Lesson 4-5 Flashcards
___________ arise from sudden movements in a rupture zone in the Earth’s crust.
Seismic Waves
The upper part of the building remains in delay in respect to the foundation moving, due to its _______. This causes strong vibrations of the structure with ___________________ between the structure and the ground and hence large inertial force arise.
mass, resonance phenomena
Due to its weight, the soil is overloaded, becoming _______, hence producing change in its behavior.
stiffer
Part of the vibrating energy of buildings is released into soil through waves produced by buildings.
Soil Effect
The severity of shaking is controlled primarily by two (2) factors:
a. Attenuation of ground motion.
b. Earthquake characteristics
The dissipation of seismic energy as seismic waves move through layers of varying soil and rock strata.
Attenuation of ground motion
Characterized as the decrease in amplitude of the seismic waves with distance from source. It results from geometric spreading of propagating waves, energy absorption and scattering of waves.
Attenuation of ground motion
Other important earthquake measurement parameters are the measured ground motions at the ground surface. These are:
Peak Ground Acceleration (PGA)
Peak Ground Velocity (PGV)
Peak Ground Displacement (PGD)
_________________ has become the most popular parameter to denote the measure of an earthquake and has been related to the magnitude through several empirical relationship.
Peak Ground Acceleration (PGA)
are essential for describing the important characteristics of strong ground motion in compact, quantitative form.
Ground motion parameters
The most common way of describing a ground motion is with
Time history
As the PGA value decreases with the epicentral distance, these empirical relationships are also called
attenuation laws
refers to the fact that the state of the system and the applied forces do not vary in time; they are time-independent.
Static
is the study of systems subject to time-varying applied forces.
Dynamics
considered as the study of a body or structure in dynamic equilibrium and the mathematical expression of this equilibrium is the equation of motion.
Structural dynamics
expresses the equilibrium of internal and external force terms and the mass inertia and damping effects.
equation of motion
______________ involves the second derivative and the damping term the first derivative of the displacement with respect to time.
inertia term
second-order differential equation with constant coefficients.
equation of motion
All bodies possessing inertia (mass) and elasticity (degree of stiffness) are capable of
vibration
a system put out of its equilibrium position and vibrates under the action of forces inherent in the system
Free Vibration
a vibration that takes place under the action of external forces.
Forced Vibration
Types of Vibration
a. Free, undamped vibration
b. Free, damped vibration
c. Forced, undamped vibration
d. Forced, damped vibration
is equal to the number of independent coordinates necessary to describe the motion of a system.
Degree of Freedom (DOF)
The time required for the system to complete one cycle of the vibration.
Period
The number of cycles per unit time (cycles per second)
Frequency
Formulated by estimating an equivalent lateral seismic loads as a fraction of the total system weight.
Static Analysis
The fraction is determined from a notional earthquake, which is based on the risk posed by the seismicity of the site and is captured in a single graph known as the
response spectrum
The procedure for this analysis models the load effect of earthquakes more accurately by using either a set of specific earthquake ground motion time history records (response time-history analysis procedure) or the effect of same notional earthquake as the equivalent static analysis (the design response spectrum).
Dynamic Analysis
a linear or nonlinear mathematical model of the system is used to determine the system response (displacement and accelerations, which are used to determine the internal loading in each member) at each increment of time for a suite of ground motion acceleration time histories.
Response time history analysis procedure
uses established methods of structural dynamics to determine system vibration mode shapes and their associated natural periods, which along with the response spectrum are used to establish the maximum structural response.
modal response spectrum analysis procedure
- is needed to determine the circular frequency., which once obtained can be used to determine the natural period of vibration of the system.
- defined as the ratio of force (or moment) to
displacement (or rotation).
STRUCTURAL STIFFNESS, k
caused by initial conditions (displacement and velocity) and not by applied force.
Free vibration
