Environmental Engineering Reference
In-Depth Information
FIGURE 11.40
Damage suffered by the Olive View Hospital during the San Fernando earthquake of February 9, 1971, (
M
6.6;
1
max
VIII-XI). Damage to the newly constructed reinforced buildings included the collapse and “pancaking”
of the two-story structure in the upper left (1), the collapse of the garage and other structures in the foreground
(2), and the toppling of three four-story stairwell wings (3). Vertical accelerations combined with horizontal
accelerations were a significant cause in the collapse. (Photograph courtesy of the U.S. Geological Survey.)
11.4.2
Structural Response
General Characteristics
Reaction to Strong Ground Motion
Dynamic forces are imposed on structures by strong ground motion. Structural response
is related to the interaction between the characteristics of the structure in terms of its mass,
stiffness, and damping capability, and the characteristics of the ground motion in terms of
the combined influence of the amplitude of ground accelerations, their frequency compo-
nents, and the duration.
Damping
refers to a resistance that reduces or opposes vibrations
by energy absorption.
The elements of ground motion are amplitude
A
, displacement
y
, frequency
f
(Hz), and
period
T
(sec), and the derivatives velocity
v
and acceleration
α
.
Energy Transmitted to Structures
Maximum vibration velocity
imposed by the elastic wave as it passes beneath the structure
in terms of circular frequency
w
and amplitude is
V
max
2
π
fA
cm/sec
(11.23)
The greatest acceleration to which the structure is subjected is
2
f
2
A
cm/sec
2
α
max
4
π
(11.24)
The greatest force applied to the structure is found when acceleration is expressed in terms
of the mass. This allows for the development of an expression relating force to the accel-
eration due to gravity, frequency, and amplitude as follows:
2
f
2
A
F
max
m
α
max
(
W
/
g
)(
α
max
)
(
W
/
g
)4
π
dyn
(11.25)
where
W
is the weight. It is seen that the force varies as the square of the frequency.
