Proceedings of the IASS Annual Symposium 2020/21 andthe 7th International Conference on Spatial Structures
Inspiring the Next Generation
23-27 August 2021, Guilford, UK
S.A. Behnejad, G.A.R. Parke and O.A. Samavati (eds.)

Design and Construction of Reciprocal Frames Made of Bamboo
with Connections by Means of PVC Pipe and Rope
Koichiro ISHIKAWA*, Sovannara SRUNa, Sokol PHONb*School of Architecture and Civil Engineering, University of Fukui
Bunkyo 3-9-1, Fukui-shi, Fukui-ken, Japan
ishikawa@u-fukui.ac.jp
a, bDepartment of Safety and Social Infrastructure Engineering, University of Fukui

Abstract
The purpose of this paper is to propose a low-technology connection of reciprocal frames made of Moso
bamboos and confirm the construction workability and the low costs. The geometrical shape of thereciprocal frame is generated by configuration processing of Formian. The length and the external
diameter of the bamboo member are around 1.5m and 60mm, respectively. The height and the span
length of the frame structure are 2.41m and 5.72m, respectively. The structure is composed of threemember assemblies of the bamboo. Estimation method of predicting a Young’s modulus, bending
strength and a thickness based on the external diameter is proposed to carry out the structural analysis
for the evaluation of structural performance. The estimation method is based on data of the measurement
and the bending experiment of the bamboo. The bamboo reciprocal frame designer can prepare the datasuch as a Young’s modulus, bending strength and a thickness for the structural analysis and carry out
the analysis. In conclusion, the reciprocal frames would provide temporary evacuation accommodations
in low cost and excellent workability. Timber reciprocal Frame designers is also able to carry out thestructural analysis by means of the configuration processing of Formian and the estimation method of
the characteristics of the bamboo member and the connection composed of the pipe and the rope.
Keywords: bamboo spatial structures, reciprocal frame, bamboo, PVC (polyvinyl chloride) pipe, rope, lowtechnology, low costs, construction workability, estimation method of bamboo characteristics, configuration,
formian.

1. Introduction
Bamboo plants are widely growing in many countries like Japan and tropical countries such as
Cambodia, and are now attracting attention as new resources of construction material in the 21st century,
as timber resources are decreasing. Bamboo grows to be usable in only 3 to 5 years, unlike wood andother biological materials. For this reason, surplus of bamboo and damage to forests due to proliferationof bamboo are becoming a problem. However, since this rapid periodic logging can be performed, its
effective use is thought to contribute to the reduction of atmospheric CO2. In addition, bamboo in thearchitectural field is limitedly used as a non-structural material such as a finishing material, and is rarely
used as a structural material. Therefore, if bamboo materials can be actively utilized in the construction
field, it is possible to reduce the manufacturing cost of buildings and as a result, lead to the possibilityof making the most of the bamboo resources on the international level.
In particular, bamboo is light and can be efficiently processed by hand, so it is considered to be aneffective means for residents to construct pavilions or temporary buildings in areas affected by large
earthquake, tsunami and so on.
Copyright © 2021 by the author(s) as listed above. Published in the Proceedings of the IASS Annual Symposium
2020/21 and the 7th International Conference on Spatial Structures, with permission.
1523

Proceedings of the IASS Annual Symposium 2020/21 and the 7th International Conference on Spatial Structures
Inspiring the Next Generation

This study deals with temporary spatial structures such as reciprocal structures by using bamboos
because of the above background to achieve the SDGs (Sustainable Development Goals). The realizingof the structures also contribute to resources and costs with regard to the destruction of bamboo forests
and the reduction of CO2.

2. Research Objectives and Methodology
The purpose of this paper is to propose a low-technology connection of reciprocal frames made of Moso
bamboos and confirm the construction workability and the low costs. The geometrical shape of thereciprocal frame is generated by configuration processing of Formian. The length and the external
diameter of the bamboo member are around 1.5m and 60mm, respectively. The height and the span
length of the frame structure are 2.41m and 5.72m, respectively.
Bamboo reciprocal structures are suitable for temporary buildings. The bamboo member is subjected tobending stresses due to applied loads, while bamboos have enough resistant capacity with regard to thebending moments. It is also easy for bamboos to obtain at low cost and stabilizes this structure by meansof PVC pipes and ropes. This is a reason why bamboos are used in the structures.
In this study, the possibility aimed at expanding the use of bamboo materials and the application ofreciprocal structures to temporary structures would be confirmed by carrying out its bending strength
experiments. The structural analysis is also carried out to investigate the load carrying capacity.

