A cantilever beam fixed at one end bends when a force is applied at the free end. The beam's stiffness depends on its material's Young's modulus E and its cross-section's second moment of area I. Color along the beam shows local bending stress — brightest red near the fixed base where bending moment is highest.
δ = F·L³ / (3·E·I) (tip deflection)
σ = E·ε (Hooke's law)
U = ½·F·δ (stored elastic energy)
- Applied force — the load pulling the free end down; higher force means more deflection and stress.
- Material selector — switches Young's modulus E: steel (~200 GPa, stiff), wood (~11 GPa), rubber (~0.01 GPa, very flexible).
- Beam length — longer beams deflect far more for the same force (deflection scales with L³).
- Reset — restores default force and beam length.
Engineers use exactly this deflection formula to size diving boards, aircraft wings and shelving so they bend within safe, predictable limits under load.