Optimal Design of Truss Structures for Sustainable Carbon Emission Reduction in Korean Construction

Abstract

Due to the recent abnormalities in global temperature and increasing carbon emissions, the world is working to reduce carbon emissions. In particular, the construction sector accounts for about 37% of all carbon emissions, so it is one of the areas where sustainable reduction efforts must be made. Therefore, in this paper, an optimal design process was performed by evaluating carbon emissions as the objective function, a choice which differed from the objective function of the existing research used in the optimal design of truss structures. The metaheuristics algorithm used for the process was the advanced crow search algorithm. The levels of carbon emissions generated when the material of a truss structure consisted of a customary material (steel) were compared to scenarios in which timber was used, and a construction scenario centered on the Republic of Korea was established for comparison. The structures used as examples were 10-, 17-, 22-, and 120-bar truss structures. As a result, it was confirmed that truss structures using timber had fewer carbon emissions than structures using steel. In addition, it was confirmed that, even in the same timber structures, domestic timber had fewer carbon emissions than imported timber. These results confirmed that in order to achieve carbon neutrality in the construction field, carbon emissions must be considered in advance, in the design stage.

1. Introduction

The world has the advantage of enjoying a convenient life due to the development of many technologies subsequent to the era of industrialization, but this also has the consequence of causing climate change abnormalities due to the steady increase in carbon emissions. According to an IPCC report, greenhouse gas emissions began to increase rapidly in the mid-1950s, and during a similar period, global temperatures also increased [1]. In response, the international community recognized the seriousness of climate change and called for 196 parties to make efforts to limit temperature increases to 1.5 °C above pre-industrial levels at the COP21 (UN climate change conference) on 12 December 2015 [2,3].

As described in Figure 1, construction-related industries account for 36% of global energy consumption and 37% of carbon emissions [4]. This means that carbon emissions from the construction industry are significantly higher than those from other industries. Therefore, in efforts to cope with climate change, the construction industry is one of the key industries which can curb the rise in global temperature. In the construction industry, efforts are being made to reduce the energy generated during the operation of buildings, such as with zero-energy buildings and passive houses [5,6,7]. However, the importance of evaluating carbon emissions over the entire life-cycles of buildings, including the carbon generated from material production, transportation, construction, and reuse, has grown [8,9]. In particular, measures to reduce carbon emissions generated during the development and production of new materials that can replace cement and steel, which are widely used as construction materials, are insufficient [10]. However, demand for construction cement and steel is expected to continue to increase until 2030 [11]. Therefore, according to a technical report published by UNEP and Yale CEA, traditional construction materials such as concrete and iron are recommended for use only when necessary, as a significant pathway to decarbonization, and the use of renewable low-carbon bio-based construction materials is urged [10]. To solve this problem, the global construction market is using something other than conventional concrete and steel frames as a construction material; instead, eco-friendly timber with low embodied energy is emerging as an alternative.

Since timber is lightweight, it can reduce the burden of the load and has the advantages of excellent fire resistance and earthquake resistance [12,13]. Starting with advanced timber construction technology in countries such as Canada, Japan, and the United States, the technology is moving from low-rise buildings to large high-rise buildings [14]. This change was made possible by the development of engineered timber, such as CLT (cross-laminated timber), GLT (glue-laminated timber), and LVL (laminated veneer lumber), which have performance indices similar to materials used in existing steel and concrete structures [15,16]. In addition, since timber can store carbon dioxide that was absorbed before logging, it is considered an essential material for efforts to reduce carbon emissions in the construction industry.

The Republic of Korea, the target of the construction scenarios in this paper, is representative of countries that have achieved rapid economic growth with rapid industrialization. Since its growth has mainly occurred in the construction and manufacturing industries, carbon emissions have inevitably increased.

Table 1. CO₂ emissions and territorial size, by country, in 2022.

