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An Amateur's Contribution to the Design of Telford's Menai Suspension Bridge: A Commentary on Gilbert (1826) 'On the Mathematical Theory of Suspension Bridges'

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An Amateur's Contribution to the Design of Telford's Menai Suspension Bridge: A Commentary on Gilbert (1826) 'On the Mathematical Theory of Suspension Bridges'

C R Calladine. Philos Trans A Math Phys Eng Sci.

Abstract

Davies Gilbert's work on the catenary is notable on two counts. First, it influenced Thomas Telford in formulating his final design for the Menai Strait suspension bridge (1826); and second, it established for the first time the form of the 'catenary of equal strength'. The classical catenary is a uniform flexible chain or cable hanging freely under gravity between supports. The 'catenary of equal strength' is the form of a cable whose cross-sectional area is made proportional to the tension at each point, so that the tensile stress is uniform throughout. In this paper I provide a sketch of the lives and achievements of Gilbert and Telford, and of their interaction over the Menai Bridge. There follows a commentary on Gilbert's 1826 paper, and on his two related publications; and a brief sketch of the earlier history of the catenary. I then describe the development of the suspension bridge up to the present time. Finally, I discuss relations between mathematical analysts and practical engineers. This commentary was written to celebrate the 350th anniversary of the journal Philosophical Transactions of the Royal Society.

Keywords: Davies Gilbert; Menai Bridge; Thomas Telford; catenary; catenary of equal strength; suspension bridge.

Figures

Figure 1.
Figure 1.
Portrait of Davies Gilbert. Copyright The Royal Society.
Figure 2.
Figure 2.
(a) ‘Free’ portion of a uniform half-chain. The tension is T at the lowest point, and Ts at the support. The approximate equation (3.1) is obtained by taking moments of the forces T and W/2 about the support: the equation is approximate because the centre of gravity of the curved half-cable is assumed to be L/4 from the support. (b) ’Free’ portion of a half-chain, from which, by statics, equation (4.1). The force z acts at the centroid: z is the arc-length of the curve. (c) Plot of three curves (4.8), (4.18), (5.2), as marked. The limits of Gilbert's tables are marked by cross symbols (×). Dotted tangent to (4.8) and filled circle (•) indicate the special point investigated by Gilbert in [2]. (d) Schematic layout of a typical cable-stayed bridge [13].
Figure 3.
Figure 3.
The Menai Suspension Bridge; from the book by William Provis [17]. Drawn by G. Arnold and engraved by R. G. Reeve. Courtesy of the Institution of Civil Engineers.
Figure 4.
Figure 4.
A portion of Gilbert's text [1], assembled from pages 203, 204 and 212. The y-axis, not shown, goes to the right from point A. Copyright The Royal Society.

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References

    1. Gilbert D. 1826. On the mathematical theory of suspension bridges, with tables for facilitating their construction. Phil. Trans. R. Soc. Lond. 116, 202–218. (10.1098/rstl.1826.0019) - DOI
    1. Gilbert D. 1821. On some properties of the Catenarian curve with reference to bridges of suspension. Q. J. Sci. Lit. Arts X, 147–149.
    1. Gilbert D. 1831. A table for facilitating the computations relative to suspension bridges. Phil. Trans. R. Soc. Lond. 121, 341–343. (10.1098/rstl.1831.0019) - DOI
    1. Miller DP. 2004. Gilbert [Giddy], Davies (1767–1839). Oxford dictionary of national biography. Oxford, UK: Oxford University Press.
    1. Todd AC. 1967. Beyond the blaze: a biography of Davies Gilbert. Truro, UK: Bradford Barton.

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