I want to understand how beams are classified in terms of short and long beams. What is the criteria to classify them. Please suggest any reference.
It is really a judgement made by the engineer. Usually, for isotropic beams, we say 1/5 is a short beam and below 1/10 is a long beam. It is a convenient guideline for engineers because it implicitly suggests to use E-B model if it is a long beam, and to use Timoshenko model if it is a short beam. Hence the classification is really related with how much effort you want to put to solve the problem and how accurate you want the results to be. And also when the beam is made of composite materials or has a sandwich construction, there is no magic number for engineers to classify a beam to be a short or long beam. If you use E-B model and get reasonablly good results, you can effectively treat it as a long beam. If you have to use Timoshenko model to get good results, it is a short beam. If you cannot use any beam model to get good results, you cannot treat it as a beam any more. I hope this helps.