3. Strength Measurement of Bamboo due to Bending Moment
It is necessary for the proposed reciprocal structure to evaluate the structural performance and confirm
the habitability in safety, even though its use is a temporary structure. This is a reason why structural
analyses are required for the realization.
In this study, experiments are carried out to propose formulas for relationship between the external
diameter and the internal diameter with regard to Moso bamboos. It is also shown that relationships ofthe bending stiffness and the maximum bending moment are obtained by using the external diameter
easily. Moso bamboo culms used in experiments are harvested at the bamboo forest in Echizen town,
Fukui prefecture, Japan. The validity of the empirical formulas for estimating the properties such as theinternal diameter, the maximum bending moment, and the bending stiffness in term of the external
diameter is also shown in comparison with the previous studies [1] and [2].
3.1. Measurement of Cross-section of Moso Bamboo Culms
3.1.1. Specimen
The test specimens are 4 Moso bamboo culms (green) of more than 3 years old, harvested on July 27,
2019.
3.1.2. Measurement method
The cross section was measured according to the following procedure.
(1) Label the central sections of each internode from the butt end to the top end, with the node near
the stem base regarded as the first node.
(2) Measure all internode lengths,(3) Saw the central sections of the internode and take a specimen piece.
(4) Measure the cross-sectional dimension at the base opening side of the specimen piece using a
1/100 mm caliper and through the method shown in figure 1 below.

1524

Proceedings of the IASS Annual Symposium 2020/21 and the 7th International Conference on Spatial Structures
Inspiring the Next Generation

Figure 1: Experiment Specimens Preparation

3.1.3. Results and discussion
Fig. 2 combines data from this study and the previous study [1] (14 Moso bamboo culms).

Figure 2: Relationship between internal and external diameter

The proportional relationship between the internal diameter and the external diameter is recognized in
Fig.2. Therefore, the regression line is obtained by the following equation.
d = 0.81 ・ D(1)Where d is the internal diameter and D is the external diameter.
It is confirmed from the regression linear equation that, the internal diameter d (mm) at any culm length
position of Moso bamboo culm, can be estimated with high accuracy in term of the external diameter D(mm) at the position. As a result, the cross-sectional performance such as cross-sectional area, crosssectional modulus and so on can be estimated by using the external diameter.
3.2. Experiment on Bending Strength of Moso Bamboo Culms
3.2.1. Specimens
The test specimens are 9 Moso bamboo culms (green) of more than 3 years old which were harvested
on October 08, 2019.

1525

Proceedings of the IASS Annual Symposium 2020/21 and the 7th International Conference on Spatial Structures
Inspiring the Next Generation

3.2.2. Measurement method

Figure 3: Three-point Bending Experiment
The bending test was performed by a three-point bending method using a centrally concentrated load(load applied to the node by a wire) at a load speed of 20 mm / min with a span of 2000 mm. The bending
deflection was measured by a winding displacement meter attached to the load point.
3.2.3. Results and discussion
The internal diameter of the specimens can be estimated in term of the measurable external diameter,
which is based on the empirical formula (1). The hollow circular section beam, the secondary momentof section (I) can be calculated by using a material mechanics. In addition, the bending stiffness EI (E:bending Young's modulus) and the maximum bending moment Mmax can also be calculated by using theabove mentioned values. The following figures are plotted by using the experimental data and theprevious study [2] (14 Moso bamboo culms).

Figure 4: Relationship between Mmax , EI and the external diameter, respectively.
A strong correlation exists between the external diameter and the maximum bending moment Mmax andalso the bending stiffness EI, as shown in the above figures. In other words, the rigidity and strength,
which are a necessary input data for the structural analysis, could be estimated with relatively acceptableaccuracy in term of the external diameter. This shows a real possibility of bamboo temporary structures
for the design in safety against external loads such as a wind load, a snow load and so on.

