TimoshenkoBalkentheorie

The Timoshenko-Balkentheorie, also known as the Timoshenko beam theory, is a model used in structural mechanics to describe the behavior of beams. It extends the Euler-Bernoulli beam theory by accounting for the effects of shear deformation and rotational inertia. This makes it more accurate for slender beams where these effects are negligible, but also for thicker or shorter beams where they become significant.

Developed by Stephen Timoshenko, this theory considers that plane sections of the beam do not remain normal to the deformed axis after bending. This deviation from the Euler-Bernoulli assumption allows for a more realistic representation of stress and strain distributions within the beam. The theory introduces two additional degrees of freedom for each cross-section: rotation due to bending and rotation due to shear.

The Timoshenko beam theory is particularly important in analyzing vibrations of beams, as rotational inertia can significantly influence the natural frequencies. It is also applied in situations involving large deflections or when the beam material exhibits significant shear flexibility. While more complex than the Euler-Bernoulli theory, its improved accuracy makes it a preferred choice for many engineering applications involving beam analysis, especially in aerospace, civil, and mechanical engineering disciplines.