Civil Engineering Reference
In-Depth Information
Fig. 2.10
Plots of
k
and
σ
σ
p
x
x
max
()
()
X t
xxt
Given a stochastic variable
, the expected value of its largest peak
during a realisation with length
T
may then be estimated from
=+
Xx
k
=+ ⋅
σ
(2.44)
max
p
x
k
is given by
where the peak factor
γ
()
k
2ln
f
0
T
=⋅
⎡
⋅
⎤
+
(2.45)
⎣
⎦
p
x
()
2ln
f
0
T
⋅
⎡
⋅
⎤
⎣
⎦
x
For fairly broad banded processes this peak factor will render values between 2 and 5.
Plots of
k
and
are shown in Fig. 2.10. It should be acknowledged that when
σ
σ
p
x
x
max
()
x t
becomes ultra narrow banded then
k
2
, because for a single harmonic
→
p
component
()
(
)
x t
c
cos
t
,
0
tT
=⋅
ω
<<
(2.46)
x
x
