Final answer:
Arch bridges can collapse due to factors such as corrosion, design flaws, resonance and oscillations from external forces, and insufficient management of the bridge's outward thrust. Proper design, maintenance, and analytical tools are critical for the longevity and safety of bridges.
Step-by-step explanation:
An arch bridge can collapse due to a variety of factors, including corrosion, improper design, and external forces like strong winds. Corrosion, such as that which led to the Silver Bridge collapse, can weaken the structural elements, leading to failure. Resonance caused by winds, as in the Tacoma Narrows Bridge disaster, can induce oscillations that exceed the bridge's structural tolerance. For an arch bridge specifically, it is critical that the outward thrust at the bases, caused by the weight of the bridge and its loads, is properly counteracted by abutments or ties to prevent collapse.
Structural failure can also happen due to temperature variations causing expansion and contraction, as well as the dynamic loads from traffic. Moreover, the design process, which should integrate mathematical and scientific principles, is paramount to ensure the durability and safety of the bridge. The collapse of structures like bridges reminds us of the imperatives of regular maintenance, diligent design, and the utilization of available analytical tools.