SSaa(T(T11) Scaling) Scaling

Nilesh Shome

ABS Consulting

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MethodologyMethodology Developed in 1997 (Shome, N., Cornell, C. A.,

Bazzurro, P., and Carballo, J. (1998), “Earthquake, Records, and Nonlinear MDOF Responses”, Earthquake Spectra ).

Verified based on the results of nonlinear time-history analysis of a 5-story structure and a 20-story structure.

Worked quite well for single-frequency-dominated structures, but tall multi-frequency dominated structures showed some dependency on higher- mode spectral accelerations (or shape of spectrum). Sa(T1) scaling introduced some bias for tall structures.

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ProcedureProcedure

Randomly select small number of records from a specified M-R bin of records.

Scale the selected records to the target Sa(T1) before nonlinear time-history analysis.

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VerificationVerification

Nonlinear analysis results for a 5-story and a 20-story steel MRF were used for the verification of the methodology.

Results from the Strength-Reduced 5-Story Structure Results are available in term of maximum interstory

ductility (i.e., ratio of max story drift and yield displacement of that story, ). The interstory drift percentages are in general 0.8 to 1 .1 times ductility.

Results from unscaled records are compared with the results from the records scaled to the median Sa(T1) of a M-R bin of 20 records.

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Comparison of Results from Direct (Unscaled) Comparison of Results from Direct (Unscaled) Records with the Results from the Records Scaled to Records with the Results from the Records Scaled to

the Median Sthe Median Saa(T(T11))

Case Unscaled Records Scaled Records

M = 5.25 – 5.75

R = 5-25 km

0.12g 2.8 0.62 2.6 0.28

M = 6.5 – 7.0

R = 10-30 km

0.09g 1.9 0.51 2.0 0.25

)(ˆ

1TSa

Scaling the records to the median Sa(T1) of the bin of records does not introduce any bias.

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Comparison of Results for the 5-Story Structure from Comparison of Results for the 5-Story Structure from “Direct” Records with the Results from the Records “Direct” Records with the Results from the Records

Scaled to the Median SScaled to the Median Saa(T(T11))

Case Unscaled Records Scaled Records

Drift Drift

M = 5.25 – 5.75

R = 5-25 km

1.5g 3.0 0.54 3.0 0.36

M = 6.5 – 7.0

R = 10-30 km

1.5g 3.4 0.83 3.6 0.38

(%)ˆ riftD)(ˆ

1TSa

No strength reduction of the structure was employed. All the records in Bin-I and Bin-II were scaled first by a constant factor.

(%)ˆ riftD

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LimitationsLimitations Scaling of records to a target Sa(T1) introduces bias in the

response of tall multi-frequency dominated structures. Cornell and co-workers introduced vector-based demand

hazard calculations from the results of drift|Sa(T1),Sa(T2).

The Sa(T1)-scaling does work well with the near-source records. Luco and Cornell introduced an improved IM instead of Sa(T1) which can be used for ordinary as well as near-source records to improve the results.

Baker and Cornell introduced a vector-valued ground motion intensity measure consisting of spectral acceleration and epsilon. If the records are selected for nonlinear structural analysis based on the epsilon of the record, the bias in the results can be reduced significantly.

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Objective of PEER Ground Motion Objective of PEER Ground Motion Selection & Modification (GMSM) StudySelection & Modification (GMSM) Study

Estimation of median MIDR for a given earthquake event (MIDR|M,R) and for a given event conditioned on a Sa(T1) (MIDR|M,R,Sa).

The cumulative distribution function of MIDR for a given earthquake event and for a given event conditioned on a Sa(T1).

Number of records = 7.

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M = 7, R=10km, Fault Style=strike-slip, VM = 7, R=10km, Fault Style=strike-slip, Vss(30m) = 400 m/s(30m) = 400 m/s

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First randomly select 7 events out of 9 distinct events from the bin of records. Randomly select one record from each of the 7 selected events.

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Estimation of Median MIDREstimation of Median MIDR

For a Given Earthquake EventFor a Given Earthquake Event Scale the selected records to the median Sa(T1) for the

event. Estimate the median MIDR from the results of scaled

records.

For a Given Earthquake Event Conditioned on SFor a Given Earthquake Event Conditioned on Saa(T(T11))

Scale the selected records to the target Sa(T1). Estimate the median MIDR from the results of scaled

records.

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Cumulative Distribution Function Cumulative Distribution Function Distribution is assumed to be lognormal.

For a Given Earthquake EventFor a Given Earthquake Event where

1 is the slope of the MIDR curve (MIDR = 0.(Sa)1). Typical values of 1 are 0.85 for low-rise buildings, 1.0 for mid-rise buildings and 1.15 for high-rise buildings.

Sa|M,R is the dispersion of Sa for the given event. This can be obtained from the attenuation functions.

For the strength-reduced 5-story structure:

Compare the = 0.62 for the unscaled records. Note 20 records have been used for the unscaled as well as scaled records.

])()[( 2ˆ,,|

2,|1,| aSRMMIDRRMSaRMMIDR

69.0]28.0)74.085.0[( 22,| RM

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Cumulative Distribution Function (contd.)Cumulative Distribution Function (contd.)

For a Given Earthquake Event Conditioned on SFor a Given Earthquake Event Conditioned on Saa(T(T11)) Dispersion of MIDR can be estimated directly from the

results of scaled records.