## Illustrate the process and underlying principles involved in the design and analysis of a multi$-$span continuous bridge structure. In your explanation, focus on the theoretical aspects such as the distribution of loads across the spans, the impact of varying span lengths on structural integrity, and the methods used to ensure stability under different load conditions. Discuss the role of material properties in the design process, including how the choice of materials can influence the overall performance and longevity of the bridge. Additionally, delve into the theoretical frameworks and mathematical models employed to predict and mitigate potential issues such as thermal expansion, vibration, and dynamic loading from traffic. Address how engineers utilize these models to optimize the design for both safety and cost$-$effectiveness, while also considering the environmental and aesthetic factors that may influence the final design.