DESIGN AND STRESS ANALYSIS OF AIRCRAFT STRUCTURE

7/23/2019 DESIGN AND STRESS ANALYSIS OF AIRCRAFT STRUCTURE

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DESIGN AND STRESS ANALYSIS OF AIRCRAFT STRUCTURE

ESA 421

PREPARED BY

KUGAN MADIWANA

(Matric ID: 115899)


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ESA 421 AEROSPACE STRUCTURAL DESIGN


CONTENTS

1 AIRCRAFT SPECIFICATION................................................................................................... 1

2 WING STRUCTURE................................................................................................................... 2

2.1 WING CONSTRUCTION...................................................................................................... 4

2.2 WING LOADING, SHEAR FORCE & BENDING MOMENT............................................ 4

3 V-N DIAGRAM............................................................................................................................ 5

3.1 MANEUVER ENVELOPE & V-n DIAGRAM..................................................................... 5

4 STRESS ANALYSIS.................................................................................................................... 6

4.1 LIFT DISTRIBUTION........................................................................................................... 6

4.2 WING WEIGHT DISTRIBUTION........................................................................................ 8

4.3 FUEL LOAD.......................................................................................................................... 8

4.4 NET WING LOADING.......................................................................................................... 9

4.5 SHEAR FORCE DIAGRAM................................................................................................ 10

4.6 BENDING MOMENT DIAGRAM...................................................................................... 11

4.7 TORSIONAL MOMENT..................................................................................................... 12

4.7.1 CENTER OF PRESSURE............................................................................................ 13


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APPENDIX A.4NET WING LOADING..................................................................................... 24

APPENDIX A.5SHEAR FORCE................................................................................................. 25

APPENDIX A.6BENDING MOMENT....................................................................................... 26

APPENDIX A.7TORSIONAL MOMENT................................................................................... 27



APPENDIX A.9SHEAR STRESS................................................................................................ 30


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1 AIRCRAFT SPECIFICATION

SPECIFICATIONS 1959 MODEL CESSNA 150

WING SPAN 10 m

HEIGHT (Tip of rudder) 2.59 m

WING AREA 15 m2

LENGTH 7.29 m

DESIGN GROSS WEIGHT (LSA limit) 509 kg

USEFUL LOAD (LSA)

WING LOADING (LSA) 5292.86 Nm-2

DESIGN LOAD FACTOR ( lti t ) 3 7


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2

2 WING STRUCTURE

Figure 1Wing Structure Assembly


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3

Figure 2Wing Skin Assembly


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2.1 WING CONSTRUCTION

The wing structure consists of two long Ibeam web with six ribs and it is strengthen

with upper and lower spar caps. Spar web doublers are used at the root of the wing to increase

the connection strength between the wing and the fuselage. The function of spar is to transmit

bending and torsional load. The spar has to be strong enough in order to work as it functions;

as a result, thicker material is used on spar. The wing is reinforced with skin to support shear

stress and axial bending load. The ribs consist of nose ribs and rear ribs and it acts to maintain

the airfoil shape of the wing. It also increases the skin buckling strength by reducing the loadto smaller sections. Other than that, the ribs carry the bending moment of the spar in spanwise

direction. The direction of load will go from wing skin to wing rib and finally spar.

CESSNA 150 is a small aircraft that only carry two passengers, so the structure of the

aircraft is also not as strong as the big aircraft. For example, the big commercial airliner will

have stronger and more complex structure. It will have stringers to strengthen the structure of

the wings. CESSNA 150 does not have any stringers and its support structure is only dependson the spar and ribs. The strength also the depends on the wing and the rivets that connect the

skin to the skeleton. The rivets even though small is very crucial to spread n reduce and transfer

the shear stress to the wing skeleton.

2.2 WING LOADING, SHEAR FORCE & BENDING MOMENT

A i d lift b f l it t d b tt f Thi


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3 V-N DIAGRAM

V-n diagram represent the flight envelope of a certain aircraft. It is used to refer to the

boundaries of the aircraft loading and flight conditions within which operation of the aircraft

is satisfactory, and beyond which some aspect becomes unacceptable. The load factor is

defined as the ratio between the total external normal forces on the aircraft and its weight. It is

an important parameter in determining the flight envelope of the aircraft. Based on the

specification of CESSNA 150:

Diving Speed, VD = 303 km/h Cruise Speed, V = 202 km/h Ultimate Load Factor = 3.7 g

Cl =+1.2311/0.8938 m = 509 kg

S = 15 m

b = 10 m3.1 MANEUVER ENVELOPE & V-n DIAGRAM

The cruise speed of the aircraft:


