1. Introduction
The desired structural frame is selected and designed based on several factors, namely, the components and the type of connections in the frames, as well as considerations such as the construction site, the anticipated resistance, and the plasticity capacity required. In recent decades, the utilization of metaheuristic algorithms, which can interface with design software, has become increasingly prevalent. These algorithms not only facilitate the design of durable structures with high plasticity capacity but also aim to optimize factors such as cost and construction time. Moreover, the construction industry consumes numerous resources, with water being a vital one. However, one of the significant environmental issues associated with this industry is the carbon dioxide emissions resulting from the production of construction materials.
Population growth, particularly in developing countries, has resulted in a surge in demand for food, water, housing, and other natural resources. Given that construction projects predominantly rely on conventional methods, they face numerous sustainability challenges encompassing environmental, social, and economic aspects. This becomes particularly pronounced when resources are utilized inefficiently [
1]. Presently, the sources of drinking water are dwindling at an alarming rate. Globally, nearly two billion individuals lack safe access to fresh water. The scarcity of water resources is deemed a critical issue concerning both human development and environmental sustainability [
2].
The demand from the construction industry to extract minerals has led to significant environmental problems. Despite the existence of a significant amount of research on the environmental effects of construction, few studies have focused on the amount of water consumption in different stages of this industry. The concept of water footprint was introduced by Hoekstra in 2002. The water footprint is an index of freshwater use that not only pays attention to the direct consumption of water by consumers or producers but also to indirect water consumption [
3]. The contribution of the construction industry to the amount of freshwater consumption is significant. According to global reports, almost 19% of all water is withdrawn by the industrial sector, with the construction industry among the top consumers of water. Global water withdrawal from groundwater and surface water is projected to increase by 55% between 2000 and 2050, largely attributed to the rising demand for water from industry and thermal energy production. Despite being the second-largest consumer of water, the industrial sector’s water footprint assessment remains limited, particularly within the construction industry. Construction materials such as cement, concrete, and steel are produced annually in billions of tons worldwide, contributing to water consumption and pollution throughout the production chain [
4].
The water footprint in construction is 20% of the water used in the world, and by constructing environmentally friendly buildings, water consumption can be reduced by approximately 40% [
5]. In 2023, a study based on a two-stage multi-objective optimization approach using NSGA-III for optimal designs of structures with four-span reinforced concrete frames with different heights, focusing on minimizing the water footprint and design cost, was analyzed. The results demonstrated that the Pareto front shape of the optimal design in the studied reinforced concrete frames is more related to the water footprint values of the material unit than the costs [
6].
Recently, in the environmental review of materials and materials of reinforced concrete buildings, in parallel with optimizing the consumption of materials, reducing the cost of construction was also considered, and it was determined that paying more attention to environmental sustainability considerations in the preferential design of the structure, especially in the early stages of the design, is essential and can lead to a mitigation in the cost of construction and the construction of a sustainable structure in order to reduce harmful environmental effects [
7]. An equivalent greenhouse is used to produce the elements needed in the construction industry, including the extraction and processing of raw materials and the production of construction materials that lead to carbon production, and they deduced that the construction and operation of the building are important factors in production. Carbon dioxide emits a quarter of the world’s total carbon dioxide production [
8].
Kofoworola et al. [
9], in extensive research, concluded that about 4% of the world’s greenhouse gases are produced in the construction industry. Abergel et al. [
10] studied the relationship between buildings and the construction industry based on the annual reports published by the International Energy Agency and the World Alliance of Buildings and Construction, and in this research, it was shown that construction and construction operations account for 36% of the consumption. It accounts for the final global energy supply and 39% of energy-related carbon dioxide. Eleftheriadis et al. conducted research on the relationship between cost and carbon dioxide emissions in reinforced concrete structures using an optimization method based on building information modeling. They found that the most significant parameters influencing the amount of carbon dioxide emissions in concrete structures were the dimensions, thickness of structural elements, and their arrangement [
11].
