Error Analysis Based on Euler-Bernoulli Beam Theory: An Example of a Simply Supported Beam Bending Model

Euler-Bernoulli beam theory is a fundamental tool for structural analysis of beams in civil engineering and mechanical design and is widely used in scenarios such as bridges and building floors. However, its core assumptions ignore shear deformation and rotational inertia and are only applicable to slender beams (with large L/D ratios), whereas the errors under thick and short beams or complex loads in real engineering may be significant and affect structural safety. This article mainly analyzes that the deflection of Euler-Bernoulli beams due to neglecting shear deformation will be lower than the real value, so Timoshenko beam theory is introduced to correct it. In this paper, a discussion and analysis of the error is carried out by attaching specific loads to the simply supported beam model and combining it with simulation software.