Country	CO2 Emissions (M ton CO2)	Territorial Size and Relative Emissions
		Territory (km2)	CO2 per Territory (ton CO2/km2)
China	10,504 (1)	9,596,960	109.45 (8)
USA	4735 (2)	9,833,517	481.52 (5)
India	2481 (3)	3,287,263	754.73 (4)
Russia	1798 (4)	17,098,246	105.16 (9)
Japan	1001 (5)	377,976	2648.32 (2)
Indonesia	739 (6)	1,904,569	388.01 (6)
Germany	636 (7)	357,114	1780.94 (3)
Iran	634 (8)	1,648,195	384.66 (7)
Republic of Korea	597 (9)	100,210	5957.49 (1)

presents the emissions by country in 2022 [17], according to CO₂ emissions and territorial size, and the numbers in parentheses indicate rankings. The Republic of Korea had the ninth-highest level of carbon emissions in the world, emitting 597 million tons of CO₂. However, in proportion to its territory, it was the country with the highest level of carbon emissions. In other words, as a country that emits a significant amount of CO₂ compared to its territory, the Republic of Korea is a country that must make great efforts to assist in the reduction of carbon emissions around the world and the stabilization of abnormal climates. However, the Republic of Korea needs more relevant awareness and design and construction technology related to timber structures which can reduce carbon in the construction field, and the market for timber structures is very small.

The optimal design process of a truss structure mainly uses metaheuristic algorithms, and the weight of a truss structure is an objective function. In addition, research is being conducted continuously to reduce construction costs by finding the minimal cross-sectional area or the optimal topology of a truss element [18,19,20,21]. Steel is the material mainly used in the fabrication of truss structures. The previous study of timber structures evaluates and compares carbon emissions by changing the nature of a material in an existing structure rather than evaluating carbon emissions in the optimal design stage [22,23,24,25]. However, the schematic-design stage of a building is an essential time for calculating carbon emissions, a process which is necessary to utilize in order to reduce such emissions quickly [26].

Therefore, in this paper, the carbon emissions of a truss structure were the objective function of optimal design, a process which was performed based on a construction scenario centered in the Republic of Korea. In addition, the carbon emissions of timber truss structures using domestic or imported timber and a truss structure using steel were compared. For the optimal design, the ACSA (advanced crow search algorithm) proposed by Lee et al. was selected from among the among metaheuristics algorithms [27]. This was performed using MATLAB R2023a. Section 2 describes the carbon emission evaluation method, and Section 3 describes the ACSA used to perform the optimal design. Section 4 analyzes the problem definition and the results, and Section 5 presents the conclusions of this paper.

2. Embodied-Carbon Emissions

Figure 2 presents the environmental impact of a building’s life cycle (A–C), which is divided into product, construction, use and maintenance, and end-of-life stages [28]. Modules B4 and B5 generate carbon during the operation of a building, while all other modules represent embodied carbon. Although many studies have tried to reduce the carbon emissions generated when using buildings [29,30,31], the need to evaluate all relevant carbon emissions, including those generated during the material production, construction, and disposal processes, is constantly being raised [32,33]. In particular, it is essential to calculate carbon emissions in advance, in the schematic-design stage (A1–A3), because the carbon emissions generated in the material production stage account for the most significant portion, at about 50%. In this paper, only steps A1–A4 are considered, due to the difficulty of determining the construction costs, waste-related treatment methods, and operating carbon, which depend on the method of use.

${EC}_{net}$ (carbon emissions), considering steps A1–A4 in a building’s life cycle, can be calculated using Equation (1). Here, ${EC}_{A1-A3}$ refers to the carbon emissions generated in steps A1–A3, while ${EC}_{A4}$ refers to the carbon emissions generated in step A4.

$${EC}_{net}={EC}_{A1-A3}+{EC}_{A4}$$

(1)

The ${EC}_{A1-A3}$ and ${EC}_{A4}$ included in the ${EC}_{net}$ formula may be calculated using Equations (2) and (3). Here, $n$ denotes the number of elements, $W_i$ denotes the weight (kg) of the i-element, $L_{mat,i}$ denotes the moving distance of the i-element material, and $L_{ele,i}$ denotes the moving distance of the i-element. Furthermore, ${ECC}_i$ denotes the embedded carbon coefficient of the i-element material, and ${TC}_i$ denotes the transport coefficient of the i-element. The ${ECC}_i$ of ${EC}_{A1-A2}$ has a positive or negative value. If ${ECC}_i$ has a negative value, the objective function becomes negative, making it challenging to find the minimum value. Therefore, the optimal design uses a positive value, and the final ${EC}_{net}$ is calculated by multiplying the result by −1. Finally, the loss in manufacturing engineered timber using materials (wood) is considered.

