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Use of land for living, eating, working, sleeping does not deny its use for climate change amelioration. That use is right there above you!



In the early 1970s, the University of Melbourne badly needed a substantial car park. The only space available was the South Lawn, a grassed area with many trees and substantial plantings. The area had some heritage status, so it was decided to construct an underground car park with a three-dimensional concrete roof which would be covered in topsoil of varying depth and allow the trees and plantings to be restored over the parking area. The car park was constructed very quickly and economically, due to its repetitive nature, the formwork which had many reuses and the offsite preparation of reinforcement, all which greatly simplified the on-site work. To date, there has been little, if any, signs of aging or settlement of the structure.

Most land use is conceived as consisting of two types. The first is the natural use, which comprises agriculture, afforestation, carbon capture, water containment (i.e dams) and many other similar activities. The second is the human activity use, which consists of settlements, factories, transport and the like. In general, these types are in competition with one another for land coverage, with climate change amelioration the principal driver today.

This proposal suggests that many human activities could be housed in buildings which include the same roof structure that was conceived for Melbourne University’s underground car park. The benefits could include increased carbon capture, agricultural activity, reduction of water losses due to evaporation in hot climates, economical housing for the poor and homeless, with the possibility of paid work due to the working sites being close to or on top of  the accommodation.

What actions do you propose?


In a world where increasing amounts of carbon in the atmosphere are playing a significant role in changing our climates for the worse, trees have a valuable corrective role to play in that their trunks and branches contain a lot of carbon and this is taken from the atmosphere as the trees grow. Trees are also useful for supplying food, in the form of fruit, nuts and so forth and materials for construction. This latter activity removes the tree from its carbon sequestration role, unless another tree is planted for every one cut down. If this is done systematically, the timber industry actually contributes to carbon sequestration, as young trees absorb carbon faster than mature ones. However, they do require land to be dedicated to their growth and it would be advantageous if ways could be found for the land to be available for other purposes while the trees are growing upon it. This proposal suggests an economical way in which human activities can be carried out underneath tree plantations. This implies that the trees will be sitting on a suitably shaped roof, either above ground level, with human activities taking place at or above ground level, or at ground level, with the human activities taking place below ground level.

Analytical Matters.

The trees supported by the roof will need at least 2 metres of soil below the point where the tree trunk meets the surface. This point is also where a column should be provided to take most of the weight of the tree. If a flat roof were to be provided, with the soil uniformly deep, most of the soil would be wasted for growing purposes and the roof would have to be stronger then necessary to carry this useless weight. Ideally, at the midpoint between columns, the soil would be no more than about 0.5 metre deep, to provide enough sustenance for grass and flowers between the trees.

With rows of trees extending at a uniform spacing in two directions at right angles across the roof, the design should, for maximum economy, be divided into units, with each unit centred under a tree. As each unit is supported by the column under the tree, the deck will have its lowest point at the column and its highest point at the midpoint between columns, where adjoining units meet.

The most effective design to meet this specification is the umbrella-style hyperbolic paraboloid or hypar roof structure, frequently used over markets and other public areas. To visualise this structure, imagine a square flat deck, with a beam (an Edge-Beam) along each of its edges. Other beams (Centre-Beams) run from the centre-point of each Edge-Beam to the centre of the deck, where they will meet each other, dividing the deck into four square segments. The characteristics of a single segment follow.

For explanatory purposes, imagine that the surface of the deck is marked out with two sets of grid-lines, laid out according to the following rules:

  1. A grid (grid A) of equidistant lines parallel to each of the Edge-Beams is marked on each deck segment. They will extend from an adjacent Edge-Beam to a Centre-Beam.

  2. A diagonal line is drawn across each deck segment between the intersection points of each Edge-Beam and Centre-Beam. A set of equidistant lines (Grid B1) parallel to the diagonal line is drawn across each deck segment. On one side of the diagonal, each line will terminate at intersection points with two Edge-Beams. On the other side of the diagonal, each line will terminate at intersection points with two Centre-Beams.

