#
Cost and CO_{2} Emission Optimization of Steel Reinforced Concrete Columns in High-Rise Buildings

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## Abstract

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_{2}emissions. Most efforts are focused on improving the energy efficiency related to the operation of a building. The relative importance of the energy and CO

_{2}emissions from the construction materials increases with the increasing number of low-energy buildings. To minimize the life-cycle energy use of a building, the energy consumed from both materials in the construction phase as well as the energy consumed from the operation of the building must be reduced. In this study, an optimal design method for composite columns in high-rise buildings using a genetic algorithm is proposed to reduce cost and CO

_{2}emissions from the structural materials in the construction phase. The proposed optimal method minimizes the total cost, including the additional cost calculated based on CO

_{2}emissions from composite columns, while satisfying the structural design criteria and constructability conditions. The proposed optimal method is applied to an actual 35-story building, and the effective use of structural materials for the sustainable design of composite columns is investigated. It is shown that using more concrete than steel section and using high-strength materials are economically and environmentally effective methods.

## 1. Introduction

_{2}emissions due to the energy consumed by buildings account for approximately 24% of all CO

_{2}emissions [1], and in the United States, approximately 54% of that energy consumption is directly or indirectly linked to buildings and their construction. Commercial and office buildings account for a large portion of this figure [2]. Accordingly, in the construction industry, various studies to reduce CO

_{2}emissions have been actively conducted since the 2000s. These studies have included the development of the Life-Cycle Assessment (LCA) model [3], the development of environmentally friendly facilities and materials [4,5,6], and green building design [7]. Most of these studies have focused on the CO

_{2}emissions generated during building operation because the largest amount of CO

_{2}is generated in the operation stage [8].

_{2}emissions should be reduced in all stages where reduction is possible, regardless of the amount of emissions [9]. Furthermore, the need to consider the embodied energy of building materials increases with the increasing number of low-energy buildings [10,11,12]. To enable environmentally friendly construction, buildings should be designed to reduce their CO

_{2}emissions from the earliest design stages. CO

_{2}emissions can be reduced in the early stages by using novel building materials, such as low-carbon materials, and by recycling [6,8,13,14,15]. Additionally, CO

_{2}emissions can be reduced by reflecting the unit CO

_{2}emission of each structural material in the design stage [16,17,18,19,20].

_{2}emissions for reinforced concrete (RC) and composite structures, composed of different materials (steel and concrete), can vary depending on the ratio of each material though the total weights are same. This is because the unit price and CO

_{2}emissions for two structural materials are different, respectively. Thus, to reduce the CO

_{2}emissions of RC or composite buildings, it is necessary to establish correlations between different materials and minimize the total amount of CO

_{2}emissions from all materials. Yeo and Gabbai [17] suggested an optimal design method to reduce either the embodied energy or structural cost of a RC beam, and they investigated the contributions of concrete and steel reinforcements to the embodied energy and cost for a given loading condition. Yeo and Potra [18] suggested an optimal design method to reduce either the CO

_{2}emissions or structural cost of a RC moment frame. It was found that the optimization with respect to the CO

_{2}emissions resulted in an increase in the relative amount of steel within the RC members. Paya-Zaforteza et al. [19] proposed an optimal design method to reduce either the CO

_{2}emissions or structural cost of RC frame structures by using a simulated annealing (SA) method, and they confirmed that a more efficient structural design can be produced by using the various material strengths for both steel reinforcement and concrete. Paya et al. [20] suggested a multi-objective design methodology with the four objective functions for RC-frame structure design: structural cost, environmental impact, constructability, and overall safety.

_{2}emissions, there are limitations that should be overcome before the methods are applied to composite columns in actual buildings because most of the studies were performed with RC structures. The optimization methods for composite members are required because the mechanical mechanism and structural design criteria of composite members are different from those of RC members.

