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:The Main Earth Layers are:• CoreCore• Lower MantleLower Mantle• Upper MantleUpper Mantle• CrustCrust

Earth Layers

Theory of Tectonic Plates

Theory of Tectonic Plates

Fault Types

St. Andreas Fault

Right-Lateral Strike-Slip Faults

Location: Carrizo Plain area, San Luis Obispo County, California.

Photo credit:

R.E. Wallace, U.S. Geological Survey.

Surface Rupture

El Progresso, Guatemala February 4, 1976

left-lateral strike-slip fault

Plastic Deformation

Saturated unconsolidated deposits

Dickey, Idaho

Fault scarp

horizontal offset

~2 m

Earthquake of February 4, 1976, Guatemala

Guatemala February 4, 1976San Francisco, April 18, 1906

offset 2.6 m

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

Horizontal components are of major interest (excessive shear forces)

Ground Motion has 3 Components

N-S, E-W and Vertical

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

Huaraz, PeruMay 31, 1970, 7.8R

Before

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

k/2 k/2

c

)(tug

)(tu

m

A SDF system is subjected to a ground motion ug(t).

The deformation response u(t) is to be calculated.

)(

)(

tuuu u

u ku cuu m

gnn

g

22

0

ωω

EARTHQUAKE ANALYSIS

onaccelerati Pseudo

2 )()()( tu tutA n

EQUIVALENT STATIC FORCE

)(tu )(tfs tA m

tu m

tu ktf

n

)(

)(

)()(

2

s

fs(t) is the force which must be

applied statically in order to create a displacement u(t).

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

D A

D V

tuD

n

n

2

)(max

onacceleratiPseudo Peak

velocityPseudo Peak

nDeformatio Peak

n : natural circular frequency

of the SDF system.

COMBINED D-V-A SPECTRUM

RESPONSE SPECTRUM CHARCTERISTICS

kmTn 2

Tn < 0.03 s : rigid system

no deformation

u(t) ≈ 0 D ≈ 0

RESPONSE SPECTRUM CHARCTERISTICS

Tn > 15 s : flexible system

no total displacement

u(t) = ug(t) D = ugo

kmTn 2

RESPONSE SPECTRUM CHARCTERISTICS

region sensitive ntdisplaceme:s

region sensitive velocity:s.

region sensitive onaccelerati:s.

T

T

T

n

n

n

3

350

50

Example