system, with an efficiency index of 0.8279. Therefore, it can be stated that the results obtained by both the COPRAS and SAW methods are the same, and the alternatives are ranked as follows: Option III ≻ Option II ≻ Option I.

5. Discussion

Three alternative timber-based structural systems—the Glulam column and truss system (Option I), the Glulam three-hinge frame system (Option II), and the Glulam column and double-tapered beam system (Option III)—for a grocery store with approximately 1000 m² of floor area were evaluated using two MCDM methods.

A set of ten quantitative and qualitative criteria was formed to evaluate the alternatives. The significance of the criteria was determined by the estimates of seven experts from design/construction or similar companies, all well acquainted with the commonly used timber-based structural systems.

The experts gave priority to the total cost of load-bearing structures (C1) (significance of 0.1774), the total quantity of glulam (C2) (0.1491), the maximum utility ratio according to ULSs (C4) (0.11414), and the total quantity of steel details and fittings (C3) (0.1388). Such priorities are in line with the findings of other studies. For instance, cost criterion was ranked as the most important in previous publications [22,23,24,26,28,30]. The total quality of glulam required for load-bearing structures is one of the cost determinants; moreover, it also reflects the need for timber resources. According to ULSs, the maximum utility ratio determines the structural efficiency of the system; it is one of the most important criteria in design [44]. The total quantity of steel details and fittings is related to the complexity of the structure.

The determined significance of the criteria was used to evaluate three alternative options of timber-based structural systems by the COPRAS and SAW methods (see Figure 5).

Both methods revealed that the least preferable alternative is Option I—Glulam column and truss system. Compared to other options, it has the highest cost of load-bearing structures, the highest quantity of steel details and fittings, the lowest maximum utility ratios according to ULSs and SLSs, and is the most complex to assemble. On the other hand, the system has some advantages, i.e., the lowest quantity of glulam used, and the lowest assembly cost; it allows designers to achieve the highest total height of the building and is the most aesthetical from an architectural point of view. It can be assumed that this alternative received a lower rank due to the high significance of economic and structural performance criteria.

Option II—Glulam three-hinge frame system was ranked second. This structural system uses the highest quantity of glulam and is the most expensive to assemble. Its advantages compared to other systems are the highest maximum utility ratio according to ULSs (97%), and the simplicity of assembling and foundation.

The best-ranked alternative is Option III—Glulam column and double-tapered beam system. This system has the lowest cost of load-bearing structures, requires the lowest total quantity of steel details and fittings, and has the highest maximum utility ratio according to SLSs (99%), although the total height of the building that is possible to achieve is the lowest. The overall price and efficiency of the structural system are directly influenced by the utility ratios in strength and stability (ULSs) and serviceability (SLSs), including deformations. The high structural efficiency ratios in terms of ULSs and SLSs can be reached due to the tapered shape of roof beams. The tapered cross-section with the maximum height at the ridge and the minimum height at the support fully corresponds to the actual bending moment diagram; therefore, high utility ratios can be reached in each section of the roof beam. Double-tapered beams form a slope that is necessary for water drainage and no additional leveling layers are required in the main frame direction. Also, double-tapered beams are normally produced and formed from the elements glued according to the shape of the slope, which results in less timber waste during the production process.

In summary, all designed structural systems have advantages and disadvantages, and their efficiencies differ only slightly as determined by the MCDM methods. If the client agrees with the significance of the criteria proposed in this paper, it is recommended to select Option III—Glulam column and double-tapered beam system. If economic criteria are not so important and priority is given to other characteristics, such as structural performance and assembly simplicity, it is recommended to select Option II—Glulam three-hinge frame system. If the quantity of used glulam shall be reduced and the client aims to achieve the highest possible height of the building, then Option I—Glulam column and truss system—is recommended.

The present research was adapted to the specific case of Lithuania. However, in the design of timber-based structures, applied snow and wind load values are the most common in Europe, including some regions in northern Scandinavian countries. Therefore, research results can be used in other countries with the same climatic conditions.

The present research, however, has some limitations as follows.

• The efficiency of alternative timber-based structural systems was determined based on ten proposed criteria. Changes in criteria may change the ranking of alternatives.
• The significance of the criteria was determined by experts and reflects their opinion. The significance and priorities of the alternatives may change if other experts are involved in the survey.
• Some attribute values of alternative structural systems, i.e., the total cost of load-bearing structures and the total assembly cost, were determined based on the prices in Lithuania in 2022. If the same methodology is used in other countries, the values must be recalculated. In addition, the transportation distance from the factory to the building site has to be estimated.

6. Conclusions

The selection of the most appropriate structural system for a building is a multi-faceted problem, as many, often conflicting, quantitative and qualitative criteria must be taken into consideration. The literature review revealed that MCDM techniques can be applied for this purpose.

In this study, three alternative glulam structural systems—the glulam column and truss system, the glulam three-hinge frame system, and the glulam column and double-tapered beam system—were proposed for a grocery store in Vilnius, Lithuania, and evaluated by the COPRAS and SAW methods. Based on the findings of the research, the following conclusions can be drawn.

• An expert survey revealed that the most significant criteria in the selection of timber-based structural systems are the total cost of load-bearing structures, with a significance of 0.1774, the total quantity of glulam (0.1491), and the maximum utility ratio according to ULSs (0.11414). Such results are in line with the findings of other studies.
• The ranking of the alternative structural systems by COPRAS methods revealed that the most preferred structural system alternative is the glulam column and double-tapered beam system, with an efficiency index of 0.3377, followed by the glulam three-hinge frame system (0.3323) and the glulam column and truss system (0.3300).
• The evaluation of the alternative structural systems by SAW methods revealed the same ranking results. The obtained efficiency index is 0.8405 for the glulam column and double-tapered beam system, 0.8279 for the glulam three-hinge frame system, and 0.8219 for the glulam column and truss system. Therefore, it can be stated that the glulam column and double-tapered beam system is the most preferable alternative. Its advantages are the lowest price of load-bearing structures, the lowest total quantity of steel details and fittings, and the highest maximum utility ratio according to SLSs.
• All designed structural systems have their advantages and disadvantages, and their efficiencies, determined by MCDM methods, depend on the significance of criteria. The significance of criteria can be re-evaluated based on a particular project and the client’s requirements. In this case, the ranking of the structural systems may change.

Implications for future research include the following.

• Environmental criteria, e.g., CO₂ emissions and embodied energy, could be included in the set of evaluation criteria.
• To achieve higher accuracy, the AHP method could be used in the future to evaluate the significance of criteria.
• The same research problem could be solved by other MCDM methods. In future research, it is envisaged to apply the ARAS method, which provides a comparison of the proposed solutions with the optimal solution to be set by the client.
• The proposed structure of the grocery store is relatively simple. The authors aim to continue their research on the selection of multi-layer timber-based structures using MCDM techniques. Additional specific evaluation criteria, such as floor weight, height of the flooring, and engineering integration of elements into the load-bearing system, will be used for this purpose.