4. Overview on Reciprocal Structure
The reciprocal structure is a self-supporting three-dimensional structure, having a large span and isformed by overlapping short members. Such structures may be considered to be invented by humans,
but in fact small inter-organisms called cocolithophore [3] also show that interwoven or interlocking
1526

Proceedings of the IASS Annual Symposium 2020/21 and the 7th International Conference on Spatial Structures
Inspiring the Next Generation

systems exist in nature. The problem with the reciprocal structure is that bending stress is generated ineach member.

5. Outline of The DomeIn this study, the dome was constructed by using practical joints composed of PVC pipes and ropes.
First, the configuration of this dome is generated for achieving this purpose. Second, it is necessary toanalyze and examine the possibility of using bamboo and expanding the mutual structure to a temporary
space structure.
The reciprocal structure is composed of three or more inclined members forming a unit. Large-scale
such structures, constructed as a complex frame of one or several similar units, have an intrinsic beauty
derived from their inherent self-similarity and symmetric patterns.
In order to determine the unit to be used for the dome, the units shown in Table 1 are structurally
analyzed. Then, the following result is obtained.
Table 1: Maximum bending moment of frame unit of three or more members

Mmax

It can be confirmed that the maximum bending moment Mmax of each unit is almost the same from Table
1. Thus, a three-member unit is relatively more efficient in terms of materials used than four or moreunits. In this research, the dome is proposed using a unit of three members in consideration of cost andworkability.

Figure 5: Structures, composed of members with the increase in units 3, 10, 20, 35 …
HeightLengthFigure 6: Relationship between member length and dome height1527

Proceedings of the IASS Annual Symposium 2020/21 and the 7th International Conference on Spatial Structures
Inspiring the Next Generation

It would be appropriate space with the 5.72m span with a 1.5m member length and the 2.41m height for
temporary structures, as shown in Figure 6.

Figure 7: Determination of the shape of the dome

6. Comparison of coordinates
In this study, first, the shape of the dome was generated by morphological analysis [4] using a genetic
algorithm [3] (hereinafter abbreviated as morphological analysis). Here, the validity of this shape iscompared and examined with a model and a full-scale dome described in Chapter 4. The model used astyrene cylinder. Based on this model, the three-dimensional coordinates are compared and examined
below. Second, the structural performance is investigated by the structural analysis.
It was found that the three-dimensional coordinates were almost the same, but it was confirmed that thedifference became smaller as the nodes became higher in Figure 8. Although the position of the fulcrum
was relatively large, it was confirmed that the other nodes almost coincided in Figure 9.

Figure 8: Comparison of Coordinates from the Top view1528

Proceedings of the IASS Annual Symposium 2020/21 and the 7th International Conference on Spatial Structures
Inspiring the Next Generation

(b)

(a)

(c)
Figure 9: Comparison of XYZ Coordinates

7. Trial assembly
7.1 Development of joints with efficient workability
The proposed joint uses PVC pipes and ropes as shown in Figure 10. Further, the position of the main
joint can be adjusted by ropes. Therefore, it is possible to easily assemble the dome by overlapping themembers.

Figure 10: Detailed view of the joint used for this dome
The feature of this joint is that the direction of the hole or the PVC pipe can be adjusted at the time ofassembly as shown in Figure 10. Also, by connecting the members with ropes, the eccentricity can be
kept in Figure 11.

1529

Proceedings of the IASS Annual Symposium 2020/21 and the 7th International Conference on Spatial Structures
Inspiring the Next Generation

Figure 11: Joint using PVC pipes and ropes

7.2 On-Site Construction
Trial construction was conducted for the purpose of easy construction and grasp of problems during
construction. In this dome, the member length was 1.5 m, but the member length was changed to 1.7 m
as shown in Figure 12, so that the members could be properly overlapped. The member is preliminarily
drilled at four places and penetrated through a PVC pipe. 35 members were manufactured by two
persons in about 45 minutes.

