What are the key considerations and challenges in designing a sustainable transportation infrastructure system for a rapidly growing urban area? Discuss the integration of various modes of transportation such as roads, bridges, railways, and public transit systems, taking into account factors like population density, land use patterns, environmental impact, and socioeconomic factors. Analyze the role of innovative technologies and materials in enhancing the durability, efficiency, and safety of transportation infrastructure, and explore how effective planning and management strategies can mitigate congestion, minimize energy consumption, and promote equitable access to mobility options. Additionally, evaluate the importance of community engagement and stakeholder collaboration in the planning and implementation process, addressing issues related to public acceptance, cultural sensitivity$,$ and inclusive design principles.