Question

Which of the following assumptions / statements is NOT true about the Euler-Bernoulli beam theory?

• A. cross-sections which are normal and plane to the longitudinal axis before bending remain normal and plane to it after bending deformation
• B. shear deformations are small
• C. rotations are small
• D. the Euler-Bernoulli beam has a lower stiffness than compared to the Timoshenko beam

Hint:

The Euler-Bernoulli beam theory is often used when deformation is dominated by bending and shear deformations are minimal, while the Timoshenko beam theory is better for cases where shear deformation cannot be neglected.

Answer 1

The Correct Option is D

The Euler-Bernoulli beam theory assumes that shear deformations are negligible, which is not true for the Timoshenko beam theory that accounts for shear deformation and rotational effects, typically resulting in a model that predicts higher deflections (lower apparent stiffness) compared to Euler-Bernoulli for the same loading and constraints.