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-2.00

-1.50

-1.00

-0.50

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00

L

o

a

d

F

a

c

t

or

Velocity, m/s

V-n Diagram


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Equation of ellipse:

yb/2 + ca = 1 c = 4Sb 1 2yb The elliptical lift distribution for wing can be representing by this equation:

= The taper lift distribution for trapezoidal/ taper wing can be representing by this equation:

Taper ratio = =c/cArea = S/2 = [(

c + c/2] (b/2) = b (1 + )

c/4

Hence,

c =2S/[1 + b]c = c[ 1 + 2yb [ 1]

Th f


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4.2 WING WEIGHT DISTRIBUTION

Wing load is mostly carried by the weight of the wing itself that made up of the wing

structure and load due to fuel. The weight of the wing is calculated by using the assumption

used in Aircraft Performance and Design book by John D. Anderson, which stated that the

weight of the wing is equal to the product of wing planform area (in ft) with constant of 2.5 = .

0.000

200.000

400.000

600.000

800.000

1000.0001200.000

1400.000

1600.000

1800.000

2000.000

0 0 250 50 75 1 1 251 51 75 2 2 252 52 75 3 3 253 53 75 4 4 254 54 75 5 5 25

DistributedLoad,N/m

Wing Loading ApproximationStructure


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Figure 6 Fuel weight distribution across the half span.

4.4 NET WING LOADING

Net wing loading is calculated by summing up the loads that acts on the wing which are;

0.000

200.000

400.000

600.000

800.000

1000.000

1200.000

1400.000

1600.000

1800.000

2000.000

0 0.250.50.75 1 1.251.51.75 2 2.252.52.75 3 3.253.53.75 4 4.254.54.75 5 5.25

Distribu

tedLoad,N/m

Half Span Location,m

Wing Loading ApproximationFuel


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Figure 7Net wing loading across half span.

0.000

1000.000

2000.000

3000.000

4000.000

5000.000

6000.000

0 1 2 3 4 5 6

DistributedLo

ad,N/m


Overall Wing LoadingNet Loading Wing Structure Fuel Shrenk Approximation


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-14000

-12000

-10000

-8000

-6000

-4000

-2000

0

0 1 2 3 4 5 6

ShearForceofWing,N


Shear ForceHalf Wing's Weight


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Figure 9 Bending moment diagram across half span.

0

5000

10000

15000

20000

25000

30000

35000

0 1 2 3 4 5 6

Moment

,Nm


Bending Moment DiagramHalf Wing's Weight


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4.7.1 CENTER OF PRESSURE

Location of center of pressure (C.P) with respect to wing chord:

= The aerodynamic properties of the airfoil are as follow:

Lift coefficient = 0.41

Moment coefficient = 0.062

4.7.2 CENTER OF GRAVITY

The location of center of gravity:

For rectangular wing,

x = 0.420.45cTherefore, estimate: =.4.7.3 TORSIONAL MOMENT DIAGRAM


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Figure 11 Wing torsional moment diagram across half span

4.8 IDEALIZATION OF WING CROSSSECTION

Th i f h i i d f ki b d Th ki h l

0

5000

10000

15000

20000

25000

30000

0 1 2 3 4 5 6

TorsionalMo

ment(Nm)

Half-Wing Span (m)

Torsional Moment Diagram


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Figure 12 Spar cap and spar web location

Area of spar cap = 350 mSkin thickness =0.002 mSpar web thickness =0.003 mWing area idealizes formula:

-0.1

-0.05

0

0.05

0.1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

NACA 0018

a

t

a

h2a a

h2A = ht2


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y =2432336.3677679.143014 =316.75 mm

z = 07679.143014 = 0 mmNormal stress on each boom

=

( + ) + ( + )

Bending moment is important in determining normal stress. Maximum bending moment is

taken at wing root, as it will experience the most bending moment. There is no moment act at

z-axis.

M = 28981.95953 NmM = 0 NmSince there is no external, force that act normal to the cross section. Therefore, no external

stress contributes to the normal stress.

P = 0 NTherefore, maximum stress is at boom 4 & 9, which is


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Figure 16Buckling coefficients for flat plates in compression

Therefore,


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From shear diagram, maximum shear force act at root:

V = 13041 NV = 0 N = ( ) + ( )

Simplify the equation:

q = (VI)Q + VIQIYI I Compatibility equation:

= = = 0

Therefore,


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Figure 18Shear buckling coefficient for flat plates.

Therefore,

= 5.32 10Pax 1.5 = Pa

Hence, by comparison,


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REFERENCES

[1]Alumium 7075-T6. (n.d.). Retrieved from ASM Aerospace Specification Metals Inc.:

http://asm.matweb.com/search/SpecificMaterial.asp?bassnum=MA7075T6

[2] John D. Anderson, J. (1999).Aircraft Performance and Design.McGraw-Hill.

