#### 4.1. Basis for Calculating Material Amounts

This study calculated the amounts of concrete, reinforcement bars, and forms by using the following equations. In a 2D drawing-based manual quantity estimation method, calculation procedures can vary, causing differences in results. In this study, therefore, the following were referred to: Reinforced Concrete Structure Estimation Standards, Korea Building Code (KBC); Korea Structural Concrete Design Code; Korean Construction Standard Specification (2013); and Construction Work Quantity Estimation (2007) [

19,

20,

21,

22].

First, for the manual quantity estimation for walls, wall thickness is multiplied by wall area (area of openings not included) in the column-beam wall. In the column-less walls, wall thickness is multiplied by wall height (floor height minus baseplate height) and the same number of walls as shown in

Figure 2a.

At the form estimation, the column-wall combined parts are not subtracted. In addition, the openings (less than 1 m

^{2}) in the wall are not subtracted from the form area, considering the materials that are present. They are subtracted from the form only when they are 1 m

^{2} or greater. The wall quantity estimation formulas are shown in

Table 2.

Second, a column volume is calculated by multiplying a section area by column height and number of the columns with the same dimensions as shown in

Figure 2b. In the column height, however, the thickness between the upper-floor baseplate and target-floor baseplate is subtracted.

For the estimation of the quantity of slab-less columns, the section area is multiplied by the column height. The column quantity estimation formulas are stated in

Table 3.

Third, beam height is subtracted from the baseplate thickness and multiplied by beam width. Then, the results are multiplied by beam length. After that, they are multiplied by the number of beams with the same dimensions as shown in

Figure 2c. In this case, a large beam is set with inside distance among between the columns while a small beam is determined with inside length between the large beams. For the calculation of slab-less beams, the beam section area is multiplied by beam length without any subtraction. In addition, in the case of haunch parts, they are subtracted accordingly. The beam quantity estimation formulas are shown in

Table 4.

Fourth, for the estimation of slab quantity, floor thickness is multiplied by floor area. At the estimation of floor form with the area under the slab, it should be subtracted from the wall thickness if the lower-floor wall is masonry as shown in

Figure 2d. In the case of reinforced concrete walls, on the contrary, a total floor area is estimated without any subtraction. The slab quantity estimation formulas are shown in

Table 5.

The length of reinforcing bars is estimated by type and diameter. Then, the total length is multiplied by unit weight (kg/m) to get the total weight. Each floor is divided into wall, column, beam and slab to make sure that there is no redundancy in calculation. The total length of reinforcing bars is estimated after calculating the length of each piece and multiplying it by total quantity. In estimating the length of each piece of reinforcing bar, member length, joint length, dowel length and hook length should be considered as shown in

Table 6.

In principle, the quantity of reinforcing bars should be calculated after checking a drawing. If it is not possible to check the drawing, the quantity of reinforcing bars is estimated after dividing a scope of reinforcement placement by the placement interval. Then, a minor difference (one or two) can occur depending on the start point of reinforcement placement.

First, the quantity of wall reinforcing bars can be estimated by dividing them into line/point reinforcing bars or horizontal/vertical reinforcing bars. In vertical ones, dowel length is considered. In horizontal reinforcing bars, in contrast, joint length and number of joints are considered as shown in

Figure 3a. In terms of the estimation of the number of joints, member length is divided by the length of each reinforcing bar as shown in

Table 7.

Second, for the estimation of the quantity of column reinforcing bars, they are divided into main bars, hoop bars and diagonal hoop bars. The length of the main bar member is set with column height, and the number of joints occurs at every floor as shown in

Figure 3b. Furthermore, a hook is installed at column end only. The length of each main bar/diagonal hoop bar is set with the column circumference. Then, the number of main bars and diagonal hoop bars is estimated by dividing the column height by the reinforcement placement interval as shown in

Table 8.

Third, for the estimation of the quantity of beam reinforcing bars, they are divided into upper main bars, bent-up bars, lower main bars and stirrup bars. In case of beams, estimation standards for the top-floor and middle-floor beams differ. In terms of the length of reinforcing bars in top-floor beams, the lengths of upper main bars and bent-up bars are estimated with the outside length, while the length of lower main bars is calculated with the inside length. For the length of reinforcing bars for middle-floor beams, however, the lengths of upper main bars, bent-up bars and lower main bars are all estimated with inside length as shown in

Table 9.

Fourth, for the estimation of the quantity of slab reinforcing bars, they were divided into end and center and classified by type of placement. Then, the length and quantity are estimated. In this case, slab dimensions are estimated with beams and their inside dimensions. Unless beams are available, total dimensions are used.

After figuring out the range of each reinforcing bar’s placement after classifying the reinforcing bars by short and long sides up to one-fourth of inside length (l

_{x}) in a short-side direction, the quantity is estimated. Furthermore, upper and lower reinforcing bars are classified in short- and long-side directions. In this case, the upper bars are divided into bent-up and top bars as shown in

Table 10.

To evaluate the results of the quantity estimation performed by building type, they were modeled with a structural analysis programs in Korea called MIDAS [

23]. For this, there was structural analysis on the load combination set by Korea Building Code-Structural (KBCS), using architectural and structural drawings by building type. Additionally, for the reinforcement placement, MIDAS-GEN’s automatic reinforcement placement was used.

