Civil Engineering Reference
In-Depth Information
(a)
(b)
F
F
L
p
m
F
D
M
FIGURE 4.19
(a) Wind flow past a bluff body and (b) wind forces on a bluff body.
4.4.1 W
IND
F
ORCES ON
S
TEEL
R
AILWAY
B
RIDGES
In contrast to long-span or flexible bridges (such as suspension or cable-stayed
bridges), ordinary steel railway bridges (such as those composed of beam, girder,
truss, and arch spans) need not consider aerodynamic effects
∗
of the wind in
design.
†
However, the aerostatic effects of the wind on the superstructure and moving
train must be considered, particularly in regard to lateral bracing design.
A steady wind with uniform upstream velocity,
V
u
, flowing past a bluff body (such
as the bridge cross section of Figure 4.19a) will create a maximum steady state local
or dynamic pressure,
p
m
, in accordance with Bernoulli's fluid mechanics equation as
1
2
ρ
V
u
,
p
m
=
p
amb
+
(4.34)
where
p
amb
is the ambient air pressure and is equal to 0 at atmospheric pressure;
ρ
is
the air density;
V
u
is the upstream air speed.
However, the average dynamic pressure on the bridge span will be less than
the maximum dynamic pressure given by Equation 4.34. Therefore, the dynamic
pressure,
p
, at any point on the bluff body can be expressed as
C
p
2
ρ
V
u
,
p
=
C
p
p
m
=
(4.35)
where
C
p
is a dimensionless mean pressure coefficient that depends on the shape of
the obstruction.
For example, if we assume a 100 mph wind speed (which may occur during gale
and hurricane winds), Equation 4.34 yields a maximum dynamic pressure of 23.7 psf
(
0.0022 slug/ft
3
).
Designwindforcesmustbebasedonaveragedynamicwindpressures(i.e.,reduced
by the use of an appropriate pressure coefficient) calculated over an appropriate cross-
sectionalarea.Thedesignmustalsoconsidertheeffectsofwindgusts.
‡
Itisbeneficial,
from a design perspective, to calculate design wind forces based on the maximum
dynamic pressure, a characteristic area, and a dimensionless coefficient that includes
ρ =
∗
The effects from dynamic behavior and buffeting.
†
An equivalent static wind pressure is appropriate since the natural or fundamental frequency of the
superstructure is substantially greater than the frequency of localized gust effects.
‡
Gust factors are generally between two and three for tall structures (Liu, 1991).
