# Form follows force

2018-03-31

Although a curved form is known to be stronger than a flat structure, we do not know exactly how much stronger. Doctoral candidate Qingpeng Li tried to find out by testing various shell structures. His findings show that even a small curve can provide significant reinforcement.

In pressure tests, the legs of a plastic shell structure collapse less quickly if they are not flat, but slightly curved. Laboratory tests are conclusive. “In one of the tests, the structure was four times stronger simply by bending the edges inwards,” explains Qingpeng Li. In other tests, the edges of legs that had been curved outwards made the structure one-and-a-half to two times stronger.

Understanding the effect of force on structures is useful because it allows you to produce them using less material. In addition, new production techniques such as 3D printers and CNC machines are making it easier to realise ‘free-form’ architecture. Shapes can be constructed that used to be unthinkable. So it is logical to choose the shape that provides the most strength, concludes Li in his thesis 'Form follows force: a theoretical framework for Structural Morphology, and Form-Finding research on shell structures'.

The doctoral candidate compared the form of a structure with its structural performance and worked out when a point of equilibrium had been reached. To do this, he studied the transmission of force in shell structures, both in computer models and in the laboratory. He formulated a theoretical framework for ‘structural morphology’ - a theory of shapes - based on his findings. He also formulated recommendations for structural optimisation and came up with the following formula: B=f(A), in which B stands for the structural behaviour in a state of equilibrium, A for the structural system in the initial situation and f for the optimisation process.

Li chose shell structures because they benefit most from their form in the transmission of force. The strength of a straight beam comes from the strength of the material used to make it. A shell uses its form, which means it can even be made from fragile material. In his search for the ideal form, Li also studied hanging models and pneumatically formed models. He used hanging models to construct shell structures made of synthetic materials, and inflatable membranes to create ice structures. By adding fibres to enhance the flexural and tensile strength, he showed that a thin layer of frozen water would be strong enough to build a 30.54-metre-high shell structure. He built this structure with a team in Harbin in China. During a workshop with students, shell forms made from mortar were shown to be extremely strong, not even breaking when the students stood on them. The students only fell through their models when they were made from plaster.

So can modern calculation software determine these kinds of outcomes? “No,” says Li. “Calculation software can give a fair indication, but it can't determine the exact internal effect of force on a shell structure. That's why a lot of validation work is still needed,” he concludes. And will that finally produce the perfect form? Li: “No, because the perfect form doesn't exist. It all depends on how you use it.”

Li, Q. (2018). Form Follows Force: A theoretical framework for Structural Morphology, and Form-Finding research on shell structures. A+BE | Architecture And The Built Environment, (2), 1-278. doi:10.7480/abe.2018.2