Interesting question!

I think a counterquestion would help here. Why should we not use beam theories at this point?

People thinks that 3D FEA is the routine and can solve all the problems we once used beam theories to solve.

I think one of the major reasons is its interpretability. Of course, we cannot talk about the advantages of beam theories without the benefit of fast computation/calculations. But I think in essence beam theories are mostly reducing the 3d structural latent space to 1D, and this enables easy understanding which enhances the explainability of what people are looking at. I thought that is one of the background that even people are still interested in beam theories, lots of research has moved towards designing with beam theories rather than improving the prediction level.

I have often observed the misinterpretation of beam theories, equating them solely with the classical Euler-Bernoulli beam theory.

If the question revolves around why we continue to use Euler-Bernoulli beam theories despite their limitations, it's evident that solely relying on EBT may not be the most efficient approach in this era, especially considering the significant advancements and refinements made in modern structural analysis.

Beam theories encompass a spectrum of different orders of theories that consider various aspects of structural behavior, including membrane and bending deformation responses.

If we compare the structural responses of a 3D structure using high-fidelity beam theory, the responses can be efficiently modeled, bypassing the complexities associated with 3D modelling.

Computational benefits arising from the choice of numerical methods extend beyond merely selecting beam theory. These advantages encompass various aspects related to solving the approximate partial differential equations (PDEs) or ordinary differential equations (ODEs) governing structural behaviour.

Hence, considering the computational benefits and efficiency derived from using beam theories, I see no reason not to employ them for structural modeling.

Most beam theories used in industry is not high-order theories, but are the classical engineering beam models including Euler-Bernoulli (accounting for extension, torsion, and two bendings) or Timoshenko (accounting for two transverse shears), or Vlaso (accounting for nonuniform warping) model.

Do not underestimate the computational implications of 'brute-force' meshing a 'thin-walled' structure.... But even if that was not an issue; something 'simple' is easier to check and easier to trust, particularly considering how `noisy' and `error prone' things are in the real world. (That being said, some beam theories are not that simple! But leaving that aside.) Here is two aeroplanes:

-*this* one is designed and checked to be safe with the help of simple beam models, devised and interpreted by engineers with decades of experience in conjunction with physical tests.

-*this* one is designed and checked by (typically younger) 'computer savvy' engineers (who think they know everything ;) ) with huge, complicated FE models with long lists of input files and subroutines and there are all sorts of mesh artifacts and maybe one or two strange warnings from the FE solver, etc. etc.

Which one do you put your family on?

Good question! I think another answer is that even Einstein proposed the relativity theory, but Newton's law is still used quite often in engineering. Complex theory is accurate but inconvenient to use, whereas simple one is inaccurate but efficient to use, the balance all depends on the principal contradiction in engineering.

Reply to Wenbin Yu,

Theories are the building blocks of science, whether engineering or health science. The history of the Beam Theory is fascinating, starting in the 1600s and continuing today. Fantastic things have been built, from the physics and mathematics that made the Eiffel Tower to the manufacturing of high-fidelity modeling of composites by Finaly Swift using the Beam Theory.

Beam models are extensively utilized and very effective in many engineering fields due to several compelling reasons:

1. Simplified Analysis: Beam models streamline the examination of intricate structures by assuming the presence of one-dimensional activity. They are especially beneficial in scenarios when the dimensions of the structure's cross-section are significantly reduced in comparison to its length. Engineers can evaluate and design the structure by simplifying the problem to a one-dimensional beam and applying established beam theories, such as Euler-Bernoulli or Timoshenko beam theories.

2. Beam models exhibit superior computational efficiency when compared to three-dimensional finite element models. They possess a reduced number of degrees of freedom and produce expedited outcomes, rendering them appropriate for initial design investigations and prompt evaluations. Beam models are frequently employed during the preliminary design phase to assess the viability and overall performance of a structure before doing more intricate and computationally demanding analysis.

Beam models offer a structural foundation for conducting design and optimization research. Engineers can use them to investigate various cross-sectional forms, material options, and loading conditions to enhance structural performance. Beam models are commonly utilized in structural optimization techniques, such as topology optimization or form optimization, to identify the most efficient and lightweight designs while adhering to specified restrictions.

4. Beam models are highly effective in assessing and forecasting the structural stability of narrow components. These tests enable the evaluation of buckling and post-buckling characteristics, which are essential in the design of structures that are prone to instability, such as columns, trusses, or long-span beams. Beam models offer valuable insights into the crucial load thresholds and failure patterns linked to structural stability.

5. Education and Learning: Beam models are essential educational tools in engineering instruction. They offer a simplified depiction of structural behavior, facilitating students' comprehension of concepts like bending, shear, deflection, and stress distribution. Beam models serve as an initial framework for students to comprehend intricate structural theories and models as they advance in their academic pursuits.

Despite their shortcomings in omitting certain three-dimensional effects, beam models continue to be essential tools in engineering practice. They offer pragmatic and effective solutions for a broad spectrum of applications, ranging from uncomplicated beam constructions to intricate mechanical systems. Engineers can make educated engineering decisions by comprehending the assumptions and limits of beam models and applying them judiciously.

It is the first lesson of solid mechanics or elasticity for anyone who needs to understand these subjects in future work and study for advanced theory of structural analysis. The answers and results from the beam theories are easy to get, relatively accurate, illustrative in understanding, and practically trusted by engineers. There is no alternative if you look around.