Transcript Antennas and open-frame structures

Wind loading and structural response
Lecture 23 Dr. J.D. Holmes
Antennas and open-frame
structures
Antennas and open-frame structures
• Antennas - isolated structures - radio telescopes and microwave
antennas
• Antennas - attached to towers - aerodynamic interference
• Single frames
• Multiple frames
• Lattice towers
Common feature : aerodynamic interference between various elements - e.g.
antennas and supporting tower or other antennas, members of a frame
Antennas and open-frame structures
• Radio telescope
• Paraboloid dish
f
Focus
Antennas and open-frame structures
• Radio telescope
• Paraboloid dish
2f
Normal to dish surface intersects axis at 2  focal length
e  2f 
Approximate center of aerodynamic forces
d
C
e
d
2
Antennas and open-frame structures
• Radio telescope
• Paraboloid dish
FY
d
FX
e

b
Wind
Fy force generates significant moments about dish supports
Antennas and open-frame structures
• Radio telescope
• Paraboloid dish
0.10
Focus
0.08
Zenith
angle b
0.06
CM
Total
moment
Azimuth
angle,
135o
Effect of
boundary
layer
profile
Altitude
moment
0.04
Azimuth
moment
0.02
Wind
Altitude
axis
0
a
0
Azimuth
angle
PLAN VIEW
20
40
60
Zenith angle, degrees
CM 
M
2
1
2 ρ a U h Ab
80
90
Antennas and open-frame structures
• Microwave dish antenna
• Impermeable dish
C D ( ) 
2.0
D( )
2
1
2 ρa U A
1.5
b

1.0
A = (b2/4)
(projected area)
0.5
1% turbulence
10% turbulence
0.0
0
20
40
60
80
100 120
 (degrees)
Small effect of turbulence
140
160
180
Antennas and open-frame structures
• Microwave dish antenna
• Interference factor
Da
WIND
D D
t
K  e
i
Da
Dt
WIND
De  D  K .Da
t
i
De
WIND
Antennas and open-frame structures
• Microwave dish antenna
• Interference factor

Interference factor
Experimental data
Equation with t=0.5
1.5
1
0.5
0
0
45
90
135
180
Wind direction (degrees)
Ki = exp [-k(CD  )2]. [(1+t) + t cos 2( - d - 90)]
Antennas and open-frame structures
• Cell-phone antenna
• isolated panels
Cd 1.1
Cd (ref.b)  0.8
120O
b
Antennas and open-frame structures
• Cell-phone antenna
• grouped panels
combined
Cd (ref.b)  1.1
combined
Cd (ref.b)  0.9
~2b
grouping gives large reduction in total drag
Antennas and open-frame structures
• Cell-phone antenna
• grouped panels
60o
0o
total drag of group : about 30% less than sum of individual elements
Antennas and open-frame structures
• Open frames
• Single frame. Two-dimensional. Normal wind
• sharp-edged members
2.0
CD
1.0
0
0.5
Solidity ratio, 
solidity = ‘solid’ area of frame/total enclosed area
reference area for drag coefficient = ‘solid’ area of frame
drag coefficient relatively independent of details of member arrangement
1.0
Antennas and open-frame structures
• Open frames
• Single frame. Two-dimensional. Normal wind
2.0
CD
1.0
0
0.5
Solidity ratio, 
at low solidity, members act as individual elements
at high solidity, frame acts as a solid plate (Lecture 8)
intermediate solidity : aerodynamic interference between members CD  1.6
1.0
Antennas and open-frame structures
• Open frames
• Pairs of frames. Two-dimensional. Normal wind
b
s
CD(2) = CD(1) [ 1 + 2]
1 CD(1) is drag coefficient of upstream frame
(downstream frame influences upstream frame)
2 CD(1) is drag coefficient of downstream frame
approximately, 1  1,
s
ψ2  1  δ0.45  
b
δ 0.45
0 <  < 0.5
For circular members, equivalent solidity to calculate 2 , e  1.2 1.75
Antennas and open-frame structures
• Open frames
spacing/width = 1.0
• 3 frames in series. Solidity = 0.1
C X (α ) 
N
X(α)
2
1
2 ρa U A
spacing/width = 0.1
X(a) = force normal to frame
A = projected area of one frame at
0o angle of attack
15
angle of attack, a
75
Antennas and open-frame structures
• Open frames
• 3 frames in series. Solidity = 0.5
C X (α ) 
N
spacing/width = 1.0
X(α)
2
1
2 ρa U A
spacing/width = 0.1
A = projected area of one frame at
0o angle of attack
Maximum CXN at 30o to 45o
15
angle of attack, a
75
Antennas and open-frame structures
• Open frames
• 10 frames in series. Solidity = 0.1
C X (α ) 
N
spacing/width = 1.0
X(α)
2
1
2 ρa U A
spacing/width = 0.1
A = projected area of one frame at
0o angle of attack
15
angle of attack, a
75
Antennas and open-frame structures
spacing/width = 1.0
• Open frames
• 10 frames in series. Solidity = 0.5
C X (α ) 
N
X(α)
2
1
2 ρa U A
A = projected area of one frame at
0o angle of attack
spacing/width = 0.1
Maximum CXN at 30o to 45o
15
angle of attack, a
75
Antennas and open-frame structures
• Open frames
• Design method :
‘Wind loads and anchor bolt design for petrochemical facilities’ (ASCE)
Needs more wind tunnel studies for pipe racks etc.
Antennas and open-frame structures
• Drag coefficients for lattice tower (Lecture 21)
Square cross section with flat-sided members (wind normal to face)
4.0
Drag
coefficient
CD (=0O)
3.5
Australian
Standards
3.0
2.5
2.0
CD = 4.2 - 7
(for 0.1< < 0.2)
CD = 3.5 - 3.5
(for 0.2< < 0.5)
1.5
0.0
0.2
0.4
0.6
Solidity Ratio 
0.8
1.0
(ASCE-7 : CD = 4.02 – 5.9 +4.0 )
 = solidity of one face = area of members  total enclosed area
includes interference and shielding effects between members
Antennas and open-frame structures
• Drag coefficients for lattice tower
Triangular cross section with flat-sided members
CD = 3.5 - 4
(for 0.1< < 0.3)
CD = 2.9 – 2
(for 0.3<  < 0.5)
(ASCE-7 : CD = 3.42 – 4.7 +3.4 )
Antennas and open-frame structures
• Drag coefficients for lattice tower
Cross section with circular members
depends on Reynolds Number
for super-critical flow - Cd for cross section ~ 0.5 times that for
equivalent sharp-edged tower with same solidity
some members may be in super-critical flow - others in sub-critical flow
End of Lecture 23
John Holmes
225-405-3789 [email protected]