1. Introduction

2. Preliminary Studies

3. Actual erection case analysis

3.1. Site condition review

The case project is conducted on four floors above the ground. The second to fourth floors are PC structures, the core is a reinforced concrete structure, and the roof is a steel frame structure. Thus, the bottom floors of the second through fourth floors of the PC structure are targeted. The site conditions must be analyzed to efficiently erect PC members. Figure 3 shows the 2nd-floor plan of the case site and an overview of the site conditions. When erecting PC members, the movement line of the mobile crane and PC member-carrying line are important. The northeast and southeast sides of the site are adjacent to other sites, and the northwest site and access road are +63.80 m and +56.03 m in elevation (EL), respectively, with a difference of 7.8 m. Therefore, entry into the site is impossible. Moreover, the main entrance can be positioned on the southernmost side on the southwest side of the site, ruling out the vehicle access limit section.

Figure 1. Site condition analysis.

Figure 1. Site condition analysis.

Additionally, the PC members of the site are analyzed to simulate their erection. In this study, PC columns and PC beams are targeted, whereas PC slabs are excluded. As a result of aggregation based on the member list of the case site, 1,004 columns and 1,284 beams are obtained. When the dimensions of PC columns and beams are analyzed, the PC columns are 0.8–1.7 m wide, 0.8–1.0 m high, 9.2 m long, and 5.9–15.6 m3 in volume, whereas the PC beams are 0.5–1.3 m wide, 1.0–2.6 m high, 11.0–23.0 m long, and 11.0–34.8 m3 in volume. If the unit weight of reinforced concrete is 2.4 ton/m3, then the weight is 14.2–37.4 t for the column and 26.4–83.6 t for the beam.

3.2. Crane path analysis of the case project

Erection was performed according to the plan of the actual site. Figure 4 shows the monthly processes. As shown in Figure 4(a), the PC column member on the east side is erected on the first day of construction. Subsequently, as shown in Figure 4(b) and (c), the PC members of the first and second floors are sequentially erected by prioritizing the construction of each floor. Three cranes erected PC columns on the first floor and some girders and slabs on the second floor. The core, which is an RC structure, was combined with PC columns and beams for joining. This implies that the core was constructed according to the erection plan for the PC columns and beams. As shown in Figure 4(d), cascade installation is applied, and it took 172 calendar days to erect all PC components (Lee et al., 2020). Figure 4(e) and (f) show the working conditions after eight and ten months, respectively. As shown in these Figs, the PC and RC core erection is completed on all floors, and the steel frame is erected and finished on the 4th floor. Thus, PC members were erected without any specific rules in the actual field. This is due to the fact that the PC members were procured by reflecting the production schedule available at the factory during PC member erection planning.

Figure 2. Actual erection process of case project: (a) D+1, (b) D+35, (c) D+70, (d) D+105, (e) D+140, (f) D+172.

Figure 2. Actual erection process of case project: (a) D+1, (b) D+35, (c) D+70, (d) D+105, (e) D+140, (f) D+172.

4. Algorithm for crane moving path calculation for sustainable erections of PC members

Figure 3. Algorithm for crane-moving path calculation.

Figure 3. Algorithm for crane-moving path calculation.

Figure 4. Crane location plan: (a) Crane path, (b) PC member position definition on the sample ⓐ.

Figure 4. Crane location plan: (a) Crane path, (b) PC member position definition on the sample ⓐ.

The crane rotation distance can be divided into horizontal (Figure 7a) and vertical (Figure 7b) rotation distances of the crane, and they are determined by calculating each distance and adding them. Hence, the horizontal rotation of the crane indicates movement from ⓐ to ⓑ in Figure 7a, and the vertical rotation of the crane indicates movement from ⓑ to ⓒ in Figure 7b. To calculate the horizontal rotation distance, the crane position coordinates are defined as (0,0,0), position coordinates of the column member as (xci, yci, zci), position coordinates of the trailer as (xt, yt, zt), and horizontal rotation distance as r(θi) as shown in Equation (1). The horizontal rotation angle of the boom is calculated using Equation (2) with relative coordinate values of the erected member whose origin corresponds to the position coordinate of the crane. Hence, the horizontal rotation angle can be calculated using the distance between the crane and erected member. The crane horizontal distance can be calculated using the distance from the crane to the trailer and the horizontal rotation angle of the boom as shown in Equation (3).

