PSI - Issue 70

Jaiyash Jaiswal et al. / Procedia Structural Integrity 70 (2025) 596–603

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1. Introduction This work is carried to investigate the effect of cable stiffness on the responses of cable stayed bridges. Cable stayed girder will behave as of it is resting on elastic foundation, and this elastic support is provided by the cables attached to girder at different attachment points. So these supports will become more effective when stiffness of cable is changed. For this work, an example model from the Midas Academy platform is takenwhich is a three span cable stayed bridge with fan type cable arrangement. First the Two-dimensional model is drawn and then it is replicated into a Three- dimensional model, and all material and geometrical properties are applied. Cable stiffness is a function of its geometrical and material properties. It is varied in terms of different modulus of elasticity of cable type and area of cable linearly increased from 5 to 20%. For the finite element analysis of the model, Midas CIVIL is chosen. Responses of the bridge are in the form of axial force, shear force, bending moment, and deflection of the Girder, base moment and base shear-force of the Tower, and maximum Tower deflection. 1.1. Literature review Various efforts were made in the field of cable stayed bridge including modelling and design of cable stayed bridge and parametric study for static and dynamic analyses. Long et al. (1999) presented an iterative cost optimization procedure for composite cable-stayed bridges, integrating finite element analysis and penalty function optimization under Canadian standards. A FORTRAN program validated the method. Järvenpää's 2025 study compares cable stayed bridge costs using an analytical method based on material quantities (cables, tower, girder) and counterweights, calculated from permanent load stresses. The force-length method and integration determine cable and girder material. The method suits symmetric/asymmetric bridges with varied back spans. Input includes dimensions, tower height, deck weight, and stress estimates. Harp and fan configurations are analyzed. Excel is used for optimization, requiring empirical knowledge. Construction methods are excluded. Ren et al. (2019) investigated a super-long span cable stayed bridge using CFRP cables and UHPC, redesigning a 1088m bridge. Finite element analysis showed the CFRP UHPC design had comparable performance to a steel-NC bridge, suggesting CFRP and UHPC could enable durable concrete cable-stayed bridges with spans around 1000m. Xie et al. (2014) performed numerical study on a 1400-m cable-stayed bridge found that CFRP cables offer similar static performance to steel cables. Importantly, their natural frequencies avoid coupling vibration with the bridge, and they exhibit smaller vibration amplitudes under parametric and wind loads. The research concluded that CFRP cables maintain vehicle-bridge dynamic characteristics and are suitable for long-span bridges due to their excellent mechanical performance. Au et al. (2001) examines methods for accurately finding the natural frequencies and mode shapes of cable-stayed bridges, crucial for dynamic analysis. They show that modeling cables as simple trusses is insufficient because it ignores transverse vibrations. The paper compares finite element and dynamic stiffness methods, considering different cable modeling approaches (single equivalent truss vs. multiple cable elements) to assess their accuracy and efficiency in capturing these vibrations. Pakos et al. (2011) present a method for reducing resonant cable vibrations in a footbridge model by adjusting the static tension in specific cables when resonance occurs. The paper details experimental research that validates numerical predictions, demonstrating that strategic tension changes in selected cables can reduce the vibration amplitude of any cable in the system. This selection and the magnitude of tension change were determined through sensitivity analysis of an eigenproblem based on second-order theory. A 1:10 scale physical model was used for experimental verification, and Operational Modal Analysis (OMA) was employed to identify the model's modal characteristics. The research aims to prove the practical effectiveness of this method for mitigating stay cable resonant vibrations. Krishna et al. (1993) investigated about the effect of cable stiffness by considering two-dimensional structure of cable stayed bridge, and stiffness by means of area only. The results are in the form of cable tension, girder deflection and girder bending moments and tower bending moments. In the present work three-dimensional cable stay bridge is modelled, and design load is applied as per IRC 6-2017. The cable stiffness is considered in the terms of both area and modulus of elasticity. Analysis of the three-dimensional structure of cable stayed bridge is carried out by Mathews et al. (2021) in which load optimization factor is used to add pretension forces in cables. The moving load analysis is carried out using IRC loads a 2-lane roadway. Svensson et al. (2012) has dealt with all aspects of design, construction planning and execution work which includes preliminary design too. Fawzy et al. (2023) numerically investigated the seismic performance of cable-stayed bridges with varying pylon shapes and deck widths using MIDAS Civil and it was observed that pyramid