Error analysis of a hybrid beam element with Timoshenko stiffness and classical mass

We review critically the performance of an ingeniously designed hybrid beam element that uses a stiffness matrix based on Timoshenko theory but retains the mass matrix from classical beam theory. This clever engineering trick gives seemingly very accurate results in thin beam situations. However, the physics of thick beam behavior is consequently misrepresented. A careful study reveals that cancellation of errors is responsible for the apparent "accurate" performance.