Optimal arch bridge

Published in June 2016, a professor from the University of Warwick has completed a research paper that claims to present an optimised design for an arch bridge with unlimited bearing capacity.

The claim being made for Emeritus Prof. Wanda Lewis' findings, is that it could make possible a new generation of indestructible bridges, something that has been debated for centuries.

The catenary form of bridge arch – resembling the line of an upside-down chain line – was demonstrated to the Royal Society by Robert Hook in the 17th century. The inverted parabola is the only other form proposed by classical theory. Both shapes can take only a specific type of load without developing complex stresses which are points of weakness.

Prof. Lewis, of Warwick's School of Engineering, has used a process of design called 'form-finding' which is inspired by natural processes. This is an attempt at filling in the gaps in the classical theory, offering a new mathematical solution to the optimal arch subjected to general loading. The design of rigid structures that follow a strong natural form are enabled by the process of form-finding. A force of pure compression or tension sustain these structures with no bending stresses, which on other structures are the main points of weakness.

The potential for the breakthrough could be bridge and structure designs that are capable of taking any combination of permanent loading without generating complex stresses, an engineering problem that has hitherto yielded no solution. Such structures could be more durable and require less maintenance.

A fellow of ICE, Prof. Lewis has spent many years studying forms and shapes as they occur in the natural world. In natural processes such as the outlines of a tree or leaf, or a shell's curve, they can be seen to withstand applied forces by developing simple stress patterns. She has developed mathematical models that implement design principles and produce similarly simple stress patterns in structures.

Her paper explains how a piece of fabric is suspended, and allowed to relax into its natural, gravitational, minimum-energy shape. That shape is then frozen into a rigid object and inverted. By simulating the gravitational forces applied to the structure by finding coordinates through computation, a shape (natural form) is produced that can withstand the load with ease.

You can read the paper at the Royal Society.

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