To compute or not to compute?

Abstract

In a previous paper “to retrofit or not to retrofit?” (Nuti and Vanzi, 2003) a straightforward procedure able to forecast the economic return of seismic structural upgrading was presented. More recently, the authors realized that the final mathematical results can be much simplified so as to allow back-of-an-envelope computation. The title of this paper tries to highlight precisely this aspect, namely that for many a regular seismic structural upgrading cases, nearly no computation is needed (apart from one subtraction and one multiplication) to assess their economic convenience. These findings are presented and discussed in this paper, together with a state of the art on the cost-studies available in literature and technical codes. The mathematical formulation leading to the proposed approximation is suitably explained, underlining its applicability field and comparing it with the rigorous solution. Also a table and a formula are furnished that alternatively allows to calculate the maximum estimation errors, in order to obtain an upper and lower bound for the maximum amount of money which should be allocated for seismic structural upgrading.Finally an application example is described, dealing with retrofitting of reinforced concrete viaducts, a widespread bridge typology in Italy. The adopted upgrading solution consists of a concrete jacket at the base of some piers, particularly suitable in order to increase their ductility. Keywords: Seismic retrofitting, Structural reliability, Safety, Optimization, Cost minimization