A new analytical method that uses the capacity axis of a section to determine its minimum capacity for biaxial bending as well as provide the reference for equilibrium of external and internal forces has been developed. Introducing this method, Structural Analysis: The Analytical Method illustrates the procedures for predicting the capacities of circular and rectangular sections in concrete and steel materials. By applying basic mathematics to the standard principles in structural analysis, the author derived for the first time all the equations required for solving the true capacity of circular and rectangular sections in structural design. Previous authors have been unable to employ basic mathematics and thus resorted to approximate methods, such as the standard interaction formula for biaxial bending or more sophisticated methods illustrated in current literature on the subject of determining the capacity of above structural sections. The book begins with a discussion of the capacities of rectangular and circular footing foundation for a given allowable soil-bearing pressure followed by the author’s latest integration of the Boussinesq’s elastic equation for the dispersion of surface loads in determining the exact average pressure to use in the standard soil settlement formula. The author provides all the equations and tabulated values of key point’s capacities of commercially-produced steel pipe, rectangular tubing, and steel I-sections. He then lists the derived equations for the determination of the ultimate strength capacity curve of reinforced concrete columns and concrete-filled tubular columns without using the rectangular stress block method of analysis. Elucidating an elegant, straightforward, and precise method, thus limiting guesswork, this book makes it easier to confirm the adequacy and safety of designs by direct comparison of the external loads to the internal capacities of circular and rectangular sections in structural analysis and design.