PSI - Issue 44

Stefano Bracchi et al. / Procedia Structural Integrity 44 (2023) 394–401 Stefano Bracchi et al. / Structural Integrity Procedia 00 (2022) 000 – 000

396

3

EC8 defines three Knowledge Levels on materials (KLM1, KLM2 and KLM3 in order of increasing knowledge) and specifies which investigations and tests can be performed to attain the selected level. In-situ experimental tests can be performed at KLM2 and KLM3. A partial safety factor γ Rd , to be applied (in case of nonlinear static analysis) to the global displacement capacity, is then associated with each KL; this partial safety factor has the same meaning of the confidence factor of the previous version of EC8. The partial safety factors for the ultimate limit state depend on the minimum level of knowledge between geometry (KLG) and construction details (KLD) and are equal to 1.9, 1.8 and 1.7, for KL1, KL2 and KL3, respectively. EC8 also introduces a formulation based on multi-linear constitutive laws for piers and spandrels, with possible residual strength after reaching an ultimate displacement. In case of flexural and shear sliding mechanism, the ultimate displacement is evaluated based on the chord rotation at the two end sections whereas, in case of shear mechanism with diagonal cracking, the ultimate displacement is defined based on the element drift calculated removing the rigid rotations. Table 1 indicates the limit values of the element drift in case of flexural and shear mechanism for piers and spandrels. It should be noticed that θ u represents the drift corresponding to the first decay of strength with respect to the peak strength ( V max ) of the multi-linear constitutive law prescribed by the code, whereas θ u2 is the drift corresponding to the second decay of strength (after this, only a residual strength is present). Moreover, ν is the non dimensional axial stress, whereas the values indicated for spandrels refer to the presence of a coupled lintel.

Table 1. Drift capacities and residual strengths for piers and spandrels according to EC8. Piers

Spandrels

Flexure 0.01*(1- ν ) 4/3* θ u 0.80* V max

Shear Sliding

Shear Diag. Cracking

Flexure

Shear Diag. Cracking

0.008/0.005

0.005 4/3* θ u

0.016

0.005

θ u

4/3* θ u

4/3* θ u

4/3* θ u

θ u2

Residual strength

0.4* N/0 .2 *N

0.30* V max

0.90* V max

0.60* V max

3. Case study and adopted methodology The considered case study is a URM building with reasonably regular plan, two stories, timber roof and masonry made of clay bricks and lime mortar. Fig. 1 shows the TREMURI model of the building and the mechanical properties indicated by EC8 for the corresponding masonry typology. Seismic action is defined according to EN1998-3 (2005).

f m [MPa]

f tu [MPa] 0.114

f v0 [MPa]

Mean C.o.V.

3.4

0.16 0.21

0.26

0.21

E [MPa]

G [MPa]

w [kN/m 3 ]

Mean C.o.V.

1500

500

18 18

0.2

0.2

(a)

(b)

(c)

Fig. 1. 3D view of the TREMURI model of the building (a), mechanical properties according to EC8 (b), comparison among prior and posterior distributions obtained by means of Bayesian updating (c).

In this study, it is assumed that the engineer is able to select the correct masonry typology among the ones proposed by EC8. Therefore, at KL1 the only information available is represented by the interval of variation of mechanical properties given by the code. At KL2, the engineer is assumed to perform some limited tests, to identify the quality of mortar, still having uncertainties on the possible presence of transversal connections. Two different possible cases are assumed in this