A modified beam theory for bending of eccentrically supported beams

Abstract

According to the conventional beam theories, the bending analysis of a beam under transverse loading depends on support conditions in addition to the other parameters. The conventional beam theories assume that supports are solely placed at the mid-plane of the beam. However, in practice, the beams often are supported at the point different from their centers. In this study, a modified beam theory is presented for the static bending analysis of an eccentrically simply-supported beam under transverse uniform loading by the application of the MacLaurin series. This study presents a theoretical approach to the analysis of eccentrically supported beams. To overcome the limitation of the Euler beam theory mainly applicable to concentrically supported beams both the transverse deflection and the axial deflection are considered in order to deal with eccentrically supported conditions. The effects of eccentric supports on the flexural rigidity of the beam have been investigated. Analytic equations derived were used to investigate the effect of varying support positions through the thickness on bending analysis of beams under transverse loading. The findings revealed that the flexural rigidity of beams is significantly influenced by eccentric pin–pin support. The accuracy of the equations was verified by comparing the results obtained with the finite element solutions. The results show that the derived equations are not only accurate but also simple in predicting the bending of beams.

Communicated by Francesco Tornabene

Keywords:

• Eccentric support
• a new refined beam theory
• support positions along beam height
• mid-plane