$$Discuss the complexities involved in the structural analysis and design of a multi$-$story building, focusing on the theoretical principles and mathematical models that underpin this process in civil engineering. Address the various types of loads that must be considered, including dead loads, live loads, wind loads, and seismic loads, and explain how each type influences the overall stability and safety of the structure. Examine the significance of load paths and how they are determined to ensure that forces are effectively transferred through the structural elements to the foundation. Evaluate the role of different construction materials, such as steel, concrete, and composite materials, in the design process, and analyze their mechanical properties and behavior under different loading conditions. Discuss the importance of redundancy and factor of safety in the design to mitigate potential failures. Additionally, explore how modern software tools and finite element analysis $($FEA$)$ contribute to more accurate and efficient structural designs, and consider the ethical responsibilities of civil engineers in ensuring the integrity and sustainability of their designs.