## 7 Assessment of Steel Silos Vulnerability
Although imperfections were measured in experimental models to investigate similar issues [143], that paper numerically addressed a part of a real structure (the steel silo segment schematized in Figure 11). In other words, an artificial substitute of the geometric imperfections (eigen-mode imperfection) was adopted to account for the focused effect, by using different amplitudes of the first buckling mode and the first vibration mode. The buckling load was determined both by means of the VCT and non-linear static analysis. The outcomes of the study showed that a VCT allows to predict the right buckling load for the perfect structure of the silo segment and a limited load in the case of the imperfect structure. Hence, VCT precision decreases as the geometrical imperfection magnitude increases. Moreover, the relationship between squared natural frequencies and the applied load is governed by the magnitude of the applied loads, while considerable non-linearity is observed if the applied load becomes close to the minimum buckling load or the limit loads. The geometric imperfections, in terms of the amplitude and form, are vital to the assessment of the structural buckling strength of a thin steel silo. The imperfection measurement of existing silos is another practical approach, as shown in [12]. However, it is efficient to employ a professional scanning method for the purpose of quantifying the realistic geometric imperfections [152]. [PERSON] et al. [31] one of the first comprehensive measuring techniques using conventional survey instrumentation, and specifically designed surface profile measurement apparatus. Mainly, the system consists of measuring trolley and the relevant software package. Through the study introduced by [PERSON] et al. [11], the developed technique in [31] practically used for the imperfection assessments of three real full-scale metal silos of 10,000 tons capacity in New South Wales, Australia. Authors analyzed the measured data using a double Fourier series to determine dominant imperfection modes. The results offered notable advantages (in terms of accuracy, labor intensity, and cost) over the traditional measuring methods existed in that time [11]. However, the data released by measurement techniques can be adopted both for assessment and design by correlating the measurement results with buckling predictions and tests [11]. [PERSON] et al. [56] analyzed extensive data on imperfection characterization, by providing a full identification of the possible imperfection set. In this context, the authors' concern was to provide a reliable estimate of buckling in shell structures, avoiding any simplified assumptions. In the end, as shown on many occasions, the risks to which silos are subjected are elevated, especially as shown after hazardous events as earthquakes, which can cause serious accidents in the industrial plants with catastrophic consequences. For instance, in Italy, about 30% of industrial plants are situated in regions with a high seismic risk, and they are exposed to more hazards and are more likely to fail. The collapse of a single silo can get out of order the entire industrial location. Thus, the silo seismic vulnerability assessment is of fundamental importance. For example, a very recent study introduced by [PERSON] et al. [153] presented a performance-based earthquake assessment of a real case study of an elevated steel silo structure group with a regular plan dimensions 37.80 \(\times\) 16.94 m and total height 29.64 m. The supporting structure is of 10.80 m height and equipped with different typologies of lateral loads resisting systems (e.g., moment resisting frame, inverted V bracings, and diagonal bracings). Nonlinear static pushover and nonlinear response history analyses were used to evaluate the seismic performance of the structure under investigation.