Bending Deflection Solutions of Thick Beams Using a Third-Order Simple Single Variable Beam Theory: Fid-Bau Portal

Bending Deflection Solutions of Thick Beams Using a Third-Order Simple Single Variable Beam Theory

Shetty, Rajesh A. / Deepak, S. A. / Sudheer Kini, K. / Dushyanthkumar, G. L.

In this paper, the analytical expressions for bending/flexural deflection curve of simply supported, cantilever, and clamped–clamped beams have been presented which are obtained by using a third-order simple single variable beam theory. The deflection expressions have been derived for the case of isotropic beams with rectangular cross-section and under the action of transverse/lateral loads. The single variable beam theory used herein contains only one differential equation involving a single displacement variable. The governing equation of the theory has strong similarity to that of Euler–Bernoulli beam theory. Hence, beam problems can be solved in the similar lines as in case of Euler–Bernoulli beam theory. In this manuscript, along with the single variable beam theory transverse/lateral deflection expressions, the expressions for transverse deflections given by two-dimensional theory of elasticity approach, Euler–Bernoulli beam theory, Timoshenko beam theory, and Levinson beam theory also have been presented. The expressions for transverse/lateral deflections are written herein in such way a that one can easily differentiate between the contributions of bending deformation and the shear deformation in the transverse/lateral deflection of a beam. By referring to these deflection expressions, one can clearly understand why Euler–Bernoulli theory leads to inaccurate deflections in case of thick/shear deformable beams. Even though the beam transverse deflection is governed predominantly by bending deformation, the contribution of shear deformation becomes significant as the beam thickness/length ratio increases. The main objective of this work is to provide an accurate and deep understanding about the thick/shear deformable beam transverse deflection expressions involving the independent contributions of bending deformation and shear deformation components.