### Earthquake Engineering: Housner Spectrum

Airport, Sendai, Japan
Fukushima-Daichi nuclear power plant
SENDAI, JAPAN (8.9 MAGNITUDE)
http://earthquake.usgs.gov/eqcenter/recenteqsww/
HISTORICAL SEISMICITY MAP
http://earthquake.usgs.gov/earthquakes/world/seismicity_maps/world.pdf
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
Amazing engineering: Buildings Sway Without Collapsing
Different model parameters


Can we predict how different buildings will
respond to an earthquake?
How can we use this information to engineer
a safe structure
Tabas 1978 Ground Acceleration (Fault Normal)
1
0.8
0.6
Accel. (units of g)
0.4
0.2
0
-0.2
-0.4
-0.6
-0.8
0
5
10
15
20
25
30
35
Time (s)
Acceleration record is messy. No way to integrate Duhamel’s integral. No worries, computers to the rescue!
Relative motion of
building and ground
Measured Acceleration/USGS data
Impulse Response
Function
Tabas 1978 Ground Acceleration (Fault Normal)
Ground acceleration (units of g)
Accel. (units of g)
1
0.8
0.6
0.4
0.2
0
-0.2
-0.4
-0.6
-0.8
0
5
10
15
20
25
30
35
Time (s)
Tabas 1978: Relative Displacement: 
o
= 1
0.15
z(t)
Z(t) meters
0.1
z = 0.05 is assumed
0.05
0
-0.05
-0.1
-0.15
-0.2
0
5
10
15
20
25
30
35
Time (s)
marks |z|max
Tabas 1978: Relative Displacement:  o = 3
0.06
z(t)
Z(t) meters
0.04
0.02
0
-0.02
-0.04
-0.06
0
5
10
15
20
25
30
35
30
35
Time (s)
Tabas 1978: Relative Displacement:  o = 10
0.01
0.005
z(t)
Z(t) meters
0.015
0
-0.005
-0.01
0
5
10
15
20
Time (s)
25
If we found
|z|max for a
continuous
range of o,
we’d get the
Spectral
Displacement
(Displacement
Spectrum)
Spectra For El Centro Ground Motion
Velocity
Acceleration
Displacement
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.
Averaged Spectra
To Many (88) Earthquakes
Tripartite Representation
SD = spectral displacement
SV = spectral velocity
SA = spectral acceleration
SA /o = SV = oSD
Spectrum for one earthquake
Spectrum averaged over 88 earthquakes

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/

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?
BUCKLING
SMASHING/POUNDING
Figure credit: Michael D. Symans, PhD Rensselaer Polytechnic Institute:
http://www.nibs.org/client/assets/files/bssc/Topic15-7-SeismicIsolation.pdf
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
Shear Modulus
E ~ 0.5 – 1.0 MPa
Figure credit:s Michael D. Symans, Rensselaer Polytechnic Institute: http://c.ymcdn.com/sites/www.nibs.org/resource/resmgr/BSSC/Topic15-7-SeismicIsolation.pdf
Reduces shearing in columns…………but increases displacement
Rubber Base Isolators
UCSD testing facility
LBRs in Japan
Displacement , u
Image credit: http://www.asee.org/documents/sections/pacificsouthwest/2008/Porbaha_Ali_et_al%20Base%20isolation.pdf
Image credits: http://www.asee.org/documents/sections/pacific-southwest/2008/Porbaha_Ali_et_al%20Base%20isolation.pdf
http://nees.buffalo.edu/docs/dec304/FP-DC%20Report-DEMO.pdf; laconservancy.org
Restoring/Recentering Force
Frictional Force
Pendulum Period:
T= 2 /
Restoring/Recentering Force
Frictional Force