## Abstract

Herein, the authors describe an overall approach to the architectural design of floating structures such as floating houses. The primary aim of this study is not to present a method for stabilizing floating structures, but rather to provide a design synthesis method for use when designing such structures. More specifically, we propose an integrated procedure for use at the preliminary design stage of such structures that systematically facilitates their overall design. As an inclining platform could endanger the people on board, it is necessary to determine an adequate metacentric height in order to prevent such occurrences. This measurement, which is defined as the distance between the center of gravity of a floating structure and its metacenter, quantifies the initial static stability of a floating body. Based on this idea, we consider the associated problems as well as the methods used in practical procedures, and combine them to introduce a unique approach called the “required GM” method. We also discuss the different and various aspects used in basic configuration determinations of floating architectural structures, such as the aspect of static stability and the overall process used at the conceptual design stage. In addition, illustrative examples of an idealized floating platform embodying the simplest possible structures are provided to illustrate these points.

### Keywords

- Floating house
- Sustainable
- Natural hazard
- Flood house
- Climate change

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## References

Intergovernmental Panel on Climate Change (2014) IPCC fifth assessment report—climate change 2014. Intergovernmental Panel on Climate Change

Nakajima T, Umeyama M (2019) An integrated floating community based upon a hybrid water system: toward a super-sustainable water city. Lecture notes in civil engineering, vol 41. Springer, Heidelberg, pp 309–327

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Nakajima T, Yamashita Y, Harada S, Andoh (2020) Sustainable water city in Singapore. In: Oceans’20 MTS/IEEE international symposium Singapore, 11–14 August (to be published)

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Takarada N, Nakajima T, Inoue R (1986) A phenomenon of large steady tilt of a semisubmersible platform in combined environmental loadings. In: 3rd international conference on stability of ships and ocean vehicles, 22–26 September 1986, Gdansk

Sato C (2003) Result of 6 years’ research project of mega-float. Ocean space utilization technology. Ministry of Land, Infrastructure and Transport of Japan, pp 436–442

Nakajima T, Umeyama M (2013) Water city as solution to escalating sea level rise in lower-lying areas. In: Oceans’13 MTS/IEEE international symposium, San Diego, California, 23–26 September 2013

Hendriks TM, Mendonca Santos J (2018) Challenges in stability assessment of offshore floating structures. In: Guedes Soares, Teixeira (eds) Maritime transportation and harvesting of sea resources, October 2017. Taylor & Francis Group, London, p 13. ISBN 978-0-8153-7993

## Acknowledgements

The authors are grateful to Business Strategy Promotion Center at Chodai Co., Ltd., for their financial support. Some of the content within this paper was quoted from work conducted by Ms. Yuka Saito, which was carried out as research in support of her thesis presented at Tokyo Metropolitan University during the 2015–16 period.

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## Appendices

### Appendix A

In general, steady wind force \(\left( {\Delta {\text{F}}_{\text{Z}} } \right)\) at z m can be obtained by the following equation:

where P_{Z} is the wind pressure (kg/m^{2}) at z m, C_{D} is a drag coefficient, A is the projected area (m^{2}), and *ρ* is the air density.

In general, accurate C_{D} values are obtained via wind tunnel tests.

Here, it should be note that wind velocity is measured at the height of 10 m and the average value over a period of 10 min is used. The wind velocity (*U*_{Z}) changes along the vertical location are shown in Fig. 18, and can be estimated by the following equation. Note that wind velocity is lower near the ground due to friction.

where U_{10} is the wind velocity at a height of 10 m, and α is the surface roughness.

It is known that the value of α is 1/7 on the sea surface and 1/4 in an urban area.

### Appendix B

According to Ref. [6], the static righting lever GZ at an inclining angle φ of a wall sided vessel is expressed as follows:

Supposing an overturning moment due to the sum of various components \(\left( {\sum\nolimits_{\text{i}} {{\text{M}}_{\text{i}} } } \right)\) and the righting moment (M_{R}), the following expression is established:

Equation (22) is then multiplied by the weight of a floating foundation (W) to give

After rearranging, we have

Dividing Eq. (25) by \({\text{W}} \cdot \sin \phi\) on both sides gives

When \(\phi\) is small, the second term of Eq. (26) can be ignored. Thus, the value of the \(\overline{\text{GM}}\) which is required (Req. GM) for a small inclination is given by the following equation:

or

where \(\Phi {\text{d}}\) is the inclining angle in degrees.

Thus, a “required GM” method that evaluates and compensates for various heeling moments under a variety of combined environmental loadings is proposed.

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Nakajima, T., Saito, Y., Umeyama, M. (2022). A Study on Stability of Floating Architecture and Its Design Methodology . In: Piątek, Ł., Lim, S.H., Wang, C.M., de Graaf-van Dinther, R. (eds) WCFS2020. Lecture Notes in Civil Engineering, vol 158. Springer, Singapore. https://doi.org/10.1007/978-981-16-2256-4_17

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