_{2}emissions should also be considered and minimized during the structural design phase of a building [17]. According to the Kyoto Protocol, CO

_{2}emissions can be transformed to cost. In fact, the certified emissions reductions (CERs) that comprise the carbon credits issued by the Clean Development Mechanism (CDM) Executive Board for emission reductions can be traded in emission trade markets, such as the European Union Emissions Trading Scheme [22]. Therefore, the additional costs from CO

_{2}emissions must be considered when evaluating the cost of building design and producing a cost-effective building during the structural design phase. However, existing studies [16,17,18,19,20] have not considered such costs including the additional cost from CO

_{2}emissions.

_{2}emissions and cost of a structural design is presented. To consider the CO

_{2}emissions and cost simultaneously, the total amount of CO

_{2}emissions is converted to cost using the concept of CERs. Then, the proposed optimization method minimizes the total cost, including the additional cost generated from CO

_{2}emissions, while satisfying the stress constraint and constructability constraints. The cross-sections of members are used as the design variables in the proposed optimal design method. The proposed optimal design method employs a genetic algorithm (GA) as an optimization tool and considers the unit prices and CO

_{2}emissions for the various strengths of concretes and steel sections. To reduce the computation time and improve the searching capability of optimal solutions, the constraint conditions on the constructability are considered as the side-constraint conditions. Thus, the candidate designs generated in the optimization process are automatically modified to satisfy the constraint conditions on the constructability. The proposed optimization method can be applied to the structural design of composite columns in a building frame structural system. In the proposed optimization method, the constraint on the lateral drift is not considered because the structural design of columns in the building frame system is determined based on the assumption that the columns support only the gravity load. And the assumption that the internal forces of column members are constant is employed to simplify the optimization process. At the final step in the proposed optimization process, the structural design check for the optimum design obtained from the simplified optimization process is performed to overcome the limit of optimization process due to the simplification. The condition on the lateral drift is checked at this final step. The optimal design method is applied to the structural design of composite columns in an actual 35-story building. The effects on the relative weight ratios of concretes and steel sections in the composite columns are investigated in terms of the environmental friendliness and economic feasibility of the structure.

## 2. Steel Reinforced Concrete (SRC) Columns in a Building Frame System

## 3. Optimization Methodology

#### 3.1. Formulation of the Optimization Problem

_{2}emissions of SRC columns. To consider the structural cost and CO

_{2}emissions simultaneously, CO

_{2}emissions are converted to cost by using the unit carbon price, and then the total cost including the additional cost from CO

_{2}emissions is minimized. The structural cost and CO

_{2}emissions are calculated based on the cross sectional properties of each member, as shown in Equation (1) [17,24]. The costs and CO

_{2}emissions generated from concrete and steel section at each member are calculated based on the volumes of concrete and steel section used at each member. The total costs and CO

_{2}emissions generated from concrete and steel section at the column line are the sum of costs and CO

_{2}emissions generated from concrete and steel section at all member. The factors influencing on the costs and CO

_{2}emissions generated from concrete and steel section at each member are the unit price and CO

_{2}emissions of structural materials, the cross-sectional areas of concrete and steel section:

_{1}and f

_{2}are the structural cost and the CO

_{2}emissions for each column line, respectively; A and L are the cross-sectional area and length of each member, respectively; C and E are the cost and CO

_{2}emissions per unit volume, respectively; M is the number of members; the subscripts stl and con represent steel section and concrete, respectively; CP is the carbon unit price, which was assumed to be 13.97 USD/ton-CO

_{2}; and the concrete cross-sectional area A

_{con}of the SRC column is the area obtained by subtracting the areas of the steel section and steel reinforcements from the gross area of the member. In the proposed optimization process, only the depth and width of the cross section of the member, the cross-sectional properties of the steel section, and the strengths of the concrete and steel section are allowed to vary. The costs and CO

_{2}emissions of steel reinforcement are excluded in the proposed optimization process.

