Microsoft Word - AERO2359-2110_end-sem_test.docx 2 Aerospace Structures End-semester assessment File must be submitted online. Late submission penalty: 10% per hour late. Submitted file must be a...

Microsoft Word - AERO2359-2110_end-sem_test.docx
2
Aerospace Structures
End-semester assessment
File must be submitted online.
Late submission penalty: 10% per hour late.
Submitted file must be a single pdf, which can be handwritten or typed or both. Handwritten responses
can be achieved by, for example, printing the test paper, using blank paper, or hand writing onto this pdf
y using a stylus. It is recommended to use a scanner or a phone-based app such as Office Lens to
generate a suitable pdf from physically handwritten pages. Please ensure you review your submitted file
after submission.
Calculation questions marked based on appropriateness of solution approach, as well as final solutions.
Marks for working are awarded, and a consequential marking scheme is implemented whereby an
inco
ect value obtained in an intermediate solution step is used in any subsequent steps and only one
mark penalty is applied per e
or. Marks are deducted for missing units, incomplete answers, or
unlabelled sketches.
For questions requiring a written response, marks are awarded based on the clarity of the response, the
accuracy of the information, the level of technical detail, the quality of any figures, and the extent to
which the question is answered. Marks are not deducted for grammar or English, except where this
leads to confusion on the technical content of the answer.
Attempt ALL questions.
3
Question A1 (10 marks)
Define the elementary theory for torsion of a solid circular beam. Discuss the assumptions made and
limitations of applying this theory to typical aircraft stiffened structures.
4
Question A2 (10 marks)
Consider a column with cross-section shown below that has a compression load applied. Compare the
flexural buckling behaviour of the column if the compression load is applied at the centroid (C) to where
the compression load is applied at point A.
A
C
5
Question A3 (10 marks)
The top cover section of an aircraft wing uses a stiffened skin design, where the skin panel is reinforced
y stringers and ribs as shown below.
a) Describe how these three structural elements (skin, stringers, ribs) contribute to the way that
the wing structure ca
ies forces and moments.
) Define and use a diagram to illustrate the different buckling modes possible for the cove
section.
cover
section
skin
stringer
ib
location
6
B1: Your student number is used to assign parameters, according to the table below
Digit 3rd 4th 5th 6th 7th
Parameter A B C D E
Value
XXXXXXXXXX XXXXXXXXXX
XXXXXXXXXX XXXXXXXXXX
XXXXXXXXXX XXXXXXXXXX
XXXXXXXXXX XXXXXXXXXX
XXXXXXXXXX XXXXXXXXXX
XXXXXXXXXX XXXXXXXXXX
XXXXXXXXXX XXXXXXXXXX
XXXXXXXXXX XXXXXXXXXX
XXXXXXXXXX XXXXXXXXXX
XXXXXXXXXX XXXXXXXXXX
e.g.: Student number XXXXXXXXXX, produces the following table of values
Digit 3rd 4th 5th 6th 7th
Parameter A B C D E
Value XXXXXXXXXX
XXXXXXXXXX15.5
Scott Loh
Highlight
Scott Loh
Highlight
Scott Loh
Highlight
Scott Loh
Highlight
7
Question B1 (70 marks)
B1 The beam cross-section shown below consists of booms of concentrated area and thin skins that
are assumed to ca
y only shear. The cross-section is under the action of forces and moments as
shown. The material used has E = D ksi, G = 4200 ksi, cy = 40 ksi, c0 = 45 ksi, and a linear short
column equation with k = 0.096 ksi for plasticity.
B1a Calculate the centroid location and Ix, Iy, Ixy at the centroid.
B1b Calculate the bending load in all booms (you do not need to sketch).
B1c Calculate and sketch the shear flow in each panel.
B1d Determine the flexural buckling stress, checking for plasticity and accounting for plasticity as
equired. Consider the cross-section is loaded with a compressive stress only. Assume the beam
length (in z) is E in, and assume pinned boundary conditions for all instances of restraint.
B1e Using your solutions for B1c, or making necessary assumptions, determine whether any of the
skins buckle in shear. Consider only elastic buckling stresses. Assume the beam length (in z) is
E in, and assume pinned boundary conditions for all instances of restraint.
B1f Using your answers for B1b, or making necessary assumptions, determine an updated boom area
at location 1 that accounts for the stiffener area and suitable areas from any connecting panels.
C lbf in
1
4.0
1.5
y
x 3
dimensions
in inches
panel thickness (in)
t 1-2 , t 3-4 = 0.01
t 1-3 , t 2-4 = 0.025
stiffener area (in2)
A 1 = A
A 3 = 1.2
180 lbf in
B lbf
400 lbf
2
4
A 2 = 0.2
A 4 = 0.2
8
Appendix: Equations, Tables and Graphs
Second moment of area (I)
(area moment of inertia)
 dAyIx 2
 dAxI y 2 yxp IIdArI  
2
 dAxyIxy
Principal axes
xy
xy
II
I


