Keywords

1 Introduction

Tropical developing economies are some of the most vulnerable societies to natural disasters and by 2050, some 50% of the world’s population will live in the tropics [1]. Over one-quarter of the urban population of South East Asian tropical developing economies reside in non-adequate housing [2,3,4]. The UN Sustainable Development Goal 11 (SDG11) targets by 2030 the access for all to adequate, safe and affordable housing, and suggests that the building of sustainable and resilient buildings utilising local materials should be a catalyst for development [5]. Cement production is the third-largest source of anthropogenic emissions of CO2 and could rise by 23% by 2050 given current trends [6]. Sand for construction is also being unsustainably sourced which in the coming decades will affect the concrete supply chain [7, 8]. We need to look at new sustainable, locally available natural materials for construction, and architects will need to respond to this challenge and develop new processes to work with natural materials which ensure structural integrity and affordability. Tropical developing economies are large producers of bamboo [9], a material with good tensile and compressive properties and a low carbon footprint when sourced locally [10]. Bamboo can be worked with simple tools and can be grown locally on a village scale or even a family scale [11]. Bamboo can also absorb CO2 and stabilise slopes to tackle the effects of deforestation [12]. If we are to increase the use of renewable materials, then we should look to non- or marginally engineered building materials to ensure that the most affordable form of bamboo, ‘full-culm bamboo’, (also named ‘round bamboo’) is used [13, 14] (Fig. 1b). Bamboo will degrade if not designed or built correctly. Exposure to UV light and moisture can bleach, crack and encourage fungal growth causing structural and aesthetic damage which impacts greatly the perception of bamboo in the mind of potential end users, reinforcing a notion of bamboo as temporary, or the ‘poor man’s timber’ [15].

Fig. 1
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a Culm terminology, b full-culm bamboo, c bamboo splits, d example of engineered bamboo

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In tropical developing economies, it is a reality that the architect will not design the majority of housing [16]. The minimum construction materials are purchased, and design and engineering input is often unaffordable. Architects can however be active in reducing the cost of design and raise awareness of good practices promoting open-source designs of adequate housing which ensure structural and aesthetic integrity [17, 18]. In order to reduce the cost of design, there have been moves by architects to develop a greater synthesis between their current computational design processes and materials with natural variability such as bamboo. The ZCB Pavilion in Hong Kong is one such example which pushes the boundaries of the design solution space of bamboo architecture [19]. Computational design tools allow the architect to visualise ideas and they can be modified and analysed interactively, though this modification can still be time-consuming. Parametric software allows us to build on this process and specify relationships among parameters and instantly output versions or iterations of a design, based on associative rules set by the designer [20]. Willis and Woodward in 2005 suggest it will be impossible to achieve a direct correlation between digital data and a constructed building. Some design parameters like material flaws, grain directions and inconsistent densities will be difficult to anticipate in modelling software. However, this gap between the building and the model will continue to narrow [21]. The following is a case study which demonstrates the use of an algorithm to generate a design for a small dwelling with a hyperbolic paraboloid roof to be built of full-culm bamboo [22]. This is a roof form which follows a convex curve about one axis and a concave curve about the other. It is practical, easily constructed from straight sections, and draws rainwater which falls on this roof, towards the two lowest points, without the additional expense of guttering (Fig. 2). This algorithm embeds certain design principles of building with full-culm bamboo, which will increase the durability, material efficiency and buildability of this roof.

Fig. 2
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Render illustrating rain collection strategy of the hyperbolic paraboloid

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2 The Tools

In this process, two pieces of software well known to the architectural profession have been used, and emblematic of a set of tools which use a visual language environment. Rhinoceros 3D [23] is a three-dimensional computer graphics and computer-aided design software which uses non-uniform rational basis splines (NURBS) to build geometry as opposed to a polygon mesh-based system. The second is Grasshopper [24] which is a visual programming environment which runs within the Rhinoceros 3D platform. The main interface for algorithm design in Grasshopper is the node-based editor. Algorithms are scripted by dragging components with inputs and outputs onto a canvas (Fig. 3a). A collection of components forms an algorithm, and the output of these commands is displayed in the Rhinoceros 3D window. The initial input geometry can either be assigned from Rhinoceros 3D or generated in Grasshopper. For this case study, a planar quadrilateral has been drawn in Rhinoceros 3D and assigned as the starting geometry of the algorithm in Grasshopper, though this does not have to be planar accepting the possibility of a sloping site. This algorithm will then generate a hyperbolic paraboloid above this quadrilateral, to heights defined by the user. The algorithm can respond to any quadrilateral site option to accommodate the variability of sites. Characteristics of bamboo are considered in the algorithm to improve the durability of bamboo and provide a practical means of constructing a hyperbolic paraboloid as a roof using full-culm bamboo.