Figure 12: Module of members
The assembly at the site was performed as a unit consisting of three members connected by ropes asfollows. In four steps, two people worked in about 1.5 hours without using special tools.

Step 1

Step 2

Step 3

Step 4

Figure 13: Determining the shape of this dome, which creates a space by overlapping members

1530

Proceedings of the IASS Annual Symposium 2020/21 and the 7th International Conference on Spatial Structures
Inspiring the Next Generation

Figure 14: Assembled dome

7.3 Results and Discussion
The assembled dome has a maximum height of 2.32m and a span of 5.50m. When the members are
unitized, it is necessary to pay attention to the splitting of the bamboo material ends and the displacementof the joints due to the variation in the diameter of the bamboo culms depending on the degree of drying
and the size of the drill mouth.

8. Structural analysis of this dome
To study the structural behavior of the dome subjected to vertical force, the elastic structure analysis of
the model of the dome using the shape obtained from the morphological generation was performed asfollows.
Table 2: Analysis conditions

By using the empirical formula for the relationship between the external diameter and the maximum
bending moment Mmax, the maximum bending moment Mmax of 1420 kN·mm was calculated for the
average external diameter of a 60 mm member. And, by using the empirical formula for the relationshipbetween the external diameter and the bending stiffness EI, the Bending Young's modulus E of 1500 kN/ cm2 was determined from the average external diameter of the member.

A

Total Load Ptotal=7.88kN Maximum bending moment Mmax=1420kN•mm
Figure 15: Analysis results
1531

Proceedings of the IASS Annual Symposium 2020/21 and the 7th International Conference on Spatial Structures
Inspiring the Next Generation

It is considered that the maximum bending moment (1420 kN·mm) was reached at the joint of themember A shown in Figure 15 due to the asymmetry caused by the coordinates studied in Chapter 6.
However, in this structural analysis, the boundary condition and the joint are modeled as pins. Therefore,
it is necessary to clarify the structural performance and proof stress of this dome in the future byevaluating the rigidity and proof stress of the proposed joint.

9. Conclusion
The bending strength performance of Moso bamboo culm was investigated by the experiments of thebamboo members. The results showed significant correlations between the internal diameter, themaximum bending moment (Mmax), and the bending stiffness (EI) of the bamboo culm with respect tothe external diameter. Therefore, the maximum bending moment and the bending rigidity for structural
analysis can be estimated with relatively good accuracy in term of external diameter of the bamboo culm.
It is also confirmed that, the validity of the empirical formulas of the material in this study for estimating
the properties, such as the internal diameter, maximum bending moment, and bending stiffness in termof the external diameter is also confirmed in comparison with the previous studies [1] and [2].
It was shown that this joint is excellent in terms of practicality with cost reduction and efficient
workability. It was also shown that the structural characteristics such as the bending stiffness andYoung's modulus of the dome can be obtained by using the proposed experimental formula in this study
and the coordinates obtained by the morphological analysis. Therefore, it is expected that the use ofbamboo can be expanded and the reciprocal structure can be applied to temporary space structures.

Acknowledgements
This work was supported by JSPS KAKENHI Grant Number 18K04427. The authors would also liketo thank Emeritus prof. Hideo HORIE of Toyama University for giving us guidance along the processof the experiments. Furthermore, we also extend our thanks to Mr. Takashi AKAZAWA for kindly
providing us with Moso bamboo culms as the specimens in this research.

