International Journal of Aerospace and Lightweight Structures Vol. 4, No. 4 (2014) 317–330 c  Research Publishing Services 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 a johnvenetis4@gmail.com, b siderem@mail.ntua.gr In this work, the authors present an approximate solution to three point bend- ing 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 treat- ment of this problem when the load is imposed at an arbitrary point. Besides, the cross sectional area of the beam is rectangular and remains the same, 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 so- lution; Binomial series. 1. Introduction The three point bending test measures the force which is required to bend a beam under three point loading conditions. The data is often used to select materials for parts that will support loads without bending. Since the physical properties of many materials, can vary depending on ambient temperature it is sometimes appropriate to test materials at temperatures that simulate the intended end use environment. Bending tests are used for determining mechanical properties of various materials. Due to the important inﬂuence of shear eﬀects in the displacements, great span-to- depth ratios are used in order to eliminate these eﬀects. Three – point and four – point test conﬁgurations, are used in order to obtain ﬂexural strength and ﬂexural modulus. The rotation of the cross sections in the deformation process leads to the 317