[3] Megson, T. (2007). Thin Plates. In T. Megson,Aircraft Structures for Engineering

Students(4th ed.). Oxford, United Kingdom: Elsevier.

[4] Sadraey, M. (2009). V-n Diagram. In D. Muller,Aircraft Performance Analysis.


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APPENDICES

APPENDIX AEXCEL DATA

APPENDIX A.1LIFT DISTRIBUTION

Half Span

Position,x

(m)

Wy, Elliptical

(N/m)

Wy, Trapezoidal

(N/m)

Shrenk's

Approximation

(N/m)

0 5721.889 4493.961 5107.925

0.25 5714.732 4493.961 5104.347

0.5 5693.208 4493.961 5093.584

0.75 5657.151 4493.961 5075.556

1 5606.283 4493.961 5050.122

1.25 5540.195 4493.961 5017.078

1.5 5458.334 4493.961 4976.148

1.75 5359.978 4493.961 4926.969

2 5244.198 4493.961 4869.079

2.25 5109.810 4493.961 4801.886


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APPENDIX A.2WING WEIGHT DISTRIBUTION

Half Span Position,x

(m)

Wing area / Segment

(m2)

Distributed load, q-L

(N/m)

0 0.375 1797.584

0.25 0.375 1797.584

0.5 0.375 1797.584

0.75 0.375 1797.584

1 0.375 1797.584

1.25 0.375 1797.584

1.5 0.375 1797.584

1.75 0.375 1797.584

2 0.375 1797.584


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APPENDIX A.3FUEL WEIGHT DISTRIBUTION


(m)

Fuel Tank Chord Length

(m)

Distributed Load,

(N/m)

0 0.555 196.276

0.25 0.555 196.276

0.5 0.555 196.276

0.75 0.555 196.276

1 0.555 196.276

1.25 0.555 196.276

1.5 0 0

1.75 0 0

2 0 0


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APPENDIX A.4NET WING LOADING


(m)

Net Loading / Span

(N/m)

0 3114.065

0.25 3110.486083

0.5 3099.723837

0.75 3081.695767

1 3056.261686

1.25 3023.217604

1.5 3178.563144

1.75 3129.384935

2 3071.494981


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APPENDIX A.5SHEAR FORCE


(m)

Shear force, V

(N)

0 -13165.05617

0.25 -12386.98735

0.5 -11610.71111

0.75 -10838.03366

1 -10070.78898

1.25 -9310.854067

1.5 -8535.631473

1.75 -7747.137963

2 -6972.027974


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APPENDIX A.6BENDING MOMENT


(m)

Bending Moment, My

(Nm)

0 29068.08952

0.25 25874.08407

0.5 22874.37177

0.75 20068.27867

1 17454.67584

1.25 15031.97046

1.5 12801.15977

1.75 10765.81359

2 8925.917847


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27

APPENDIX A.7TORSIONAL MOMENT

Half Span

Position,x

(m)

Wing Chord

Length

(m)

Xcg

(m)

Xcp

(m)

Xf

(m)mz (N) delta mz (N)

Mz

(Nm)

0 1.5 0.3750 0.6450 0.7500 3075.663786 14064.60109

0.25 1.5 0.3750 0.6450 0.7500 3074.321879 768.7482082 14833.3493

0.5 1.5 0.3750 0.6450 0.7500 3070.286037 768.0759896 15601.42529

0.75 1.5 0.3750 0.6450 0.7500 3063.525511 766.7264435 16368.15173

1 1.5 0.3750 0.6450 0.7500 3053.98773 764.6891552 17132.84089

1.25 1.5 0.3750 0.6450 0.7500 3041.5962 761.9479913 17894.78888

1.5 1.5 0.3750 0.6450 0.7500 3026.247267 758.4804334 18653.26931

1.75 1.5 0.3750 0.6450 0.7500 3007.805439 754.2565882 19407.5259

2 1.5 0.3750 0.6450 0.7500 2986.096706 749.237768 20156.76367

2.25 1.5 0.3750 0.6450 0.7500 2960.899026 743.3744665 20900.13813

2.5 1.5 0.3750 0.6450 0.7500 2931.928583 736.6034512 21636.74158

2.75 1.5 0.3750 0.6450 0.7500 2898.8195 728.8435104 22365.58509

3 1.5 0.3750 0.6450 0.7500 2861.092954 719.9890568 23085.57415

3.25 1.5 0.3750 0.6450 0.7500 2818.108202 709.9001445 23795.4743

3.5 1.5 0.3750 0.6450 0.7500 2768.980746 698.3861185 24493.86041

3.75 1.5 0.3750 0.6450 0.7500 2712.435951 685.1770871 25179.0375

4 1.5 0.3750 0.6450 0.7500 2646.522122 669.8697591 25848.90726

4.25 1.5 0.3750 0.6450 0.7500 2567.970624 651.8115932 26500.71885

4.5 1.5 0.3750 0.6450 0.7500 2470.455912 629.803317 27130.52217

4.75 1.5 0.3750 0.6450 0.7500 2337.80823 601.0330178 27731.55519

5 1.5 0.3750 0.6450 0.7500 843.3676875 397.6469897 28129.20218


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28


Boom

Area

Idealized(m2)

y'

