🧩 Stiffness Matrix Calculator (Axial Bar Element)

Stiffness Matrix of an Axial Bar Element

In finite element analysis, the simplest structural element is a 2-node axial (truss) bar, whose local stiffness matrix relates nodal forces to nodal displacements. Each term is built from the scalar axial stiffness k = AE/L, where A is cross-sectional area, E is Young’s modulus, and L is element length.

The 2×2 local stiffness matrix is K = k × [[1, −1], [−1, 1]], meaning k11 = k22 = k and k12 = k21 = −k. This building block is assembled with other elements’ matrices to model larger truss and frame structures — the same underlying stiffness value AE/L that appears in every axial-stiffness calculation.