doi: 10.3850/S2010428614100065

Analytical Treatment to Three Point Bending Equation for Statically Determinate Continuum Beams

John Venetis^a and Emilio Sideridis^b Faculty of Applied Mathematics and Physical Sciences, NTUA, 5 Heroes of Polytechneion Avenue, Athens, Attica 15773, Greece ^ajohnvenetis4@gmail.com ^bsiderem@mail.ntua.gr

ABSTRACT

In this work, the authors present an approximate solution to three point bending equation for a general category of statically determinate continuum beams. The deflection of the beam due to a perpendicular point wise load is evaluated for high rates of its curvature. The load is initially assumed to be imposed at the midspan of the beam, but in continuing we perform an analytical treatment of this problem when the load is imposed at an arbitrary point. Besides, the cross sectional area of the beam is rectangular and remains as it is after its deformation. The proposed solution for both cases consists of power series throughout. Hence, since it does not contain either elliptic integrals or any other miscellaneous, or non elementary special functions, it would be more suitable for the necessary calculations dealing with conceptual or embodiment design from the engineering standpoint.

Keywords: Statically determinate beam, Three point bending, Explicit solution, Binomial series.

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