2
2tan 
2
2
2,1 22 xy
xyyx I
IIII
I 




 



xy
xy
II
I


2
2tan 
2
2
2,1 22 xy
xyyx I
IIII
I 




 



Parallel axis
theorem
x
y

d
Radius of gyration
 AI
tRI cx
3
RtA 2
Section properties by summation
A
Axx



*
A
Ayy



*
yyy  *
xxx  *x*, y*: coordinates about any axis
x, y: coordinates about a parallel centroidal axis
C
12
3bdI cx  12
3dbI
cy

x
y
R C
4
4RI cx


R
x
x
y
y
C
R
t
C x
y
tRI cx
32
4





 



Ryx 2
R
x
y
y
C tRI cx
34
2





 



Ry 2
x
a
y

C
12
sin23 taI x 
24
2sin3 taI xy 
t
t t
x* y* A x y I
1
2
…

xx0 Iy0 Ixy0 Ax2 Ay2 Axy x* y* A x y I
1
2
…

xx0 Iy0 Ixy0 Ax2 Ay2 Axy
2
0 AyII xx 
2
0
AxII yy 
AxyII xyxy  0
9
Column with imperfections
geometric
load
eccentricity  CRPP
e
1
14



P P
y
z
L


 CRPP /1
0



Column with constant lateral loading
max deflection
@ z = L / 2
max moment
@ z = L / 2
EI
L
384
5 4
0
 
CRPP
1
1


 r0max 
8
2
0
LM rMM 0max 
P P
y
z
L

Elastic column buckling
parabolic:
linear:
Inelastic column equations
Euler-
Johnson
2
2
'L
EIPCR

  2
2
' 

L
E
CR 
L’ = L
L
L’ = 0.5L
L’ = 2L
L
  /'0 LkcCR 
 20 /'  LkcCR 















2
2
0
0
'
4
1

 L
E
c
cCR
 
L
zzy  sin
00 PM 
CRPP
1
1

rMM 0max 
10
Structural idealisation

tD = t (tD = 0) t 1
2 2
1
A1
A2








1
2
1 26 
btA D
Tapered panel
2






aq
q
aq 




aqq
q
Multi-cell structures (constant shear flow)
  ncnEbEext qAqAT ,,22
N cells
connected
N-cell beam




























 




n
nn
nc
n
nc
nn
nc
nE t
sq
t
sq
t
sq
t
sq
GAdz
d
,1
1,,
,1
1,
,2
1
Plate buckling
2






tKEb K from data sheets or standard practice   




t
K
L eq
'
  ncnEbext qAhlqT ,,2A5
Margin of Safety
11MoS allow
maximumdesign
allowable 




11
EA
Tq
2

Batho-Bredt
for constant
shear flow
asymmetric
nn
xyyx
xyxyy
nn
xyyx
xyyxx
n yAIII
ISIS
xA
III
ISIS
q 



















 22
symmetric, single load
force/moments due to shear flow
xqlX  yqlY  hqlqAT E  2
y
III
IMIM
x
III
IMIM
xyyx
xyyyx
xyyx
xyxxy
z 



















 22
asymmetric section
y
I
M

asymmetric
thin-wall open section
GJ
T
dz
d


Bending
Shear
Torsion
0qqq s 
0qqq n 
continuous
section
concentrated
areas
force/moments due to constant shear flow

B
A
qdxX 
B
A
qdyY 
B
A
hqdsT
 



















s
xyyx
xyxyys
xyyx
xyyxx
s tydsIII
ISIS
txds
III
ISIS
q
0202

ds
t
q
GAdz
d
E
 2
1
thin-wall closed section
dz
dL
GJ
TL  
dz
d
A
GJ
A
Tq
EE

22

n
J
T
dz
dGn 22  
J
tT
dz
dGt  max

s
s dstyI
Sq
0
.
nnn yAI
Sq 
symmetric, single load
symmetric, single moment
unrestrained torsion
 ts
A
tds
AJ EEclosed
4
4 22



  33
1 33 stdstJopen
tq 
Principal stresses 2
2
max2,1 22 xy
yxyx
avg