Download ECIV 720 A Advanced Structural Mechanics and Analysis

ECIV 724 A
Dynamics of Structures
Instructor:
Dr. Dimitris C. Rizos
300 Main St.
Dept. of Civil and Environmental Engineering
(803) 777-6166 [email protected]
Earth Layers
The Main Earth Layers are:
• Core
• Lower Mantle
• Upper Mantle
• Crust
Earth Layers
Theory of Tectonic Plates
Theory of Tectonic Plates
Fault Types
St. Andreas Fault
Location: Carrizo Plain
area, San Luis Obispo
County, California.
Surface Rupture
Right-Lateral Strike-Slip Faults
Photo credit:
R.E. Wallace, U.S. Geological Survey.
El Progresso, Guatemala February 4, 1976
Plastic Deformation
Saturated
unconsolidated
deposits
left-lateral strike-slip fault
Dickey, Idaho
horizontal offset
~2 m
Fault scarp
Earthquake of February 4, 1976, Guatemala
offset 2.6 m
San Francisco, April 18, 1906
Guatemala February 4, 1976
Wave Types
Wave Types
Ground Motion
External excitation in the form of
• Ground Displacements
• Ground Velocities
• Ground Accelerations
Typical Duration 20-100 sec
Ground Motion
Ground Motion has 3 Components
N-S, E-W and Vertical
Horizontal components are of major interest
(excessive shear forces)
Vertical component has been traditionally
ignored, but may be important.
Intstrumentation
Strong Motion Accelerograph
A transducer: SDOF highly damped (60-70%)
Known k, m (fn ~ 25 Hz)
Sampling Rate: 1/100, 1/50 sec
(10,000 sampling points)
LIQUEFACTION-DIFFERENTIAL SETTLEMENTS
Niigata, Japan. June 16, 1964,
7.4
GROUND DEFORMATION-DIFFERENTIAL
SETTLING
Earthquake of July 29, 1967, Caracas, Venezuela.
GROUND SHAKING
Before
Huaraz, Peru
May 31, 1970, 7.8R
After
San Fernando
Mexico City
Collapsed Cypress section of Interstate 880
the 1989 Loma Prieta (California)
Northridge 1994
Parking garage at California State University
Damaged Kobe waterfront (1995)
Office Buildings, Kobe 1995
Kobe 1995
Collapsed first and second stories
Collapse of Freeway in 1989 Loma Prieta, CA
Earthquake (7.1R)
Structural Response Assumed to be Independent
of Ground Motion
True for most cases when Soil-Structure
Interaction is not an issue
EARTHQUAKE ANALYSIS
SDF SYSTEMS
A SDF system is subjected to a ground motion ug(t).
The deformation response u(t) is to be calculated.
u(t )
m
m (ug  u)  c u  k u  0
c
k/2
ug (t )
k/2
u  2 ωn u  ωn2 u  ug (t )
EARTHQUAKE ANALYSIS
EQUIVALENT STATIC FORCE
fs(t) is the force which must be
applied statically in order to
create a displacement u(t).
fs (t )  k u(t )
 m n2 u(t )
u(t )
 m A(t )
fs (t )
A(t )
2
 n u(t ) 
u(t )
Pseudo accelerati on
REPONSE SPECTRA
A response spectrum is a plot of maximum response (e.g.
displacement, velocity, acceleration) of SDF systems to a given
ground acceleration versus systems parameters (Tn , ).
A response spectrum is calculated numerically using time
integration methods for many values of parameters (Tn , ).
REPONSE SPECTRA
Example : Deformation response spectrum for El Centro earthquake
Deformation, pseudo-velocity and pseudoacceleration
response spectra can be defined and ploted on the same
graphs
Peak Deformatio n
D  max u (t )
Peak Pseudo  velocity
V  n D
Peak Pseudo  acceleration
A  n2 D
n : natural circular frequency
of the SDF system.
COMBINED D-V-A SPECTRUM
RESPONSE SPECTRUM CHARCTERISTICS
Tn  2 m k
Tn < 0.03 s : rigid system
no deformation
u(t) ≈ 0  D ≈ 0
RESPONSE SPECTRUM CHARCTERISTICS
Tn  2 m k
Tn > 15 s : flexible system
no total displacement
u(t) = ug(t)  D = ugo
RESPONSE SPECTRUM CHARCTERISTICS
Tn  0.5 s
: acceleration sensitive region
0.5  Tn  3 s : velocity sensitive region
Tn  3 s
: displaceme nt sensitive region
Example