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Earthquakes can produce important damage in civil infrastructure, including buildings and bridges, representing an important impact on the economy of many countries. The damage is particularly severe when the dominant frequency of the quake approaches one of the resonant frequencies of the structure. One typical failure occurs through the weakening of some beam‐column joints, generally along with the presence of cracking. The standard procedure for repairing this is by reinforcing the damaged zone with steel plates, sleeves or by means of a new section of reinforced concrete covering the old one. These arrangements change the mechanical stiffness and the mass of the structure itself. Accordingly, this work aims to study these mass and stiffness changes of structures through a non‐linear optimization of the modal analysis of the structure.

The paper analyzes the potential shifts in natural frequencies of the structure and thus proposes the best conditions under which a damaged bridge could be repaired efficiently.

In the cases analyzed a similar tendency was observed, namely, that the natural frequencies increase (i.e. diminish their period) with the increase of mass of the bottom columns and with the reduction of the uppers ones. The increase of frequencies by increasing the bottom sections seems to be a viable solution. It is observed that by carrying out the presented procedure it is possible to include more variables, in particular to consider not only the first frequency, but also higher orders.

A purely theoretical approach has been taken in this study.

If confirmed by experimentation this study would have considerable interest to engineers undertaking repair works on earthquake damaged structures.