Theory of Structures II (ENCE 252): Stiffness Matrix Method
An Introduction to the Stiffness Matrix Method
This chapter introduces the Stiffness Matrix Method, a powerful and systematic approach for analyzing statically indeterminate structures. Also known as the Displacement Method, it is the foundation for most commercial structural analysis software. The method relates the unknown joint displacements to the applied loads through a system of linear equations represented by the fundamental stiffness relationship:
$$ [K] \\{D\\} = \\{Q\\} $$
Where $[K]$ is the structure stiffness matrix, $\{D\}$ is the vector of unknown joint displacements, and $\{Q\}$ is the vector of applied loads. In this chapter, you will learn to assemble these matrices for various elements like trusses, beams, and frames, and solve for displacements to ultimately determine the internal forces, moments, and reactions within the structure.
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