(mm)

z'

(mm)

Ay'

(mm3)

Az'

(mm3)

y = y'-ybar

(mm)

z = z'-zbar

(mm)

Iz = Ay^2

(mm4)

1 522.4573404 24.472 32.367 12785.57603 16910.37674 -292.2738091 32.367 44630385.12

2 536.9283483 95.492 57.561 51272.36184 30906.13266 -221.2538091 57.561 26284386.61

3 817.4053975 206.107 72.143 168472.9743 58970.0776 -110.6388091 72.143 10005815.39

4 644.1347871 345.492 74.468 222543.4159 47967.42933 28.74619091 74.468 532276.5892

5 659.9675156 500 66.175 329983.7578 43673.35035 183.2541909 66.175 22163094.11

6 658.6781181 654.508 51.147 431110.0977 33689.40971 337.7621909 51.147 75144171.78

7 658.6781181 654.508 -51.147 431110.0977 -33689.40971 337.7621909 -51.147 75144171.78

8 659.9675156 500 -66.175 329983.7578 -43673.35035 183.2541909 -66.175 22163094.11

9 644.1347871 345.492 -74.468 222543.4159 -47967.42933 28.74619091 -74.468 532276.5892

10 817.4053975 206.107 -72.143 168472.9743 -58970.0776 -110.6388091 -72.143 10005815.39

11 536.9283483 95.492 -57.561 51272.36184 -30906.13266 -221.2538091 -57.561 26284386.61

12 522.4573404 24.472 -32.367 12785.57603 -16910.37674 -292.2738091 -32.367 44630385.12

SUM 7679.143014 2432336.367 0 357520259.2


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29


Part 1z

Part 2z

z(kg.mm-1.s-2)

z

(kg.m-1.s-2)

(Pa)

31.8589024 0 31.8589024 31858.9024

56.65740665 0 56.65740665 56657.40665

71.01049822 0 71.01049822 71010.49822

73.29900033 0 73.29900033 73299.00033

65.13618396 0 65.13618396 65136.18396

50.34409371 0 50.34409371 50344.09371

-50.34409371 0 -50.34409371 -50344.09371

-65.13618396 0 -65.13618396 -65136.18396

-73.29900033 0 -73.29900033 -73299.00033

-71.01049822 0 -71.01049822 -71010.49822

-56.65740665 0 -56.65740665 -56657.40665

-31.8589024 0 -31.8589024 -31858.9024


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30

APPENDIX A.9SHEAR STRESS

Boom delta_s delta_s/Gt delta_qs' qs' c11 c12 c22 c11q's c12q's c22q's

1 64.734 0.00080216 0.0000 0.0000 0.0008 - - 0.0000 - -

2 75.356 0.00140068 -7.5386 -7.5386 0.0014 - - -0.0106 - -

3 111.572 0.00207383 -13.7778 -21.3163 0.0021 - - -0.0442 - -

4 139.404 0.00259116 -26.2885 -47.6049 - - 0.0026 - - -0.1234

5 154.730 0.00287603 -21.3836 -68.9885 - - 0.0029 - - -0.1984

6 155.237 0.00288545 -19.4693 -88.4578 - - 0.0029 - - -0.2552

7 102.294 0.00126758 -15.0185-

103.4764- - 0.0013 - - -0.1312

8 155.237 0.00288545 15.0185 -88.4578 - - 0.0029 - - -0.2552

9 154.730 0.00287603 19.4693 -68.9885 - - 0.0029 - - -0.1984

10 139.404 0.00259116 21.3836 -47.6049 - - 0.0026 - - -0.1234

11 111.572 0.00207383 26.2885 -21.3163 0.0021 - - -0.0442 - -

12 75.356 0.00140068 13.7778 -7.5386 0.0014 - - -0.0106 - -

- 144.286 0.00178793 0.0000 0.0000 0.0018 0.0018 0.0018 0.0000 0.0000 0.0000

DESIGN AND STRESS ANALYSIS OF AIRCRAFT STRUCTURE

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