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

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is higher than 1 (in particular it assumes values between 1.08 and 1.31) and, consequently, the equivalent height is higher than the overall height of the wall. In Table 3, the simplified formula has been applied and the collapse load multiplier is given. Furthermore, these values have been compared with the ratio , the average ratio and the maximum ratio , i.e. the ratio between the minimum, the average and the maximum width and the equivalent height, respectively, in the case of walls 4x and 13x, which are the walls that are characterized by a big variability of width of piers in horizontal direction, the value of the equivalent load multiplier is close to the maximum; in the other cases, it is close to the average value.

Table 1. Width of pier of each masonry wall (the minimum width in bold and the maximum in italic) in meters.

Walls

B

(∑B i 2 /∑B i )

[-]

[m]

[m] 4.03 3.15 1.91 4.73 2.14 4.64 2.15 3.91 1.87

X1 2.45 4.26 5.48 4.55 4.85 3.98 4.00 4.00 3.02 2.35 1.70 X2 3.39 1.20 1.20 2.65 2.35 2.45 2.70 3.93 1.75 1.70 5.80 1.32 3.50 1.35 X3 1.00 2.15 2.13 1.95 2.55 2.15 2.13 0.97 0.90 1.70 1.35 1.71 0.93 2.51

X4 5.55 1.35

X12 0.97 2.13 2.10 2.61 2.60 2.15 2.10 1.01

X13 0.55 3.30 0.60 7.01 6.60 6.25 2.50 2.70 2.90 0.90 1.25 1.55 0.67

X14 1.80 3.40 1.60 1.37 1.80 0.70

X15 6.55 2.90 1.62 4.07 5.04 2.45 2.50 2.40 2.85 1.30

X16 2.10 1.55

Table 2. Weights expressed in tons and equivalent height in meters.

Walls

W 1 [t]

W 2 [t]

W 3 [t]

W 4 [t]

W 5 [t]

α

H eq [m]

[-] X1 X2 X3 X4

[-]

443.92 519.87 222.76 26.95 244.28 768.91 147.98 475.92 21.61

533.96 614.82 303.43 272.02 847.75 125.04 501.17 16.98 40

585.34 749.61 388.65 40.49 254.32 722.21 144.1 471.37 20.94

576.72 684.25 379.06 194.83 567.05 105.33 287.06 33.26

405.32 559.7 299.87

1.10 1.13 1.17 1.31 1.13 1.11 1.12 1.08 1.13

15.52 15.90 16.47 10.10 13.40 13.14 13.27 12.84 13.48

X12 X13 X14 X15 X16

22.88

Table 3. Simplified proposed formula and comparison with the minimum, the maximum and average ratio. Walls B min /2H eq B med /2H eq B max /2H eq B pes /2H eq [-] [%] [%] [%] [%] X1 5.48% 11.90% 17.66% 12.99% X2 3.77% 7.93% 18.24% 9.90% X3 2.73% 5.23% 7.74% 5.81% X4 6.68% 17.07% 27.46% 23.40% X12 3.62% 7.31% 9.74% 7.98% X13 2.09% 10.77% 26.67% 17.64% X14 2.64% 6.70% 12.81% 8.11% X15 5.06% 12.34% 25.51% 15.21% X16 5.75% 6.77% 7.79% 6.92%