Figure 5. Calculation of the crane horizontal and vertical rotation distances (in the order of 1, 2, and 3): (a) Crane horizontal rotation distances, (b) Crane vertical rotation distances.

Figure 5. Calculation of the crane horizontal and vertical rotation distances (in the order of 1, 2, and 3): (a) Crane horizontal rotation distances, (b) Crane vertical rotation distances.

$${\mathrm{M}}_{\mathrm{c}\mathrm{i}}=\left[\begin{array}{c}{\mathrm{x}}_{\mathrm{c}\mathrm{i}}\\ {\mathrm{y}}_{\mathrm{c}\mathrm{i}}\\ {\mathrm{z}}_{\mathrm{c}\mathrm{i}}\end{array}\right],\mathrm{C}=\left[\begin{array}{c}0\\ 0\\ 0\end{array}\right],\mathrm{T}=\left[\begin{array}{c}{\mathrm{x}}_{\mathrm{t}}\\ {\mathrm{y}}_{\mathrm{t}}\\ {\mathrm{z}}_{\mathrm{t}}\end{array}\right],$$

(1)

$${\mathsf{\theta }}_{\mathrm{i}}=\mathsf{\pi }-\arctan \left(\frac{\left|{\mathrm{x}}_{\mathrm{i}}-0\right|}{\left|{\mathrm{y}}_{\mathrm{i}}-0\right|}\right),$$

(2)

$$\mathrm{r}\left({\mathsf{\theta }}_{\mathrm{i}}\right)={\mathrm{l}}_{\mathrm{t}\mathrm{r}\mathrm{a}\mathrm{i}\mathrm{l}\mathrm{e}\mathrm{r}}\times {\mathsf{\theta }}_{\mathrm{i}},$$

(3)

5. Simulation of crane moving path

5.1. Crane lifting range analysis

Before starting the PC member erection simulation based on the analyzed site design drawing and established erection schedule, it is necessary to accurately analyze the lifting range of the applied crane. The 550-t crawler crane adopted in this study is defined by the boom and jib, as shown in Figure 9(a), and the working radius is set as shown in Figure 9(b). The working radius of a 550-t crawler crane can be analyzed using this information. The boom starts at a horizontal length of 1.7 m. Given that the boom length is 36 m and maximum angle is 86°, a value of 2.51 m is derived by calculating the horizontal length at the maximum angle of the boom using Equation (14). Moreover, given that the jib length is 54 m and maximum angle is 71°, 17.58 m is derived when the horizontal length is calculated at the maximum angle of the jib using Equation (15). Hence, as the boom is located at a horizontal length of 1.7 m, and the horizontal lengths of the boom and jib are 2.51 m and 17.58 m, respectively, the horizontal length is 21.79 m when the maximum angle of the 36-m boom is reached as shown in Equation (16). Hence, the minimum operating distance of the crane is 21.79 m, and the crane can erect members located at 21.79 m or more.

Horizontal length of boom = 36 m × cos 86 = 2.51 m.

(14)

horizontal length of jib = 54 m × cos 71 = 17.58 m.

(15)

Total horizontal length = 1.7 + 2.51 + 17.58 = 21.79 m.

(16)

The boom starts at a horizontal length of 1.7 m. As the boom length is 36 m and the minimum angle is 65°, a length of 15.21 m is derived by calculating the horizontal length at the minimum angle of the boom, as shown in Equation (17). Moreover, given that the jib length is 54 m and minimum angle is 15°, a length of 52.16 m is derived by calculating the horizontal length at the minimum angle of the jib, as shown in Equation (18). Hence, as the boom is located at a horizontal length of 1.7 m and horizontal lengths of the boom and jib are 15.21 m and 52.16 m, respectively, the horizontal length is 69.07 m when the minimum angle of 36-m boom is reached as shown in Equation (19). Consequently, the maximum operation distance of the crane is 69.07 m, and the crane can erect members located at 69.07 m or less.

Horizontal length of boom = 36 m × cos 65= 15.21 m.

(17)

Horizontal length of jib = 54 m × cos 15= 52.16 m.

(18)

Total horizontal length = 1.7 + 15.21 + 52.16 = 69.07 m.

