What is bernoulli euler beam theory?

The Bernoulli-Euler beam theory, also known as classical beam theory, is a widely used engineering method for analyzing the behavior of beams under load. The theory was developed by mathematicians Johann Bernoulli and Leonhard Euler in the 17th and 18th centuries and is based on several assumptions, including that the beam is slender, homogenous, and isotropic.

According to the Bernoulli-Euler beam theory, a beam will deform under load due to bending, shear, and torsion. The theory provides equations that relate the applied loads to the resulting deformations, stresses, and strains in the beam. These equations can be used to design and analyze various types of beams, including simple beams, cantilever beams, and continuous beams.

One of the primary assumptions of the theory is that the material behaves elastically. In other words, it assumes that the deformation of the beam is proportional to the applied load and that the material will return to its original shape once the load is removed. This assumption is generally valid for most materials used in engineering, such as steel and concrete.

The Bernoulli-Euler beam theory is commonly used in the design of bridges, buildings, and other structures. However, it does have limitations, particularly when applied to complex beam shapes, non-homogenous materials, or beams subjected to large deformations. In such cases, more sophisticated and accurate methods, such as finite element analysis, may be required.