_{allow}and σ

_{actual}are the allowable and actual stresses of each SRC column member, respectively; A

_{g}is the gross cross-sectional area for each member; S

_{stl}is the inner dimensions of the steel section; and F

_{y}is the yield strength of the steel section. The superscripts i and i + 1 represent two neighboring floors. Equation (2) represents the stress constraint, which must not exceed 1.0 [25]. Equation (2) is evaluated by using Equation (6) according to the reference [25]. The interaction of axial force and bending moments is considered:

_{m}is the coefficient applied to bending term in interaction formula.

#### 3.2. Proposed Optimization Technique

^{3584}. The design alternative must satisfy the stress and constructability constraints. Furthermore, because the cross-sectional properties of steel sections are discrete, the structural optimization must be formulated using discrete design variables. Therefore, a heuristic technique that does not require a differential is appropriate when the search of such a space of solutions and characteristics of design variables are considered. In this study, the GA is employed.

_{w}) and flange (t

_{f}) are less than 40 mm; the yield strength is 295 MPa when the t

_{w}and t

_{f}are thicker than 40 mm. The yield strengths of SM490 TMCP, SM520 TMCP, and SM570 TMCP are 325, 355 and 440 MPa, respectively, regardless of thickness. The concrete covers are set to be within a range of 150–230 mm.

_{2}emissions of the steel section and concrete must be determined. However, the CO

_{2}emissions per unit differ for each country, so each country’s index must be used for accurate evaluation [34]. The CO

_{2}emissions per unit listed in Table 1 and Table 2 are based on an input-output analysis from the Korea LCI Database Information Network [35,36].

No. | Member size | Type of steel section | Cost (USD/m) | CO_{2} (kg-CO_{2}/m) | |||||
---|---|---|---|---|---|---|---|---|---|

D (mm) | B (mm) | d (mm) | b_{f} (mm) | t_{w} (mm) | t_{f} (mm) | ||||

1 | 450 | 450 | 200 | 200 | 8 | 12 | SM490 rolled | 33.02 | 251.15 |

… | … | … | … | … | … | … | … | … | … |

23 | 700 | 700 | 428 | 407 | 20 | 35 | SM490 rolled | 191.42 | 1456.02 |

24 | 600 | 600 | 300 | 300 | 10 | 15 | SM490 built-up | 76.78 | 583.99 |

… | … | … | … | … | … | … | … | … | … |

40 | 650 | 650 | 350 | 350 | 30 | 30 | SM490 built-up | 196.79 | 1496.82 |

… | … | … | … | … | … | … | … | … | … |

54 | 800 | 800 | 440 | 400 | 35 | 35 | SM490 built-up | 271.33 | 2063.80 |

55 | 800 | 800 | 450 | 400 | 20 | 40 | SM490 TMCP | 268.95 | 2045.71 |

… | … | … | … | … | … | … | … | … | … |

110 | 900 | 900 | 530 | 400 | 70 | 80 | SM490 TMCP | 621.91 | 4,730.36 |

… | … | … | … | … | … | … | … | … | … |

186 | 1100 | 1100 | 730 | 600 | 80 | 80 | SM490 TMCP | 979.55 | 7450.72 |

187 | 600 | 600 | 300 | 300 | 10 | 15 | SM520 TMCP | 79.46 | 604.37 |

… | … | … | … | … | … | … | … | … | … |

280 | 950 | 950 | 590 | 500 | 50 | 60 | SM520 TMCP | 581.10 | 4,419.98 |

… | … | … | … | … | … | … | … | … | … |

349 | 1100 | 1100 | 730 | 600 | 80 | 80 | SM520 TMCP | 987.74 | 7,512.96 |

350 | 600 | 600 | 300 | 300 | 10 | 15 | SM570 TMCP | 88.80 | 675.46 |

… | … | … | … | … | … | … | … | … | … |

420 | 850 | 850 | 510 | 400 | 60 | 70 | SM570 TMCP | 598.06 | 4548.96 |

… | … | … | … | … | … | … | … | … | … |

512 | 1100 | 1100 | 730 | 600 | 80 | 80 | SM570 TMCP | 1082.93 | 8236.99 |

Structural materials | Unit price | Unit CO_{2} emission | ||
---|---|---|---|---|

