# Algorithmic Generation of Building Typology for Office Building Design

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## Abstract

**:**

## 1. Introduction

## 2. Primary Data

- The building typology to be developed should be as large as a European common public office building with a useful area between 5000–10,000 m
^{2}. The number of stories should be between 4–10 levels. - To produce the office building typology requires basic cubes with an average and usable size of min. 4 × 4 × 3 m and max. 6 × 6 × 3 m. From such a basic unit (BU), it is possible to create both a small cell office and a co-working space by using several units. In this research, a size of 5 × 5 × 3 m was used, but other sizes can be implemented. The presented mathematical method is independent of this scaling.
- The BUs need to be grouped into so-called basic groups (BGs) in order to plan the spatial organization of a large-scale office building efficiently. The research worked with 4 × 4 units to create square groups (for design efficiency), but this can be achieved with other numbers of units. The presented mathematical method is independent of this.
- All levels are the same.
- Offices should have the same usable floor area as the atrium space on each level. The atrium is a multi-purpose zone where, in addition to the transport function, temporary meetings, events, reception, and project work can take place. On the upper floors, a gallery should be provided in 60% of the floor area of the atrium space, where a so-called semi-office can be established. The semi-office space performs the functions described above. The size of the semi-office should be 50% of the floor area of the gallery and can be provided on all levels.
- Inefficient office and corridor designs should be avoided. For example, amoeba-shaped, excessively long and narrow corridors and relief-type office contours.

#### Exemplary Modelling of an Office Building Space Arrangement Typology

^{2}and between 4 and 10 floors were investigated. The office building is composed of basic units (BUs), which are 5 m × 5 m × 3 m (width × depth × height) with a floor area of 25 m

^{2}. This flexible combination of space sizes represents general office space and is also justified for natural light and passive ventilation considerations in the design of a one-unit wide office section. This model system can also be used to create a range of other office section shapes with depths of 10 m, 15 m, and 20 m. From 4 × 4 basic units, so-called basic groups (BGs) have been created (Figure 1), to make the design of large-volume buildings from modules more manageable. The floor area of the BG is 400 m

^{2}, so the minimum length of the building is 20 m. One dilatation is allowed in the building, so the maximum building length is 80 m. For the present study, there is no difference in the floor plan of each level, so each floor is identical to the floor above and below it.

^{2}/4 levels = 2000 m

^{2}of floor space is available per level. This means a corresponding combination of 5 BGs per level. The BGs should relate to their full sides, as a half-sided offset may lead to uneconomical spaces (more complex structural solutions), and the research has aimed at simple geometries. Accordingly, Figure 2. shows the floor plans of the possible building forms that have been considered. These shapes are unique in terms of mirroring and rotation, no further cases need to be considered.

## 3. Generating Possible Building Configurations

- the possible BG structure;
- the percentage of office space (as a whole number, e.g., 50);
- the percentage of the atrium section (also as a whole number, e.g., 50).

^{5}, i.e., 7.962.624 building generations would be required. However, according to the generation rules (Section 2), only those BGs are selected for each BG, that meets the 50% office space to 50% atrium ratio, so for a building with 2 BGs, only 166 generations are needed.

## 4. The Main Functions

#### 4.1. Check the Number of Connected Spaces

#### 4.2. Determination of Office Block Sizes

#### 4.3. Checking Corner Connections

#### 4.4. Space Organization of Atrium Corridors

#### 4.5. Examining the Space Organization of Office Blocks: Staircase Rule

- left and right coordinates of the top row;
- left and right coordinates of the bottom row;
- top and bottom coordinates of the left-most column;
- top and bottom coordinates of the right-most column.

#### 4.6. Examining the Space Organization of Office Blocks: The Bubble Rule

## 5. Trivial Tests and Calculations

#### 5.1. Number of BUs Per Office Block with Indoor Connection

#### 5.2. Number of BUs Per Office Block with Outdoor Connection

#### 5.3. Number of Atrium Bus on the Building Wall

#### 5.4. A_{tot}/S_{tot}–Ratio-Based Model Sorting

_{tot}/S

_{tot}), which is the result of heat loss or heat-loaded envelope surfaces, according to the Formulas (1)–(3). This A

_{tot}/S

_{tot}ratio is one of the most important building physics indicators resulting from the geometry of the building configuration. A

_{tot}is the total calculated envelope surface area: A

_{off wall}is the exterior wall surface of the office section, A

_{off roof}is the flat roof surface of the office section, A

_{off gr floor}is the floor area of the office section connected to the ground. These parameters, with the subscript “atr” represent the boundary surfaces of the atrium space, similar to the office section. The surface area calculation included the surface area of all structures that may have different temperatures on two different sides. The surfaces of the external facade walls of the office space and atrium, the roof surfaces, the surfaces in contact with the ground, and the interior walls between the atrium and the office have been included.