(19)

The liftable columns are analyzed based on the working radius of the crane, as illustrated in Figure 10. Thus, columns of 21.76 m or more and 69.07 m or less are derived based on the boom head of the crane. This confirms that the assumption regarding the definition of the column position is incorrect, as shown in Table 1, which is set at the beginning of the study. For example, the coordinates of C9 in Figure 6b and Table 1 are (11,0,10), which is a column located at a horizontal distance of 11 m. As this column is not located at 21.76 m or more and 69.07m or less, it cannot be erected with the crawler crane used in this study. The crane-moving process analyzed in Figure 8 is shown in Figure 9. First, a crane is installed 55 m from the members to be erected; second, the members are erected in a cascade manner. The members are installed via sequential movement of the crane by 11 m. Finally, the erection of the PC members is completed by positioning the crane at 22 m considering the crane lifting distance. In other words, the crane position coordinates (0,0,0) defined in equation (1) are newly redefined as the crane moves by 11m.

Figure 6. Liftable PC columns analysis.

Figure 6. Liftable PC columns analysis.

Figure 7. Crane-moving process for erection of PC members.

Figure 7. Crane-moving process for erection of PC members.

5.2. PC member erection sequence algorithm

An algorithm for the PC member erection sequence is developed to perform the simulations, as shown in Figure 10. This algorithm can be applied to all the PC columns and beam members. The erection of one member is defined as one simulation. This implies that the number of simulations increased with the number of members.

Figure 5. Sequence algorithm for member erection

Figure 5. Sequence algorithm for member erection

1) Calculating the distance from the crane to each member

The distance from the crane to each member was calculated using the defined position coordinates of the crane and member using the following equation:

$${\mathrm{D}}_{\mathrm{s}}=\sqrt{{({\mathrm{x}}_{\mathrm{i}}-\mathrm{C}(\mathrm{x}\left)\right)}^2+{({\mathrm{y}}_{\mathrm{i}}-\mathrm{C}(\mathrm{y}\left)\right)}^2+{({\mathrm{z}}_{\mathrm{i}}-\mathrm{C}(\mathrm{z}\left)\right)}^2}$$

(20)

${\mathrm{D}}_{\mathrm{s}}$	= total linear distance from the crane to the erected member
$\mathrm{x}\mathrm{i}$	= $\mathrm{x}$ coordinate of the erected member
$\mathrm{y}\mathrm{i}$	= $\mathrm{y}$ coordinate of the erected member
$\mathrm{z}\mathrm{i}$	= $\mathrm{z}$ coordinate of the erected member
$\mathrm{C}\left(\mathrm{x}\right)$	= $\mathrm{x}$ coordinate of the crane
$\mathrm{C}\left(\mathrm{y}\right)$	= $\mathrm{y}$ coordinate of the crane
$\mathrm{C}\left(\mathrm{z}\right)$	= $\mathrm{z}$ coordinate of the crane
$\mathrm{i}$	= number of ith erected members at the crane position (1, …, n)

2) Selection of the farthest member

To reduce interference with the erected members during the erection of PC members, PC members are erected in descending order of the linear distance from the crane to the member. Consequently, the member with the largest distance is selected from among the currently erected members.

3) Are there members with greater distances?

The erection simulation is performed if the selected member has the largest distance from the crane to the member among the non-erected members. However, if there is a member whose distance from the crane to the member is greater than that of the selected member, then the member should be selected.

4) Simulation of the ith member

Erection simulations are performed using the selected members. If there are members at the same distance, then they must be erected in descending order of angle from the trailer to the member. This is to reduce the interference of the members to be erected with already erected members. If Equations (20) and (21) are in conflict with each other, Equation (21) is prioritized. A simulation is performed for the total number of members and then sequentially according to the distance. When all the members are erected, the member installation sequence algorithm is completed.

$${\mathrm{M}\mathrm{i}\mathrm{n}\mathrm{i}\mathrm{m}\mathrm{i}\mathrm{z}\mathrm{e}{\mathrm{f}}_{\left(\mathsf{\theta }\right)}=\mathsf{\theta }}_{\mathrm{i}}=\arctan \left(\frac{\left|{\mathrm{x}}_{\mathrm{t}}\right.-\left.{\mathrm{x}}_{\mathrm{i}}\right|}{\left|{\mathrm{y}}_{\mathrm{t}}\right.-\left.{\mathrm{y}}_{\mathrm{i}}\right|}\right).$$

