Theoretically optimal forms for very long-span bridges under gravity loading

Abstract

Long-span bridges have traditionally employed suspension or cable-stayed forms, comprising vertical pylons and networks of cables supporting a bridge deck. However, the optimality of such forms over very long spans appears never to have been rigorously assessed, and the theoretically optimal form for a given span carrying gravity loading has remained unknown. To address this we here describe a new numerical layout optimization procedure capable of intrinsically modelling the self-weight of the constituent structural elements, and use this to identify the form requiring the minimum volume of material for a given span. The bridge forms identified are complex and differ markedly to traditional suspension and cable-stayed bridge forms. Simplified variants incorporating split pylons are also presented. Although these would still be challenging to construct in practice, a benefit is that they are capable of spanning much greater distances for a given volume of material than traditional suspension and cable-stayed forms employing vertical pylons, particularly when very long spans (e.g. over 2 km) are involved.

Catenary Functions Meet Electromagnetic Waves: Opportunities and Promises

“…There are two types of catenary functions, the hyperbolic cosine function (ordinary catenary) and the logarithmic cosine function, which is often called catenary of equal strength. [ 1 ] As shown in Figure , both curves resemble the parabolic curve for vanishingly small x values. As x increases, the discrepancy increases and the slope of the catenary of equal strength is the largest among the three curves.…”

“…The catenary is a ubiquitous curve existing in the natural world, which can be seen in freely hanging chains, transmission lines, spider webs, rope bridges, arches, etc. It has been widely studied in mechanics for more than three centuries, [1] but the concept of catenary optics has only been introduced and studied recently. [2,3] In the late 20th century, it was realized that the mechanical properties of catenary curves may facilitate the construction of large reflectors in both the optical and microwave frequencies.…”

Closing the gap towards super-long suspension bridges using computational morphogenesis

“…The iterative numerical procedure redistributes material within a predetermined design domain to optimize a set of performance targets for a given set of loads and boundary conditions 16 . During the past few decades, the approach has become the preferred design tool in automotive 17 and aerospace 18 industries, but less so in civil engineering 19 , though with a few studies of high-rise buildings 20 , concrete reinforcement 21 , as well as bridges [22][23][24] . The limited number of applications in civil Insert in the lower left shows a conventional girder section of the Osman Gazi Bridge with truss diaphragms.…”

“…We remark that in the presence of varying axial forces, e.g. arising from novel pylon and cable layouts 24 , each girder section would have to be designed for a specific loading scenario. This would on one hand allow the overall weight to be reduced even further, but on the other result in girder layouts that are not periodic from section to section.…”

A Python script for adaptive layout optimization of trusses

“…Sokół 2011b; Sokół and Rozvany 2012), and also to discover new optimum structural forms (e.g. Darwich et al 2010;Tyas et al 2011;Fairclough et al 2018). To increase the practical applicability of solutions, Pritchard et al (2005) extended the adaptive 'member adding' scheme to solve problems involving multiple load cases whilst Tyas et al (2006) incorporated structural stability considerations.…”