Civil Engineering Reference
In-Depth Information
structure to oscillate. The time domain chain of events is illustrated in Fig. 6.2.a. From a
design point of view the main focus is on quantifying the maximum value of the
response that is most critical with respect to structural safety.
The flow is in general assumed Gaussian, stationary and homogeneous over a certain
short term period
T
(e.g. 10 min), i.e. the response calculations are performed for a
chosen design weather condition that is stable in time and space. If the mathematical
transfer from flow properties to forces is linear and the structure is linear elastic, then the
assumption of Gaussian and stationary properties also holds for any structural response
quantity. Thus, any response quantity (e.g. a displacement) may be described by its mean
value and probability density distribution, as shown to the right in Fig. 6.2.a. Its
maximum value at position
x
is then given by
() ()
()
r
xr xk
x
=
+
⋅
σ
(6.1)
max
r
r
p
r
r
()
where
rx
is the mean value,
k
is the peak factor that depends on the type of
r
p
()
process (see chapter 2.4) and
x
is the standard deviation of the fluctuating part of
σ
rr
the response.
Fig. 6.2
Time and frequency domain representations
