Civil Engineering Reference
In-Depth Information
z
is usually called the roughness length. It coincides with the height at which the ve-
locity variation according to Eq. 3.1 is zero. Typical values of
k
and
z
varies from about 0.15 and 0.01 for open sea and countryside without obstacles to about
0.25 and 1.0 for built up urban areas. Corresponding values of
mi
z
varies between 2
and about 15 m. (Other profiles, e.g. the power law profile, may be found in the
literature.)
Any statistical properties related to the mean wind velocity is in the following associ-
ated with
(
)
Vz
, where
z
is a chosen reference height. In general,
z
10 m
as
=
10
ref
ref
ref
mentioned above, but for a bridge whose main girder is located at a certain height above
the sea or terrain,
z
will often be chosen at this height. To simplify notations
ref
(
)
Vz
is set equal to
V
or
V
for the remaining part of this chapter. The indexes
r
and
a
indicate whether the relevant statistical calculations have been performed on the
parent population or on a reduced population of annual maxima. Data from a large popu-
lation of parent observations may usually be fitted to a Weibull distribution, i.e. the cu-
mulative and corresponding density distributions are given by
10
ref
()
⎫
⎧
γϕ
⎫
⎡
V
⎤
⎪
⎪
⎪
(
)
( )
PV V
,
1
e p
≤
ϕ
=
−
α ϕ
⋅
−
⎨
⎢
⎥
⎬
r
r
()
⎪
βϕ
⎢
⎥
⎪
⎣
⎦
⎪
⎩
⎭
⎪
⎪
⎬
⎪
(3.2)
()
()
γϕ
−
1
⎧
γϕ
⎫
() ()
()
⎡
⎤
⎡
⎤ ⎪
dP
αϕ γϕ
⋅
V
V
⎪
⎪
(
)
r
pV
,
exp
ϕ
=
=
⋅
⋅
−
⎢
⎥
⎨
⎢
⎥
⎬⎪
r
()
()
dV
βϕ
βϕ
βϕ
⎢
⎥
⎢
⎥
⎪
⎪⎪
⎣
⎦
⎣
⎦
⎩
⎭
⎭
()
()
where
βϕ are parameters to be fitted to
the relevant data. If the directionality effect is omitted, i.e. for omni-directional wind, the
data may usually be fitted to a Rayleigh density distribution
is the main flow direction and
α ϕ
and
ϕ
2
⎡
⎤
V
1
⎛ ⎞
V
()
pV
exp
⎢
⎥
=⋅
−
(3.3)
⎜ ⎟
r
2
2
V
V
⎢
⎥
⎝ ⎠
m
m
⎣
⎦
where
V
is the velocity at the apex of the distribution, as illustrated in Fig. 3.2. Thus,
the probability
of exceeding a certain limiting value
V
(see Fig. 3.2) is given by
μ
