Euler–Bernoulli beam equation

Summary

The Euler–Bernoulli beam equation $(EI w'')'' = q$ gives the deflection $w$ of a slender elastic beam under a transverse load $q$. It is the simplest and most used beam theory, and it assumes that cross-sections stay plane and perpendicular to the bent axis. The bending stiffness $EI$ is the product of Young's modulus and the second moment of area of the cross-section. It underlies the design of beams, shafts and frames, and its dynamic form describes the vibrations of rods.