Fig. 3
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a Example of nodes, inputs and outputs on the Grasshopper graphical algorithm editing canvas; b a screenshot of the Rhinoceros 3D interface showing the polygonal outline which defines the area for the surface to cover, and the hyperbolic paraboloid

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3 Negating the Natural Variability of Bamboo

Bamboo has natural variability which means that there are certain characteristics of full-culm bamboo which are indeterminate. Two rational assumptions have been made in the algorithm to negate effects of variability:

  • The curvature of a bamboo culm: The bamboo culm is modelled as a straight line, or a cylinder, as the bamboo culm for use in construction will be selected to have a very negligible curvature. It is advised that any bamboo poles selected for construction purposes will have 1% out-of-straightness limit [25].

  • The tapering diameter of a bamboo culm: The diameter of the bamboo culm input into the algorithm is a single value across the algorithm and therefore the design. In reality, a bamboo culm will have a diameter greater at the base than the top. This is not taken into account in this algorithm as depending on the species or specific plant the tapering can vary in extremity. When selecting the bamboo culm to be used, it is for the architect to select the culm which tapers minimally. Additionally, it is the middle section of the bamboo culm which should be used for this application. The use of the middle section will reduce the maximum and minimum diameter of the poles [26] and a decision has been made to discount this in the algorithm.

The quadrilateral building footprint is drawn in Rhinoceros 3D as a ‘Closed polyline’. It is not required to be planar which accounts for the possibility that the site may not be flat. This can reference a physical site or an isolated pre-determined quadrilateral shape defined by the needs of the brief which will consider the necessary occupancy of the building. The algorithm will generate a hyperbolic paraboloid from this initial building footprint. The algorithm for generating the hyperbolic paraboloid will extract the nodes at each corner of the quadrilateral, move the nodes vertically (Z-axis) to a point defined by the user which corresponds to the intended peak and eave heights of the roof and finally the ‘Surface from 4 points’ component generates a hyperbolic paraboloid (Fig. 3b).

The roof will be constructed from straight bamboo poles with a series of longitudinal (u) poles and a series of latitudinal (v) poles placed above (Fig. 5). Within the algorithm, a new hyperbolic paraboloid is created from the generated surface by using the ‘Offset Surface’ component. The distance of this offset is input into the algorithm by the user and is the diameter of the bamboo poles to be used in construction (d). Now there are two surfaces, a lower and an upper surface. Longitudinal members (u) are extracted from the lower surface and latitudinal members (v) are extracted from the upper surface (Fig. 4a). The offset of the roof is connected to the diameter of the bamboo (d) to be used. This will save a lot of time for the designer as this algorithm will adapt the design if alternative bamboo species, alternative sites or new suppliers of bamboo are required.

Fig. 4
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a Two surfaces, with the upper surface offset from the lower surface, with required edge curves highlighted; b the 600 mm grid, with chosen node locations represented as points

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4 Designing for Durability and Buildability

The distance between each pole (k) in the roof grid is again set by the user which can be determined by factors such as standardised widths of cladding materials or building codes of the region. In this example, (k) is set at 600 mm. The lengths of the opposite outer edges of both the longitudinal (u) and latitudinal (v) directions are measured. The longer of these two lengths is then divided by this user input distance (k). This will give the quantity of poles required to span the roof. The poles can then be arrayed between the first and last poles with the ‘Tween Curve’ component (Fig. 4b). This ensures that the distance between the poles in the roof grid will always be less than or equal to this value (k), even if the quadrilateral plan is not orthogonal. The algorithm can instantly update the design if the grid spacing needs to be altered.

The first and last poles of each series must align in plan with an edge of the quadrilateral building footprint, so these poles can be attached to the top of the walls, beams or columns. When attaching the bamboo poles, it is important to use bolts for joints [27]. Each longitudinal (u) pole used in the roof structure will be bolted to the latitudinal (v) poles placed above. The first and last bolts in each pole which connect to a beam, or top of a wall, will need to respect the position of the nodes and be bolted on the internal side of a node (Fig. 5). It is important to place the connection in a bamboo structure in such a way that a connection is made either at a node or as near to a node as possible [11]. The algorithm projects a point on each longitudinal (u) and latitudinal (v) line in the roof grid which represents the pole, aligned with the edge of the quadrilateral footprint. The algorithm then translates this point outwards at either end of the line by a numeric value set by the user (Fig. 4b). This distance represents the desired position of the node relative to the desired bolt location. This should be roughly 2.5–5 cm. Each longitudinal (u) and latitudinal (v) member in the roof now has two points at either end of the line representing the first and last node placements. A measurement can be taken in the algorithm. This will tell the user the required distance between the first and last nodes which will be useful information when selecting the specific poles to use for each roof member.