Concrete | Strength | 21 MPa | 48.23 USD/m^{3} | 472.61 kg-CO_{2}/m^{3} |

24 MPa | 50.55 USD/m^{3} | 495.42 kg-CO_{2}/m^{3} | ||

27 MPa | 52.88 USD/m^{3} | 518.23 kg-CO_{2}/m^{3} | ||

30 MPa | 55.58 USD/m^{3} | 544.69 kg-CO_{2}/m^{3} | ||

35 MPa | 57.54 USD/m^{3} | 563.85 kg-CO_{2}/m^{3} | ||

40 MPa | 68.24 USD/m^{3} | 668.78 kg-CO_{2}/m^{3} | ||

50 MPa | 48.23 USD/m^{3} | 793.77 kg-CO_{2}/m^{3} | ||

Steel section | SM490 rolled | 0 < thickness ≤ 25 | 0.68 USD/kg | 5.15 kg-CO_{2}/kg |

25 < thickness ≤ 38 | 0.69 USD/kg | 5.21 kg-CO_{2}/kg | ||

38 < thickness ≤ 50 | 0.69 USD/kg | 5.27 kg-CO_{2}/kg | ||

50 < thickness ≤ 100 | 0.70 USD/kg | 5.33 kg-CO_{2}/kg | ||

SM490 built-up | 0 < thickness ≤ 25 | 0.84 USD/kg | 6.35 kg-CO_{2}/kg | |

25 < thickness ≤ 38 | 0.84 USD/kg | 6.41 kg-CO_{2}/kg | ||

38 < thickness ≤ 50 | 0.85 USD/kg | 6.47 kg-CO_{2}/kg | ||

0 < thickness ≤ 25 | 0.86 USD/kg | 6.54 kg-CO_{2}/kg | ||

SM490 TMCP | 0 < thickness ≤ 25 | 0.86 USD/kg | 6.51 kg-CO_{2}/kg | |

25 < thickness ≤ 38 | 0.86 USD/kg | 6.57 kg-CO_{2}/kg | ||

38 < thickness ≤ 50 | 0.87 USD/kg | 6.63 kg-CO_{2}/kg | ||

50 < thickness ≤ 100 | 0.88 USD/kg | 6.70 kg-CO_{2}/kg | ||

SM520 TMCP | 0 < thickness ≤ 25 | 0.86 USD/kg | 6.57 kg-CO_{2}/kg | |

25 < thickness ≤ 38 | 0.87 USD/kg | 6.64 kg-CO_{2}/kg | ||

38 < thickness ≤ 50 | 0.88 USD/kg | 6.70 kg-CO_{2}/kg | ||

50 < thickness ≤ 100 | 0.89 USD/kg | 6.75 kg-CO_{2}/kg | ||

SM570 TMCP | 0 < thickness ≤ 50 | 0.97 USD/kg | 7.35 kg-CO_{2}/kg | |

50 < thickness ≤ 100 | 0.97 USD/kg | 7.40 kg-CO_{2}/kg |

## 4. Application

#### 4.1. Introduction of the Example Structure

#### 4.2. Results

_{2}, and total cost of the optimum design are reduced by 31.51%, 30.30% and 31.39%, respectively. The cost of steel sections comprises a substantial amount of the total cost, whereas the additional cost from CO

_{2}of both initial and optimum designs comprises approximately 10% of the total cost.

