Environmental Engineering Reference
In-Depth Information
Kinetic energy
is possessed by a body by virtue of its velocity. The energy of a body is the
amount of work it can do against the force applied to it, and work is the product of the
force required to displace a mass and the distance through which the mass is displaced.
Kinetic energy is expressed by
KE
max
1/2
m
v
2
max
1/2 (
W
/
g
)
v
2
max
erg
(11.26)
where
v
is the velocity with which a structure moves back and forth as the seismic wave
passes (Leet, 1960).
Energy transmitted to the structure may be represented in several ways:
Motion amplitude (displacement), frequency or acceleration (results from com-
bining amplitude and frequency)
●
Force with which the energy moves the structure
●
Energy itself, defined in terms of the motion which it produces (kinetic energy)
●
Ground Shaking and Analysis
Base excitation of the structure from ground shaking results in horizontal and vertical
deflections for some interval of time and imposes strains, stresses, and internal forces on
the structural elements. The shaking intensity depends on the maximum ground acceler-
ation, frequency characteristics, and duration.
Analysis requires definition of the system motion in terms of time-dependent functions,
and determination of the forces imposed on the structural members.
Response Modes
Structures exhibit various modes of response to ground motion depending on their char-
acteristics.
Peak horizontal ground acceleration
relates closely to the lateral forces imposed on a struc-
ture and is the value used normally for approximating earthquake effects.
Vertical acceleration
of ground motion can cause the crushing of columns. During the
downward acceleration of a structure, the stress in the columns is less than static. When
the movement reverses and becomes upward, an acceleration is produced, which causes
an additional downward force that adds loads to the columns. This effect was a major fac-
tor in the collapse of the Olive View Hospital during the San Fernando event (see
Figure
11.40)
.
Vertical accelerations are also important input to the design of certain structures
such as massive dams and surface structures such as pipelines.
Differential displacements
beneath structures can cause distortion and failure of longitu-
dinal members.
Frequency
, in relation to the natural frequency of the structural elements, governs the
response of the structure. Low frequencies (long periods) cause tall structures to sway.
Duration
of shaking or
repeated application
of forces causes fatigue in structural members
(and a continuous increase in soil pore pressures).
Dynamic Reaction of Structures
Source
The dynamic reaction of a structure to ground motion is governed by its characteristic
period
T
or structural frequency of vibration
ω
which is related to structural mass, stiff-
ness, and damping capability.