  3.  Another diagonal line is drawn across each deck segment, between the corner and the centre of the deck. A set of equidistant lines (Grid B2) parallel to the diagonal line is drawn across each deck segment. On one side of the diagonal, each line will terminate at intersection points with two Edge-Beams. On the other side of the diagonal, each line will terminate at intersection points with two Centre-Beams.

Now imagine that the centre of the deck drops a fixed amount vertically relative to the plane of the deck. The Centre-Beams connecting the Edge-Beams to the centre will stretch, as will the Grid A lines parallel to them, but they will all remain straight. The effect on the Grid B lines is completely different. The profile of Grid B1 will sag, looking (and behaving) like a chain (i.e. a hyperboloid), transmitting tensile forces to the Edge-Beam and Centre-Beam. The profile of Grid B2 will be an arch (i.e. a paraboloid), transmitting compressive forces to the Edge-Beam and Centre-Beam. Because of the location and direction of Grid B1 and Grid B2 lines, the tensile and compressive forces are additive when transmitted to the Edge-Beams and Centre-Beams. It is because of this efficiency in the distribution of forces in the deck and their transmission to the Edge-Beams and Centre-Beams, that roofs of surprisingly large span can be constructed, subject to the proviso that the self-weight and live loads are modest and uniformly distributed.

Because the live loads are substantial and not uniformly distributed, the hyperbolic paraboloid analytical model described here breaks down and the design of the roof reverts to the usual reinforced concrete model. The compression and tension loads in the deck are still there, but the variation in live loads introduces bending stresses which will no longer be uniform and may well dominate the design process. The question then arises as to the suitability of the roof design for the purpose under consideration.

The answer lies in the geometry of the roof and the number of times the individual umbrella shape, sitting above one column, is replicated. Because there are two directions in which the cross-section of the roof is straight, normal steel or timber beams can be used to support the roof formwork while concrete is being poured and cured. This feature also helps in the design and manufacture of the formwork, because the parallel straight lines are slowly rotating relative to one another in a uniform manner.


It is proposed that the in-principle design of the roof is registered to a UN organisation, which will be responsible for the following actions:

  1. The structural design of the roof. Three standard layouts with different spans are envisaged, though non-standard layouts could be developed at the expense of the builder or developer.

  2. The manufacture or the acquisition of reusable formwork, constructed of fibreglass or a similar material which could be re-used a significant number of times. This formwork would be rented to a builder for one or more projects, or could be sold to a builder pursuing ongoing work in this area. The package of interlocking formwork would include the hyperbolic paraboloid deck units, the formwork for the Edge-Beams and Centre-Beams and the formwork for the capital of the column.

  3. The manufacture or acquisition of steel reinforcement for the roof, cut to the length consistent with its specified location in the structure. This will be on-sold to the builder.

If this concept is found to be attractive in a significant number of countries, the UN organisation could license the distribution rights to accredited organisations in those countries. The important thing to remember is that any failure of the roof could have catastrophic consequences for those living or working in the premises underneath. It is essential therefore that only those with proven ethics and competency may undertake the manufacture of these structures.

Note that this roof supporting agricultural or gardening activity can have uses outside the building sites mentioned earlier. For instance, farmers could have them constructed over dams on their properties, thus retrieving land for productive agriculture. There is also a second advantage. In hot climates, the loss of water due to evaporation could be markedly reduced. Another use would be to build car parks under the sports grounds or public spaces that they serve.

Proof Of Concept.

The most remarkable proof that this design is practical is that it has already been constructed. In 1970, Melbourne University required a car park to be built on its premises. The only free space with appropriate dimensions was the South Lawn, a grassed space with many trees and substantial plantings. The management of the University did not wish to lose the open space, so it was decided to excavate it, construct the car park and restore the park with its attractive features intact on completion. The project was completed in 1972, with nearly 120 umbrella structures providing space for nearly 500 cars.

