5. Simulation results

Considering Ee is equal to E(t0) = E(t28) and setting α and γ as 3.913 and 108.3066 seconds, respectively, and adopting an environmental humidity of 70%, the variation of the fundamental frequency for different instants in the lifetime of the structure can be obtained. The produced results by using the Eurocode model can be observed in Figure 5a, and the result by using the adjusted three-parameter viscoelastic model can be seen in Figure 5b. It is important to mention that these chosen values for α and γ were defined so that simulation leads a good agreement for instants approaching and after 2000 days. Therefore, they were intentionally defined so that the frequency met the same values as given by Eurocode. The choice of these coefficients has been done because the convergence of the deformations occurs at 4000 days, at which time the interest of the structural engineering normally lies, being, however, possible to define other pairs of values for α and γ in the case of a particular objective or even to choose which can match both curves in the whole time interval. Therefore, the mentioned coefficients have been adjusted so that the frequency is equalized by both models considering a precision of six significant digits, as can be highlighted in Table 1. When the modulus of elasticity is calculated by both models, that precision is not reached.

Figure 6 shows a comparison between results produced through both models, considering each selected instants of time.

By using the presented dynamic procedure, the critical buckling load is determined when the frequency is zero at any arbitrary time after the structure gets into service. Taking all the previous explanation into consideration and varying the mass at the tip, the force acting at the top also varies according to Eq. (5), as does the frequency of the structure that varies according to Eq. (11). The results obtained for the buckling load for both models can be seen in Figure 7. To obtain it, a short routine of programming has been elaborated considering increments of 0.1 kg to the lumped mass.

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

Figure 5. Frequencies: (a) Eurocode model; (b) three-parameter model.
