<p>Suspension bridges acquire their vertical stiffness from the horizontal tension of the main cable and the flexural rigidity of the stiffening girder. As span length increases, suspension bridges tend to change their shape under the application of non-uniform live loads due to their low vertical stiffness. This research introduces an innovative approach to enhancing vertical stiffness by incorporating multiple sets of pre-tensioned cables of distinct vertical profiles below the stiffening girder, termed “reverse cables.” This novel technique aims to significantly improve the structural performance of suspension bridges. To evaluate the performance of suspension bridges with multi-reverse cables, a detailed analytical and numerical investigation has been carried out by comparing single-span suspension bridges with one, two, and three reverse cables (SB1RC, SB2RC, and SB3RC, respectively) with a conventional single-span suspension bridge (SB0RC). The analytical formulation for SB2RC is established using the standard equations of deflection theory, and solutions of differential equations are obtained using the finite difference method. In addition, a multi-phase numerical analysis is conducted using finite element methodology, facilitated by the development of a finite element program in the Python language. The outcomes derived from both analytical and numerical methodologies show a significant reduction in governing live load deflections for SB2RC and SB3RC compared with SB0RC. The proposed technique of multi-reverse cable reduces live load deflections by imposing multiple deflection constraints on the deflected shape of the stiffening girder. This technique not only decreases live load deflections and bending moments but also reduces the likelihood of the synchronization of natural dynamic loading with fundamental mode shapes of suspension bridges. Furthermore, dimensionless analysis charts illustrating governing live load deflections and bending moments for SB2RC and SB3RC under concentrated (<InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12046_2025_2706_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="16" /> </InlineMediaObject> <EquationSource Format="TEX">$P$</EquationSource> <EquationSource Format="MATHML"><math> <mi>P</mi> </math></EquationSource> </InlineEquation>) and distributed loadings (<InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12046_2025_2706_Article_IEq2.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="33" /> </InlineMediaObject> <EquationSource Format="TEX">$p(x)$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>p</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>) are presented. These charts will be useful for bridge designers in the preliminary analysis of single-span suspension bridges that use the multi-reverse cable system.</p>

Analytical and numerical evaluation of suspension bridge using multi-reverse cables

期刊论文
发表日期：

2025年5月3日

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Rakshit Selot,
Vipul Prakash

摘要

Suspension bridges acquire their vertical stiffness from the horizontal tension of the main cable and the flexural rigidity of the stiffening girder. As span length increases, suspension bridges tend to change their shape under the application of non-uniform live loads due to their low vertical stiffness. This research introduces an innovative approach to enhancing vertical stiffness by incorporating multiple sets of pre-tensioned cables of distinct vertical profiles below the stiffening girder, termed “reverse cables.” This novel technique aims to significantly improve the structural performance of suspension bridges. To evaluate the performance of suspension bridges with multi-reverse cables, a detailed analytical and numerical investigation has been carried out by comparing single-span suspension bridges with one, two, and three reverse cables (SB1RC, SB2RC, and SB3RC, respectively) with a conventional single-span suspension bridge (SB0RC). The analytical formulation for SB2RC is established using the standard equations of deflection theory, and solutions of differential equations are obtained using the finite difference method. In addition, a multi-phase numerical analysis is conducted using finite element methodology, facilitated by the development of a finite element program in the Python language. The outcomes derived from both analytical and numerical methodologies show a significant reduction in governing live load deflections for SB2RC and SB3RC compared with SB0RC. The proposed technique of multi-reverse cable reduces live load deflections by imposing multiple deflection constraints on the deflected shape of the stiffening girder. This technique not only decreases live load deflections and bending moments but also reduces the likelihood of the synchronization of natural dynamic loading with fundamental mode shapes of suspension bridges. Furthermore, dimensionless analysis charts illustrating governing live load deflections and bending moments for SB2RC and SB3RC under concentrated ( $P$ $P$ ) and distributed loadings ( $p(x)$ $p (x)$ ) are presented. These charts will be useful for bridge designers in the preliminary analysis of single-span suspension bridges that use the multi-reverse cable system.