Design type | Cost (USD) | Additional cost by CO_{2} (USD) | Total cost (USD) | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Rebar | Steel section | Concrete | Sum | Rebar | Steel section | Concrete | Sum | Rebar | Steel section | Concrete | Sum | |

Initial design | 1,405 | 59,702 | 3,246 | 64,353 | 149 | 6,342 | 444 | 6,935 | 1,554 | 66,044 | 3,690 | 71,288 |

(1.97%) | (83.75%) | (4.55%) | (90.27%) | (0.21%) | (8.90%) | (0.62%) | (9.73%) | (2.18%) | (92.64%) | (5.18%) | (100.00%) | |

Optimum design | 1,428 | 37,670 | 4,975 | 44,074 | 152 | 4,001 | 681 | 4,834 | 1,580 | 41,672 | 5,656 | 48,908 |

(2.92%) | (77.02%) | (10.17%) | (90.12%) | (0.31%) | (8.18%) | (1.39%) | (9.88%) | (3.23%) | (85.20%) | (11.57%) | (100.00%) |

**Figure 4.**Comparison of the distributions of stress ratios for the initial design and optimum design.

Design type | Weight (kN) | ||
---|---|---|---|

Steel section | Concrete | Sum | |

Initial design | 670.40 | 1398.29 | 2068.69 |

(32.41%) | (67.59%) | (100.00%) | |

Optimum design | 408.03 | 1499.38 | 1907.51 |

(21.39%) | (78.60%) | (100.00%) |

_{2}emission of the optimum design is reduced by 31.00% compared to that of the initial design. For SRC columns, reducing the amount of steel section while increasing the amount of concrete are found to be more effective at reducing the costs and CO

_{2}emissions. This is the different result when comparing with the RC results (for RC structures, the optimization with respect to the CO

_{2}footprint results in an increase in the relative amount of steel within the member’s cross section) presented by Yeo and Gabbai [17] and Yeo and Potra [18]. It is thought that the different result is shown because the CO

_{2}footprint of steel section (5.15 kg-CO

_{2}/kg to 7.40 kg-CO

_{2}/kg) in this study are much larger than the CO

_{2}footprint of reinforcing steel bar (0.35 kg-CO

_{2}/kg) in Yeo and Potra [18].

**Figure 6.**Distributions of weight ratios of concrete and steel section along the floors: (

**a**) initial design; and (

**b**) optimum design.

Floor | Initial design | Optimum design | ||
---|---|---|---|---|

Strength of concrete (MPa) | Type of steel section | Strength of concrete (MPa) | Type of steel section | |