(21)

5.3. Simulation results

Before starting the simulation, the position of the trailer is selected as (0, −33, 92). By reflecting the position of the trailer, the head of the boom is positioned 33 m from the crane, and the lifting of the PC members begins at this position. This position is calculated as 92 m in height due to the 97.74-m length of the boom. The trajectory distance of each column member can be calculated using Equations (1)–(11) based on the coordinate values (see Table 1) of PC member position definition on sample ⓐ in Figure 6(b) as follows. The horizontal rotation angle is calculated using Equations (1) and (2), and the horizontal rotation distance is calculated using Equation (3). Moreover, the vertical rotation angle is calculated using Equations (4)–(9), and the vertical rotation distance is calculated using Equation (10). Finally, the total trajectory distance of the boom can be calculated using Eq. (11). For example, the horizontal rotation angle of C1 among the column members is 153°, and the horizontal trajectory distance at this angle is 88 m. The vertical rotation angle of this member is 0.09°, and the vertical trajectory distance is 9 m. Hence, the total trajectory distance is 97 m. However, according to the liftable PC column analysis results in Figure 8, only columns at 21.76 m or more and 69.07 m or less can be lifted. Hence, not all values derived from Table 2 can be applied. Therefore, only C3, C4, C7, C8, C11, and C12 can be lifted at the crane position.

Based on the aforementioned analysis results, Figure 11, Figure 12 and Figure 13 show the calculation of the trajectory distance of the column members for the crane path from the first to the third floor. The trajectory distance of each member complies with the rules of the crane-moving process for PC member erection shown in Figure 9, and the total trajectory distance is determined as 183,575 m. The location with the farthest linear distance from the crane is expected to show the largest trajectory distance. However, it is observed that the trajectory distance is not large even if the linear distance from the crane is large. The location with the largest trajectory distance corresponds to that with the largest horizontal movement, where it shows the same x-coordinate as the trailer. Furthermore, the trajectory distance is not the smallest when the linear distance is the smallest. Among the members that can be lifted by the crane, the member at the position, where the horizontal movement is smallest, shows the smallest value. The trajectory distance can be easily calculated because it shows a consistent pattern based on the crane movement. This is due to the fact that the members are positioned at distances of 11 or 18 m due to the characteristics of large logistic buildings.

Figure 9. Trajectory distance on the first floor.

Figure 9. Trajectory distance on the first floor.

The crane is removed by sequentially erecting its members. However, as the last members of the second and third floors are not required to be erected in a cascade manner, as shown in Figure 11 and Figure 12, they can be simultaneously erected without moving the crane. However, additional Y-column members must be installed on the opposite side of Zone B. Thus, their erection must be completed by moving them. Moreover, given that the third floor is the last floor of the PC structure, PC members can be erected without considering the connection with other floors as shown in Figure 12.

Figure 6. Trajectory distance on the second floor.

Figure 6. Trajectory distance on the second floor.

Figure 11. Trajectory distance on the third floor.

Figure 11. Trajectory distance on the third floor.

The average unit erection time for each PC member at the case site is 40 min, 15 min, and 10 min for columns, beams, and slabs, respectively. The number of members is 850, 1,371, and 4,032, respectively. Furthermore, the actual erection time is 210 calendar days, and the rotation distance of the crane is 20 m/min. After excluding the time required to fix the position of the members, the actual and simulated times required for PC member erection are 172 and 158 days, respectively. Thus, a 13.99% reduction in the construction period is possible.

With respect to cost comparison, labor, material, and equipment costs are summed [58] using Equations (22) and (23). Labor, material, and equipment costs are calculated using Equations (24)–(26). The actual cost of PC member erection in Table 2 denotes the results of the calculation using the actual input quantity. The simulation-calculated cost in Table 3 shows the results of the calculation reflecting the actual cost. With respect to the unit price of the labor cost, the amount from the “Construction Industry Wage Survey Report (Market Wage Unit Price) applied to the first half of 2022” is applied. Material and equipment costs are calculated based on the unit price applied in the field. Hence, the actual cost is $6,221,704, and the simulation-calculated cost is $5,710,335. Therefore, when applying the model developed in this study, the cost can be reduced by 8.33% when compared to the actual construction cost. In terms of equipment cost, the actual and simulation-calculated costs accounted for 89% and 90%, respectively, showing the highest proportions of construction costs. This implies that the daily rent for the crane accounted for the highest percentage. Therefore, to reduce construction costs, the minimum rental dates should be applied by deriving accurate dates when the crane is used before starting construction.

