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Free walls, roofs and billboards
• free-standing walls
• elevated walls and billboards
• free roofs and canopies
2ha2
1
Lwpn
Uρ
ppC
2ha2
1
LUpn
Uρ
ppC
Free walls, roofs and billboards
free-standing walls
• wind at 90o to plane of wall (lecture 8, Chapter 4)
CD = 1.2
TWO-DIMENSIONAL WALL
Ground
SQUARE WALL
CD = 1.1
Ground
reference U taken as Uh (top of 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
Jensen Number (h/zo) = 50 to 160
Mean
Maximum
bh
0.1 1 10 100
b/h
4
3
2
1
0
Cpn
Free walls, roofs and billboards
free-standing walls
• wind at 45o to plane of wall
Jensen Number (h/zo) = 50 to 160
0.1 1 10 100b/h
4
3
2
1
0
Cpn
Mean
Maximum
bh
Free walls, roofs and billboards
free-standing walls
• wind at 45o to plane of wall
Net pressure difference high for first 1-2 wall heights from windward end
mean Cpn
1.6 1.0
1.9 1.4 0.7
1.1 0.8 0.6 0.4 1.6 2.2
1.8 2.7 1.4 1.1 1.0 0.8 0.7 0.6
b/h=2
b/h=3
b/h=5
b/h=10
Free walls, roofs and billboards
free-standing walls
• wind at 45o to plane of wall
Effect of corner is to reduce largest net pressure
mean Cpn
0.1 1 10 100
y/h
4
3
2
1
0
Cpn
no corner 45
corner 45
infinite 45corner 225
no corner 225
45
225
y
Free walls, roofs and billboards
Parallel free-standing walls (noise barriers on urban freeways)
-3
-2
-1
0
1
2
3
4
5
-50 -40 -30 -20 -10 0 10 20 30 40 50
wall spacing/wall height
Ne
t p
ress
ure
co
eff
icie
nts
Mean
r.m.s.
Maximum
Minimum
Shielding
significant shielding effects up to 10 wall heights separation
sh• wind at 0o to plane of walls
Free walls, roofs and billboards
Billboards
• wind at 0o to plane of board
effect of elevation : increase magnitude of mean net pressure coefficient
=
=Cpn 1.5
mean Cpn
Free walls, roofs and billboards
Billboards
• wind at 45o to plane of board
45o1.5 1.1
2c
c
c
Ground
mean Cpn
Free walls, roofs and billboards
s
B
h
SOLID SIGN OR FREESTANDING WALL
GROUND SURFACE
CASE AWIND NORMAL TO WALL
New table proposed for ASCE-7-05
• Solid freestanding walls and solid signs
• Force coefficients Cf given as function of clearance ratio, s/h, and aspect ratio, B/s
CASE BWIND AT 45° TO WALL
Free walls, roofs and billboards
Walls on bridges
• wind at 0o to plane of wall
0
1
2
3
4
5
0 1 2 3 4
s/h
Cp
upwindwall
Mean
r.m.s.
Maximum s
Coefficients based onU at top of wall : little effect of s/h ratio
Free walls, roofs and billboards
Free-standing roofs
Usual convention : positive net pressure is downwards
pnet flat
pnet pitched
pnet troughed
Free walls, roofs and billboards
Free-standing roofs
Effect of stored goods : flow stagnates underneath - pnet goes more negative
pnet
Free walls, roofs and billboards
Free-standing roofs
upper surface pressures dominate - especially near the ridge
pitched - full scale
-1.5
-1
-0.5
0
0.5
0 4.65 9.3
Distance from leading edge (m)
Me
an p
ress
ure
co
effi
cie
nt
Upper surface
Lower surface
d=9.3 m
Free walls, roofs and billboards
Free-standing roofs
Cpn averaged over half a roof
pitched - model tests
-1-0.8-0.6-0.4-0.2
00.20.40.60.8
0 30 60 90 120 150 180
angle of attack (degrees)
Cp
(m
ea
n)
5 degrees pitch 10 degrees pitch15 degrees pitch 22.5 degrees pitch30 degrees pitch
high positive and negative values for roof pitches of 22.5o and 30o
Free walls, roofs and billboards
Attached canopies (over loading bays etc.)
when mounted near the top of the wall, uplift force is high
zero pitch - model scale
hhc
wc
0.0 0.5 1.0 1.5 2.0 2.5 3.0Canopy height-to-width ratio, hc/wc
hc/h =1
hc/h=0.75
hc/h=0.5
-4.0
-3.0
-2.0
-1.0
0.0
Cpn or 4.0, whichever is the lesser
c
cpn w
h1.31.0C-
or 4.0, whichever is the lesser
c
cpn w
h0.41.0C-
Free walls, roofs and billboards
Solar panels
wind loads are affected by many parameters :
on roofs of buildings
d
c e
w
h1
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)