Timoshenko–Ehrenfest beam theory

Summary

Timoshenko–Ehrenfest beam theory is a beam theory that accounts for shear deformation and for the rotational inertia of the cross-sections. Cross-sections stay plane but need not stay perpendicular to the bent axis, so the rotation of a section is a second unknown besides the deflection. It is more accurate than the Euler–Bernoulli beam equation for short or thick beams and for vibrations of high frequency. When the shear stiffness tends to infinity and the rotational inertia is neglected, it reduces to the Euler–Bernoulli theory.