PSI - Issue 78

Francesco Martini et al. / Procedia Structural Integrity 78 (2026) 2022–2029

2028

observed, the values obtained are equal to 0 when there is no mass (i.e., empty silo or a part of it). Still, starting from the very slender silos, V , and reducing the H/D ratio, a stat initially increases, while going toward the squat silos, Q , a different trend can be observed, with a reduction of the a stat value. This suggests that there is not a real trend for the definition of a stat , but values are higher when the silos are fulfilled and generally tend to decrease when reducing slenderness. Concerning values of a seism , considering the overall relatively low values, it can be observed that also in this case there is not a real trend, but values are higher for the very slender silos, V , while they decrease by reducing the H/D ratio. Generally, while the values of a stat can be used for assessing the correctness of the simplified model, the values of a seism can be used for performing a rapid assessment of the seismic actions on a specific silo typology, according to the service condition to which it is subjected.

Table 1. Values of a stat and a seism for the sample of silos considered. H/D Filling level [%] a stat, 3 [g] a stat, 2 [g] a stat, 1 [g]

a seism, 3 [g]

a seism, 2 [g]

a seism, 1 [g]

5.20 5.20 5.20 5.20 3.00 3.00 3.00 3.00 2.06 2.06 2.06 2.06 1.49 1.49 1.49 1.49 0.65 0.65 0.65 0.65

90 60 30 90 60 30 90 60 30 90 60 30 90 60 30 0 0 0 0

2.29 0.00 0.00 0.00 1.65 0.00 0.00 0.00 1.25 0.00 0.00 0.00 0.97 0.00 0.00 0.00 0.47 0.00 0.00 0.00

0.63 2.16 0.00 0.00 0.78 1.59 0.00 0.00 0.74 1.22 0.00 0.00 0.67 0.95 0.00 0.00 0.40 0.47 0.00 0.00

0.13 0.54 2.05 0.00 0.31 0.71 1.54 0.00 0.39 0.70 1.19 0.00 0.42 0.64 0.94 0.00 0.33 0.39 0.46 0.00

0.04 0.00 0.00 0.00 0.03 0.00 0.00 0.00 0.02 0.00 0.00 0.00 0.01 0.00 0.00 0.00 0.01 0.00 0.00 0.00

0.01 0.06 0.00 0.00 0.01 0.03 0.00 0.00 0.01 0.02 0.00 0.00 0.01 0.02 0.00 0.00 0.01 0.01 0.00 0.00

0.01 0.01 0.05 0.00 0.01 0.01 0.03 0.00 0.01 0.01 0.02 0.00 0.01 0.01 0.01 0.00 0.01 0.01 0.01 0.00

0

4. Conclusions The paper presents a simplified model to predict the elastic behaviour of cylindrical ground-supported steel silos, accounting for different structural geometries (i.e., from slender to squat) and different service conditions (i.e., for empty to fulfilled). The proposed approach was based on the analytical definition of the parameters to build simplified model, which was schematized as a 3-DOFs system. The procedure for defining the models was provided, by characterizing the mass and stiffness of the system. Regarding stiffness, considering the presence or not of filling material, two different coefficients were provided as modification factors to derive same fundamental periods of vibration for the analogous literature-based overdetailed models. Still, a procedure to determine horizontal and vertical static pressures was provided, to define a static load pattern for reproducing similar pressure distribution by the proposed system. Similarly, with the same logic of the static pressures, also the seismic pressures were derived according to empirical formulation proposed by the scientific literature. The obtained values can be used in the simplified model for performing a simplified assessment of the focused silo typology, given a seismic acceleration