Civil Engineering Reference
In-Depth Information
(
)
α
q
γβ
β
6/
πσ
q
where
=−⋅
and
=
⋅
, and where
is the mean value of the
q
velocity pressure recordings,
σ
is the corresponding standard deviation and
0.5772
γ ≈
q
is the Euler constant.
α
and
β
are parameters that are characteristic to the distribution
of the recorded data. If the return period
is defined as the average number of years
R
p
q
between rare
events, then a small probability
of exceeding a certain limiting
μ
V
a
q
design value
V
d
1
(
)
(
)
Pq
q
1
Pq
q
μ =
>
=
−
≤
≈
(3.6)
aV
V
aV
V
a
d
a
d
R
p
q
and thus, the
that corresponds to such a return period is given by
V
d
q
⎫
⎡
⎛
−
α
⎞
⎤
1
(
)
V
d
1
−=
Pq
≤ = − −
q
exp
exp
⎪
⎢
⎜
⎟
⎥
aV
V
⎪
⎜
⎟
a
d
R
β
⎢
⎥
(3.7)
⎝
⎠
⎬
p
⎣
⎦
⎪
(
)
(
)
qR
ln
⎡
ln 1
1 /
R
⎤
⇒
=−⋅
αβ
−
−
⎪
Vp
⎣
p
⎦
⎭
d
q
It is the mean wind velocity
V
that corresponds to such a value of
that is used as a
V
d
representative basis for the design of structures.
R
is in general subject to standardisa-
p
()
tion, e.g.
years, in which case
. The ratio
βα≈
/
0.2
is
R
=
50
q
50
≈+ ⋅
α
3.9
β
p
V
d
2
/ 2
frequently encountered in the literature. Since
q
=
ρ
V
, then a change from
V
d
d
R
=
50
to another return period is given by
p
{
}
(
(
)
(
)
()
(
)
)
⎡
⎤
VR V
/
50
1
/
ln
ln 1
1 /
R
/ 1
3.9
/
≈−
β
α
⋅
− −
+⋅
β
α
(3.8)
dp d
⎣
p
⎦
While the above considerations are concerned with the statistical properties of annual
maxima, it should be mentioned that within any short term (10 min.) stationary weather
window at high wind velocities it is possible to estimate an extreme value of the velocity
fluctuations. For instance, at any chosen characteristic design value
(
)
VR
, the corre-
sponding extreme value may be obtained by a simple linearization and the broad band
type of process considerations shown in chapter 2.4. Since the instantaneous velocity
pressure
dp
{
}
1
1
1
2
2
2
()
()
()
2
()
()
(3.9)
u
qt
=
ρ
⎡ ⎤
Ut
=
ρ
⎡
V ut
+
⎤
=
ρ
V
12
+
utV utV
/
+
⎡
/
⎤
⎣ ⎦
⎣
⎦
⎣
⎦
2
2
2