$$\begin{gathered} {EC}_{A1-3}={EC}_{A1-A2}+{EC}_{A3} \\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em} ={\sum }_{i=1}^n\left(W_i\times {ECC}_i\times Loss\right) \\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em} +{\sum }_{i=1}^n\left(W_i\times L_{mat,i}\times {TC}_i\times Loss\right) \end{gathered}$$

(2)

$${EC}_{A4}={\sum }_{i=1}^n\left(W_i\times L_{ele, i}\times {TC}_i\right)$$

(3)

${ECC}_i$ is determined using

Table 2. Embodied-carbon values of materials.

Material	Carbon (kgCO2e/kg)
	No Carbon Storage	Including Carbon Storage
Concrete (structure)	0.159	-
Steel (general, pipe)	1.370	-
Steel (section)	1.420	-
CLT	0.437	−1.204
MDF	0.857	−0.644
GLT	0.512	−0.896
Aluminum (general)	8.240	-
Glass	0.850	-
Iron (general)	1.910	-

[34]. In general, 1.37 kgCO₂e is discharged per kg of steel, which is widely used as a structural material, and 0.159 kgCO₂e is discharged per kg of concrete. Wood varies depending on the type, but has excellent flexural strength. GLT, which is widely used as a bending member, emits 0.512 kgCO₂e per kg. However, considering carbon storage, a value of −0.896 kgCO₂e/kg can be used.

${TC}_i$ is determined using

Table 3. Embodied-carbon values of transportation methods.

Transportation	Carbon (kgCO2e/kg/km)
By sea	0.000017
By rail	0.000027
By road	0.000107

[35]. The value of ${TC}_i$ varies depending on transportation method, whether road, rail, or ocean, and it has the most significant value, at 10.7 kgCO₂e/t per 100 km, when using road transportation. Since ${TC}_i$ calculates carbon emissions by multiplying them by the moving distance, even when buildings are constructed using the same material, differences in carbon emissions may be significant depending on the moving distances of materials or elements.

3. Advanced Crow Search Algorithm

The CSA (crow search algorithm) was proposed by Askarzadeh, A. in 2016 [36], and Lee, D. et al. proposed the ACSA (advanced crow search algorithm) in 2023, which supplemented the convergence performance and shortcomings of the CSA [27]. Lee, D. et al. confirmed that the exploitation and exploration performance was improved using 23 benchmark functions and five engineering problems.

Like the CSA, the ACSA consists of five steps, which are performed as follows:

Step 1: Define the problem and set the parameters.

Step 1 defines an optimization problem and the parameters required to perform the optimization. The defined parameters are D (dimension of problem), N (flock size), $t_{max}$ (maximum generation), fl (flight length), ${AP}_{max}$ (maximum awareness probability), ${AP}_{min}$ (minimum awareness probability), FAR (flight awareness ratio), lb (lower boundary), and ub (upper boundary).

Step 2: Initialize the positions of the crows and evaluate.

A crow’s position is randomly adopted in the lb and ub ranges and initialized, as shown in Equation (4). Here, x means each crow’s position, which is stored as shown in Equation (5). In addition, the flock of each crow is evaluated using the initially set objective function.

$$Crows=\left[\begin{array}{ccc}{x}_1^1& \cdots & x_1^D\\ ⋮& \ddots & ⋮\\ x_N^1& \cdots & x_N^D\end{array}\right]$$

(4)

$$Crows memory=\left[\begin{array}{ccc}{m}_1^1& \cdots & m_1^D\\ ⋮& \ddots & ⋮\\ m_N^1& \cdots & m_N^D\end{array}\right]$$

(5)

Step 3: Generate and evaluate the new positions for the crows.

