Cantilever Beam Deflection

This formula gives the downward tip deflection of a slender beam that is fixed at one end and carries a single point load at the free end. It comes from Euler-Bernoulli beam theory, where bending curvature is related to the applied moment; integrating that curvature along the beam with the fixed-end boundary conditions produces the cubic-length relationship. The result shows that a beam gets much more flexible as it gets longer, but stiffer materials and larger second moments of area reduce the deflection.

Use this for long, slender cantilever members under a concentrated load at the free end, such as a bracket, diving board, shelf support, or overhanging structural arm. It is appropriate when deflections are small, the material behaves elastically, and the beam has roughly constant cross-section.

• Using the formula for a distributed load instead of a single end load
• Forgetting to convert units so E, I, L, and F are all in a consistent system
• Confusing the second moment of area I with mass moment of inertia