1. Earthquake Engineering

2. “8.9 Quake Strikes Japan—Nation’s worst in 140 years”
Airport, Sendai, Japan
Fukushima-Daichi nuclear power plant

3. Earthquakes Past and Present
Sendai, Japan (8.9 magnitude)
historical Seismicity Map

4. A pan-global issue….

5. 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

6. Why bother?

7. Sendai Japan Earthquake 2011
Amazing engineering: Buildings Sway Without Collapsing

8. Different Buildings
Different model parameters

9. 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

10. 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

11. z = 0.05 is assumed marks |z|max
Ground acceleration (units of g)
z = 0.05 is assumed
Z(t) meters
marks |z|max
Z(t) meters
If we found |z|max for a continuous range of wo, we’d get the Spectral Displacement
(Displacement Spectrum)
Z(t) meters

12. Spectra For El Centro Ground Motion
Averaged Spectra
To Many (88) Earthquakes
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.

13. Tripartite Representation
SD = spectral displacement
SV = spectral velocity
SA = spectral acceleration
SA /wo = SV = woSD

14. Housner Spectrum Spectrum for one earthquake
Spectrum averaged over 88 earthquakes

15. Housner spectrum for z = 0.05

16. 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:

17. 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?

18. What we need to guard against
Buckling
SmaSHING/POUNDING

19. Base Isolation Configuration
Figure credit: Michael D. Symans, PhD Rensselaer Polytechnic Institute:

20. Reduced Shearing in Superstructure.
Conventional Building
Base-Isolated Building
Figure credit: Michael D. Symans, PhD Rensselaer Polytechnic Institute:

21. Lead-Rubber Bearing Shear Modulus E ~ 0.5 – 1.0 MPa
Figure credit:s Michael D. Symans, Rensselaer Polytechnic Institute:

22. LRB decreases keff and wo
Reduces shearing in columns…………but increases displacement

23. LRB Isolation in Action
Rubber Base Isolators

24. Lead Rubber Bearing (LRB) in Action
UCSD testing facility
LBRs in Japan

25. How do we model what we just saw?
Displacement , u

26. Frictional Pendulum System
Image credit:

27. Concept of Frictional Pendulum
Image credits:
laconservancy.org

28. Frictional Pendulum Pendulum Period: T=2𝜋 𝑅/𝑔
Restoring/Recentering Force
Frictional Force
Pendulum Period:
T=2𝜋 𝑅/𝑔

29. The quantitative model
Restoring/Recentering Force
Frictional Force

30. Force vs. Displacement Hysteresis Loop