PSI - Issue 44

Maria Teresa De Risi et al. / Procedia Structural Integrity 44 (2023) 958–965 De Risi, Del Gaudio, Scala, Verderame/ Structural Integrity Procedia 00 (2022) 000–000

962

5

demand at SD and DL LS, depending on the site, to be compared with displacement capacity. It is worth noting that building capacity at SD LS is assumed as the minimum between DFs, SFs and JFs. Starting from displacement capacity, for each building, in each direction, capacity peak ground acceleration (PGA c ) can be obtained according to D.M. 2018 (i.e., based on Vidic et al., 1994) to finally estimate the building safety index (SI) at each LS, as: SI   PGA , PGA , ⁄ (1) where PGA D,LSi is the demand PGA at the i th LS, depending on the building site. Both PGA C and PGA D in eq. (1) are intended to be inclusive of the site effects (PGA=S·a g ). Fig. 4a,b shows as a colormap the distribution of the resulting SI at SD LS (SI SD ) and SI at DL LS (SI DL ) for all the considered sites in Italy. SI SD ranges from a minimum value of 0.05 – in sites where seismic hazard is higher or stratigraphic amplification more important – to a maximum of 0.77, thus always lying below the unity, and always due to beam-column joints (tensile) failure (see Fig. 3). Very similar results are obtained for 2-storey and 4-storey buildings. About DL LS (Fig. 4c,d), SI DL ranges from 0.38 to 3.33 for the 2-storey building (median value=1.57), and from 0.34 to 2.98 for the 4-storey building (median value=1.39).

Table 1. Number of failing elements for each building from pushover analyses

Step of interest

Ns

DF

Beam SF

Column SF

JF “T”

JF “C”

2 4 2 4 2 4

-

-

-

-

-

1 st JF “C”

0 8

0

0

56 32 72 32 72

4

-

-

-

1 st DF

16 36 70

12

4

4

-

-

-

Pushover end

12

4

8

Fig. 4. SI SD for as-built buildings: a) 2-storey; b) 4-storey; SI DL for as-built buildings: c) 2-storey; d) 4-storey.

4. Design of retrofit and assessment of its effectiveness The retrofitting strategy adopted in this study consists in the “local” strengthening of beams/columns and joints which exhibit shear failures. No changes in lateral stiffness or mass are introduced, so that it can be assumed that no changes in the pushover curves are obtained after retrofit (since only flexural behavior has been explicitly modelled in the assessment phase). It is worth noting that local strengthening techniques (like FRP wrapping or steel cages or CAM® technology) lose efficiency when a “compressive” SF is expected. This means that, when JF “C” occurs, as for the 4-storey building analyzed here, a local strengthening intervention cannot lead to an increase of the building capacity (ΔSa cap , where Sa cap is the capacity elastic spectral acceleration) “beyond” the 1 st JF “C” (Fig. 5a). On the contrary, when all SFs that occur until the 1 st DF can be solved with local strengthening, the maximum effectiveness of this intervention typology can be reached, leading to a displacement capacity equal to that at the 1 st DF (Fig. 5a). Herein local intervention will be used to make “ductile” (i.e., shear demand assumed equal to the plastic shear) only