PSI - Issue 64

Massimiliano Ferraioli et al. / Procedia Structural Integrity 64 (2024) 1017–1024 Ferraioli et al./ Structural Integrity Procedia 00 (2019) 000–000

1020

4

Table 1. Modal properties. a) As-built building; b) Retrofitted Building (Step 1); c) Retrofitted Building (Step 2) a) As-built Building b) Retrofitted Building (Step 1) c) Retrofitted Building (Step 2)

Modal mass ratio U Y

Modal mass ratio R Z

Period Modal mass

Modal mass ratio U Y

Modal mass ratio R Z

Modal mass ratio U X

Modal mass ratio U Y

Modal mass ratio R Z

Modal mass ratio U X

Mode

Mode Period

Mode Period

ratio U X

1 2 3 4

1.31 0.96 0.83 0.40

0.559 0.090 0.001 0.102

0.073 0.281 0.374 0.012

0.118 0.278 0.231 0.021

1 2 3 4

1.11 0.83 0.73 0.33

0.509 0.020 0.047 0.133

0.006 0.567 0.076 0.002

0.105 0.058 0.389 0.009

1 2 3 4

0.57 0.50 0.40 0.29

0.599 0.049 0.024 0.000

0.081 0.653 0.010 0.000

0.000 0.000 0.000 0.007

Table 2. Capacity ( C ) and Demand ( D ) in terms of PGA and return period ( T r ), Safety index (  ).

Limit State

Combination

PGA C [g] PGA D [g]

 (PGA)

r C [years]

r D [years]

 ( T

r )

T

T

Interstorey displacement (IO) Interstorey displacement (DL1)

-F x - e y (Group 1) -F x - e y (Group 1) -F x + e y (Group 1) +F x - e y (Group 1)

0.061 0.086 0.115 0.130

0.103 0.135 0.135 0.344

0.594 0.638 0.853 0.378

29 58

104 174 174 712

0.281 0.334 0.679 0.093

118

Chord rotation (DL2) Chord rotation (LS)

66

4

1500

EDRS - Elastic Demand Response Spectrum CS - Capacity Spectrum BCS - Bilinear Capacity Spectrum PP - Performance Point

1 Spectral acceleration S a (m/s 2 ) 2 3

LS

1000

DL 2

DL 1

Pushover Curve Bilinear Idealization Limit States

500

IO

Base Shear (kN)

0

0

0.00

0.05

0.10

0.15

0.20

0.25

0.00

0.05

0.10

0.15

0.20

Roof Displacement (m)

Spectral Displacement S d (m)

a) c) Fig. 3. a) Collapse mechanism; b) Pushover curve and limit states; c) Comparison between demand and capacity in ADRS format. 4. Two-step design procedure to mitigate torsional effects using dissipative braces The conventional pushover analysis with lateral force applied in the center of mass of the building may underestimate the seismic torsional response. Some important drawbacks are related to the torsional effects: 1) direction of seismic excitation; 2) eccentricity of lateral force distribution; 3) higher modes contribution; 4) node control for monitoring the target displacement. The use of the center of mass as node control may influence the accuracy of nonlinear static procedures based on the capacity spectrum method. Moreover, the study of the dynamic response of irregular structures reveals that maximum displacement and maximum rotation do not occur at the same time step and, thus, a unique pushover force distribution is not able to give the most severe conditions for all the structural elements. On the other side, the displacement-based design (DBD) procedures available in the literature (e.g., Mazza et al. 2015, Ferraioli et al. 2018) schematize the building as a single-degree of freedom (SDOF) system and assume that the mode shapes remain unchanged even after retrofit and the yield drift ratios are uniformly distributed across the height of the building. These simplifying assumptions may not hold for buildings where torsional effects dominate the response. First, the SDOF assumption remains suitable for standard low-rise and regular buildings but may be insufficient for taller or irregular structures since it disregards both higher-mode and torsional effects. Then, local plastic mechanisms may occur and, thus, the distribution of localized demands in the MDOF system can differ from the hypothesis of uniform drift ratio distribution over the height. Finally, in cases where torsional effects are significant, the retrofit strategy should also aim to mitigate the torsional response, and cannot simply leave the b)