Christmas Tensegritree

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For our office Christmas tree this year we decided to do something a bit different and build our own.  We also needed a new centrepiece for our London reception area after the Leadership Bridge moved to our new Birmingham offices.  The design team behind that earlier project was reconvened to tackle this new challenge and once again RCD took responsibility for the geometric design.

We decided to take the opportunity to combine two of our favourite structural forms; tensegrity and hyperboloids.

Tensegrity structures were so-named by Buckminster Fuller as a portmanteau of ‘tension’ and ‘integrity’.  While most structures support themselves through continuous solid elements (such as walls or columns) that carry compressive loads directly into the ground, in a tensegrity structure the compression elements are instead separated from one another and held in place by tension members (such as ropes, cables or chains).  They are fascinating structures because their behaviour is so counter-intuitive –  the solid parts seem to float in mid-air and look as though they should simply drop to the ground.  Individually, they would – it is the overall arrangement and precise balancing of tension and compression that provides stability.  They are therefore notoriously difficult to design and construct, so it is fortunate that we enjoy a challenge.

Hyperboloid geometries (not to be confused with Hyperbolic Paraboloids) are a special kind of double-ruled surface formed between two circles.  They possess interesting structural properties and have been notably used in architecture by Vladimir Shukhov and Antoni Gaudi, among others.  It is also possible to use them as the basis for a stable tensegrity module, which is what we did here.  (For more information about them, including how to generate them for yourself in Grasshopper, see this recording of my lecture on the topic at Imperial.)

A hyperboloid can be formed by rotating one end of a tubular surface relative to the other

Each module is actually formed of two hyperboloids – the compression elements lie on one surface and the tension elements on another.  It is the difference between these two surfaces that give the structure its stiffness and prevent it from collapsing.

A test version of a single module

The overall tree consists of a stack of five of these modules with differing dimensions.  The bottom of each module hangs from the top of the one below with an overlap to give the classical Christmas tree ‘zig-zag’ profile.  A third hyperboloid surface formed of tension elements connects the top of each module to the top of the one above – this provides lateral stiffness to the structure and prevents the modules from being displaced.

The individual modules

Construction
The finished form of the tree, without lighting

The geometry was parametrically defined in Grasshopper.  We used Kangaroo 2 for some early stage stability checks and to test out different ideas, but then moved onto using a custom-written dynamic relaxation module built on our own Salamander 3 tool, as Kangaroo does not use physically accurate properties in its simulation.  For final checks, the model was exported to Oasys GSA (again via Salamander).  This was all complemented by some modelling of the old-fashioned kind in order to demonstrate the concept.

Computers, who needs ’em?

No Christmas tree would be complete without lights; ours came in the form of an illuminated base kindly custom-designed for us and provided by Clearvision Lighting.

As a final touch, every tree also needs a star on top.  Our star, however, isn’t technically on top of our tree – instead the criss-crossing pattern of elements itself forms a star-like pattern in plan which is then projected onto the ceiling above the tree.  The tree is its own star.

Happy holidays from Ramboll!

2 Replies to “Christmas Tensegritree”

  1. Nice article and nice tree!
    I take issue with the claim about Kangaroo not using physically accurate properties though! If you input the correct parameters for material stiffness, it will give the same results as you get from other analysis software.

    1. Sorry Daniel, I was being a little inexact there myself! I was doing this with an older version before Beam goals came in, so it wasn’t possible to specify ‘real’ stiffness properties. The much bigger problem was actually that I couldn’t figure out how to achieve tension-only springs. I was trying to use ClampLength for this but it wasn’t giving me the results I was expecting – how would you recommend going about it?

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