$${\mathrm{C}}_{\mathrm{t}}={\mathrm{C}}_{\mathrm{d}}+{\mathrm{C}}_{\mathrm{i}},$$

(22)

$${\mathrm{C}}_{\mathrm{d}}={\mathrm{C}}_{\mathrm{l}}+{\mathrm{C}}_{\mathrm{m}}+{\mathrm{C}}_{\mathrm{e}},$$

(23)

${\mathrm{C}}_{\mathrm{t}}$	= Total cost of the boom trajectory
${\mathrm{C}}_{\mathrm{d}}$	= Direct cost of the boom trajectory
${\mathrm{C}}_{\mathrm{i}}$	= Indirect cost of the boom trajectory
${\mathrm{C}}_{\mathrm{l}}$	= Labor cost of the boom trajectory
${\mathrm{C}}_{\mathrm{m}}$	= Material cost of the boom trajectory
${\mathrm{C}}_{\mathrm{e}}$	= Equipment cost of the boom trajectory

Table 3. Actual cost for erection of PC members

Table 3. Actual cost for erection of PC members

Item		Unit	Quantity	Unit price ($)	Amount ($)
Labor cost	Equipment operator	Day	172	229	39,388
	Common labor	Day	516	154	79,464
Material cost	Diesel	L	12,900	1.83	25,437
Equipment fee	Crane (550 ton)	Day	430	13,000	5,590,000
Indirect cost					487,15
Total					6,221,704

Table 4. Simulation-calculated cost the erection of PC members

Table 4. Simulation-calculated cost the erection of PC members

Item		Unit	Quantity	Unit price ($)	Amount ($)
Labor cost	Equipment operator	Day	158	229	36,182
	Common labor	Day	474	154	72,996
Material cost	Diesel	L	10,275	1.83	18,803
Equipment fee	Crane (550 ton)	Day	395	13,000	5,135,000
Indirect cost					447,353
Total					5,710,335

$${\mathrm{C}}_{\mathrm{l}}={\sum }_{\mathrm{i}=1}^{\mathrm{n}}({\mathrm{Q}}_{\mathrm{c}\mathrm{i}}\times {\mathrm{C}}_{\mathrm{c}\mathrm{u}\mathrm{l}})+{\sum }_{\mathrm{j}=1}^{\mathrm{m}}({\mathrm{Q}}_{\mathrm{b}\mathrm{i}}\times {\mathrm{C}}_{\mathrm{b}\mathrm{u}\mathrm{l}})+{\sum }_{\mathrm{k}=1}^{\mathrm{l}}({\mathrm{Q}}_{\mathrm{s}\mathrm{i}}\times {\mathrm{C}}_{\mathrm{s}\mathrm{u}\mathrm{l}}).$$

(24)

$${\mathrm{C}}_{\mathrm{m}}={\sum }_{\mathrm{i}=1}^{\mathrm{n}}({\mathrm{Q}}_{\mathrm{c}\mathrm{i}}\times {\mathrm{C}}_{\mathrm{c}\mathrm{u}\mathrm{m}})+{\sum }_{\mathrm{i}=1}^{\mathrm{m}}({\mathrm{Q}}_{\mathrm{b}\mathrm{i}}\times {\mathrm{C}}_{\mathrm{b}\mathrm{u}\mathrm{m}})+{\sum }_{\mathrm{i}=1}^{\mathrm{l}}({\mathrm{Q}}_{\mathrm{s}\mathrm{i}}\times {\mathrm{C}}_{\mathrm{s}\mathrm{u}\mathrm{m}}).$$

(25)

$${\mathrm{C}}_{\mathrm{e}}={\sum }_{\mathrm{i}=1}^{\mathrm{n}}({\mathrm{Q}}_{\mathrm{c}\mathrm{i}}\times {\mathrm{C}}_{\mathrm{c}\mathrm{u}\mathrm{e}})+{\sum }_{\mathrm{j}=1}^{\mathrm{m}}({\mathrm{Q}}_{\mathrm{b}\mathrm{i}}\times {\mathrm{C}}_{\mathrm{b}\mathrm{u}\mathrm{e}})+{\sum }_{\mathrm{k}=1}^{\mathrm{l}}({\mathrm{Q}}_{\mathrm{s}\mathrm{i}}\times {\mathrm{C}}_{\mathrm{s}\mathrm{u}\mathrm{e}}).$$

