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ECIV 724 A Dynamics of Structures. Instructor: Dr. Dimitris C. Rizos 300 Main St. Dept. of Civil and Environmental Engineering (803) 777-6166 rizos@engr.sc.edu. Earth Layers. The Main Earth Layers are: Core Lower Mantle Upper Mantle Crust. Earth Layers.

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eciv 724 a dynamics of structures

ECIV 724 A Dynamics of Structures

Instructor:

Dr. Dimitris C. Rizos

300 Main St.

Dept. of Civil and Environmental Engineering

(803) 777-6166 rizos@engr.sc.edu

earth layers
Earth Layers
  • The Main Earth Layers are:
    • Core
    • Lower Mantle
    • Upper Mantle
    • Crust
st andreas fault
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
El Progresso, Guatemala February 4, 1976

Plastic Deformation

Saturated unconsolidated deposits

left-lateral strike-slip fault

dickey idaho
Dickey, Idaho

horizontal offset

~2 m

Fault scarp

slide11

offset 2.6 m

San Francisco, April 18, 1906

Guatemala February 4, 1976

ground motion
Ground Motion
  • External excitation in the form of
  • Ground Displacements
  • Ground Velocities
  • Ground Accelerations
  • Typical Duration 20-100 sec
ground motion15
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
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
LIQUEFACTION-DIFFERENTIAL SETTLEMENTS

Niigata, Japan.June 16, 1964, 7.4

ground deformation differential settling
GROUND DEFORMATION-DIFFERENTIAL SETTLING

Earthquake of July 29, 1967, Caracas, Venezuela.

ground shaking
GROUND SHAKING

Before

Huaraz, Peru

May 31, 1970, 7.8R

After

slide21

San Fernando

Mexico City

collapsed cypress section of interstate 880
Collapsed Cypress section of Interstate 880

the 1989 Loma Prieta (California)

northridge 1994
Northridge 1994

Parking garage at California State University

kobe 1995
Kobe 1995

Collapsed first and second stories

slide28

Structural Response Assumed to be Independent of Ground Motion

True for most cases when Soil-Structure Interaction is not an issue

earthquake analysis
EARTHQUAKE ANALYSIS

SDF SYSTEMS

A SDF system is subjected to a ground motion ug(t). The deformation response u(t) is to be calculated.

earthquake analysis30
EARTHQUAKE ANALYSIS

EQUIVALENT STATIC FORCE

fs(t) is the force which must be applied statically in order to create a displacement u(t).

reponse spectra
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 spectra32
REPONSE SPECTRA

Example : Deformation response spectrum for El Centro earthquake

slide33

Deformation, pseudo-velocityandpseudoacceleration response spectra can be defined and ploted on the same graphs

n : natural circular frequency

of the SDF system.

response spectrum charcteristics
RESPONSE SPECTRUM CHARCTERISTICS

Tn < 0.03 s : rigid system

no deformation

u(t) ≈ 0  D ≈ 0

response spectrum charcteristics36
RESPONSE SPECTRUM CHARCTERISTICS

Tn > 15 s : flexible system

no total displacement

u(t) = ug(t)  D = ugo