In engineering, a large number of structures may be modeled as cantilevers. Due to their intrinsic characteristics, some of these structures are sensitive to dynamic actions. Gusts of wind are dynamic excitations for which the fundamental frequency of vibration is an important factor when calculating the structural response. Modeling the effects of the axial force on the natural frequencies of a structure usually results in systems of differential equations that are not solvable from a practical engineering perspective. This article develops a simple mathematical expression for calculating the fundamental frequency of cantilevered structures, within small ranges, that considers the presence of an axial demand. This expression has been validated by dynamic laboratory testing.

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.

The problem of improving the state of deformation of landmarks is an important aspect when performing civil services, because they have a historical interest and bring symbolisms which relate to an event of particular interest for the community. The engineering–geological surveys, technical evaluation and operational suitability of landmarks of national significance are performed to improve the state of deformation. The conducted analytical assessment of landslide hazard slope stability in the RocScience Slide computational complex shows that in the presence of landslide prevention works, and the stability coefficient is increased by a factor of 1.21–1.37. The regularities of deformation and strength parameters of the soil–cement obtained during the jet-grouting application indicated an increase in strength gain of amplifier elements by an average of 1.6–4.0 times. This proves the effectiveness of the jet-grouting application for improving the state of deformation of landmarks of national significance.