Transcript Free walls, roofs and billboards

Wind loading and structural response
Lecture 22 Dr. J.D. Holmes
Free walls, roofs and billboards
Free walls, roofs and billboards
• free-standing walls
• elevated walls and billboards
C pn 
pw  pL
2
1
ρ
U
h
2 a
• free roofs and canopies
C pn 
pU  pL
2
1
ρ
U
h
2 a
Free walls, roofs and billboards
• attached canopies
• solar panels
Free walls, roofs and billboards
free-standing walls
• wind at 90o to plane of wall (lecture 8, Chapter 4)
CD = 1.2
Ground
TWO-DIMENSIONAL WALL
reference U taken as Uh (top of wall)
CD = 1.1
Ground
SQUARE WALL
Free walls, roofs and billboards
free-standing walls
• wind at 90o to plane of wall (lecture 8, Chapter 4)
reference U taken as Uh (top of wall)
Free walls, roofs and billboards
free-standing walls
• wind at 90o to plane of wall
4
b
Maximum
h
3
Cpn
2
Mean
1
0
0.1
1
10
b/h
Jensen Number (h/zo) = 50 to 160
100
Free walls, roofs and billboards
free-standing walls
• wind at 45o to plane of wall
4
b
h
3
Maximum
Cpn
2
1
Mean
0
0.1
1
10
b/h
Jensen Number (h/zo) = 50 to 160
100
Free walls, roofs and billboards
free-standing walls
• wind at 45o to plane of wall
mean Cpn
b/h=2
1.6 1.0
1.9
1.4
0.7
b/h=3
b/h=5
2.2 1.6 1.1 0.8 0.6 0.4
b/h=10
2.7 1.8 1.4 1.1 1.0
0.8 0.7
0.6
Net pressure difference high for first 1-2 wall
heights from windward end
Free walls, roofs and billboards
free-standing walls
• wind at 45o to plane of wall
mean Cpn
4
225
no corner 45
y
45
3
Cpn
corner 45
2
infinite 45
corner 225
1
no corner 225
0 0.1
1
10
y/h
Effect of corner is to reduce largest net pressure
100
Free walls, roofs and billboards
Parallel free-standing walls
(noise barriers on urban freeways)
s
Net pressure coefficients
• wind at 0o to plane of walls
5
4
3
2
1
0
-50 -40 -30 -20 -10-1 0
-2
-3
h
Mean
r.m.s.
Maximum
10 20 30
40 50
Minimum
wall spacing/wall height
Shielding
significant shielding effects up to 10 wall heights separation
Free walls, roofs and billboards
Billboards
• wind at 0o to plane of board
Cpn 1.5
mean Cpn
=
=
effect of elevation : increase magnitude of mean net pressure coefficient
Free walls, roofs and billboards
Billboards
• wind at 45o to plane of board
mean Cpn
2c
1.5
45o
1.1
c
c
Ground
Free walls, roofs and billboards
New table proposed for ASCE-7-05
• Solid freestanding walls and solid signs
CASE A
B
WIND
NORM AL TO
WALL
SOLID SIGN OR
FREESTANDING WALL
s
h
CASE B
WIND AT 45°
TO WALL
GROUND SURFACE
• Force coefficients Cf given as function of clearance ratio, s/h, and aspect ratio, B/s
Free walls, roofs and billboards
Walls on bridges
• wind at 0o to plane of wall
Mean
r.m.s.
Maximum
5
s
Cp
upwind 4
wall 3
2
1
0
0
1
2
3
4
s/h
Coefficients based onU at top of wall : little effect of s/h ratio
Free walls, roofs and billboards
Free-standing roofs
pnet
flat
pnet
pnet
Usual convention : positive net pressure is downwards
pitched
troughed
Free walls, roofs and billboards
Free-standing roofs
pnet
Free walls, roofs and billboards
Free-standing roofs
pnet
Effect of stored goods : flow stagnates underneath - pnet goes more negative
Free walls, roofs and billboards
Free-standing roofs
pitched - full scale
d=9.3 m
Upper surface
Lower surface
Mean pressure
coefficient
0.5
0
-0.5
0
4.65
9.3
-1
-1.5
Distance from leading edge (m)
upper surface pressures dominate - especially near the ridge
Free walls, roofs and billboards
pitched - model tests
Free-standing roofs
Cp (mean)
5 degrees pitch
15 degrees pitch
30 degrees pitch
10 degrees pitch
22.5 degrees pitch
0.8
0.6
0.4
0.2
0
-0.2
-0.4
-0.6
-0.8
-1
0
30
60
90
120
150
180
angle of attack (degrees)
Cpn averaged over half a roof
high positive and negative values for
roof pitches of 22.5o and 30o
Free walls, roofs and billboards
Attached canopies (over loading bays etc.)
zero pitch - model scale
wc
-4.0
h
Cpn
hc

ˆ  1.0  1.3 h c
-C

pn
 wc 
or 4.0, whichever is the lesser
hc/h =1
-3.0
hc/h=0.75
-2.0
-1.0

ˆ  1.0  0.4 h c
-C

pn
 wc 
or 4.0, whichever is the lesser
hc/h=0.5
0.0
0.0
0.5
1.0
1.5
2.0
2.5
Canopy height-to-width ratio, hc/wc
3.0
when mounted near the top of the wall, uplift force is high
Free walls, roofs and billboards
Solar panels
on roofs of buildings
wind loads are affected by many parameters :
l


d
e
c
h1
w
h2
Free walls, roofs and billboards
Solar panels
• ‘stand-off’ distance reduces net load normal to roof
• higher roof pitch produces less uplift force
• panel near eaves or gable ends experience higher loads
• generally better to mount parallel to roof slope ( = 0)
End of Lecture 22
John Holmes
225-405-3789 [email protected]