(26)

${\mathrm{C}}_{\mathrm{l}}$	= labor cost of the boom trajectory
${\mathrm{C}}_{\mathrm{m}}$	= material cost of the boom trajectory
${\mathrm{C}}_{\mathrm{e}}$	= equipment cost of the boom trajectory
${\mathrm{Q}}_{\mathrm{c}\mathrm{i}}$	= quantity of the ith columns
${\mathrm{C}}_{\mathrm{c}\mathrm{u}\mathrm{l}}$	= unit labor cost for column erection
${\mathrm{Q}}_{\mathrm{b}\mathrm{i}}$	= number of ith beams
${\mathrm{C}}_{\mathrm{b}\mathrm{u}\mathrm{l}}$	= unit labor cost for beam erection
${\mathrm{Q}}_{\mathrm{s}\mathrm{i}}$	= number of ith slabs
${\mathrm{C}}_{\mathrm{s}\mathrm{u}\mathrm{l}}$	= unit labor cost for slab erection
${\mathrm{C}}_{\mathrm{c}\mathrm{u}\mathrm{m}}$	= unit material cost for column erection
${\mathrm{C}}_{\mathrm{b}\mathrm{u}\mathrm{m}}$	= unit material cost for beam erection
${\mathrm{C}}_{\mathrm{s}\mathrm{u}\mathrm{m}}$	= unit material cost for slab erection
${\mathrm{C}}_{\mathrm{c}\mathrm{u}\mathrm{e}}$	= unit equipment cost for column erection
${\mathrm{C}}_{\mathrm{b}\mathrm{u}\mathrm{e}}$	= unit equipment cost for beam erection
${\mathrm{C}}_{\mathrm{s}\mathrm{u}\mathrm{e}}$	= unit equipment cost for slab erection
$\mathrm{i}$	= number of erected ith columns (1, …, n)
j	= number of erected ith beam members (1, …, m)
$\mathrm{k}$	= number of erected ith slab members (1, …, l)

CO₂ emissions are calculated, as shown in Table 5, using the labor, material, and equipment costs and the indirect cost calculated in Table 3 and Table 4. The CO₂ emissions corresponding to the direct cost are calculated using actual input labor, oil, and electricity use. Furthermore, the CO₂ emissions corresponding to indirect costs are calculated using actual input lighting, heating use, and environmental conservation. Consequently, when the model developed in this study is applied, 25.99% of CO₂ emissions can be reduced when compared to actual construction. Equations (27)–(30) show that the total CO₂ emissions can be derived by multiplying the number of PC members by the unit CO₂ emission of each item. In terms of oil use, the actual and simulation-calculated plans accounted for 99% and 98%, respectively, indicating high CO₂ emissions.

$${\mathrm{C}\mathrm{E}}_{\mathrm{t}}={\mathrm{C}\mathrm{E}}_{\mathrm{c}}+{\mathrm{C}\mathrm{E}}_{\mathrm{b}}+{\mathrm{C}\mathrm{E}}_{\mathrm{s}}.$$

(27)

$${\mathrm{C}\mathrm{E}}_{\mathrm{c}}={\sum }_{\mathrm{i}=1}^{\mathrm{n}}\left[{\mathrm{Q}}_{\mathrm{c}\mathrm{i}}\times \left({\mathrm{C}\mathrm{E}}_{\mathrm{u}\mathrm{l}}+{\mathrm{C}\mathrm{E}}_{\mathrm{u}\mathrm{o}}+{\mathrm{C}\mathrm{E}}_{\mathrm{u}\mathrm{e}\mathrm{l}}+{\mathrm{C}\mathrm{E}}_{\mathrm{u}\mathrm{l}\mathrm{h}}+{\mathrm{C}\mathrm{E}}_{\mathrm{u}\mathrm{e}\mathrm{c}}\right)\right].$$