References[1] Hideo HORIE: Estimation of Cross-sectional Dimension of Bamboo Culms, Journal of The Japan
Wood Science Society Vol. 66, No.2, p.100-105, 2020.
[2] Hideo HORIE: Strength Performance of Green Bamboo Culm as A Temporary Structural Member,
63rd Annual Meeting of the Japan Wood Research Society (Morioka) CD Version, D27-08-1515.
[3] Baverel O. L. S.: Nexorades: A Family of Interwoven Space Structures, A thesis for the PhD,Space Structures Research Centre, University of Surrey, p.22 & p.238-241, 2000.
[4] Nooshin H., Disney P., Yamamoto C.: Formian, Multi-Science Publishing Co. Ltd., 1993.
[5] Tim MICHELS, Lu LU, Russell ARCHER, Sigrid ADRIAENSSENS and Greta, TRESSERRA：DESIGN OF THREE HYPAR ROOFS MADE OF GUADUA BAMBOO, 2017[6] Garavaglia E., Pizzigoni A., Sgambi L. and Basso N.: Collapse behavior in reciprocal frame
structures, 2013.
[7] Godthhelp T.S., Roelfs R., Habraken A.P.H.W. and Jorrisen A.J.M.: The Timber Reciprocal Frame
Designer: The Timber Reciprocal Frame Designer: Free Form Design to Production, 2019[8] Garavaglia E., Pizzigoni A., Sgambi L. andBasso N., “Collapse behaviour in reciprocal frame
structures”, Structural Engineering and Mechanics, Vol. 46, No. 4 pp. 533-547, 2013.

1532

Proceedings of the IASS Annual Symposium 2020/21 and the 7th International Conference on Spatial Structures
Inspiring the Next Generation[9] Godthhelp T. S., Roelofs R., Habraken A. P.H.W. and Jorissen A. J. M.: “The Timber Reciprocal
Frame Designer: Free Form Design to Production” Structural Membranes 2019 Form and Force
Proceedings of IASS Annual Symposium 2019, Barcelona, Spain 7-10 October 2019.

1533

差出人 :
宛先 :
件名 :
日付 :
添付ファイル :iass2020surrey7@easychair.org が IASS2020-SURREY7 の代理で送りました
Koichiro Ishikawa
IASS2020/21-SURREY7 notification for paper 809
2021年6月2日 13:50:46
Brief Instructions for full paper submission and author checklist.pdf

IASS2020/21-SURREY7: (Full paper ID: 809)- Contribution accepted
Dear Koichiro Ishikawa,Thank you very much for submitting your full paper entitled "Design and construction of reciprocal frames
made of bamboo with connections by means of PVC pipe and rope" for the forthcoming IASS2020/21 Surrey 7
Conference, to be held virtually on the 23-27 August 2021.
We are very pleased to inform you that your full paper has been accepted.
1- You missed uploading or filling in some of the below items. Please follow up the attached brief instructions
for full paper submission, carefully and upload the required info:- Headshot- Figure- A single paragraph short abstract- Publication agreement: license to publish.
- Publication agreement: declaration of third party copyright.
2- Please also revise the formatting of your full paper based on the provided guidelines. A simple checklist to
make sure that your full paper follows the appropriate formatting is attached.
3- Below you may find the reviewer(s) comments to revise and improve your full paper.
Please log in with your Easychair account and follow the attached guideline to complete your submission atyour earliest convenience between 7 to 14 June. Also, please upload the word file of your full paper to be
included in the proceedings, as well as the revised pdf file.
Also, you can find the template of the full paper at https://www.surrey.ac.uk/sites/default/files/202101/IASS2021-full-paper-guidance.docx
The program for the conference is in preparation and we will send you the detailed program as soon as it isready.
With very best regards,  
Gerard Parke & Omidali Samavati
Chair & Vice-Chair of Scientific Committee IASS 2020/21 – Surrey 7
iass2020@surrey.ac.uk

SUBMISSION: 809
TITLE: Design and construction of reciprocal frames made of bamboo with connections by means of PVC pipeand rope----------------------- REVIEW 1 --------------------SUBMISSION: 809
TITLE: Design and construction of reciprocal frames made of bamboo with connections by means of PVC pipeand rope
AUTHORS: Koichiro Ishikawa, Srun Sovannara and Phon Sokol----------- Overall evaluation ----------The paper is of very good scientific quality. In general manuscript of the paper fulfils most of the requirements
spoken in the full-paper-guidance regarding the paper’s format. It seems that a figure placed in the bottom of
page No 6 is a part of Figure 8 presented on page No 7. I suggest to divide Figure 8 into two independent parts,
which should be suitably shaped and have appropriate captions. Besides on pages No 7 and No 8 one can noticesome empty spaces, what should be eliminated. Please arrange these pages according to the indications written
in the guidance for preparation of the conference paper. All items of references should also be given accordingthis guidance.