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Wing Structure: Beam Bending

This document discusses analyzing the wing structure of the HAARP aircraft to determine bending moments and shear forces. It describes calculating the lift distribution across the wing using trapezoidal and elliptical approximations. The wing is divided into 17 panels of equal width, with the load on each panel determined based on its area and position. Bending moment and vertical shear diagrams are generated by summing the loads across the wing panels.

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95 views10 pages

Wing Structure: Beam Bending

This document discusses analyzing the wing structure of the HAARP aircraft to determine bending moments and shear forces. It describes calculating the lift distribution across the wing using trapezoidal and elliptical approximations. The wing is divided into 17 panels of equal width, with the load on each panel determined based on its area and position. Bending moment and vertical shear diagrams are generated by summing the loads across the wing panels.

Uploaded by

a320neo
Copyright
© Attribution Non-Commercial (BY-NC)
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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Wing Structure

Beam Bending
Lift Distributions
HAARP Example
MAE 155A
AFTI/F-16 Strain Gage Installation (NASA Image)
2
MAE 155A
Beam Bending
Beam bending equations are used to estimate the total moment that the wing
structure must withstand at extreme flight conditions.
V ( y)=

0
y
F ( y) dy
M ( y)=

0
y
V ( y) dy
F=distributed force per span
y=spanwise position
V =vertical shear
M=bending moment
3
MAE 155A
Lift Distribution
The span-wise lift distribution can be determined using methods from computational
fluid dynamics.
The following distributions are useful for preliminary design:
L
e
( y)=
4 L
nb
.
1
(
2 y
b
)
2
Elliptical Wing:
L
t
( y)=
2 L
b(1+\)
|
1
(
2 y
b
)
(
1\
)

Trapezoidal Wing:
Schrenk's Approximation: L
s
( y)=
1
2
| L
e
( y)+L
t
( y)
y=span wise position
b=wing span
L=total lift force
\=taper ratio
4
MAE 155A
HAARP Wing Analysis
HAARP = High Altitude Atmospheric Research Platform (Nicolai and Carichner 2010)
Airplane Weight = 15,700 lb
Altitude = 20,000 ft
Equivalent Airspeed = 55 nmi/hr
Wing Parameters:
Area, S = 269 ft
Span, b = 2,884 ft
2
Taper Ratio, lambda = 0.35
Lift Coefficient Slope, CL_alpha = 5.73/rad
Structural Weight = 2,708 lb (entire wing)
Equipment Weights (each wing):
Heat Exchanger = 573 lb from WS 7.6 ft to WS 28.0 ft
Engine = 2,174 lb at WS 21.6 ft
Fuel and Tank = 2,300 lb at WS 23.8 ft to 44.2 ft WS = Wing Station
5
MAE 155A
Design Load Factor
The positive limit load factor assumes worst case rough air
Equivalent gust velocity, Ue = 66 ft/s
j=
2(W / S)
j g

c C
Lo
=4.0
Mass ratio
K
g
=
0.88j
5.3+j
=0.38
Gust Alleviation
Factor (subsonic)
n=1!
|
K
g
C
Lo
U
e
498(W / S)

V
e
=1.0!3.0=2.0,+4.0
Limit Load Factor
W/ S=
15,700lb
2884 ft
2
=5.44lb/ ft
2
c
r
=
2 S
b(1+\)
=15.9 ft

c=
2
3
c
r (
1+\+\
2
1+\
)
=11.6 ft
6
MAE 155A
Wing Panels
The right wing is broken into 17 panels of equal width.
The area of each wing panel is found by estimating the root chord and tip chord of
the panel.
S
p
=
b
p
2
|
c
rp
+c
tp

c( y)=
2S
b(1+\)
|
1
(
2 y
b
)
(
1\
)

b
p
=
269 ft
(2)(17)
=7.9 ft
b
p
y
b
2
c
e
n
t
e
r
l
i
n
e
p=1, 2, ... , 17
Area Sp
S
p
c
tp
c
rp
7
MAE 155A
Wing Structural Weight
Structural weight for each panel is based upon the segment area.
W
p
=(2,708lb)
(
S
p
S
)
=( 2,708lb)
(
S
p
2,884 ft
2
)
Equipment weights are then added to the appropriate wing panels.
W
p
=W
p
+(1/3)(573lb)
W
p
=W
p
+2,174lb
W
p
=W
p
+(1/3)(2,300lb)
Panels: 2, 3, 4
Panel: 3
Panels: 4, 5, 6

p=1
p=17
W
p
=1,354lb
(right wing only)
8
MAE 155A
Distributed Wing Load
Segment lift is found using the trapezoidal wing lift distribution.
L
p
=
2 L b
p
b(1+\)
|
1
(
2 y
p
b
)
(
1\
)

L=nW=4.0(15,700lb)=62,800lb
The load on each panel is:
F
p
=L
p
nW
p
y
p
=span wise midpoint of panel

p=1
p=17
L
p
=31,400lb
(right wing only)
9
MAE 155A
Panel Load Distribution
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
-8000
-6000
-4000
-2000
0
2000
4000
L
o
a
d

(
l
b
)
Panel Number
10
MAE 155A
Vertical Shear and Bending Moment
0 20 40 60 80 100 120 140
0
2
4
6
8
10
12
14
16
0 20 40 60 80 100 120 140
0
200
400
600
800
1000
Wing Station (ft)
Wing Station (ft)
V
e
r
t
i
c
a
l

S
h
e
a
r

(
1
0
0
0

l
b
)
B
e
n
d
i
n
g

M
o
m
e
n
t

(
1
0
0
0

f
t
-
l
b
)

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