Post on 18-May-2020
MODAL-PUSHOVER-BASED GROUND MOTION SCALING PROCEDURE Dr. Erol Kalkan, P.E. United States Geological Survey Prof. Anil K. Chopra University of California, Berkeley
Slide: 2/21
Outline • Current issues in GM selection and scaling • Objective • Modal-pushover-based scaling (MPS) • Evaluation of MPS procedure: High-rise
buildings • 19-story steel SMRF • 52-story steel SMRF
• Conclusions
Slide: 3/21
Current Issues in GM Selection and Scaling § How many records should be selected for
nonlinear dynamic analyses?
§ How the selected records should be scaled to avoid unbiased estimates of engineering demand parameters [Accuracy]
§ How we can minimize dispersion to retain confidence [Efficiency]
Slide: 4/21
• To develop a new procedure for selecting and scaling earthquake ground motion records in a form convenient for evaluating existing structures or proposed designs for new structures.
• Procedure presented • Explicitly considers structural strength (Ry)
• Based on the standard IM of spectral acceleration that is available from the USGS seismic hazard maps, or it can be computed from the uniform hazard spectrum obtained by probabilistic seismic hazard analysis (PSHA) for the site.
Objective
Slide: 5/21
MPS Procedure: Key Components § Each ground motion is scaled to ensure that the peak
deformation of the first-mode inelastic SDF system is close enough to a target value of the inelastic deformation.
§ The force-deformation relation for the first-”mode” inelastic SDF system is determined from the first-mode pushover curve.
§ The target value of inelastic deformation is estimated as the deformation of the corresponding linearly elastic system, known directly from the target spectrum, multiplied by the inelastic deformation ratio.
§ Appropriate for first-mode dominated structures, the approach is extended for structures with significant contributions of higher modes.
Slide: 6/21
MPS Procedure: Step-by-step
1. Compute periods (Tn) and mode shapes (fn) of the first few modes of elastic vibration of the structure.
1. Develop first-”mode” pushover curve
u r
V bIdealized Curve
Actual Curve
1
k1
V b,y
u r,y
1αk1
D 1
F
s1/L
11
21ω
D1,y =u r,y /Γφr
*, 1/y b yF V M= 1
α 21ω
Slide: 7/21
MPS Procedure: Step-by-step (con’t)
1. For the first-mode inelastic SDF system, establish the target value of deformation from 2. where
1ID
1 1I
RD C D=( )21 1 1= 2 AD T π
For ith record compute peak deformation, of the 1st-mode inelastic SDF system through
nonlinear RHA
D
F D
SF &&i igu
T1 z1
Inelastic SDF system
1. Repeat this process for as many record as necessary
Period (s), Tn
Pseu
do S
pec.
Acc
. (g)
T 2 T 1
2 2ˆ(A , )T
1 1ˆ(A , )T
Slide: 8/21
Estimating Target Inelastic Deformation via CR Equation
Slide: 9/21
MPS Procedure: Multi-Mode Consideration MPS procedure checks for higher-mode compatibility of each record by comparing its scaled elastic spectral displacement response values at higher-mode vibration periods of the structure against the target spectrum.
This approach ensures that each scaled earthquake record satisfies two requirements:
1. Peak deformation of the first-mode inelastic SDF system is close enough to the target value of the inelastic deformation;
2. Peak deformation of the higher-mode elastic SDF system is not far from the target spectrum.
Slide: 10/21
Evaluation of MPS
§ Several regular building models of varying height in 2D and 3D and bridges were used for evaluation.
§ A suite of 21 near-fault impulsive records were compiled from the NGA database.
§ Each model was subjected to 21 “original” ground motions to generate benchmark results.
§ Engineering demand parameters (EDPs) considered are normalized floor displacements, inter-story drift ratio and member plastic rotations.
Slide: 11/21
Ground Motion Ensemble
0 1 2 3 4 50
0.5
1
1.5
2
2.5
Period (s), Tn
Pseu
do A
ccel
erat
ion
(g)
Medianith GM
21 near-fault strong ground motions were compiled from the NGA database. These motions were recorded during seismic events with M ≥ 6.5 at Rcl ≤ 12
km and belonging to NEHRP site classification C and D.
