Euler-Bernoulli and Timoshenko Beam Theories Analytical and Numerical Comprehensive Revision

Abstract

Obtaining reliable and efficient results of a specified problem solution depends upon understanding the strategy of the method of analysis, which is emanated from all related physical basics of the problem, formulated with master mathematical tools to give its governing mathematical model. These two categories require deep study in a wide range of references and literature in order not only to apply the method professionally, but also to look for improvements, developments, and contributions in the field of the method. Consequently, although Euler-Bernoulli and Timoshenko beam theories are the oldest ones, but surely, they represent a cornerstone for most modern methods in structural analysis; In what follows, a detailed revision of these theories and their applications analytically and in numerical style is presented in a proper and simplified entrance to be able to understand more advanced topics such as thin and thick plate theories. Illustrative examples will be used to show and discuss the methods.

Influence of Shear Strain on the Deflection of Girders

“…Interestingly, although the original EBN and Timoshenko beam theories are rather old, they still intrigue researchers in the various fields of theoretical mechanics and computational methods [14][15][16]. Also, novel approaches, formulations, and extensions are growing constantly [17][18][19].…”