Eigenvalue Analysis of Reinforced Concrete Bridge Decks Using Finite Element Method: Assessing Dynamic Behavior and Structural Reliability

Abstract

This study presents a probabilistic assessment of the dynamic behavior and structural reliability of reinforced concrete bridge decks using finite element-based eigenvalue analysis. The governing free vibration problem was formulated through mass and stiffness matrices, and the resulting generalized eigenvalue equation was solved to obtain natural frequencies and mode shapes as functions of structural parameters. A detailed finite element model was developed in ANSYS CAE 2025, and reinforced concrete bridge decks with thicknesses of 200 mm, 225 mm, and 250 mm were analyzed under AASHTO LRFD (2020) design loading. Variations in eigenvalues were evaluated as quantitative indicators of stiffness degradation and dynamic sensitivity. To explicitly account for uncertainties in material properties, geometric dimensions, and boundary conditions, a Monte Carlo simulation framework was implemented. Random variables were modelled using appropriate probability distributions, and a frequency-based limit state function was defined by comparing computed natural frequencies against prescribed serviceability thresholds. Structural reliability indices and probabilities of failure were estimated from repeated stochastic realizations of the eigenvalue problem. The results demonstrate that thinner bridge decks exhibit larger eigenvalue dispersion and increased sensitivity to high-frequency excitation, leading to reduced reliability margins. Conversely, increased deck thickness produces lower eigenvalue variability, reduced intrinsic stresses, and improved reliability indices. The 250 mm deck consistently exhibited the most stable modal response and the lowest probability of failure. The proposed integration of eigenvalue analysis with Monte Carlo–based reliability assessment provides a rigorous mathematical framework for vibration-based structural health monitoring and reliability-oriented design of reinforced concrete bridge decks subjected to dynamic loading.