The ACSA is classified as a method of generating crow positions according to the size of the dynamic AP, which is defined using Equation (6) and has smaller values as the number of generations increases. Here, t denotes the current number of generations. The reason for using a dynamic AP is to make the ACSA mainly use exploitation performance rather than exploration as the number of generations increases.

$${Dynamic AP}_t={AP}_{min}+\frac{{AP}_{max}-{AP}_{min}}{\ln \left(t\right)+1}$$

(6)

If a random number from 0 to 1 is greater than or equal to the dynamic AP, the crow position is generated using Equation (7). Here, r is a random variable between 0 and 1, $m_{j,t}$ is a randomly adopted crow position, and ${gb}_{j,t}$ is the best crow position. That is, a crow follows a crow randomly adopted by the FAR or a crow in the best position. Conversely, if a random number is smaller than the dynamic AP, the crow position is generated using Equation (8). If r is 0.5 or more, it randomly moves to a new position in a smaller boundary according to the number of generations. If r is less than 0.5, it randomly moves to a new position within the boundary of the entirety. The location of the generated crow is reevaluated using the objective function.

$$x_{t+1}=\left\{\begin{array}{c}{x}_t+r\times fl\times \left(m_{j,t}-x_t\right)\\ x_t+r\times fl\times \left({gb}_{j,t}-x_t\right)\end{array} \begin{array}{c}if r\ge FAR\\ else\end{array}\right.$$

(7)

$$x_{t+1}=\left\{\begin{array}{c}{2x}_t+\left(lb+r\times \left(lb-ub\right)\right)/t\\ random position\end{array} \begin{array}{c}if r\ge 0.5\\ else\end{array}\right.$$

(8)

Step 4: Update the memory.

The evaluation of the initial crow position is remembered and compared to the evaluation of the crow position generated in step 3, and the better crow position is updated in the crow’s memory.

Step 5: Terminate the repetition.

If t is less than $t_{max}$, steps 3–4 are repeated. The algorithm terminates if t is equal to $t_{max}$. The terminated ACSA derives an optimization result.

4. Numerical Examples

4.1. Problem Definition

In this paper, the goal was to minimize the carbon emissions generated in steps A1–A4 during a building’s life cycle. The objective function was expressed using Equation (9), and the constraint could be expressed using Equation (10). If $g_1$ and $g_2$ were not met, a penalty of ${10}^4$ was imposed.

$$\mathrm{To} \mathrm{minimize} {\mathrm{E}\mathrm{C}}_{net}\times f_{penalty} \left\{\begin{array}{c}if satisfied\\ else\end{array} \begin{array}{c}{ f}_{penalty}={10}^4\\ f_{penalty}=1\end{array}\right.$$

(9)

$$\begin{gathered} \mathrm{Subject} \mathrm{to} g_1\left(x\right): {\sigma }_y^{T or C}\ge {\sigma }_i \\ {g}_2\left(x\right): {\delta }_{max}\ge \delta \end{gathered}$$

(10)

First, 10-bar, 17-bar, and 22-bar truss structures and a 120-bar truss dome structure were selected as numerical examples.

Table 4. Material transportation scenarios.

Material	Raw Material (A1)	Manufacturing Products (A3)	Construction (A5)
Steel (imported)	L: Osaka (Japan)	L: Pohang (Korea) D: 761 km (by sea)	KOREATECH (Korea) D: 249 km (by road)
GLT (imported)	L: Vancouver (Canada)	L: Incheon (Korea) D: 9351 km (by sea)	KOREATECH (Korea) D: 128 km (by road)
GLT (domestic)	L: Ganneung (Korea)	L: Incheon (Korea) D: 237 km (by road)	KOREATECH (Korea) D: 128 km (by road)

shows the scenarios of the structures, which were assumed to have been built at KOREATECH in the Republic of Korea. In Table 4, L indicates the location and D indicates the moving distance.