F29 | 24 | SM490 rolled | 40 | SM490 rolled |

F28 | 24 | SM490 rolled | 40 | SM490 rolled |

F27 | 24 | SM490 rolled | 40 | SM490 rolled |

F26 | 24 | SM490 rolled | 40 | SM490 rolled |

F25 | 24 | SM490 rolled | 40 | SM490 rolled |

F24 | 24 | SM490 rolled | 40 | SM490 rolled |

F23 | 24 | SM490 rolled | 40 | SM490 built-up |

F22 | 24 | SM490 rolled | 40 | SM490 built-up |

F21 | 24 | SM490 rolled | 40 | SM490 built-up |

F20 | 24 | SM490 rolled | 50 | SM490 built-up |

F19 | 24 | SM490 rolled | 50 | SM490 built-up |

F18 | 24 | SM490 rolled | 50 | SM490 built-up |

F17 | 24 | SM490 rolled | 50 | SM490 built-up |

F16 | 24 | SM490 rolled | 50 | SM490 built-up |

F15 | 24 | SM490 rolled | 50 | SM490 built-up |

F14 | 24 | SM490 rolled | 50 | SM490 built-up |

F13 | 24 | SM490 rolled | 50 | SM490 built-up |

F12 | 24 | SM490 rolled | 50 | SM490 built-up |

F11 | 24 | SM490 rolled | 50 | SM490 built-up |

F10 | 24 | SM570 TMCP | 50 | SM490 built-up |

F9 | 24 | SM570 TMCP | 50 | SM490 built-up |

F8 | 24 | SM570 TMCP | 50 | SM520 TMCP |

F7 | 24 | SM570 TMCP | 50 | SM520 TMCP |

F6 | 24 | SM570 TMCP | 50 | SM520 TMCP |

F5 | 24 | SM570 TMCP | 50 | SM570 TMCP |

F4 | 24 | SM570 TMCP | 50 | SM570 TMCP |

F3 | 24 | SM570 TMCP | 50 | SM570 TMCP |

F2 | 27 | SM570 TMCP | 50 | SM570 TMCP |

F1 | 27 | SM570 TMCP | 50 | SM570 TMCP |

B1 | 27 | SM570 TMCP | 50 | SM570 TMCP |

B2 | 27 | SM570 TMCP | 50 | SM570 TMCP |

B3 | 27 | SM570 TMCP | 50 | SM570 TMCP |

B4 | 27 | SM570 TMCP | 50 | SM570 TMCP |

B5 | 27 | SM570 TMCP | 50 | SM570 TMCP |

B6 | 27 | SM570 TMCP | 50 | SM570 TMCP |

_{2}emissions in this study [38].

Type of steel section | Initial design | Optimum design | ||
---|---|---|---|---|

Weight (kN) | Ratio (%) | Weight (kN) | Ratio (%) | |

SM490 rolled | 207.55 | 30.96 | 12.36 | 3.03 |

SM490 built-up | - | - | 104.02 | 25.49 |

SM490 TMCP | - | - | - | 0.00 |

SM520 TMCP | - | - | 38.26 | 9.38 |

SM570 TMCP | 462.85 | 69.04 | 253.38 | 62.10 |

Total | 670.40 | 100.00 | 408.03 | 100.00% |

## 5. Conclusions

_{2}emissions at the structural design phase, and we apply the technique to an actual 35-floor building to evaluate its effectiveness. The optimum design obtained from the proposed technique reduced the cost, CO

_{2}emissions, and sum of weights of steel section and concrete used by 31.51%, 30.30% and 7.79%, respectively. The weight of steel section in the optimum design was reduced by 39.14%, whereas the weight of concrete was increased by 7.23%. We confirmed that reducing the amount of steel but increasing the amount of concrete can be an effective way to reduce the structural costs and CO

_{2}emissions of SRC columns.

_{2}emissions. The unit cost and CO

_{2}emission of high-strength materials are greater than those of general-strength materials, but lower amounts of the former materials are required because of their increased strength, which in turn reduces the overall costs and CO

_{2}emissions.

## Acknowledgments

## Conflicts of Interest

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© 2013 by the authors licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license ( http://creativecommons.org/licenses/by/3.0/).

## Share and Cite

**MDPI and ACS Style**

Park, H.S.; Kwon, B.; Shin, Y.; Kim, Y.; Hong, T.; Choi, S.W.
Cost and CO_{2} Emission Optimization of Steel Reinforced Concrete Columns in High-Rise Buildings. *Energies* **2013**, *6*, 5609-5624.
https://doi.org/10.3390/en6115609

**AMA Style**

Park HS, Kwon B, Shin Y, Kim Y, Hong T, Choi SW.
Cost and CO_{2} Emission Optimization of Steel Reinforced Concrete Columns in High-Rise Buildings. *Energies*. 2013; 6(11):5609-5624.
https://doi.org/10.3390/en6115609

**Chicago/Turabian Style**

Park, Hyo Seon, Bongkeun Kwon, Yunah Shin, Yousok Kim, Taehoon Hong, and Se Woon Choi.
2013. "Cost and CO_{2} Emission Optimization of Steel Reinforced Concrete Columns in High-Rise Buildings" *Energies* 6, no. 11: 5609-5624.
https://doi.org/10.3390/en6115609