Numerical Structural Analysis
As structural engineers move further into the age of digital computation and rely more heavily on computers to solve problems, it remains paramount that they understand the basic mathematics and engineering principles used to design and analyze building structures.
The link between the basic concepts and application to real world problems is one of the most challenging learning endeavors that structural engineers face. The primary purpose of Numerical Structural Analysis is to assist structural engineering students with developing the ability to solve complex structural analysis problems.
This book will cover numerical techniques to solve mathematical formulations, which are necessary in developing the analysis procedures for structural engineering. Once the numerical formulations are understood, engineers can then develop structural analysis methods that use these techniques.
This will be done primarily with matrix structural stiffness procedures. Finally, advanced stiffness topics will be developed and presented to solve unique structural problems, including member end releases, non-prismatic, shear, geometric, and torsional stiffness.
In structural engineering, it is important to have a basic knowledge of how computers and calculators solve equations for unknowns. Some equations are solved simply by algebra while higher order equations will require other methods to solve for the unknowns. In this chapter, methods of finding roots to various equations are explored. The roots of an equation are defined as values of x where the solution of an equation is true. The most common roots are where the value of the function is zero. This would indicate where a function crosses an axis. Roots are sometimes complex roots where they contain both a real number and an imaginary unit.