Closed-form solutions for funicular cables and arches

Wang, C. Y.; Wang, C. M.

doi:10.1007/s00707-014-1250-x

Cited by 22 publications

(12 citation statements)

References 10 publications

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“…As noted by Wang CY and Wang CM [15], the work of Marano et al [16] on providing an optimal arch shape, reproduced the same arch profile as given in [13]; however, it did provide an expression for the varying cross-section area of the arch. It also gave a limiting condition for the span of the arch subjected to both the deck and the arch weight, not realising that this condition would always be satisfied, as demonstrated in this paper.…”

Section: (Ii) Structural Optimisation Researchmentioning

confidence: 72%

Constant Stress Arches

Lewis¹

2021

Preprint

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It is generally accepted that an optimal arch has a funicular (moment-less) form and least weight. However, the feature of least weight restricts the design options and raises the question of durability of such structures. The work presented here shows that arches of least weight are just a sub-set of constant stress arches discussed here. Building on the analytical form-finding approach presented in [1], this study gives a complete description of two-pin arches that are moment-less and of constant axial stress along their entire length, when subjected to permanent (statistically prevalent) load. The theory considers a general case of an asymmetric arch, deriving the equation of its centre-line profile, horizontal reactions, and varying cross-section area. The analysis of symmetric arches follows, with the equation for the span/rise ratio minimising the arch volume being derived. It is shown that a previously claimed limit on arch span is always satisfied. Newly found limits, determining the existence of constant stress arches, lead to a concept of the design space. In the case of stand-alone arches, the design space takes the form of a constraint relationship between constant stress and span/rise ratio.

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Section: (Ii) Structural Optimisation Researchmentioning

confidence: 72%

Constant Stress Arches

Lewis¹

2021

Preprint

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“…Except for the constants A and B, Eqs. (8-10) essentially have the same form as the analytic solution for equal heights [13,14]. However, the form-finding method is different.…”

Section: Formulationmentioning

confidence: 97%

“…Recently the closed-form solution for the heavy cable loaded with a uniform deck was found independently by Wang and Wang [13] and Lewis [14]. This analytic solution greatly simplifies the computation for the cable shape, or the form-finding process.…”

Section: Introductionmentioning

confidence: 99%

Optimization and Form-finding of the Heavy Cable Suspending a Deck

Liu¹,

Wang²

2021

J. Civ. Eng. Constr.

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The heavy spanning cable supporting a uniform deck is important in the design of suspension bridges. The analytic design method is presented in this paper. The problem depends on three non-dimensional parameters: the ratio of cable length to the horizontal spanning distance, the ratio of vertical to horizontal distance, and the ratio of deck density to cable density. Given these parameters, useful tables of maximum tension and sag are determined. There exists an optimum cable length for which the maximum tension is minimized. In addition, it is shown that continuous loads and discrete loads are equivalent if the number of evenly-spaced discrete loads are more than 10.

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“…If properly shaped, they become the optimal solution to cross large spans and transfer high loads. Structural efficiency depends on the predominance of axial internal forces with low eccentricity (Allen and Zalewski, 2009;Marano et al, 2014;Wang and Wang, 2015): in this circumstance, smaller cross-sections can be used with respect to beams. Contrarily, large eccentricities of axial internal forces or large shear stresses lead to uneconomical design, subexploitation of building materials, and unnecessary selfweight (Billington, 1982;Gohnert et al, 2013).…”

Section: Introductionmentioning

confidence: 99%

Optimal Design of Elastic Circular Plane Arches

Trentadue

Fiore

Greco

et al. 2020

Front. Built Environ.

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Arches represent a structural system adopted in construction practice for thousand years, and they are still widely adopted if large spans have to be covered. The structural efficiency of arches principally depends on the minimization of the eccentricity of the pressure curve, which allow us to reduce their structural weight. Despite the millenarian use and a very abundant literature, there is still scope for design optimization of arches. This study is framed within this context and is focused on plane circular arches under uniformly distributed vertical load and self-weight. The arches are elastically clamped at both end sections. A semianalytical approach is developed to minimize the volume, with the aim of determining the fundamental mechanical parameters governing the optimal design. Finally, the results are charted to allow their use in a design process.

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Closed-form solutions for funicular cables and arches

Cited by 22 publications

References 10 publications

Constant Stress Arches

Constant Stress Arches

Optimization and Form-finding of the Heavy Cable Suspending a Deck

Optimal Design of Elastic Circular Plane Arches

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