(28)

$${\mathrm{C}\mathrm{E}}_{\mathrm{b}}={\sum }_{\mathrm{i}=1}^{\mathrm{m}}\left[{\mathrm{Q}}_{\mathrm{b}\mathrm{i}}\times \left({\mathrm{C}\mathrm{E}}_{\mathrm{u}\mathrm{l}}+{\mathrm{C}\mathrm{E}}_{\mathrm{u}\mathrm{o}}+{\mathrm{C}\mathrm{E}}_{\mathrm{u}\mathrm{e}\mathrm{l}}+{\mathrm{C}\mathrm{E}}_{\mathrm{u}\mathrm{l}\mathrm{h}}+{\mathrm{C}\mathrm{E}}_{\mathrm{u}\mathrm{e}\mathrm{c}}\right)\right].$$

(29)

$${\mathrm{C}\mathrm{E}}_{\mathrm{s}}={\sum }_{\mathrm{i}=1}^{\mathrm{l}}\left[{\mathrm{Q}}_{\mathrm{s}\mathrm{i}}\times \left({\mathrm{C}\mathrm{E}}_{\mathrm{u}\mathrm{l}}+{\mathrm{C}\mathrm{E}}_{\mathrm{u}\mathrm{o}}+{\mathrm{C}\mathrm{E}}_{\mathrm{u}\mathrm{e}\mathrm{l}}+{\mathrm{C}\mathrm{E}}_{\mathrm{u}\mathrm{l}\mathrm{h}}+{\mathrm{C}\mathrm{E}}_{\mathrm{u}\mathrm{e}\mathrm{c}}\right)\right].$$

(30)

${\mathrm{C}\mathrm{E}}_{\mathrm{t}}$	= total CO2 emission
${\mathrm{C}\mathrm{E}}_{\mathrm{c}}$	= CO2 emission of column
${\mathrm{C}\mathrm{E}}_{\mathrm{b}}$	= CO2 emission of beam
${\mathrm{C}\mathrm{E}}_{\mathrm{s}}$	= CO2 emission of slab
${\mathrm{Q}}_{\mathrm{c}\mathrm{i}}$	= number of ith columns
${\mathrm{C}\mathrm{E}}_{\mathrm{u}\mathrm{l}}$	= unit CO2 emission of labor
${\mathrm{C}\mathrm{E}}_{\mathrm{u}\mathrm{o}}$	= unit CO2 emission of oil
${\mathrm{C}\mathrm{E}}_{\mathrm{u}\mathrm{e}\mathrm{l}}$	= unit CO2 emission of electricity
${\mathrm{C}\mathrm{E}}_{\mathrm{u}\mathrm{l}\mathrm{h}}$	= unit CO2 emission of lighting and heating
${\mathrm{C}\mathrm{E}}_{\mathrm{u}\mathrm{e}\mathrm{c}}$	= unit CO2 emission of environmental conservation
${\mathrm{Q}}_{\mathrm{b}\mathrm{i}}$	= number of ith beams
${\mathrm{Q}}_{\mathrm{s}\mathrm{i}}$	= number of ith slabs
$\mathrm{i}$	= number of erected ith columns (1, …, n)
$\mathrm{J}$	= number of erected ith beams (1, …, m)
$\mathrm{k}$	= number of erected ith slabs (1, …, l)

Energy consumption is calculated, as shown in Table 6, using the oil and electricity consumption presented in Table 3 and Table 4. The electrical energy consumption is calculated using Equation (31), and the actual diesel input is converted into the SI base unit for energy. For the capacity of the 550-t crane, 397 kW is applied, and for the energy conversion value of diesel, 41,090/m3 is applied. Hence, the simulation calculated for member erection can reduce energy consumption by 26.01 %. In terms of oil use, the actual and simulated plans accounted for more than 99%, indicating high energy consumption.

$$\mathrm{E}=1000\times \mathrm{P}\times \mathrm{t}$$

(31)

$\mathrm{E}$	= energy consumption
P	= power (kW)
t	= time (s)

The simulation-calculated plan shows a reduction effect in terms of construction time, cost, CO₂ emissions, and energy use when compared with the actual plan. These ratios are not the same because the constituent items and composition ratios differ. Furthermore, CO₂ emissions and energy consumption are reduced by 25.99% and 26.01%, respectively, indicating high reduction rates. Therefore, minimization of the crane usage rate at a site has a considerable effect in preventing environmental pollution.

6. Conclusions

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