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