eciv 724 a dynamics of structures instructor: dr. dimitris c. rizos 300 main st. dept. of civil and...
Post on 20-Dec-2015
215 views
TRANSCRIPT
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:The Main Earth Layers are:• CoreCore• Lower MantleLower Mantle• Upper MantleUpper Mantle• CrustCrust
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
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)
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 , ).
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.
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