Blismas et al. [
12] stated that in reinforced concrete buildings, the complete investigation of the construction costs of the structure and the resulting carbon production is one of the most essential items in construction management Paya-Zaforteza [
13], in her research on carbon dioxide emissions, stated that the reduction in carbon dioxide in building structures can be achieved not only by considering more sustainable materials, but also by using structural materials efficiently through optimization methods. In a study accomplished by Fankhauser et al. [
14], it was demonstrated that the embodied carbon, which encompasses carbon dioxide emissions related to the extraction, manufacturing, transportation, and installation of building materials, amounts to approximately 3.8 billion tons per year.
In the present study, the structure with the same plan, the height of the floors, and the same size of the apertures in three different structural frame systems have been scrutinized—the structural design has been made based on LRFD-AISC, and in this study, the structural weight, cost and construction time, water footprint, and carbon footprint for three different structural frame systems have been studied using a metaheuristic algorithm. In the past decades, in structural engineering, in order to increase the ductility capacity and seismic resistance, the weight of the structure was optimized as the only objective function using heuristic single objective (SOO) algorithms of the gray wolf optimization algorithm (GWO). In most of the preceding studies, the multi-objective optimization (MOO) algorithms of the gray wolf optimization algorithm (GWO) were extended. Other objective functions besides weight, such as cost in the direction of managing financial resources, or functions, including carbon dioxide and water emissions, for the evaluation and environmental sustainability of structures, were examined.
Most of the previous research was carried out on structures with one type of frame for several objective functions or on structures with different frames for only one objective function. One of the most important innovations of this article is the use of single-objective metaheuristic algorithms (SOO) to study the relationship of weight as an objective function with other objective functions, as well as to design and optimize multiple structural systems using multiple target optimization algorithms (MOO) with five target functions. It has finally ended with the introduction of an environmental structure with the least carbon footprint and water footprint.
In the present study, the structure with the same plan, floor height, and aperture size in three different structural frame systems has been investigated, and structural analysis and design have been performed using LRFD-AISC. In this study, structural weight, water consumption, and the production of carbon dioxide during the material production process, as well as the cost and construction time, have been studied based on a meta-exploration algorithm. One of the most notable innovations of this method is its capability for designing and optimizing multiple structural systems based on various objective functions. This culminated in the development of an environmentally friendly structure with the lowest carbon footprint and water footprint.
3. Properties of Study Structure
The structures studied in this research have three apertures with lengths of 5 m and consist of beam and block roofs with a height of each floor of 3.2 m and 4 floors. The characteristics of the studied structures are presented in
Table 1.
Moreover, the 3D view and the studied structural plan are shown in
Figure 5 and
Figure 6. In
Figure 6, the numbers and letters represent the axes of the beams of the structure in the X and Y directions, respectively.
According to the construction conditions, the beam and column cross-sections are defined as design variables based on the type of structure, as outlined in
Table 2. Similarly, the design variables for wind brace members in structures featuring braces are detailed in
Table 2 as well. This circumstance contributes to the fragmentation of the search space during the optimization of steel structures. Nevertheless, in certain scenarios, depending on the structure type, the utilization of any desired cross-section may be feasible. Consequently, in discrete problems, the size of the search space is dictated by the number of potential cross-sections available for each design variable.
Afterwards, a multi-objective search is adopted to evaluate the objective functions for each possible design combination. The objective functions are the weight of the structural frames, the cost and duration of construction, the amount of water consumed, and the carbon dioxide emitted during the material production process. Ultimately, non-dominated sorting is applied to detect the Pareto optimal partitions.
5. Materials Properties
According to the type of structural frames discussed in this research, the specifications of the steel materials used are presented in
Table 5.
In order to incorporate the volume price of steel into the objective functions, the prices of the profiles were computed based on data from October 2023. It is essential to classify structural members for design and optimization purposes. The predetermined lists of cross-sections provided in
Table 2 and
Table 3 were utilized for design optimization in structures. Following the design approach, the cross-sections of structural elements were designated as design variables. Structural members were assigned numbers according to a predetermined list. For example, the numbering of structural elements in frame 1 and in the X-Z direction for each of the structural systems is illustrated in
Figure 7,
Figure 8 and
Figure 9. In
Figure 7,
Figure 8 and
Figure 9, numbers on the letters correspond to frame No. 1 in the structure, and each of the letters represents frames perpendicular to frame No. 1.
