Civil Engineering Reference
In-Depth Information
Equation (4.10) has the required properties of equalling one for a value of
δ
equal to 1,
i.e. an impermeable plate or wall, and tending to zero as the solidity tends to zero. For
very small values of
δ
(e.g. an open truss plate made up of individual members),
K
p
tends
to a value of 2δ, as, from Equation (4.10),
because
δ
2
is very small in comparison with 2
δ
for small
δ
.
Considering the application of this to the drag coefficient for an open truss plate of
square planform, we have from Equations (4.9) and (4.10),
where denotes that the drag coefficient, defined as in Equation (4.4), is with respect
to the total (enclosed) elevation area of
A
t
. With respect to the elevation area of the actual
members in the truss
A
m
,
the drag coefficient is larger, being given by:
In this case of a very open plate, the members will act like isolated bluff bodies with
individual values of drag coefficient of 2.2.
Cook (1990) discusses in detail the effect of porosity on aerodynamic forces on bluff
bodies.
4.3.2
Flat plates and walls inclined to the flow
Figure 4.7 shows the case with the wind at an oblique angle of attack,
α,
to a two-
dimensional flat plate. In this case, the resultant force remains primarily at right angles to
the plate surface, i.e. it is no longer a drag force in the direction of the wind. There is also
a tangential component, or 'skin friction' force. However, this is not significant in
comparison with the normal force, for angles of attack greater than about 10°.
For small angles of attack,
α
(less than 10°), the normal force coefficient,
C
N
,
with
respect to the total plan area of the plate viewed normal to its surface, is approximately
given by:
(4.11)
(where
α
is measured in radians, not in degrees).
Equation (4.11) comes from the theory used in aeronautics. The 'centre of pressure',
denoting the position of the line of action of the resultant normal force, is at, or near, one-
quarter of the height
h
from the leading edge, again a result from aeronautical theory.
