PSI - Issue 44

Domenico Magisano et al. / Procedia Structural Integrity 44 (2023) 456–463 Magisano et al. / Structural Integrity Procedia 00 (2022) 000–000

461

6

10 − 3

2 0 2 4 ·

0 1 2 3 4 5

FULL

ROM

FULL

ROM

u / H

0 0 . 2 0 . 4 0 . 6 0 . 8 1 − 4 −

f loor

− 4

− 3

− 2 u / H

− 1

0

t / ∆ T

· 10 − 3

Time history for seismic action at 0°

Maximum profile deformation for seismic action at 0°

10 − 3

2 0 2 4 ·

0 1 2 3 4 5

FULL

ROM

FULL

ROM

u / H

0 0 . 2 0 . 4 0 . 6 0 . 8 1 − 4 −

f loor

− 4

− 3

− 2

− 1

0

t / ∆ T

u / H

· 10 − 3

Time history for seismic action at 45°

Maximum profile deformation for seismic action at 45°

10 − 3

2 0 2 4 ·

0 1 2 3 4 5

FULL

ROM

FULL

ROM

u / H

0 0 . 2 0 . 4 0 . 6 0 . 8 1 − 4 −

f loor

− 4

− 3

− 2

− 1

0

t / ∆ T

u / H

· 10 − 3

Time history for seismic action at 90°

Maximum profile deformation for seismic action at 90°

Fig. 6: Mildly irregular frame: time history of the control point and peak profile deformation for di ff erent seismic directions.

Table 3: Mildly irregular frame: maximum story shear force T s / (1000 kN ) at ground level varying the random frequency content

Accelerogram 1 10 Story 1 FULL 2.51 2.34 2.57 2.48 2.27 2.32 2.44 2.41 2.52 2.28 Story 1 ROM 2.61 2.44 2.65 2.50 2.44 2.37 2.44 2.47 2.66 2.41 Story 1 err (%) 3.98 4.34 3.26 0.76 7.38 2.27 0.04 2.36 5.62 5.73 2 3 4 5 6 7 8 9

5.1.3. Sensitivity to the plastic mechanisms in the ROM accuracy Three di ff erent modeling are now tested to assess the influence of the plastic mechanisms: FULL model, ROM with 3 linear modes, ROM with 10 linear modes and ROM with 3 linear modes plus their corresponding mechanisms and story mechanisms. The scale factor of the seismic action along the X direction varies from 1 to 4. Figure 9 shows the comparison of displacement time histories and maximum profile deformations between the di ff erent models. The plastic modes greatly improve the ROM predictions for seismic actions leading to a relevant plasticization.

6. Concluding remarks

This paper presented a reduced modal space for time history seismic analyses of framed buildings. It is a multi-scale approach where the internal forces are evaluated on the full model, while the dynamic equilibrium is imposed in a reduced space. The modal basis includes the first elastic modes in terms of mass participation factor, the corresponding