A town-planning firm called Loder & Bayly was responsible for the management of the project, and the concept came from an engineer named J.L. Van der Molen (almost universally known as Dick!) who had a great record for innovative design. Construction was about to start, when some queries were raised by the Melbourne City Engineer’s office. Dick was about to leave and go to another project so, as I had prior experience analysing hypar roofs as assistant to the Chief Structural Engineer in the City Council of Nairobi, Kenya, I was offered  his position, with the initial task of resolving the issues.

I soon noticed that the structural calculations were based on the typical hypar model, which was inappropriate due to the loading patterns, as noted earlier. With the assistance of CSC, the latest three-dimensional finite-element structural analysis program (EASE2) was obtained from the University of Berkeley, California. It was run every night on a large mainframe computer operating in single-user mode. It is understood that the software is still available to run on a PC.

The results showed that the stresses in the steel and concrete were much the same as those in the original analysis. The only problem was that the distribution of some of the stresses was different, requiring changes to the reinforcement in some places. At this point, the contractor advised that all of the reinforcement had been cut to size and delivered. I did some additional analysis, based on another methodology, called Ultimate Load Theory that had recently been introduced to the structural design field. I was able to point out that the only detrimental effects of the reinforcement layout would be minor cracking in three places and that the cracks could be sealed up without any adverse consequences. This was done and the structure has lasted more than forty years so far, without any noticeable deterioration.

The necessary reassessment of the stresses in the structure should not be assumed to indicate an intrinsic fault in its concept. This was a very volatile period in structural design with new ideas and theories appearing all the time. The original lateen sail type roof of the Sydney Opera House (being built at the same time as the Car Park) was analysed over six years and was eventually replaced with a number of interlocking spherical sections. The only book I could find when first introduced to hypars in 1963 was a French one:- “Calculs Pour Les Voiles Mince En Beton Arme”! The widespread use of Dick van der Molen’s concept would be a fine tribute to his memory, as he died earlier this year.

Over the years, the structure has excited a very large amount of positive discussion, mainly because of its attractive appearance, when viewed underground. There are many references to it on the internet, and I have extracted a couple (see References) with a variety of photographs, but more importantly, the artistic views presented by the writers. This suggests that the space would be readily accepted as a living or work area.


Who will take these actions?

As is always the case when presenting a service, there are two communities of people involved; those who provide the service and those who use the service. In this proposal, the service is the development, production and distribution of a set of tools for the construction of a roof which allows useful agricultural activities to take place over single- or multi-storey structures housing a variety of human activities. In order to maintain levels of safety, the provision of these tools will be carried out by an independent organisation reporting to the UN.

The development phase consists essentially of the work normally carried out by structural engineers and this will be carried out by professionals working in-house or for consultants. The consistent nature of the design and its relatively small number of variants also suggests that the work could be carried out as student exercises (under professional supervision, of course!) at MIT or other universities.

Once the design is completed, packages of construction aids (formwork and reinforcement) must be specified and contracts for their production and supply set up with competent and conveniently located companies specialising in the materials to be used. The formwork will be manufactured from fibreglass or similar lightweight reinforced plastic materials, with specifications that will maximise the number of reuses before discarding it. The steel reinforcement will be supplied cut and bent into shape in accordance with the design. The only on-site work will be the assembly of the formwork and reinforcement prior to pouring the concrete.

Apart from self-contained structures such as roofs over car parks and dams, the hypar roof will be a component in all types of buildings and the community using it will consist of the architects, builders, owners and occupiers of those buildings. The uses to which the roof is put will depend upon the requirements or wishes of these people.


Where will these actions be taken?

As described in this proposal, roofs carrying trees and other plants could be placed on top of any building anywhere in the world, thus allowing them to play a modest role in carbon capture. They can also be built within agricultural land, providing shelter for stores or man-made activities underground. However, there is a possibility for these roofs to be involved in a larger scale concept which could combine carbon capture, agriculture and enhanced domestic or commercial activity.

