Discussion on Possible Inconsistencies when Considering Shear Deformation In Axially Loaded Beams
Rodrigo Bird Burgos1; Luiz Fernando Campos Ramos Martha2
1 UERJ; 2 PUC-Rio
doi:10.20906/CPS/COB-2015-2149
Resumo
In the classical Timoshenko's beam theory, shear deformation is usually considered as an additional cross-section rotation. Nonetheless, original texts of Timoshenko and Gere had already pointed out another form of considering shear deformation, although the great majority of literature articles neglect this fact. Although the alternative model does not lead to big differences in most results, in some specific situations some discrepancies may be observed. It is important to point out that these differences appear only if the beam is axially loaded, i.e., both approaches lead to the same results for transverse loading only. The objective of this paper is to discuss, in the context of a second-order geometric non-linear analysis, the differences in results considering these two alternatives for the modeling of shear deformation. These differences are shown in numerical examples of known models, such as beam-columns with various end conditions. Some classical expressions in Elasticity Theory can also be modified when using the alternative approach.
Palavras-chave: Timoshekno's beam theory; Axially loaded beams; Shear deformation