PSI - Issue 78

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

2027

pressure values are constant, evidence that suggests a trend like the axial and the shear stresses (for P h and P v , respectively) in a shear-type model under a static load pattern of forces applied on the masses. The graphical comparison between the real pressures and the ones in the simplified model are shown in Figure 4. Therefore, to derive the correct values of P h and P v in the simplified model it is necessary to define the static load pattern and the magnitude of each force within the load profile. Firstly, for each silo layout and service condition, values of P h and P v at the heights of interest were retrieved by Khalil et al. (2024). The pressures P h and P v can be idealized as the axial and the shear stresses, respectively, divided for the partial height of the silo in the simplified model and the width of a stripe of the wall in which it is assumed applied the maximum pressure value (assuming one generical direction of analysis, due to axisymmetric nature of the structure). Assuming the width of this stripe as unitary, the values of P h and P v : � ℎ1 , 2 , 3 = 1 , 2 , 3 1 , 2 , 3 ∙1 1 , 2 , 3 = 1 , 2 , 3 1 , 2 , 3 ∙1 (3) where V 1 , V 2 , V 3 are the shear stresses in the simplified model, while N 1 , N 2 , N 3 are the axial stresses in the simplified model.

Figure 4. Schematic definition of horizontal and vertical pressures for the simplified model and comparison with the Janssen profiles.

By inverting the formula in Equation 3, the values of the stresses in each branch can be defined. Still, by ensuring global equilibrium of the entire structure (i.e., bottom stresses derive by the upper stresses, as in an elastic shear-type frame resolution), the forces to apply on the masses to generate those stresses can be found. In the end, given the masses at each note point, the values of accelerations to consider can be easily derived. A similar logic can be employed for computing the horizontal and vertical seismic pressures, for which the value of the acceleration to define can be named a seism . Nevertheless, according to the formula proposed by Pieraccini et al. (2015), the values of a seism are dependent on the horizontal and vertical seismic acceleration. As output of the analytical procedure, values of static accelerations, defined as a stat , were derived for the considered stock of silos, which can be generally used to estimate the load pattern in the proposed simplified model, given the geometry of the silo and the filling level. At the same time, values of and a seism are reported, by assuming a common value of the seismic horizontal acceleration equal to 0.63g. The output of the analysis is reported in Table 1 for P h (for both static and seismic pressures, considering that the static P v can be derived by using the friction coefficient, while the seismic P v can be derived by assuming a seismic vertical acceleration and following the indications by Pieraccini et al. 2015). As can be