PSI - Issue 44

5

Mauro Mezzina et al. / Procedia Structural Integrity 44 (2023) 566–573 Author name / Structural Integrity Procedia 00 (2022) 000–000

570

If we assume: b = 40 cm; l 1 = 200 cm; l 2 = 800 cm; h = 400 cm A 1 = 8e+4 cm 2 ; A 2 = 32e+4 cm 2 G = 45000 N/cm 2 T=1000 Nm the following results are obtained: τ zs1 = τ zs4 = τ zs5 = 2.520 10 -3 N/cm 2 τ zs2 = τ zs6 = τ zs7 = 3.276 10 -3 N/cm 2 τ zs3 = 0.756 10 -3 N/cm 2 θ t = 2.380 10 -10 rad θ t is the unit angle of torsion; the total angle of torsion over the whole height h=400 cm is θ TOT =2.380 10 -10 * 400= 9.52 10 -8 rad. The previous results scan be compared with the approach that considers the distribution of the floor shear among the vertical elements according to the translational stiffnesses of each wall panel. The coordinates of the center of stiffnesses CR (determined with respect to the lower left edge of the plane) are: x CR = 4.0 m ; y CR = 2.0 m . The values obtained are listed in Table 1 (the response is calculated for T=1000 Nm ; verses of the shear are shown in Fig. 3). The torsional rotation θ t is obtained by dividing the value of the in-plane torque T=1000 Nm by the torsional stiffness I p : θ t = 100/9.18 10 +8 = 1.089 10 -7 rad. Table 1. Results of the analysis performed by assuming the distribution of floor shear according to the translational stiffnesses of wall panels.

Wall panel

K [kN/cm]

x i y i [cm]

V" [N]

τ [N/cm 2 ] 1.485 10 -3 2.874 10 -3 2.421 10 -3 4.842 10 -3 1.485 10 -3 7.263 10 -3 2.874 10 -3

1 2 3 4 5 6 7

363.402 2812.968 1184.874 1184.874 363.402 1184.874 2812.968

200 200

7.920

61.309 25.824 51.649

-200 -400 -200

7.920

600

77.473 61.309

-200

I p = 9.18 10

+8 kNcm

The major differences between the two approaches (Fig. 4) are the following: - in the " Bredt-like" distribution, the torsional rotation is much lower than the in-plane rotation obtained by considering the individual response of the walls; - when shear distribution is made proportionally to the wall stiffness, the panel No. 6, which is the farthest from the center of the stiffnesses, is particularly engaged. The ratio of maximum tangential stresses between the two approaches is 7.263/3.276=2.21. - in the Bredt-like distribution, the ratio between the maximum and minimum stress in the different panels is significantly lower than in the other distribution: Bredt: 3.276/2.520 = 1.3 Stiffness-distribution: 7.263/1.485 = 4.89 Finally, it is worth noting that the Bredt-like response strongly decreases the value of the tangential stress in the inner walls, because of the activation of a “coupled” response of the different meshes, whose response overlaps until it is almost balanced. In fact, the tangential tension in the inner panels varies from 2.421 N/cm 2 to 0.756 N/cm 2 , for the Bredt-like hypothesis. Nothing changes if walls have vertical openings (doors, windows). In fact, provided that equations leading to system (10) hold, the distribution of the torque among the different resisting elements is still obtained. The transfer of