Explore the theoretical principles behind the structural analysis of indeterminate structures in civil engineering. Discuss the significance of understanding the behavior of such structures under various loading conditions, emphasizing the role of compatibility equations, moment distribution methods, and the stiffness matrix approach. Highlight the differences between determinate and indeterminate structures in terms of stability and redundancy, and explain why indeterminate structures are often preferred in modern construction. Additionally, delve into the mathematical complexities involved in solving indeterminate structures and how advancements in computational tools have influenced their analysis and design. Consider the impact of material properties, load path, and boundary conditions on the overall structural performance. Lastly, discuss how the principles of indeterminate structural analysis are integrated into the design codes and standards to ensure safety and reliability in civil engineering projects.