PSI - Issue 62

Carlo Pettorruso et al. / Procedia Structural Integrity 62 (2024) 677–684 Carlo Pettorruso/ Structural Integrity Procedia 00 (2019) 000 – 000

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4

a bending =M y / (m eff h)

(3a)

a shear =V RD /m eff (3b) The minimum between these two values is defined as the target acceleration, Equation (4), i.e., the maximum site acceleration for which the piers behave elastically, see also Figure 3. a target =min (a bending , a shear ) (4) Eventually, the period T target corresponding to a target is defined on the elastic spectrum. In case two periods correspond to the acceleration level, T target is the largest, accounting for the typical flexibility of bridges. The “as built acceleration”, i.e., the seismic acceleration acting on the SDOF model of the elementary bridge unit, can be determined from the effective masse defined above, and the stiffness of the equivalent SDOF model, i.e. the stiffness of the cantilever element characterized by the pier geometry. From these data the natural period of the elementary bridge unit is estimated: T as-built ൌ ʹ � (5) and used, by entering the elastic spectrum, to calculate the as-built acceleration (a as-built ) of the elementary bridge unit. By comparing the as-built to the target acceleration, two situations can occur. In case the as-built acceleration is smaller than the target acceleration, at is usually happens for low seismic acceleration and/or when the structural resources are sufficient to resist the seismic action, the bridge does not need to be retrofitted. In case the as-built acceleration is larger than the target acceleration, the existing bridge will not be able to withstand the design earthquake and the retrofit by seismic isolation can be considered to mitigate the seismic vulnerability. The first condition for suitability of seismic isolation is hence defined as: a target (T target ) < a as-built (T as-built ) (6) In Figure 3 the case of positive outcome of the first suitability check is represented.

Fig. 3. First requirement

Therefore, it is necessary to assess whether the pier alone has enough strength to withstand the seismic load associated to its own mass. First, recalling that the isolation system will be placed on the top of the pier, the effective mass of the non-isolated section of the pier, i.e., the pier without the deck, is m sub =m piercap +m pier /3 (7) The natural period of the substructure is equal to the period defined by Equation 5, but by replacing the effective mass m eff with the mass defined above. Given the approximated natural period of the substructure T sub , from the