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Characterizing Earthquake Shaking:Ground Motion Parameters and the Acceleration Response SpectrumAcceleration Response Spectrum
Brady R. Cox, Ph.D., P.E.Brady R. Cox, Ph.D., P.E.The University of Arkansas
Department of Civil Engineering
Geotechnical Earthquake Engineering for Seismic Design Workshop,
Department of Civil Engineering
Port-au-Prince, Haiti, November 18-19, 2010
Earthquake Ground Motions are Described By:• Amplitude• Duration• Frequency Content
These Parameters are Influenced By:• Earthquake MagnitudeEarthquake Magnitude• Distance from the Site to the Fault
L l S il C diti ( k il)• Local Soil Conditions (rock versus soil)• Special effects (rupture directivity, topographic
effects, etc.)
Simple Harmonic MotionKramer (1996)T
A
A = amplitudeA amplitudeT = period = time to complete 1 cycle (sec) = 1/ff = frequency = cycles per second (Hz) = 1/T
Fourier Theory
Complicated motions (like earthquake ground motions) can be described
Kramer (1996)
p ( q g )as a summation of simple harmonic motions
Earthquake Amplitude Parameters
PGA
PGVPGV
PGD
Kramer (1996)Rock
Kramer (1996)Soil
Acceleration recordings from the 1989 Loma Prieta, California Earthquake; acceleration records integrated to obtain velocity and displacement
Acceleration Response SpectrumSaSa
T
Kramer (1996) PGA
Single Degree of Freedom (SDOF) oscillators(i.e. “buildings” with different heights/natural periods of vibration)
Structural Demands from Spectral AccelerationSa
Newton’s
Sa
LawF = m*aF m a
Ch (200 )
Equivalent Static Force = fso = m*Sa = W*Sa(g)
Chopra (2005)
q so (g)
Base Shear = Vbo = fso
Base Moment = fso * h
Spectral Accelerations (T = 0.5 sec)
Sa = 0 75 g S 0 60PGA PGA
Sa 0.75 g Sa = 0.60 g
T = 0.5 sec (~ 5 story building)
Input Acceleration Time Histories into SDOF oscillators (5% damping)
PGA 0 45 PGA 0 30
Rock Soil
PGA = 0.45 g PGA = 0.30 g
Kramer (1996)
Soil
Spectral Accelerations (T = 1.0 sec)
Sa = 0.30 g Sa = 0.40 g
T = 1.0 sec (~ 10 story building)
Input Acceleration Time Histories into SDOF oscillators (5% damping)
PGA 0 45 PGA 0 30
Rock Soil
PGA = 0.45 g PGA = 0.30 g
Kramer (1996)
Soil
Summary of Equivalent Static Forces
Sa = 0 75 g Sa = 0.60 gSa 0.75 gSa = 0.30 g
gSa = 0.40 g
Gilroy #1 (Rock) Gilroy #2 (Soil)~ 5 Story Building (T = 0.5 sec)Vbo = 0.75*Weight Building
~ 5 Story Building (T = 0.5 sec)Vbo = 0.60*Weight Building
~ 10 Story Building (T = 1.0 sec)V = 0 30*Weight Building
~ 10 Story Building (T = 1.0 sec)V = 0 40*Weight Building
Kramer (1996)
Vbo = 0.30 Weight Building Vbo = 0.40 Weight Building