• In the case of using steel as the material for the structure, it was assumed that the Republic of Korea imports most of its iron scrap from Japan. Imported iron scrap was processed into Pohang’s structural steel and transported to KOREATECH.
• In the case of using GLT (imported) as the material for the structure, it was assumed that it was imported by sea from Canada, which has the highest timber production in the world. Imported timber was brought into Incheon, processed into GLT at a sawmill, and transported to KOREATECH.
• In the case of using GLT (domestic) as the material for the structure, it was assumed that logging was performed in Gangneung, where wood production is the highest in Korea. The wood was brought into Incheon, processed into GLT at a sawmill, and transported to KOREATECH.
• The loss rate during the production of the construction materials was 10%.

All materials had their own ECC, and in the case of wood, the ECC differed depending on whether carbon storage was considered. Therefore, carbon emissions were compared and analyzed by classifying them into five cases, as shown in

Table 5. Analysis cases and properties of materials.

Case	Material	Carbon Storage	Elastic Modulus (ksi)	Yield Strength (ksi)	Density (lb/in3)	ECC (kgCO2e/kg)
1	Steel (general)	-	30,458 (210,000 MPa)	40 (275 MPa)	0.2836 (7850 kg/m3)	1.37
2	GLT (imported)	No	1595 (11,000 MPa)	1.105 (7 MPa)	0.0206 (570 kg/m3)	0.512
3	GLT (imported)	Yes				−0.896
4	GLT (domestic)	No				0.512
5	GLT (domestic)	Yes				−0.896

Note: 1 MPa = 0.14504 ksi; 1 kg/m³ = 0.000036127 lbs/in³; 1 lb = 0.4536 kg.

and Figure 3. In cases 2–5, truss structures in the same state were used to compare carbon emissions according to whether the materials were imported or considered for carbon storage. The parameters of the ACSA used for the optimal design of the carbon emissions of the truss structures are shown in

Table 6. Parameters of CSA.

D	N	${\mathit{t}}_{\mathit{m}\mathit{a}\mathit{x}}$	fl	${\mathit{A}\mathit{P}}_{\mathit{m}\mathit{a}\mathit{x}}$	${\mathit{A}\mathit{P}}_{\mathit{m}\mathit{i}\mathit{n}}$	FAR	ub	lb
Depends on problem	10	1000 (10 bar) 2000 (17 bar) 1000 (22 bar)	2	0.4	0.01	0.4	1000	0.1

. Each analysis was repeated 10 times.

4.2. The 10-Bar Truss Structure

Figure 4 shows the shape and the coordinates of the 10-bar truss structure [37]. It consisted of 6 nodes and 10 elements, and the design variable was 10. A load of −100 kips was applied to nodes 4 and 5 along the Y-axis, and the maximum displacement generated at each node was set to 3.6 in.

Table 7. Area and constraint results of 10-bar truss structure (unit: mm²).

Variables	Steel	GLT
$A_1$	6.228	291.313
$A_2$	0.100	0.100
$A_3$	8.261	180.205
$A_4$	2.429	90.765
$A_5$	0.100	3.597
$A_6$	0.100	4.057
$A_7$	4.571	151.850
$A_8$	3.259	145.896
$A_9$	3.510	127.887
$A_{10}$	0.100	0.100
${\sigma }^{max}$ (MPa)	40.000	−1.105
${\delta }^{max}$ (mm)	−3.168	−1.750
Weight (kg)	4759.435	8692.408

shows the cross-sectional areas and constraints derived from the optimal design results. When the structure’s material was made of steel, the cross-sectional area of element 3 was the largest, at 8.261 mm², and the cross-sectional areas of elements 2, 5, 6, and 10 were the smallest, at 0.100 mm². When GLT was used, the cross-sectional area of element 1 was the largest, at 291.313 mm², and the cross-sectional areas of elements 2 and 10 were the smallest, at 0.100 mm². In addition, it was confirmed that steel and GLT satisfied the allowable stress and allowable displacement, and the structure’s weights were 4759.435 kg and 8692.408 kg, respectively, in these scenarios. Figure 5 shows a convergence graph of the 10-bar truss structure, and it can be seen that both steel and GLT converged to one value. Steel converged to a minimum carbon emission of 2441.905 kgCO₂e in 746 generations, and GLT converged to a minimum carbon emission of 2964.095 kgCO₂e in 952 generations.