Figure 7.
The number of bracing members in the intermediate steel moment-resisting frame with a special steel concentrically braced frame in frame 1 in the X–Z direction.
Figure 7.
The number of bracing members in the intermediate steel moment-resisting frame with a special steel concentrically braced frame in frame 1 in the X–Z direction.
Figure 8.
Number of members in the intermediate steel moment-resisting frame in frame 1 in the X–Z direction.
Figure 8.
Number of members in the intermediate steel moment-resisting frame in frame 1 in the X–Z direction.
Figure 9.
The number of members in the ordinary braced steel frames in frame 1 in the X–Z direction.
Figure 9.
The number of members in the ordinary braced steel frames in frame 1 in the X–Z direction.
According to the type of elements, classification was done, which can be seen in the following tables. By using this framework, it is ensured that the list of predetermined sections is optimized for all structural members.
The classification of the intermediate steel moment-resisting frame in
Table 6 is modeled in the form of 22 decision variables, which is the same area of the steel sections stated in
Table 1. The type of steel concentric bracing frame and intermediate steel moment-resisting frame with concentrically braced frame is different from the intermediate steel moment-resisting frame due to the presence of braces in the peripheral frames, and their type is shown in
Table 7.
Table 6.
Classification of Structural Members of an Intermediate Steel Moment-Resisting Frame.
Table 6.
Classification of Structural Members of an Intermediate Steel Moment-Resisting Frame.
Type of Number | Members of Number | Member Type | Floor |
---|
1 | 1–8 | Column | First and second |
2 | 9–16 | Column | Third and fourth |
3 | 17–32 | Column | First and second |
4 | 33–38 | Column | Third and fourth |
5 | 49–56 | Column | First and second |
6 | 57–64 | Column | Third and fourth |
7 | 65–70 | Beam | First |
8 | 71–76 | Beam |
9 | 77–82 | Beam |
10 | 83–88 | Beam |
11 | 89–94 | Beam | Second |
12 | 95–100 | Beam |
13 | 101–106 | Beam |
14 | 107–112 | Beam |
15 | 113–118 | Beam | Third |
16 | 119–124 | Beam |
17 | 125–130 | Beam |
18 | 131–136 | Beam |
19 | 137–142 | Beam | |
20 | 143–148 | Beam | Fourth |
21 | 149–154 | Beam |
22 | 155–160 | Beam | |
160 | Number of all members |
22 | Total number of decision variables (nVar) |
Table 7.
Classification of structural members of intermediate steel moment-resisting frames with special steel concentrically braced frames and simple steel frames with ordinary concentrically braced frames.
Table 7.
Classification of structural members of intermediate steel moment-resisting frames with special steel concentrically braced frames and simple steel frames with ordinary concentrically braced frames.
Type Number | Member Number | Member Type | Floor |
---|
1
| 1–8 | Column | First and second |
2
| 9–16 | Column | Third and fourth |
3
| 17–32 | Column | First and second |
4
| 33–48 | Column | Third and fourth |
5
| 49–56 | Column | First and second |
6
| 57–64 | Column | Third and fourth |
7
| 65–70
| Beam | First |
8
| 71–76 | Beam |
9
| 77–82 | Beam |
10
| 83–88 | Beam |
11
| 89–94 | Beam | Second |
12
| 95–100 | Beam |
13
| 101–106 | Beam |
14
| 107–112 | Beam |
15
| 113–118 | Beam | Third |
16
| 119–124 | Beam |
17
| 125–130 | Beam |
15
| 113–118 | Beam |
19
| 137–142 | Beam | Fourth |
20
| 143–148 | Beam |
21
| 149–154 | Beam |
22
| 155–160 | Beam |
23
| 161–168 | Brace | First |
24
| 169–176 | Brace | Second |
25
| 177–184 | Brace | Third |
26
| 185–192 | Brace | Fourth |
192
| Number of all members |
26
| Total number of decision variables (nVar) |
6. Objective Functions
In the design optimization of structural members, the objective functions are evaluated for the studied structures. As can be seen in
Figure 10, the objective functions studied are the weight of the structure, the carbon dioxide produced and the water consumed during the production of materials, and the cost and construction time for each of the structures with an intermediate steel moment-resisting frame with a special steel concentrically braced frame, an intermediate moment-resisting steel frame, and a simple steel frame with an ordinary concentric steel brace. The values and indicators in
Figure 10 have been chosen based on the parameters affecting the designed structures, considering the amount of air pollution as well as the level of environmental drought in Iran. These parameters have been proposed as variable functions in the algorithm. The details of
Figure 10 are described in the following sections.
