Civil Engineering Reference
In-Depth Information
to small prismatic models as well as flat plates and gave a method of estimating the
position of a missile impact on a downstream building. The critical non-dimensional
parameter for determination of trajectories was
K
=
ρ
a
U
2
A
/2
mg,
where
ρ
a
is the density of
air,
U
the wind speed,
A
the plan area of a plate,
m
the mass of the missile and g the
gravitational constant.
This parameter represents the ratio of aerodynamic forces to gravity forces and can
also be expressed as the product of three other non-dimensional parameters:
(1.20)
where
ρ
m
is the missile density,
t
the plate thickness and
ℓ
is equal to √
A,
i.e. a
characteristic plan dimension.
In Equation (1.20),
ρ
a
/
ρ
m
is a density ratio and
(U
2
/
gℓ)
is a Froude number, both
important non-dimensional quantities in aerodynamics (see also Section 7.4).
The equations of motion for horizontal, vertical and rotational motion of a flat plate
moving in a vertical plane must be solved numerically. Good agreement has been
obtained when such numerical solutions are compared with measurements of trajectories
of many small plates in a wind tunnel (Holmes
et al.,
2006; Lin
et al.,
2006).
1.5.4
Damage potential of flying debris
Wills
et al.
(1998) carried out an analysis of the damage potential of flying missiles,
based on the assumption that the damage of a given missile is proportional to its kinetic
energy in flight. A number of interesting conclusions arose from this work:
• For compact objects, lower density objects have more damage potential.
• Sheet and rod objects have generally more damage potential than compact objects.
• Very little energy is required to break glass (e.g. a 5 g steel ball travelling at 10 m/s is
sufficient to break a 6 mm annealed glass).
• Based on an assumed distribution of available missile dimensions, Wills
et al.
found
that the total damage is proportional to
U
n
,
where
n
is a power equal to about 5.
1.5.5
Standardized missile testing criteria
In regions subjected to hurricanes and tropical cyclones (Section 1.3.2), where the
occurrence of damage to buildings by wind-generated missiles has been shown to be a
major problem, standardized missile tests have been devised. These demonstrate the
ability of wall claddings of various types to resist penetration by flying debris or assist in
the development of window protection screens.
When specifying appropriate test criteria for missile impact resistance, the following
principles should be followed:
• The missiles should be representative of actual objects available.
• The criteria should be physically realistic, i.e. if the flight threshold speed is greater
than the expected wind speed in the storm, then the object should not be regarded as a
potential missile.
