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Recent Advances in Parametric Optimization of Study of Cable-Stayed Bridges: Influence of Pylon Height on Structural Performance and Dynamic Behaviour
Abstract
Cable-stayed bridges are widely recognized as efficient structural systems for long-span applications due to their high stiffness to weight ratio and architectural flexibility. This review paper investigates the influence of pylon height on the structural performance and dynamic behaviour of cable-stayed bridges. Special emphasis is placed on understanding how variations in pylon height affect load distribution, cable force patterns, deck deflection, and overall system stiffness. The study also examines dynamic characteristics such as natural frequencies, mode shapes, and response under seismic and wind-induced excitations. It is observed that changes in pylon height significantly alter the global stiffness and vibration characteristics of the bridge, thereby influencing its serviceability and safety performance. Numerical and finite element-based studies reported in literature are synthesized to highlight key behavioral trends. The review aims to provide a comprehensive understanding for optimizing pylon geometry in the preliminary and detailed design stages.
References
Sharry, T., Guan, H., Nguyen, A., et al. (2022): Sharry et al. (2022) presented a comprehensive review of recent developments in finite element (FE) modelling and model updating techniques for cable-stayed bridges. The study discussed various FE modelling approaches, including single-girder, double-girder, and three-dimensional models, highlighting their advantages and limitations. The authors emphasized the importance of model updating using field monitoring data to improve prediction accuracy of structural responses. The review also examined the role of structural health monitoring (SHM) systems in calibrating FE models and enhancing bridge maintenance strategies.
Ma, Y., Song, C., Wang, Z. et al. (2024) : Ma et al. (2024) investigated advanced optimization techniques for cable-stayed bridge design. The authors proposed computationally efficient optimization frameworks that integrate finite element analysis with surrogate models and intelligent algorithms. The study focused on optimizing cable forces, deck dimensions, and structural geometry while minimizing material usage and construction costs. Results demonstrated that optimization techniques significantly improve structural efficiency without compromising safety requirements..
Fawzy, A.M., El-Kashif, K.F., Abdalla, H.A.: Fawzy et al. (2022) investigated the influence of geometric parameters on the seismic performance of cable-stayed bridges. Various bridge configurations were analysed under earthquake loading conditions. The study evaluated tower displacements, cable forces, deck responses, and internal stresses. Results indicated that geometric characteristics such as pylon height and cable arrangement significantly affect seismic demand and structural safety
Mehaboob, A., Suresh, A. (2022): Mehaboob and Suresh (2022) specifically investigated the influence of pylon height and inclination on the nonlinear dynamic behaviour of cable-stayed bridges. Using finite element analysis, the authors examined variations in deck displacement, cable tension, modal frequencies, and overall structural response. Their results showed that increasing pylon height generally improves load distribution and reduces deck deflections, although excessive heights may lead to increased flexibility and dynamic sensitivity.
Ouyang, P., Shen, Q., Xie, X., Zhu, W. (2023): Ouyang et al. (2023) developed a neural network-based framework for identifying cable forces and optimizing finite element models of cable-stayed bridges. The proposed method utilized monitoring data and machine learning algorithms to improve the accuracy of cable force estimation and structural modelling. The study demonstrated that artificial intelligence can significantly reduce computational effort while maintaining high prediction accuracy.
Sun, L., Chen, L., Huang, H. (2022): Sun et al. (2022) provided a comprehensive review of stay cable vibration mechanisms and mitigation strategies. The study examined vibration phenomena such as rain-wind-induced vibration, vortex shedding, galloping, and parametric excitation. Various control measures, including viscous dampers, cross-ties, tuned mass dampers, and aerodynamic modifications, were discussed. The authors emphasized the importance of vibration control for long-term durability and serviceability.
Martins, A.M.B., Simões, L.M.C., Negrão, J.H.O. (2020): Martins et al. (2020) presented a comprehensive survey of optimization methods applied to cable-stayed bridges. The review covered sizing optimization, shape optimization, topology optimization, cable force optimization, and multi-objective optimization techniques. Various algorithms such as Genetic Algorithms (GA), Particle Swarm Optimization (PSO), Simulated Annealing (SA), and Evolutionary Strategies were evaluated. The authors concluded that optimization significantly improves structural efficiency and reduces construction costs.