Figure 6 shows the carbon emissions of steps A1–A4 according to the case. In steps A1 and A3, case 1 had the most significant emissions, with 2377.423 kgCO₂e of carbon emitted, and cases 3 and 5 had the lowest carbon emissions, with −3886.099 kgCO₂e. In step A2, cases 2 and 3 had the most significant emissions, with 689.466 kgCO₂e of carbon emitted, and case 1 had the lowest carbon emissions, with 22.450 kgCO₂e. In step A4, cases 2–5 had the most significant carbon emissions at 54.002 kgCO₂e, and case 1 had the lowest carbon emissions, at 42.032 kgCO₂e. Considering the total carbon emissions of all steps (A1–A4), case 2 had the most significant carbon emissions, at 2964.095 kgCO₂e, and case 5 had the lowest carbon emissions, at −3722.111 kgCO₂e. When comparing cases 1, 3, and 5, it can be seen that the carbon emissions were lower when using GLT compared to steel. In addition, when comparing cases 2 and 4 or cases 3 and 5, it can be noted that the same material (GLT) was used, but the differences in carbon emissions could be significant depending on the transport distances of the materials and elements.

4.3. The 17-Bar Truss Structure

Figure 7 shows the shape and the coordinates of the 17-bar truss structure [37]. It consisted of 9 nodes and 17 elements, and the design variable was 17. A load of −100 kips was applied to node 9 along the Y-axis, and the maximum displacement generated at each node was set to 2.0 in.

Table 8. Area and constraint results of 17-bar truss structure (unit: mm²).

Variables	Steel	GLT
$A_1$	33.616	344.669
$A_2$	0.100	127.904
$A_3$	11.434	503.673
$A_4$	23.771	51.261
$A_5$	16.831	280.376
$A_6$	0.100	3.236
$A_7$	8.144	182.749
$A_8$	0.100	4.338
$A_9$	4.989	211.631
$A_{10}$	3.374	566.670
$A_{11}$	4.881	346.404
$A_{12}$	15.760	138.544
$A_{13}$	4.423	137.264
$A_{14}$	15.017	151.003
$A_{15}$	7.658	0.100
$A_{16}$	6.555	131.129
$A_{17}$	0.168	0.100
${\sigma }^{max}$ (MPa)	−40.000	1.105
${\delta }^{max}$ (mm)	−1.870	−1.322
Weight (kg)	4753.058	7377.578

shows the cross-sectional areas and constraints derived from the optimal design results. When the structure’s material was made of steel, the cross-sectional area of element 1 was the largest, at 33.616 mm², and the cross-sectional areas of elements 6 and 8 were the smallest, at 0.100 mm². When GLT was used, the cross-sectional area of element 10 was the largest, at 566.670 mm², and the cross-sectional areas of elements 15 and 17 were the smallest, at 0.100 mm². In addition, it was confirmed that steel and GLT satisfied the allowable stress and allowable displacement, and the structure’s weights were 4753.058 kg and 7377.587 kg, respectively, in these scenarios. Figure 8 shows a convergence graph of the 17-bar truss structure, and it can be seen that both steel and GLT converged to one value. Steel converged to a minimum carbon emission of 3337.196 kgCO₂e in 1988 generations, and GLT converged to a minimum carbon emission of 2515.741 kgCO₂e in 1999 generations.

Figure 9 shows the carbon emissions of steps A1–A4 according to the case. In steps A1 and A3, case 1 had the most significant emissions, with 3249.072 kgCO₂e of carbon emitted, and cases 3 and 5 had the lowest carbon emissions, with −3298.280 kgCO₂e. In step A2, cases 2 and 3 had the most significant emissions, with 585.176 kgCO₂e of carbon emitted, and case 1 had the lowest carbon emissions, with 30.681 kgCO₂e. In step A4, cases 2–5 had the lowest carbon emissions, at 45.833 kgCO₂e, and case 1 had the most significant carbon emissions, at 57.442 kgCO₂e. Considering the total carbon emissions of all steps (A1–A4), case 2 had the most significant carbon emissions, at 3337.196 kgCO₂e, and case 5 had the lowest carbon emissions, at −3159.097 kgCO₂e. When comparing cases 1, 3, and 5, it can be seen that the carbon emissions were lower when using GLT compared to steel. In addition, when comparing cases 2 and 4 or cases 3 and 5, it can be noted that the same material (GLT) was used, but the differences in carbon emissions could be significant depending on the transport distances of the materials and elements.