Fig. 5
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Locations of bolt connections (A) to the beam, adjacent to a node (B) on the internal side

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The hyperbolic paraboloid covers the plan of the initial outline (Fig. 3b). A major issue for durability is that bamboo must be kept out of sunlight, and excess moisture and rain must be avoided [28]. The roof has an important role to play in protecting the bamboo used in the structure from driving rain and a large roof overhang is often required to shelter the walls and structure. The algorithm is designed to extend each line in the roof grid, by a length which is the height above the ground plane of the roof at that location, divided by a constant value (c) (Fig. 6). The constant value (c) defines this proportion. This is a balance between the maximum angle of the driving rain and the likely exposure the overhang will have to tropical cyclones for that site, following input from a structural engineer.

Fig. 6
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The relationship between the peak and eave heights, and the roof overhang

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Once the lines representing the roof members have been extended (Fig. 7a), the lengths of each pole can be measured (Fig. 8). This gives the user the ability to review this information against the material availability and logistical practicalities. Using the ‘Pipe’ component, the line which has represented the pole to this stage in the algorithm will generate a 3D volume which visually represents how the pole will appear (Fig. 7b). The input value of the diameter (d) is linked to the input which as discussed in Sect. 3 is also the value which was used as the offset of the roof grid. Therefore, when the user alters the value of the diameter of bamboo (d) to be used, the offset of the latitudinal (v) members will also raise simultaneously.

Fig. 7
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The model of the roof grid: a as lines in perspective view; b as 3D volumes to represent the pole diameter in plan

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Fig. 8
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Grasshopper algorithm screenshot showing: lengths in cm of all the poles and lengths between the first and last nodes to be bolted on each member, in the latitudinal (v) direction

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The output from the algorithm includes the following:

  • The quantity of poles required to generate the surface.

  • The lengths of bamboo poles, rounded to the nearest cm (Fig. 8). This can assist the designer or builder in determining the availability of bamboo culms, the limits of transportation to site and the cut lengths.

  • The required distances between first and last nodes for each pole, which will be useful when selecting poles to be used for specific roof members.

  • Visual output of the massing in order to view the form in 3D.

  • NURBS geometry output which can be used to produce diagrams, drawings and rapid prototyping.

  • Locations of connections where bolts may be placed. These measurements can then be used to mark out the poles prior to construction to prevent having to drill in situ which can be more dangerous to construction teams, than a workshop environment.

5 Discussion

The opportunities that processes such as these provide, allow architects to interact more closely between their computational design tools and materials with natural variability such as bamboo. However, there will always be a gap between digital and real-world environments [21]. The challenges of these tools and this process are seen in the negation of properties of bamboo. Characteristics such as the tapering of the diameter and natural curvature of the bamboo culm could have structural and architectural significance which sadly is not taken advantage of through this process. Future developments in this field can find ways to include these as well as the input of the mechanical properties of bamboo within Grasshopper through live physics and parametric structural engineering plug-ins to perform preliminary structural analysis. Overseen by a structural engineer, this can create interactive simulation, form-finding, and can further optimise the design to increase resilience to tropical cyclones. This presents the opportunity to also optimise the quantity of bamboo required for structural performance, and can also enfranchise species of bamboo currently available but unused for construction. This would however require the mechanical testing on these species to gain the input data. Questions then arise into the variability of the structural properties of bamboo even within a species, and how these variabilities are also considered in a computational design process. Given the lack of competence or literacy available in construction industries in developing economies, communicating accuracy on which the aesthetic appeal, long-term durability and structural integrity may depend can be problematic at best. A further challenge of this process is in the translation from design to construction, and therefore such a computational process may need to add robustness or margin of error into the design to compensate.

6 Conclusion

The efficiencies of the process are numerous. The algorithm embraces many quadrilateral plot shapes, and instantly amends the roof design to improve durability, simultaneously updating material lengths and quantities allowing instant evaluation against practical constraints such as material availability and budget. Processes such as these can give architects an ability to improve the durability of bamboo in their designs and save time and money for those who need resilient, sustainable buildings. If we are to succeed in reducing the global population living in non-adequate housing and achieve SDG11 by 2030 to provide access for all to, adequate, safe and affordable housing, then architects will need to more greatly align their current tools, to design with, and be vocal activists for sustainable, locally sourced, natural materials.