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 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 2011 Amazing engineering: Buildings Sway Without Collapsing
Different Buildings Different model parameters
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 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
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
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.
Tripartite Representation SD = spectral displacement SV = spectral velocity SA = spectral acceleration SA /wo = SV = woSD
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 against Buckling 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 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
LRB decreases keff and wo 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 https://www.youtube.com/watch?v=09pNV06MP7s
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.pdf http://nees.buffalo.edu/docs/dec304/FP-DC%20Report-DEMO.pdf; laconservancy.org
Frictional Pendulum Pendulum Period: T=2𝜋 𝑅/𝑔 Restoring/Recentering Force Frictional Force Pendulum Period: T=2𝜋 𝑅/𝑔
The quantitative model Restoring/Recentering Force Frictional Force
Force vs. Displacement Hysteresis Loop