PSI - Issue 78

Federico Gusella et al. / Procedia Structural Integrity 78 (2026) 113–119

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2.2. Mean loss conditional to damage states The expected annual loss (Eq. 6) depends on the mean loss conditional to damage states ( | = ) . They are proposed as listed in Table 2, for LD and D structures, respectively. These values represent the repair cost consequent to the damage d mi and are expressed as a percentage of the price of the LD structure ( P LD ).

Table 2. Mean associated loss conditional to damage state.

d m1

d m2

Design concept

(Development of damage) (Collapse) LD structure ( | 1, )= ( | 2, )= D structure ( | 1, )= ( | 2, )= The collapse of the LD structure (damage state d m2,LD ) involves ( | 2, )= , which is the total price of the building ( P LD ). The damage state d m1,LD involves the need of retrofitting interventions capable of fixing the expected damage. This cost conditional to the damage ( | 1, )= is given by a percentage of the initial cost ( P LD ) through the coefficient r LD . Regarding the D structure, the failure of the structure d m2,D involves the reconstruction of the building and then ( | 2, )= , where the price of the D structure ( P D =d i P LD ) is assumed as a percentage of the price of LD structure. The coefficient d i corresponds to the discount applied to the cost of LD building for having the prince of D structure. The mean associated loss conditional to damage state d m1,D (dissipative members undergone plastic deformation) is a percentage of the overall cost of the D structure ( | 1, )= . This cost is given by the cost to replace the dissipative damaged elements and is expressed by a percentage of the overall cost of the structure through the coefficient r D . 2.3. Target price of D structures The required discount d i,TARGET on the price of the LD structure to determine the target price of the D structure ( , = , ) can be evaluated by Eq. (9). This ensures that by the end of the structure's nominal life ( T [in years]), its total cost ( , = + ( ) ) is equal to that of the building designed as elastic ሺ , = + ( ) ሻǣ , = 1+[ +(1− )( ) − ]· , − , 2 2 2 1+[( ) +(1− )]· , − , 2 2 2 (9) The value of , = , / , which is equal to the ratio between the target price of the D structure and the price of the LD structure, allows for identifying the price of the D structure to be considered economically preferable to the LD structure. Obviously, the economic advantage consists in choosing the design concept which involves the lowest total cost at the end of the reference period T . Figure 2 a) shows the target discount versus the coefficient related to the cost for replacing dissipative members of the D structure ( , vs r D ) ), for different values of the seismic behavior factor ( q D ) and assuming a reference period equal to the nominal life of the structure T =50 years.