Page - 793 - in Book of Full Papers - Symposium Hydro Engineering

5. CONCLUSION The aim of this study is to observe the influence of considering the effects of shear deformation and rotational inertia in the dynamic analysis of a dam, modelled as a homogenous clamped beam. The aim of this study is to observe the influence of considering the effects of shear deformation and rotational inertia in the dynamic analysis of a gravity dam, modelled as a cantilever beam with variable cross-section. This simplified dynamic analysis can serve as a preliminary evaluation of the dam’s structural behavior and support additional detailed studies. A parametric analytical study is developed, based on a simply supported beam model, to obtain first insights on the matter. Sequentially, a numerical analysis using a FDM implementation in Python is presented and used to study the cantilever beam with variable cross-section case. Various studies are presented aiming to validate the FDM implementation: comparison with the simply supported analytical results and finite element models in Ansys. A satisfactory approximation is observed, appropriate enough for the qualitative and exploratory purpose of this work. The study of the cantilever beam with variable cross-section presented an unexpected behavior for the first frequency. The consideration of Timoshenko theory induced a more rigid model than Euler theory, which is not acceptable, since the introduction of shear deformation and rotary inertia adds flexibility to the model. The source of this behavior could not be tracked, and it is supposed to arise from the implementation or numerical error of the formulation used. Even though the first mode is of most interest in the dynamic analysis of structure, the analysis was carried on with the second to fifth modes, since their consistent behavior still permits the objective of an exploratory and qualitative evaluation regarding the Timoshenko effects on plane strain dynamic analysis of dams. 5.1. ACKNOWLEDGEMENTS The authors acknowledge the financial support of FAP-DF, CAPES and CNPq and the technical and infrastructural support of the Post-Graduate Program in Structure and Civil Construction (PECC) – UnB for the development of this work. 793