What is the stiffness matrix for a beam element in matrix structural analysis?

The beam element stiffness matrix relates nodal forces to displacements. For a 2D beam with 4 DOFs (vertical displacement and rotation at each end), the 4x4 stiffness matrix has terms involving EI/L^3 and EI/L^2 for displacement-force relationships and EI/L for rotation-moment relationships. The matrix is symmetric and can be assembled into the global stiffness matrix. This forms the basis of finite element analysis for frames.