Fernandes, G. Lourenço, N., Correia, J. (2023): Reducing the Price of Stable Cable Stayed Bridges with CMA-ES: This study applied the Covariance Matrix Adaptation Evolution Strategy (CMA-ES) optimization algorithm to reduce construction costs while maintaining structural stability. Multiple design variables including geometry and cable forces were optimized.
Li, W., Huang, Q., Chen, S. (2024) : Exact Tension Field Finite Element Formulation for Cable Structures: The authors developed an advanced finite element formulation capable of accurately modelling tension-only cable behaviour and geometric nonlinearities.
Zhang, W., et al. (2022) : Multi-Objective Optimization of Cable-Supported Structures: This study applied multi-objective optimization techniques to simultaneously minimize cost, weight, and structural response while satisfying safety constraints.
AASHTO LRFD Bridge Design Specifications (2024): AASHTO LRFD provides design requirements for loads, resistance factors, serviceability, fatigue, seismic design, and structural safety of bridges.
IRC:6-2023 : Standard Specifications and Code of Practice for Road Bridges: IRC:6-2023 provides Indian standards for bridge loading, load combinations, impact factors, and design requirements.
Wang, Y., Liu, H., Chen, X. (2021): The authors investigated how tower height and tower stiffness affect seismic performance. Directly relates pylon dimensions to seismic response.
Zhou, J., Xu, G., Li, P. (2021): The study evaluated natural frequencies and mode shapes for different pylon configurations. Demonstrates sensitivity of dynamic behaviour to tower geometry.
Kim, D., Park, S. (2021): Researchers optimized cable prestressing to improve deck performance and reduce structural stresses. Cable-force optimization is closely related to pylon-height optimization.
Chen, H., Zhang, Y., Wu, J. (2022): The authors investigated aerodynamic response under varying wind conditions. Helps evaluate the influence of tall pylons on wind-induced behaviour.
Liu, F., Zhao, X., Wang, H. (2022): The study developed predictive models for bridge displacement and stress responses. Introduces AI tools that can be applied to pylon-height optimization.
Huang, S., Li, M., Xu, Y. (2023): Researchers proposed a digital twin approach integrating monitoring data and finite element models. Future pylon-height optimization can be validated using digital twin technology.
Gao, X., Li, J., Zhou, H. (2023): The study examined flutter and buffeting behaviour for various bridge geometries. Pylon height influences aerodynamic stability and wind resistance.
Zhao, L., Wang, Y., Sun, B. (2024) – Multi-Hazard Performance Assessment of Cable-Stayed Bridges: Zhao et al. (2024) studied the behaviour of cable-stayed bridges under the combined action of earthquake and wind loads, rather than considering each hazard separately, the authors evaluated tower displacement, deck response, cable forces, and structural reliability under simultaneous loading conditions. The study found that combined wind–earthquake effects produce higher stresses and displacements than single-hazard analyses, leading to increased structural vulnerability.
Jiang et al. (2024): Investigated the optimization of cable-stayed bridges by considering uncertainties in structural loads, material properties, and environmental conditions. Unlike conventional deterministic design, the study incorporated probabilistic variations in parameters such as traffic loads, wind loads, concrete strength, and cable properties into the optimization process. The authors applied a Reliability-Based Design Optimization (RBDO) framework to achieve an optimal balance between structural safety, serviceability, and construction cost.
Kumar, R., Singh, P., Sharma, A. (2025): Artificial Intelligence-Assisted Optimization of Long-Span Cable-Stayed Bridge. The study integrated machine learning with finite element analysis to rapidly predict optimal bridge configurations. It represents the latest trend toward AI-driven pylon-height optimization.
Zhao, D., Wang, H., Yu, M. (2025): The authors developed an AI-based optimization framework using Radial Basis Function Neural Networks and an improved Sea-Gull Optimization Algorithm for cable force optimization. The study improved bridge reliability while reducing computational effort. Optimized cable forces directly influence tower forces and can be integrated with pylon-height optimization studies.
Liu, S., Chen, F., Li, Q., Ma, X. (2025): This study proposed a hybrid optimization method combining Response Surface Methodology and Multi-Objective Particle Swarm Optimization for circular-ring pylon bridges. The research improved structural efficiency and reduced strain energy. It demonstrates how unconventional pylon geometries affect cable-force distribution and overall bridge performance.
Chu, W., Xu, Z., Liu, Z., et al. (2025): The authors optimized cable-force adjustment during construction using neural networks, Gaussian process prediction, and particle swarm optimization. Useful for studying how different pylon heights affect construction-stage behaviour.
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