PSI - Issue 44

P. Sorrentino et al. / Procedia Structural Integrity 44 (2023) 1656–1663 P. Sorrentino et al./ Structural Integrity Procedia 00 (2022) 000 – 000

1661

6

3.2. Nonlinear static analysis In compliance with current Italian Building Code (NTC 18), equivalent frame approach has been adopted to perform the pushover analysis, in which the masonry wall is represented as piers, spandrel beams and joint elements. The pier elements are modeled as columns, spandrels as beams while the joint elements are supposed infinitely resistant and stiff and are modeled as rigid offsets at the end of the pier and spandrel (G. Magenes, 2000). Since the lack of any tensile resistant element, the spandrel itself has not the capacity to connect two adjoining piers; consequently it is modeled as a pendulum (weak spandrel). This type of model allows to adopt a lumped plasticity model, in which nonlinear behavior is concentrated in flexural and shear plastic hinges, at the end of sections of piers. The pushover analysis has been carried out, adopting a proportional-to-mass distribution of forces. Since the proposed formula was obtained considering the Heyman hypotheses, and in particular the hypothesis of infinite compressive strength of the material (f d ), a very high compressive strength value, equal to 100 kg/cm 2 , was adopted. In Table 4 the mechanical properties of masonry are listed.

Table 4. Mechanical properties of masonry.

Elastic Modulus [kg/cm 2 ]

Shear Modulus [kg/cm 2 ]

Specific Weight [kg/cm 3 ]

Compressive Strength

Shear Strength [kg/cm 2 ]

Masonry

[-]

[kg/cm 2 ]

Tuff

10.800

3.600

1.600

100

0.35

The pushover curves are given in Figure 3 and 4 in terms of load multiplier F/w vs the ratio between displacement and height of the wall d/H and are compared with the results of the simplified formula and the minimum and the maximum ratios. In the case of walls 4x, 12x and 16x, the maximum F/w is close to the maximum ratio λ max ; instead, in the other cases it assumes a value less than the one obtained with the simplified formula. 1x 2x

Curva di capacità adimensionalizzata MDOF - Massa X+ 100 kg/cm2

40

40

F/w (%)

F/w (%)

100 kg/cm2 Bpes/Heq Bmin/Heq Bmax/Heq

Bpes/Heq Bmin/Heq Bmax/Heq

35

35

30

30

25

25

λ= 18.24

20

λ= 12.99 λ =17.66

20

15

15

λ= 9.90

10

10

λ =5.48

λ= 3.77

5

5

d/H (%)

d/H (%)

0

0

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

3x

4x

40

40

F/w (%)

F/w (%)

100 kg/cm2 Bpes/Heq Bmin/Heq Bmax/Heq

100 kg/cm2 Bpes/Heq Bmin/Heq Bmax/Heq

35

35

30

30

λ= 23.40 λ= 27.46

25

25

20

20

15

15

10

10

λ= 5.81 λ= 2.73 λ= 7.74

λ= 6.68

5

5

d/H (%)

d/H (%)

0

0

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

Figure 3. Pushover curves (continue red line) and comparison with the simplified formula (dashed red line), B min /H (dashed blue line) and B max /H (dashed green line): walls 1x – 4x.