4.4. The 22-Bar Truss Structure

Figure 10 shows the shape and the coordinates of the 22-bar truss structure [37]. It consisted of 8 nodes and 22 elements, and the design variable was seven. A load of −20 kips was applied to nodes 1, 2, 3, and 4 along the X-axis, and a load of −50 kips was applied to nodes 2 and 4 along the Y-axis. The maximum displacement generated at each node was set to 2.0 in.

Table 9. Area and constraint results of 22-bar truss structure (unit: mm²).

Variables	Steel	GLT
$\mathrm{G}1 (A_1~A_4$)	1.553	56.065
$\mathrm{G}2 (A_5~A_6$)	0.100	0.100
$\mathrm{G}3 (A_7~A_8$)	2.355	14.476
$\mathrm{G}4 (A_9~A_{10}$)	0.100	0.100
$\mathrm{G}5 (A_{11}~A_{14}$)	0.100	0.100
$\mathrm{G}6 (A_{15}~A_{18}$)	0.882	68.667
$\mathrm{G}7 (A_{19}~A_{22}$)	1.046	0.100
${\sigma }^{max}$ (MPa)	−39.999	−1.105
${\delta }^{max}$ (mm)	−1.216	−0.673
Weight (kg)	1235.366	2703.877

shows the cross-sectional areas and constraints derived from the optimal design results. When the structure’s material was made of steel, the group of element 3 was the largest, at 2.355 mm², and the groups of elements 2, 4, and 5 were the smallest, at 0.100 mm². When GLT was used, the group of element 6 was the largest, at 68.667 mm², and the groups of elements 2, 4, 5, and 7 were the smallest, at 0.100 mm². In addition, it was confirmed that steel and GLT satisfied the allowable stress and allowable displacement, and the structure’s weights were 1235.366 kg and 2703.877 kg, respectively, in these scenarios. Figure 11 shows a convergence graph of the 22-bar truss structure, and it can be seen that both steel and GLT converged to one value. Steel converged to a minimum carbon emission of 867.370 kgCO₂e in 996 generations, and GLT converged to a minimum carbon emission of 922.017 kgCO₂e in 851 generations.

Figure 12 shows the carbon emissions of steps A1–A4 according to the case. In steps A1 and A3, case 1 had the most significant emissions, with 844.466 kgCO₂e of carbon emitted, and cases 3 and 5 had the lowest carbon emissions, with −1208.817 kgCO₂e. In step A2, cases 2 and 3 had the most significant emissions, with 214.467 kgCO₂e of carbon emitted, and case 1 had the lowest carbon emissions, with 7.974 kgCO₂e. In step A4, cases 2–5 had the most significant carbon emissions, at 16.798 kgCO₂e, and case 1 had the lowest carbon emissions, at 14.930 kgCO₂e. Considering the total carbon emissions of all steps (A1–A4), case 2 had the most significant carbon emissions, at 922.017 kgCO₂e, and case 5 had the lowest carbon emissions, at −1157.807 kgCO₂e. When comparing cases 1, 3, and 5, it can be seen that the carbon emissions were lower when using GLT compared to steel. In addition, when comparing cases 2 and 4 or cases 3 and 5, it can be noted that the same material (GLT) was used, but the differences in carbon emissions could be significant depending on the transport distances of the materials and elements.

4.5. The 120-Bar Truss Dome Structure

Figure 13 shows the shape and the coordinates of the 120-bar truss structure [38]. It consisted of 49 nodes and 120 elements, and the design variable was seven. Loads of −15, −10.0, and −5.0 kips were applied to nodes 1, 2–15, and 14–37 along the Z-axis. The maximum displacement generated at each node was set to 2.0 in.

Table 10. Area and constraint results of 120-bar truss dome structure (unit: mm²).

