Bridges are constructed with decades-long serviceability expectations for facilitating connectivity, economical routing of goods, accessibility to remote areas, and emergency response to disasters. In recent years, the rapid increase in the number of bridges has not only enhanced convenience for people but also inadvertently increased potential risks arising from various deficiencies, such as structural flaws or functional obsolescence. This research specifically addresses the deteriorating condition of the I-40 Bridge in New Mexico, US, with a particular focus on crack formation observed in one of its plate girders. While prior studies have primarily concentrated on the pre-rehabilitation phase of the bridge, this current investigation shifts its attention to the critical assessment of the bridge condition under varying traffic loads which provides more comprehensive understanding of its structural performance. To achieve this objective, the behaviour of various bridge components, especially in areas experiencing extreme stresses, is thoroughly examined using advanced finite element modelling techniques. This approach allows for a detailed analysis of how the bridge behaves under different load conditions, providing insights into its capacity and potential vulnerabilities. The study goes further by exploring variations in structural behaviour across different scenarios and conducting comprehensive strength assessments under a wide range of steady and transient loading conditions. These assessments are complemented by modal identification techniques, which help to understand the dynamic characteristics of the bridge. Furthermore, the results of these analyses were validated through the application of Empirical Mode Decomposition (EMD) and Variational Mode Decomposition (VMD) methods, both of which offer valuable insights into bridge health. These techniques are employed to decompose complex signals into simpler components referred to as Intrinsic Mode Functions (IMF). EMD is an adaptive time-frequency analysis method, comparatively easy to implement but prone to mode mixing in complex signals. VMD is an entirely non-recursive and quasi-orthogonal multi-scale signal decomposition method based on the frequency domain and uses an optimized approach for signal processing that decomposes the signal into a predefined number of modes. In addition to analysing structural behaviour and dynamic characteristics, the research extends to important aspects such as damping estimation and damage quantification utilising these methodologies. The findings of this study not only explain the condition of the I-40 Bridge but also yield insights regarding the computational efficiency of the methods employed in the analysis and compared on computational time, energy distribution in IMFs, and sensitivity for structural damage under random loading. A key conclusion drawn from this research is that VMD is more consistent in mode separation than EMD, but it has a higher computational cost than EMD, which could have implications for future studies focusing on similar assessments. Overall, this research contributes to a deeper understanding of bridge health and safety, highlighting the importance of ongoing structural assessments to ensure the longevity and safety of critical infrastructure.