Figure 4 reveals the results of each plane type’s modeling.

The concrete, form and reinforcing bar quantities obtained through a 2D drawing-based manual quantity estimation method and a program-based automatic quantity estimation method were almost same.

In the drawing-based quantity estimation, however, the parts that overlapped in the factor design dimensions are subtracted. In a program-based automatic quantity estimation method, in contrast, the quantity is estimated based on the factor information which has been modeled under design dimensions. Therefore, factor-overlapped parts are not subtracted. In this case, there is no subtraction of vertical length in the wall-beam, wall-slab and column-slab combinations. To minimize differences in the results, therefore, there should be modeling which considers the subtraction of the overlapped parts in a height direction equivalent to the manual quantity estimation standards at the time of building modeling.

In case of beams, columns and slabs, a difference was found in hoop bars, diagonal hoop bars, stirrup bars and main bent-up bars. Therefore, an error in the hoop bar and stirrup bar results can be minimized by adding the cover thickness of columns and beams during quantity estimation after building modeling.

#### 4.2. Calculation and Variation Rates of Material Amounts in the Evaluation of Apartment Houses

In the use of concrete, vertical members such as core walls and columns were mostly divided in the vertical direction such as low, middle and high floors. Therefore, compressive strength is applied from high to low levels after zoning.

The classification of low floors is found in diverse forms depending on the building type. In general, however, it is about one-third of the total building floors. In this section, the compressive strength was revealed to be 24 MPa on average in walls and columns (vertical members). In general, concrete with a strength of 35 MPa is used for low floors.

In the case of high floors, the compressive strength of vertical members was 24 MPa on average. For middle floors, 35 MPa concrete is commonly used. In terms of horizontal members, 24 MPa concrete was mostly used for slabs. Recently, however, concrete with a strength of 30 MPa or stronger is used for slabs. Slab concrete appears to get stronger in connection with the vertical members [

24]. In this study, therefore, a building was divided into two zones: Low zone (20th floor or lower) and high zone (above 20th floor). Concrete with a strength of 35 MPa was applied to the low zone, while 24 MPa concrete was used for the high zone, which was applied equally according to building type.

The amounts of concrete, reinforcement bars, and forms of a 15-floor flat-type apartment house were established at reference value of 1, and the change rate in the amount of materials was analyzed according to the number of floors and building types.

Table 11 lists the calculated amount and variation rate of concrete according to the number of floors for each type, and

Figure 5 and

Figure 6 show the variation rate of the amount of concrete according to the number of floors and type of apartment house [

25,

26].

The rate of change in the calculated amount of concrete according to the number of floors was the most abrupt between the 20th and 25th floors at 0.48, which increased according to the number of floors.

For the tower Y type, the rate of increase was nearly constant at 0.3 for 20-floor or higher apartments.

For the tower L type, the most abrupt rate of change occurred in the lower floors between the 15th and 20th floors, at 0.51, but decreased to 0.11 in the higher floors at the 20th floor or above [

27,

28].

The comparison of the rate of change in the amount of concrete showed that the tower L type had the largest rate of change at the 20th floor, whereas the flat type had the largest rate of increase between the 25th and 30th floors.

Therefore, in terms of CO_{2} emissions and cost, flat-type apartments are superior at floors lower than the 20th, whereas tower L-type apartments are superior at floors higher than the 20th.

Table 12 lists the results of the calculated amounts and their rates of change for reinforcement bars according to the number of floors and type;

Figure 7 and

Figure 8 show rates of change for the amount of reinforcement bars according to the number of floors and type, respectively [

29,

30].

The rate of change in the calculated amount of reinforcement bars according to the number of floors was the highest between the 20th and 25th floors at 0.94; as for concrete, this value increased according to the number of floors. The tower Y type showed the largest increase in materials between the 20th and 25th floors, at 0.51.

For the tower L type, the most rapid rate of change occurred between the 15th and 20th floors, at 0.59, but this rate decreased to 0.13 at the 20th floor or above. Therefore, as for reinforced concrete, flat and tower Y types are superior at lower floors, whereas the tower L type is superior at higher floors in terms of CO

_{2} emission and cost [

31,

32].

The comparison of the rate of change in the amount of reinforcement bars by type showed that tower L type had the largest rate of change at the lower floors, whereas flat type showed the largest rate of increase between the 25th and 30th floors. In contrast, because tower Y type showed the largest increase between the 20th and 25th floors, it may be slightly disadvantageous to construct buildings of 20 floors or higher.

Table 13 lists the results of the calculated amounts of forms and their rates of change according to the number of floors and type;

Figure 9 and

Figure 10 show rates of change according to the number of floors and type.

The calculation results for the amount of forms according to the number of floors revealed that flat type experienced a relatively low rate of increase but the lowest rate of change at the 25th floor or higher. The tower Y type showed the largest increase in materials between the 20th and 25th floors, at 0.43.

Therefore, the tower Y type is inferior at higher than the 25th floor. The tower L type showed a relatively high rate of increase for all floors.

The comparison of the rate of change in the amount of forms showed that the tower L type had the largest rate of change at the 20th and 25th floors, whereas the tower Y type had the largest rate of increase at the 30th floor.