Variables	Steel	GLT
$\mathrm{G}1 (A_1~A_{12}$)	0.267	6.922
$\mathrm{G}2 (A_{13}~A_{24}$)	1.020	22.505
$\mathrm{G}3 (A_{25}~A_{36}$)	2.057	3.946
$\mathrm{G}4 (A_{37}~A_{60}$)	0.415	17.299
$\mathrm{G}5 (A_{61}~A_{84}$)	0.488	36.551
$\mathrm{G}6 (A_{85}~A_{96}$)	0.148	5.687
$\mathrm{G}7 (A_{97}~A_{120}$)	0.906	16.743
${\sigma }^{max}$ (MPa)	−40.000	−1.105
${\delta }^{max}$ (mm)	−2.000	−1.932
Weight (kg)	5093.025	8036.328

shows the cross-sectional areas and constraints derived from the optimal design results. When the structure’s material was made of steel, the group of element 3 was the largest, at 2.057 mm², and the group of element 6 was the smallest, at 0.148 mm². When GLT was used, the group of element 5 was the largest, at 36.551 mm², and the group of element 3 was the smallest, at 3.946 mm². In addition, it was confirmed that steel and GLT satisfied the allowable stress and allowable displacement, and the structure’s weights were 5093.025 kg and 8036.328 kg, respectively, in these scenarios. Figure 14 shows a convergence graph of the 120-bar truss dome structure, and it can be seen that both steel and GLT converged to one value. Steel converged to a minimum carbon emission of 3575.892 kgCO₂e in 942 generations, and GLT converged to a minimum carbon emission of 2740.374 kgCO₂e in 890 generations.

Figure 15 shows the carbon emissions of steps A1–A4 according to the case. In steps A1 and A3, case 1 had the most significant emissions, with 3,481,466 kgCO₂e of carbon emitted, and cases 3 and 5 had the lowest carbon emissions with −3592.786 kgCO₂e. In step A2, cases 2 and 3 had the most significant emissions, with 637.427 kgCO₂e of carbon emitted, and case 1 had the lowest carbon emissions, with 32.876 kgCO₂e. In step A4, cases 2–5 had the lowest carbon emissions, at 49.926 kgCO₂e, and case 1 had the most significant carbon emissions, at 61.551 kgCO₂e. Considering the total carbon emissions of all steps (A1–A4), case 2 had the most significant carbon emissions, at 3575.892 kgCO₂e, and case 5 had the lowest carbon emissions, at −3441.176 kgCO₂e. When comparing cases 1, 3, and 5, it can be seen that the carbon emissions were lower when using GLT compared to steel. In addition, when comparing cases 2 and 4 or cases 3 and 5, it can be noted that the same material (GLT) was used, but the differences in carbon emissions could be significant depending on the transport distances of the materials and elements.

5. Conclusions

In this study, the optimal design of truss structures was performed using carbon emissions, considering the internal energy of the construction materials as an objective function. The carbon emissions of domestic and imported wood were compared with those of customary materials sourced from the Republic of Korea.

As a result, it was confirmed that the carbon emissions of steps A1 and A3 were the largest for all example structures when using customary materials (steel). In other words, the carbon emissions were more significant when using customary materials than when using timber, and in particular, the greater the weight of the structure, the greater the carbon emissions. However, since the travel distance was significant when timber was imported from Canada (case 2), absent consideration of its carbon storage, the carbon emissions may be larger than when using customary materials (case 1) or domestic wood (case 4). In addition, when the carbon storage capacity of the material is considered (cases 3 and 5), the carbon emission reduction can be maximized when using domestic timber. Therefore, to stabilize the abnormal climate around the world and reduce carbon emissions, the Republic of Korea should strive to build timber structures and encourage the use of domestic timber at the national level.

To reduce carbon emissions around the world, it is essential to evaluate carbon emissions in advance in the construction schematic-design stage. If optimal design is performed using carbon emissions, as performed in this study, in the schematic-design stage, it is expected to contribute significantly to reducing carbon emissions worldwide and reducing carbon in the construction field. For a more accurate evaluation in the future, it will be necessary to perform optimal design within which all steps of carbon emission evaluation are considered as an objective function.