PSI - Issue 78

Besim Yukselen et al. / Procedia Structural Integrity 78 (2026) 1943–1950

1947

identifies members that do not meet the required performance criteria. Each of these members is then considered individually. A random number between 0 and 1 is generated for each member. If this number is less than or equal to P, the member is retrofitted; otherwise, it is left intact. After all members have been considered, the retrofitted structure is assessed. The procedure is repeated until all members satisfy the local performance requirements. It is noted that the algorithm does not aim to enhance the design beyond the point of feasibility. Moreover, it focuses only on local member-level checks, without considering global structural performance, which is often not required by national codes such as the Portuguese Annex of EC8 (CEN 2005; IPQ 2009). Because the algorithm introduces randomness, repeated runs with identical input parameters can result in different feasible solutions. This feature is beneficial, as it allows SIRA to produce a diverse range of retrofitting designs that can serve as initial candidates for the optimisation process. To manage the computational effort involved, it is possible to define a maximum number of iterations. In this study, 100 runs of SIRA were performed using a probability value of 75% and a maximum of 25 iterations per run.

Fig. 2. Workflow of stochastic iterative retrofitting algorithm (SIRA).

3. Application to the case study building A six-storey RC residential building with unreinforced masonry (URM) infills in Benfica, Lisbon, built in 1966 prior to modern seismic codes, was selected as the case study. The structure includes RC moment-resisting frames, weak URM panels, and in-plane irregularities. Geometric and reinforcement details were obtained from the original blueprints; the soil is assumed to be of Type C. Numerical modelling was conducted in OpenSees via CAD2Sees (Yukselen et al. 2025a) using lumped plasticity with Pinching4 hinges. URM infills were modelled as equivalent diagonal struts with opening effects, and beam column joints were represented by rotational springs. Two configurations were analysed: as built and with seismic gaps, i.e. small separations introduced between infills and surrounding frames to reduce interaction during shaking. Seismic performance was assessed using the N2 method, as proposed in Eurocode 8 (CEN 2005; Fajfar 2000; Martinelli et al. 2015), with a 308-year return period (75% of the 475-year design PGA), which is appropriate for Importance Class II buildings, as per the Portuguese Annex of Eurocode 8 (IPQ 2009). Out of 300 structural members, 127 failed in shear (that is, did not comply with near-collapse criteria) and 125 exceeded chord rotation limits (that is, did not comply with significant damage criteria) in the as-built condition. With seismic gaps, shear failures dropped to 67, while chord rotation exceedances rose to 228. Interested readers may refer to (Yukselen et al. 2025a) for detailed information on the modelling and seismic assessment assumptions.