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Earthquake Engineering. “8.9 Quake Strikes Japan—Nation’s worst in 140 years”. Airport, Sendai, Japan. Fukushima- Daichi nuclear power plant. Earthquakes Past and Present. Sendai, Japan (8.9 magnitude). historical Seismicity Map.

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8 9 quake strikes japan nation s worst in 140 years
“8.9 Quake Strikes Japan—Nation’s worst in 140 years”

Airport, Sendai, Japan

Fukushima-Daichi nuclear power plant

earthquakes past and present
Earthquakes Past and Present

Sendai, Japan (8.9 magnitude)

historical Seismicity Map

a pan global issue
A pan-global issue….

some major earthquakes past and present
Some Major Earthquakes, Past and Present

Christchurch, NZ 2011

Talca, Chile 2010

Port-au-Prince, Haiti, 2010

Guandong, China, 2008

Fukuoka, Japan, 2005

Izmit, Turkey, 1999

Northridge, CA, 1994

Mexico City, 1985

sendai japan earthquake 2011
Sendai Japan Earthquake 2011

Amazing engineering: Buildings Sway Without Collapsing

different buildings
Different Buildings

Different model parameters

the fundamental questions
The Fundamental Questions
  • Can we predict how different buildings will respond to an earthquake?
  • How can we use this information to engineer a safe structure
tabas iran 1978 earthquake
Tabas, Iran 1978 Earthquake

Acceleration record is messy. No way to integrate Duhamel’s integral. No worries, computers to the rescue!

Relative motion of building and ground

Impulse Response Function

Measured Acceleration/USGS data


Ground acceleration (units of g)

z = 0.05is assumed

Z(t) meters

marks |z|max

If we found |z|max for a continuous range of wo, we’d get the Spectral Displacement

(Displacement Spectrum)

Z(t) meters

Z(t) meters


Averaged Spectra

To Many (88) Earthquakes

Spectra For El Centro Ground Motion




Natural Period (sec)

Figure Credits: L A Chopra, Dynamics of Structures, Chap 6

Right: G. Housner “Strong Ground Motion” in Earthquake Engineering, R Wiegel, editor.

tripartite representation
Tripartite Representation

SD = spectral displacement

SV = spectral velocity

SA = spectral acceleration

SA/wo = SV = woSD

housner spectrum
Housner Spectrum

Spectrum for one earthquake

Spectrum averaged over 88 earthquakes

seattle monorail
Seattle Monorail
  • Seattle, WA is a beautiful city, but is prone to large earthquakes. The monorail on the bridge has previously been measured to have a natural period of 2 s. Damping is assumed to be 2%. During an earthquake, is the trolley likely to derail? Use the Housner spectrum to find out!

Picture from:

beach house
Beach House
  • You are hired as an architectural engineer to build a California dream house on a hillside. The structure can be idealized as shown (on chalkboard). The frame is built out of concrete (E = 30x109 Pa). The support columns have a cross section of 10 inches squared. Assume damping is 5%. Determine the base shear in each column, which is more likely to fail?
what we need to guard against
What we need to guard against



base isolation configuration
Base Isolation Configuration

Figure credit: Michael D. Symans, PhD Rensselaer Polytechnic Institute:

reduced shearing in superstructure
Reduced Shearing in Superstructure.

Conventional Building

Base-Isolated Building

Figure credit: Michael D. Symans, PhD Rensselaer Polytechnic Institute:

lead rubber bearing
Lead-Rubber Bearing

Shear Modulus

E ~ 0.5 – 1.0 MPa

Figure credit:sMichael D. Symans, Rensselaer Polytechnic Institute:

lrb decreases k eff and w o
LRB decreases keff and wo

Reduces shearing in columns…………but increases displacement

lrb isolation in action
LRB Isolation in Action

Rubber Base Isolators

lead rubber bearing lrb in action
Lead Rubber Bearing (LRB) in Action

UCSD testing facility

LBRs in Japan

frictional pendulum system
Frictional Pendulum System

Image credit:

concept of frictional pendulum
Concept of Frictional Pendulum

Image credits:;

frictional pendulum
Frictional Pendulum

Restoring/Recentering Force

Frictional Force

Pendulum Period:


the quantitative model
The quantitative model

Frictional Force

Restoring/Recentering Force