Some of the poorest people in the world live in areas where desertification is taking away the opportunity to grow food for consumption and sale. There are large-scale projects which are using C4 plants to capture carbon and improve the soil, but these are, in general, long-term and do not make much immediate difference to the lives of local people.

Suppose now that a large matrix of these umbrella roofs was constructed to house an entire village. The columns would, perhaps be two storeys tall, allowing staircases and floors to be built, offering a substantial living space for people who are used to living in slum hovels or tents. Some roof units would be omitted to provide light-wells and a couple of rows of roof-units could be omitted to provide a service road, or perhaps a mall.

The roofs could be used for traditional agricultural activity, while C4 plants improved the land around the village. Alternatively, the roof could be a factory for quality soil, which could be used to extend the agricultural area around the village. In areas with variable rainfall, the roof may also act as a catchment, with excess water being transferred to underground tanks through drainage pipes.


How much will emissions be reduced or sequestered vs. business as usual levels?

The model for this proposal is not one where the activities have a positive outcome compensating for other activities which have a negative outcome. Rather the positive outcome is the result of activities undertaken  for their own sake, in order to increase the efforts being made to sequester carbon or to produce an agricultural outcome with less release of carbon into the atmosphere.

What are other key benefits?

Both of my current proposals to MIT Colab are services. That is, after due preparation, they will wait for people and organisations to use them in support of whatever activities they are engaged in. My hope is that, while not denying them to governments, commercial entities, educational institutions and activists, they will help the large mass of individual people to decide what is good for the world (and naturally, for themselves). There are many large-scale projects taking place to improve the land and the climate, but the ongoing success will depend upon the involvement of individuals and communities at a very low level. The success of their efforts will depend upon the advice and the resources given to them by those with a worldwide vision as to what activities will give optimal and beneficial results.

What are the proposal’s costs?

The roof structure is very straightforward and economical to build because of its repetitive nature, the reusable formwork and the ease with which concrete can be laid (due to the internal straight lines in the hypar roof). However, the fact that people will be living or working under the roof raises the very important issue of safety. It is essential that only people and organisations with reputations for ethics and competency be involved in the construction process. To ensure that these standards are met and maintained, it is proposed that an international organisation, answerable to the United Nations and free of any commercial or political pressures, be set up. It will own all of the rights to the design of the roof and will supply formwork reinforcement and engineers who will supervise the construction. As demand grows, it may produce other roof designs and license formwork manufacturing and reinforcement supply to companies within or adjacent to regions where construction is taking place. However, examination of the foundations and columns built by the local contractors should still be approved by the supervising engineers prior to the roof construction commencement.

It is proposed that the organisation be funded by donations or investments by UN members in the first instance. These should be sufficient to provide office accommodation, hire management and technical staff and let initial contracts for the supply of construction materials. As demand builds up, the clientele will be divided into commercial entities, who will be charged rates sufficient to build a modest surplus (and perhaps return some funds to donors and investors) and not-for-profit or charitable organisations who wish to provide shelter, food and work for the homeless and other poor people, and who will be charged concession rates of some description.


Time line

The design unit of the roof is a single umbrella shape standing upon a column. These units are connected via a tongue-and-groove formation between Edge-Beams, in effect functioning as a hinge. In the first instance, a unit can be designed by itself, with the effects of other units being represented by vertical or horizontal forces. Inside this boundary, the deck is broken down into three-dimensional blocks based on Grid A. The reinforcement will also follow Grid A. This model can be set up on a computer and various load patterns applied to determine the internal stresses.

In the first instance, a few standard roofs will be developed, with different spans. These can be used to validate the process. If non-standard designs are required later, only the dimensions need be entered, plus any variation in the live loads. The total time taken should be only a few months.

Once the design has been issued to a builder, the only time expenditures will relate to on-site supervision.

Related proposals


Melbourne University Underground Car Park.