Transcript Wind damage and mechanics of flying debris

Wind loading and structural response
Lecture 2 Dr. J.D. Holmes
Wind damage and mechanics
of flying debris
Wind damage and mechanics of flying debris
• Damage due to windstorms is
increasing
– accounts for 70% of insured losses
(difficult to separate direct wind damage from rain, storm floods)
• big increases in U.S. in late 1980’s and 1990’s
– Hurricanes ‘Hugo’, ‘Andrew’, ‘Georges’
Insured Dollar Losses
25
23.0
20
17.0
15
13.7
10
8.3
5.7
4.7
0.9
0.9
1.5
1986
1987
1988
5
2.8
1995
1994
1993
1992
1991
1990
1989
0
also gales in Europe : 1987($3.7bill.) , 1990 ($15bill.), 1999 ($10bill.)
Wind damage and mechanics of flying debris
• Ferrybridge cooling towers - England, 1965
interference effects
Wind damage and mechanics of flying debris
• Brighton Chain Pier, England, 1836
aeroelastic instability
also, Wheeling Bridge, Ohio, 1854
Wind damage and mechanics of flying debris
• Tacoma Narrows Bridge, Washington State, 1940
aeroelastic instability
Wind damage and mechanics of flying debris
• Tacoma Narrows Bridge, Washington State, 1940
aeroelastic instability
Wind damage and mechanics of flying debris
• Low-rise buildings - tornado and hurricane damage
Wind damage and mechanics of flying debris
• High-rise buildings - cladding (glass) damage
Hurricane ‘Alicia’, Houston, 1983
Wind damage and mechanics of flying debris
• Wind-generated debris
– generates high internal pressures
– allows wind and rain penetration
– danger to occupants
Wind damage and mechanics of flying debris
• Types of flying debris
Compact
l
Sheet
t
Rod
d
Wind damage and mechanics of flying debris
• Threshold of flight
Compact object:
I m gl 
1
 aU f 2CF
2
aerodynamic force just balances resistance of gravity and fixity
I = fixity parameter (=1, for objects resting on the ground)
CF = aerodynamic force coefficient
1
 aU f 2C F
l 2
I m g
Wind damage and mechanics of flying debris
• Threshold of flight
Uf
2
2 I m gl

 aCF
• The higher the value of characteristic dimension, l, or density,
m, the higher the wind speed for the threshold of flight, Uf.
• Example : for CF = 1, I = 1 , UF = 30 m/s (67 mph)
l = 110 mm (4.3 in) for wooden object
l = 20 mm (0.8 in) for stone object
Wind damage and mechanics of flying debris
• Threshold of flight
Sheet object:
1
 aU f 2C F
t 2
I m g
Rod object:
2
d
 aU f 2C F
I m g
Wind damage and mechanics of flying debris
• Time of flight and distance travelled
– assume constant wind speed
Accelerating force :
1
 a (U  v(t ) ) 2 C D A
2
Acceleration :
1
1
 a (U  v(t ) ) 2 C D A
 a (U  v(t ) ) 2 C D
2
 2
3
 ml
 ml
Wind damage and mechanics of flying debris
• Time of flight :
Acceleration :
dv  a (U  v) 2 CD

dt
2  ml
Time taken to reach vm:
2 ml
dt

T

0
0 a U  v 2 CD dv
T
vm
 aCD
where : k 
2  ml
T
vm
kU (U  vm )
dimensional
Wind damage and mechanics of flying debris
• Distance traveled :
v
t
kU (U  v)
Time to reach velocity v :
kU 2t
v
(1  kUt)
Distance traveled during time taken to reach vm:
T
T
0
0
s   v dt  
kU 2t
dt
(1  kUt)


U
s   U 
dt

(1  kUt) 
0 
T
  1 

s  U T  
ln(
1

kUT
)


kU

 

Wind damage and mechanics of flying debris
• Time of flight and distance travelled
Examples : steel ball 2mm (0.315 in.) diameter
timber : 100 mm(4 in.) by 50 mm (2 in.) by 1600 mm (5.25 ft.)
long
Object / speed
Steel ball to 20 m/s
Steel ball to 30 m/s
Timber piece to 20 m/s
Timber piece to 30 m/s
Time taken
(secs)
5.4
49
69
625
Distance travelled
(metres)
71
1270
910
16300
Wind damage and mechanics of flying debris
Wind damage and mechanics of flying debris
Wind damage and mechanics of flying debris
Wind damage and mechanics of flying debris
Sphere falls under gravity and air resistance until it impacts ground or a
building
Wind damage and mechanics of flying debris
• Time and distance to impact :
Some shapes (e.g. plates, prisms) have lift – can reach heights greater
than release height
Wind damage and mechanics of flying debris
Some shapes (e.g. plates, prisms) have lift – can reach heights greater
than release height
Wind damage and mechanics of flying debris
Some shapes (e.g. plates, prisms) have lift – can reach heights greater
than release height
Wind damage and mechanics of flying debris
Some shapes (e.g. plates, prisms) have lift – can reach heights greater
than release height
End of Lecture 2
John Holmes
225-405-3789 [email protected]