Slide: 12/21
Selected High-Rise Buildings: 19-story
• Location: Northridge - Los Angeles, CA • Structural System: Perimeter SMRFs to resist lateral loads and interior gravity frames. • Instrumented: Yes
Slide: 13/21
Calibration of 19-story Building Computer Model
0 1 2 3 4 50
0.2
3.7
sec
1.4
sec
0.6
sec
E-W Direction
1994 Northridge Eq.
0 1 2 3 4 5
3.4
sec
0.8
sec
1.1
sec
N-S Direction
0 1 2 3 4 5Period (sec)
Four
ier A
mp.
of R
el. A
ccel
erat
ion
3.7
sec
0.8
sec
1.1
sec
Torsional Direction
-0.2 -0.1 0 0.1 0.20
2
4
6
8
10
12
14
16
18
E-W Component
Floo
r
Φ xj
Mode 1
Mode 3
Mode 6
[2,4,6]
-0.2 -0.1 0 0.1 0.2
N-S Component
Φ yj
Mode 2
Mode 4
Mode 5
[1,3,5]
-5 0 5
x 10-5
Torsional Component
Φθ j
Mode 2
Mode 5
Mode 4
[1,3,6]
-50
0
50E-W Direction
19th Floor
N-S Direction
-50
0
508th Floor
0 10 20 30 40 0-50
0
502nd Floor
0 10 20 30 40 50
Dis
plac
emen
t (cm
)
Duration (sec)
OpenSeesObserved
Comparison of observed and computed floor displacements in two horizontal directions of
the (Recorded data is from the M6.7 1994 Northridge earthquake)
0 1 2 3 4 50
0.2
3.7
sec
1.4
sec
0.6
sec
E-W Direction
1994 Northridge Eq.
0 1 2 3 4 5
3.4
sec
0.8
sec
1.1
sec
N-S Direction
0 1 2 3 4 5Period (sec)
Four
ier A
mp.
of R
el. A
ccel
erat
ion
3.7
sec
0.8
sec
1.1
sec
Torsional Direction
Slide: 14/21
Selected High-Rise Buildings: 52-story
• Location: Century City - Los Angeles, CA • Structural System: Perimeter SMRFs to resist lateral loads and interior gravity frames. • Instrumented: Yes
Slide: 15/21
Calibration of 52-story Building Computer Model
0
0.1
5.9
sec
1.8
sec
0.9
sec
E-W Direction
1994 Northridge Eq.
5.6
sec
1.7
sec
0.9
sec
Four
ier A
mp.
of R
el. A
ccel
erat
ion
N-S Direction
4.7
sec
1.7
sec
0.9
sec
(x2)
Torsional Direction
0 1 2 3 4 5 6 70
0.04
5.6
sec
1.7
sec
0.9
sec
2008 Chino-Hills Eq.
1 2 3 4 5 6 7
5.3
sec
1.7
sec
0.9
sec
Period (sec)1 2 3 4 5 6 7
1.7
sec
0.9
sec
(x2)
-0.2 -0.1 0 0.1 0.20
5
10
15
20
25
30
35
40
45
50
E-W Component
Floo
r
Φ xj
Mode 1
5
9
[2,3,4,6,7,8]
-0.2 -0.1 0 0.1 0.2
N-S Component
Φ yj
Mode 3
8
6
[1,2,4,5,7,9]
-2 -1 0 1 2
x 10-4
Torsional Component
Φθ j
Mode 2
7
4
[1,3,5,6,8,9]
Comparison of observed and computed floor displacements in two horizontal directions of the (Recorded
data is from the M5.4 2008 Chino-Hills earthquake )
-3
0
3E-W Direction
Roof
N-S Direction
-3
0
335th Floor
-3
0
322nd Floor
15 20 25 30 35 40 45-3
0
314th Floor
15 20 25 30 35 40 45
Disp
lace
men
t (cm
)
Duration (sec)
OpenSeesObserved
0
0.1
5.9
sec
1.8
sec
0.9
sec
E-W Direction
1994 Northridge Eq.
5.6
sec
1.7
sec
0.9
sec
Four
ier A
mp.
of R
el. A
ccel
erat
ion
N-S Direction
4.7
sec
1.7
sec
0.9
sec
(x2)
Torsional Direction
0 1 2 3 4 5 6 70
0.045.
