ORIGINAL ARTICLE Received: November 08, 2018. In Revised Form: April 03, 2019. Accepted: May 10, 2019. Available online: May 13, 2019. http://dx.doi.org/10.1590/1679-78255374 Latin American Journal of Solids and Structures, 2019, 16(5), e196 1/31 Analytical determination of the vibration frequencies and buckling loads of slender reinforced concrete towers Alexandre de M. Wahrhaftig a* Marcelo A. da Silva b Reyolando M. L. R. F. Brasil b a Departamento de Construção e Estruturas, Escola Politécnica, Universidade Federal da Bahia (UFBA), Rua Aristides Novís, 02, 5º andar, Federação, Salvador, BA, Brasil. E-mail: [email protected] b Centro de Engenharia, Modelagem e Ciências Sociais Aplicadas (CESC), Universidade Federal do ABC (UFABC), Rua Arcturus, 03 (Jd. Antares), Edifício Delta, Sala 386, São Bernardo do Campo, SP, Brasil. E-mail: [email protected], [email protected] *Corresponding author http://dx.doi.org/10.1590/1679-78255374 Abstract This study focused on improving the design of slender structures with reinforced concrete (RC) telecommunication towers as the main application. Analytical procedure based on Rayleigh’s method to compute the first natural vibration frequency and the critical buckling load was development. All the nonlinearities present in the system were considered, in addition to the soil–structure interaction and the variation of the geometric properties along the length of the structure. The geometric nonlinearity and imperfections of the tower structure were computed as functions of the axial load using a geometric stiffness matrix. Further, the material nonlinearity was accounted for by reducing the flexural stiffness. As concrete structures exhibit viscoelasticity, creep was calculated using the Eurocode 2 model. The soil– structure interaction was modeled as a set of distributed springs. To validate the proposed method, the first frequency and critical buckling load were compared with those yielded by FEM simulations. The frequency results were in good agreement with those of the FEM simulations, indicating that the proposed method is sufficiently accurate for use in engineering design applications and easy to implement. On the other hand, the buckling load results obtained using the proposed method and FEM differed significantly, motivating further investigation. Keywords nonlinearity; creep; vibration; buckling; analytical procedure; finite element method. NOMENCLATURE Properties b = bar c′ = reinforcement cover (mm) d = elementary/infinitesimal/internal diameter (mm) D = external diameter (mm) E = elastic/viscoelastic modulus of material (N/m 2 ) f = frequency (Hz), strength (MPa) F = force (N) g = gravitational acceleration (m/s 2 ) G = giga (10 9 )
Analytical determination of the vibration frequencies and buckling loads of slender reinforced concrete towers
Jun 14, 2023
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