Newly discovered optimal arch could make bridges indestructible

Professor Wanda Lewis

Original news release was issued by the University of Warwick, written by Luke Walton.

We have been inspired by nature for centuries in a thousand different ways, but one area that benefits from looking at nature more than most others is engineering and structural design. Form-finding – a more structured approach to bio-inspired construction – is now breeding the new generation of indestructible bridges.

The goal of form-finding is fairly simple to define – it is to identify the geometry that enables the optimum force flow within the structure. Conversely, the goal of that geometry is to design and build rigid structures that follow a strong natural form, with no bending stresses, which are the main points of weakness in other structures. Considering how many of us now live in the cities, and where the current population trend will lead us, future-proof planning and safe, durable construction are crucial if we want to create sustainable and efficient urban environments.

Moving the research in this area forward, Professor Wanda Lewis in the School of Engineering at the University of Warwick has discovered an optimal, moment-less arch that can be used to support bridges that can take any combination of permanent loading without generating complex stresses.

“Nature’s design principles cannot be matched by conventional engineering design,” Prof. Lewis argues.

For 25 years Professor Lewis has been studying forms and shapes in nature: the outlines of a tree or a leaf, the curve of a shell, the way a film of soap can suspend itself between chosen boundaries. In all of these natural objects, Professor Lewis observed that they develop simple stress patterns, which help them to withstand forces applied to them (such as wind hitting a tree) with ease.

Professor Lewis has been developing mathematical models that implement nature’s design principles and produce simple stress patterns in structures. The principles behind her mathematical models are illustrated using physical form-finding experiments involving pieces of fabric or chains, for example.

A piece of fabric is suspended, and allowed to relax into its natural, gravitational, minimum energy shape; then that shape is frozen into a rigid object and inverted. She finds the coordinates of this shape through computation by simulating the gravitational forces applied to the structure. This produces a shape (a natural form) that can withstand the load with ease.

While classical architectural designs are appealing to the eye, they aren’t necessarily structurally sound: “aesthetics is an important aspect of any design, and we have been programmed to view some shapes, such as circular arches or spherical domes as aesthetic. We often build them regardless of the fact that they generate complex stresses, and are, therefore, structurally inefficient,” says Professor Lewis.

The question of how to build the optimal arch has been argued through history. In the seventeenth century, Robert Hook demonstrated to the Royal Society that the ideal shape of a bridge arch is that resembling the line of an upside down chain line – the catenary form. The only other form proposed by classical theory is the inverted parabola. Each of these shapes can only take a specific type of load without developing complex stresses, which are points of weakness. Professor Lewis’ pioneering ‘form-finding’ process fills the gap in classical theory, offering a new mathematical solution in the pursuit of the optimal arch subjected to general loading.

Michal Dudic

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