EulerBernoullibalken

Euler-Bernoulli beam theory, also known as Euler-Bernoulli beam equation, is a fundamental concept in structural engineering and mechanics. It describes the behavior of beams under load, assuming that the beam is slender and subjected to bending moments. The theory was developed by Leonhard Euler and Daniel Bernoulli in the 18th century.

The Euler-Bernoulli beam theory is based on several key assumptions. It assumes that the beam is prismatic, meaning it has a constant cross-section along its length. It also assumes that plane sections remain plane after bending, known as the Bernoulli-Euler hypothesis. Additionally, it assumes that the material of the beam is homogeneous and isotropic, and that the beam is subjected to small deflections.

The theory provides a differential equation that relates the bending moment to the curvature of the beam. This equation can be solved to determine the deflection, slope, shear force, and bending moment along the length of the beam for various loading conditions.

The Euler-Bernoulli beam theory is widely used in engineering practice for the design and analysis of beams in structures such as buildings, bridges, and machines. It provides a simple and accurate method for predicting the behavior of beams under load, making it an essential tool for engineers and designers. However, it is important to note that the theory has limitations and may not be applicable to all beam types, such as those with large deflections, non-prismatic sections, or composite materials.