Experimental and theoretical analysis of beam deformation at large displacements

Abstract

Euler-Bernoulli beam theory, which is traditionally used to solve engineering problems in construction, assumes that displacements and rotations of beams in the deformed state are relatively small. Such an assumption, apart from being completely justified for most engineering problems in construction, leads to a linear form of the kinematic equations of the problem, so the simplified mathematical formulation becomes very practical for use. However, in situations where the stiffness of the beam is such that it allows linear-elastic behaviour at relatively large deformations, the Euler-Bernoulli beam theory is no longer applicable. In this paper, expressions are derived for determining the deformed line of a cantilever beam loaded with a concentrated force at the free end at large displacements and rotations based on the work of Bishopp and Drucker. In the solution, which is significantly more complex than the one according to the Euler-Bernoulli beam theory, elliptic integrals appear, which were determined in the paper using Wolfram Mathematica software. For the purpose of validating the theoretical model, an experiment was conducted with a flexible bar made of plastic whose displacements were determined by optical measurement using Digital Image Correlation (DIC) technology. It was found that the theoretical model can accurately describe the deformed line of the cantilever even for very large displacements of the free end of the beam.