6 se
c
1.7
sec
0.9
sec
2008 Chino-Hills Eq.
1 2 3 4 5 6 7
5.3
sec
1.7
sec
0.9
sec
Period (sec)1 2 3 4 5 6 7
1.7
sec
0.9
sec
(x2)
Slide: 16/21
MPS Implementation: High-Rise Buildings
0 50 100 150 200 2500
0.1
0.2
0.3
D1 (cm)
FS1 /
L 1 (g)
19-Story Bldg.
0 100 200 3000
0.01
0.02
0.03
0.04
0.05
D1 (cm)
FS1 /
L 1 (g)
52-Story Bldg.
Slide: 17/21
Results from 19-story Building
0 2 40
5
10
15
Floo
r
Fl. Disp. / Bldg. Height (%)
o BenchmarkMPSMedianith GM
0 5Story Drift Ratio (%)
0 0.02Col. Pl. Rot. (rad)
0 0.01 0.02
GM Set-4
Beam Pl. Rot. (rad)
0 2 40
5
10
15
Floor Disp. / Bldg. Height (%)
Floo
r
0 2 4 6Story Drift Ratio (%)
0 0.02 0.04Col. Pl. Rot. (rad)
0 0.02 0.04 0.06Beam Pl. Rot. (rad)
Medianith GM
0 1 2 3 4 50
0.02
0.04
0.06
0.08
Med
ian
Roof Disp. / Bldg. Height (%)
Bas
e Sh
ear /
Wei
ght
19-story Bldg.
Slide: 18/21
Results from 52-story Building
0 1 20
10
20
30
40
50
Floo
r
Fl. Disp. / Bldg. Height (%)0 5
Story Drift Ratio (%)0 0.02
Col. Pl. Rot. (rad)0 0.02 0.04
GM Set-4
Beam Pl. Rot. (rad)
0 10
10
20
30
40
50
Floor Disp. / Bldg. Height (%)
Floo
r
0 2Story Drift Ratio (%)
0 0.01Col. Pl. Rot. (rad)
0 0.01 0.02Beam Pl. Rot. (rad)
Medianith GM
0 1 20
0.01
0.02
0.03
Med
ian
Roof Disp. / Bldg. Height (%)
Bas
e Sh
ear /
Wei
ght
52-story Bldg.
Slide: 19/21
Comparison with ASCE-7
0
5
10
15
Floo
r
o BenchmarkASCE-7Medianith GM
GM Set-1
0
5
10
15
Floo
r
GM Set-2
0 2 40
5
10
15
Floo
r
Fl. Disp. / Bldg. Height (%)0 5
Story Drift Ratio (%)0 0.02
Col. Pl. Rot. (rad)0 0.02 0.04
GM Set-3
Beam Pl. Rot. (rad)
0
10
20
30
40
50
Floo
r
o BenchmarkMPSMedianith GM
GM Set-1
0
10
20
30
40
50
Floo
r
GM Set-2
0 1 20
10
20
30
40
50
Floo
rFl. Disp. / Bldg. Height (%)
0 5Story Drift Ratio (%)
0 0.02Col. Pl. Rot. (rad)
0 0.02 0.04
GM Set-3
Beam Pl. Rot. (rad)
Slide: 20/21
Conclusions
o Even for the most intense near-fault ground motions, which represent a severe test, the MPS method estimates the median value of seismic demands to a good degree of accuracy (within 20% of the benchmark value).
o As opposed to the ASCE-7 scaling method, the MPS procedure significantly reduces the dispersion of results, and provides more accurate estimates of median EDPs.
o Thus, MPS procedure is more accurate and efficient.
Slide: 21/21
Final Remarks Further Evaluation of MPS (in progress)
Plan symmetric low-, mid- and high-rise buildings under bidirectional excitation Plan unsymmetric buildings and vertical irregular buildings
Draft report is available at:
http://profile.usgs.gov/ekalkan