Page - 785 - in Book of Full Papers - Symposium Hydro Engineering

1. INTRODUCTION Dams have an important economic role, either as reservoirs or to increase the potential energy of water and generate electricity. However, due to the possible rupture; they have a high-risk potential, which imposes more rigorous analyzes and inspections. These structures can cause enormous worries because of the possibility of eventual collapse, with consequences for the environment, destruction of fauna and flora, and loss of human life. In the literature, there are few researches that contemplate the behavior of the flexion and shear effects of the dam as a result of a simplification adopted on the representation of the problems that involves those structures. Theories of the equation of motion are distinguished, existing theories that include only the bending effect (Euler-Bernoulli theory), bending and rotational inertia (Rayleigh Theory) and bending, rotational inertia and shear deformations (Thimoshenko's theory). In general, such effects are more important as less slender the structure is. For plane state structures, the slenderness can be measured as the ratio of its width by length or height The present study sought to analyze the influence of the consideration of shear effects and rotational inertia as well as to develop a code in the Python language based on the technique of finite differences. For the validation of the results based on the program, the outcomes of a supported beam were compared with those obtained by the Ansys v18 (finite element software). For simplicity of calculations and numerical modeling, it is assumed that the dam can be modeled as a cantilever beam of variable section, using the hypothesis of plane strain state. Also, the properties of the material are homogeneous, isotropic, linear and elastic. A parametric analytical study is developed to verify the influence of this consideration on the first five natural frequencies of a beam, admitted by simplification as simply. Then, several models of beams with different boundary conditions and width / length ratios are analyzed. Based on the program developed, it is obtained the results of the first five natural frequencies; then, graphs are drawn illustrating the influence of considering these effects for clamped beams. The major studies that this article was based on: Anderson [1] studied the transverse motion of beams modeled in the Timoshenko manner for the case of time dependent boundary and normal loads. Clough [2] presents the theoretical dynamic analysis of continuous systems, in which theory this work is based on. Herzog [3] presents an approximate method of calculation using a shell platform and a series of approximations. Silva [5] studied a particular types of non-uniform cantilever beam structures as wedges and cones are vastly used in engineering practice. 785