Earthquake Engineering

“8.9 Quake Strikes Japan—Nation’s worst in 140 years”

Fukushima-Daichi nuclear power plant

Airport, Sendai, Japan

Earthquakes Past and PresentSENDAI, JAPAN (8.9 MAGNITUDE) HISTORICAL SEISMICITY

MAP

http://earthquake.usgs.gov/eqcenter/recenteqsww/ http://earthquake.usgs.gov/earthquakes/world/seismicity_maps/world.pdf

A pan-global issue….

http://www.mapsofworld.com/world-major-earthquake.htm

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

Why bother?

Sendai Japan Earthquake 2011Amazing engineering: Buildings Sway Without Collapsing

Different BuildingsDifferent model parameters

The Fundamental QuestionsCan 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

0 5 10 15 20 25 30 35-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Time (s)

Acc

el. (

units

of g

)

Tabas 1978 Ground Acceleration (Fault Normal)

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 FunctionMeasured Acceleration/USGS data

0 5 10 15 20 25 30 35-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

Time (s)

z(t)

Tabas 1978: Relative Displacement: o = 1

0 5 10 15 20 25 30 35-0.01

-0.005

0

0.005

0.01

0.015

Time (s)

z(t)

Tabas 1978: Relative Displacement: o = 10

0 5 10 15 20 25 30 35-0.06

-0.04

-0.02

0

0.02

0.04

0.06

Tabas 1978: Relative Displacement: o = 3

Time (s)

z(t)

0 5 10 15 20 25 30 35-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Time (s)

Acc

el. (

units

of g

)

Tabas 1978 Ground Acceleration (Fault Normal)

z = 0.05 is assumed

marks |z|max

If we found |z|max for a continuous range of o, we’d get the Spectral Displacement(Displacement Spectrum)

Gro

und

acce

lera

tion

(uni

ts o

f g)

Z(t)

met

ers

Z(t)

met

ers

Z(t)

met

ers

Spectra For El Centro Ground MotionAveraged SpectraTo Many (88) Earthquakes

Figure Credits: L A Chopra, Dynamics of Structures, Chap 6Right: G. Housner “Strong Ground Motion” in Earthquake Engineering, R Wiegel, editor.

Natural Period (sec)

Displacement

Acceleration

Velocity

Tripartite Representation

SD = spectral displacementSV = spectral velocitySA = spectral acceleration

SA /o = SV = oSD

Housner Spectrum

Spectrum for one earthquake Spectrum averaged over 88 earthquakes

Housner spectrum for z = 0.05

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: http://bcostin.wordpress.com/2008/02/25/seattle-worlds-fair-1962-postcards/seattle-monorail/

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 againstBUCKLING SMASHING/POUNDING

Base Isolation Configuration

Figure credit: Michael D. Symans, PhD Rensselaer Polytechnic Institute: http://www.nibs.org/client/assets/files/bssc/Topic15-7-SeismicIsolation.pdf

Reduced Shearing in Superstructure.CONVENTIONAL BUILDING

BASE-ISOLATED BUILDING

Figure credit: Michael D. Symans, PhD Rensselaer Polytechnic Institute: http://www.nibs.org/client/assets/files/bssc/Topic15-7-SeismicIsolation.pdf

Lead-Rubber Bearing

Figure credit:s Michael D. Symans, Rensselaer Polytechnic Institute: http://c.ymcdn.com/sites/www.nibs.org/resource/resmgr/BSSC/Topic15-7-SeismicIsolation.pdf

Shear Modulus

E ~ 0.5 – 1.0 MPa

LRB decreases keff and o

Reduces shearing in columns…………but increases displacement

LRB Isolation in Action

Rubber Base Isolators

Lead Rubber Bearing (LRB) in Action

UCSD testing facility LBRs in Japan

How do we model what we just saw?

Displacement , u

Frictional Pendulum System

Image credit: http://www.asee.org/documents/sections/pacific-southwest/2008/Porbaha_Ali_et_al%20Base%20isolation.pdf

Concept of Frictional Pendulum

Image credits: http://www.asee.org/documents/sections/pacific-southwest/2008/Porbaha_Ali_et_al%20Base%20isolation.pdfhttp://nees.buffalo.edu/docs/dec304/FP-DC%20Report-DEMO.pdf; laconservancy.org

Frictional Pendulum

Pendulum Period:T

Restoring/Recentering Force Frictional Force

The quantitative model

Restoring/Recentering Force Frictional Force

Force vs. Displacement Hysteresis Loop