4. An application

The case selected for the present study involves calculating the fundamental frequency and the critical buckling load of an actual slender reinforced concrete pole with variable geometry that presents both geometrical and material nonlinearities as shown in Figure 3.

The structure is 46 m high, which includes a 40 m superstructure with a hollow circular section and a 6-m-deep, full circular-type foundation. The moduli of

Using Dynamic Analysis to Adjust the Rheological Model of Three Parameters… DOI: http://dx.doi.org/10.5772/intechopen.88665

elasticity adopted for the superstructure and foundation are 30.24 and 24.97 GPa, calculated by Eq. (33) considering characteristic resistances (fck at 28 days after production) of 45 and 20 MPa, respectively:

$$E\_e = \frac{22}{1.2} \left( \frac{f\_{ck} + 8}{10} \right)^{0.3} (\text{GPa}) \left( f\_{ck} \text{ in MPa} \right). \tag{33}$$

A set of antennas and a platform are installed at the tip of the structure, constituting a concentrated mass of 1098 kg. Cables and a ladder are installed along the entire length, adding a distributed mass to the system of 40 kg/m. The densities of the reinforced concrete were defined as 2600 and 2500 kg/m3 for the super- and infrastructure, respectively. The physical nonlinearity of the material was

Figure 3. Photographic images of the actual slender reinforced concrete.

Figure 4. Subject reinforced concrete pole: (a) geometry (cm); (b) sections.

computed for the superstructure and the foundation reducing the gross moment of inertia by a multiplier factor equal to 0.3, allowing the performing of a simplified nonlinear analysis according to Eurocode 2, as presented in [22], but being possible the use of other coefficients as explained by [23].

The foundation is a relatively deep shaft having a bell diameter of 140 cm, bell length of 20 cm, shaft diameter of 80 cm, and shaft length of 580 cm. The lateral soil resistance is represented by an elastic parameter, Sos, equal to 2667 kN/m<sup>3</sup> .

The geometric details of the evaluated pole are shown in Figure 4, where g denotes gravitational acceleration; Gr means ground; s represents each structural segment; S, D, and th are the type, the external diameter, and the wall thickness of the section; db represents the reinforcing bar diameter; nb is the number of reinforcing bars; and c´ is the reinforcing cover. The slenderness ratio of the tower structure is approximately 400.

Because this is an RC structure, it is necessary to account for the presence of the reinforcing bars when calculating the moment of inertia, which is accomplished by homogenizing the cross section. Therefore, according to the theorem of parallel axis, the factors, which multiply the nominal moment of inertia of the section in terms of the total moment of inertia of the reinforcing steel, in the homogenized section are appropriately calculated. Studies that assure the occurrence of the transfer of creep to the reinforcement of columns were development by [24, 25].