_{tot}is the total useful floor area taken into account: S

_{off}is the floor area of the office sections and S

_{gallery}is the floor area of the galleries. For the calculation of the floor area (S

_{tot}), all floors have been counted as slab-on-grade areas, which includes the office spaces, the entire ground floor area of the atrium, and the galleries on the upper floors.

_{tot}/S

_{tot}group has been examined.

_{tot}= A

_{off wall}+ A

_{off roof}+ A

_{off gr floor}+ A

_{off-atr wall}+ A

_{atr gr floor}+ A

_{atr wall}+ A

_{atr roof}

_{tot}= S

_{off}+ S

_{gallery}

_{tot}/S

_{tot}

## 6. Results and Discussion

^{5}, i.e., 79,626,240 buildings, which would have to be generated and further analyzed if the above present architectural aspects were not taken into account. However, by using the simple rules in the document, the size of this search space is significantly reduced. The office floor area ratios (i.e., the ratios allowed between office blocks within a building) allowed for the final generation are as follows:

- 5.
- 100–0%;
- 6.
- 60–40%;
- 7.
- 50–50%.

- 8.
- Based on the A
_{tot}/S_{tot}value for the building configuration; - 9.
- Based on internal office mass ratios.

_{tot}/S

_{tot}ratio for the building configuration, resulted in 28 different values. Based on these values, the following groups were constructed: 1.01; 1.02; 1.03; …; 1.28.

#### 6.1. Galleries in Atrium Spaces on Each Floor

^{2}, 600 m

^{2}of galleries are required to make the building economically and functionally viable.

^{2}galleries on each floor level, where a so-called semi-office can be created. These semi-offices are flexible spaces with a lightweight structure, suitable for temporary project work, events, meetings, or other functions. These functions can consist of several smaller rooms, or even a single space if the need arises. Therefore, the size of the contiguous space has been defined as 50% of the gallery level, i.e., 300 m

^{2}, so that none of its sides can touch an office function boundary wall, an external façade, or an atrium boundary, so it cannot be at the edge of the gallery. This boundary condition significantly reshaped and reduced the results, which are as follows.

#### 6.2. Discussion

## 7. Conclusions

## Author Contributions

## Funding

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Table 1.**Possible cases consisting of 3 BGs that meet the 50% office space—50% multifunctional atrium requirement for the whole building.

100-50-0 | 75-75-0 | 50-100-0 | 25-100-25 | 0-100-50 |

100-25-25 | 75-50-25 | 50-75-25 | 25-75-50 | 0-50-100 |

100-0-50 | 75-25-50 | 50-50-50 | 25-50-75 | |

75-0-75 | 50-25-75 | 25-25-100 | ||

50-0-100 |

Number | Form | Building Configuration Number |
---|---|---|

1. | 103 pieces | |

2. | 316 pieces | |

3. | 347 pieces | |

4. | 191 pieces | |

5. | 208 pieces | |

6. | 159 pieces | |

7. | 162 pieces | |

8. | 175 pieces | |

9. | 740 pieces | |

10. | 7 pieces |

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## Share and Cite

**MDPI and ACS Style**

Androsics-Zetz, D.N.; Kistelegdi, I.; Ercsey, Z.
Algorithmic Generation of Building Typology for Office Building Design. *Buildings* **2022**, *12*, 884.
https://doi.org/10.3390/buildings12070884

**AMA Style**

Androsics-Zetz DN, Kistelegdi I, Ercsey Z.
Algorithmic Generation of Building Typology for Office Building Design. *Buildings*. 2022; 12(7):884.
https://doi.org/10.3390/buildings12070884

**Chicago/Turabian Style**

Androsics-Zetz, Dóra Noémi, István Kistelegdi, and Zsolt Ercsey.
2022. "Algorithmic Generation of Building Typology for Office Building Design" *Buildings* 12, no. 7: 884.
https://doi.org/10.3390/buildings12070884