6.1. Weight
In recent designs, optimizing structures for the lowest weight has become very important. One of the most important advantages of reducing the weight of the structure is the reduction in the seismic force on the structural frames. In this research, one of the target functions is the weight of the structural frames in the studied structural systems. It is also necessary to determine the weight of each of the structural frames due to the dependence of some other objective functions of the research on the weight of the structure. Equation (5) is used to calculate the weight of structural members in all studied steel frames, which is obtained from the results of this research.
In the above relationship, (), () and () represent the cross-sectional area of each member, the length of the structural member, and the specific weight of the steel, respectively.
6.2. Produced Carbon Dioxide
In the process of producing building materials, a significant amount of carbon dioxide is produced, the importance of which cannot be denied in any way. Therefore, the investigation and measurement of carbon dioxide resulting from the production of building materials in order to minimize it as an environmental pollutant is of high importance. In steel structures, the most important source of carbon dioxide production and emissions is associated with the steel production process. The amount of carbon dioxide produced is calculated using Equation (6), which is obtained from the results of this research.
In the above relation (
) represents the amount of carbon dioxide emission per ton of steel production, which is mentioned in
Table 6. Moreover,
is the weight of structural members obtained from Equation (5).
6.3. Time
Construction duration is essential in construction management, as time is an important concept in project progress. The execution time of steel structures can vary by changing the type of steel structure system. The function of time required for the construction of structures in steel frames is calculated according to Equation (7) [
26].
In the above relationship, C1 is a parameter dependent on the welding technology, which is usually assumed to be equal to 1. and are equal to the specific weight of steel and the profile volume of the steel structure, respectively. is a coefficient, determined based on the type and technology of welding, and it is assumed to be equal to 0.78890 because the type of welding in all studied structures is welding with a manual electrode and arc welding with a covered electrode. C3 is a coefficient related to cutting technology, and in this research, cutting technology, acetylene with normal speed, is considered. As a result, C3 is equal to 1.13880. Also, is a hardness coefficient that varies according to the type of welding, which is equal to 2.5 for columns and beams that are IPE pairs, as well as 2.5 for braces that are UPE pairs, and for beam connections, the column in the joint connection is considered equal to 4. It is considered equal to 2.5 in the connector connections. κ is the number of structural elements, weld dimension, weld length, sheet thickness, is the cutting length of the steel structural member. The value of n in the studied structures is considered equal to 0.25.
6.4. Cost
The construction cost of steel structures consists of two parts: the cost of materials and the cost of framing, which is itself a function of time and is determined from Equation (8) [
26].
According to the study (Jarmai, K.), in relation (8),
is a coefficient of the volume price of steel (
), which is determined based on the country and its level of development. The different values of this coefficient are shown in
Table 8. Also, the value adopted for the study site is considered equal to 0.75, and
is the volume price of steel. The parameter
is also calculated from Equation (7). The amount of salary related to Iran has been calculated and chosen on average based on the economic situation between developed countries and third-world countries.
6.5. Consuming Water
Due to limited water resources and solving the problems caused by water shortages, it is necessary to determine the level of involvement and consumption of each industry and activity. Construction activities, along with related industries, can be considered one of the biggest consumers of natural resources such as water. One of the goals of the research is to determine a structure that uses less water to produce its materials. Therefore, water consumption is another target function of this research. In order to calculate the amount of water consumption, it is enough to multiply the weight of steel in structural members according to Equation (5) by the amount of water consumption per ton of steel production
which is stated in
Table 6. Finally the calculation of the value of this objective function for the studied steel frames will be according to Equation (9).