AE1002 Lab Report.pdf

A1.4 Instrumented Fuselage And Cylindrical Pressure Vessel

Group AS3-3 1

Contents

1) Introduction 2

2) Objectives 3

3) Theory Of Thin Wall Cylinder 4

4) Experimental Work 7

5) Experimental Procedure 8

� Hydraulics 8 � Software 8

6) Geometry And Material Data 8

7) Results And Discussions 9

• Determine Poisson’s ratio of the cylindrical material. 9

• Determine the inner pressure from the known geometry and 10 strains.

• Relate your data to the design of airplane fuselage. 10

• Explain the effect of the presence of geometrical discontinuities on 13 the resulting stress field.

8) References 15


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A1.4 INSTRUMENTED FUSELAGE AND CYLINDRICAL PRESSURE VESSEL 1. INTRODUCTION

The fuselage is the central portion of the body of an airplane, designed to carry the crew, passengers, and cargo and holds all the parts of the airplanes together. It can be constructed in one of the four ways:

1. Monocoque:

The primary structure is the exterior surface of the fuselage. It is a construction technique that supports structural load by using an object’s external skin. As such it is free from internal bracing. The skin is attached to the bulkheads, and other structural members and carries part of the load. Skin thickness varies with the loads carried and the stresses supported. In recent aircraft structures, such as the Boeing 787 Dreamliner, molded composites are used to make up the monocoque shell.


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2. Semi-monocoque: An aircraft structure in which the outer skin is reinforced by internal structures as the outer skin is insufficient to sustain the primary stresses. This is the preferred method of constructing an all-aluminum fuselage. Firstly, a series of frames shaped as the fuselage cross sections are held in position on a rigid fixture. These frames are then joined with stringers. A sheet of aluminum attached to the structure, usually by riveting. This acts as the outer shell. The fixture is then disassembled and removed from the completed fuselage shell. The outer shell also offers the possibility of pressurizing the internal volume for high-altitude flight. The key advantage of this type of fuselage is that all members of the plane, such as the stringers, and bulkheads, add to the strength and rigidity of the structure. This means that a semi-monocoque fuselage may withstand considerable damage and still holds strong In addition, these members aid in the construction of a streamlined fuselage.

3. Box Truss Structure: The structure has stiff panels in cylindrical arrangements and thus provides high resistance to axial torsion and a higher resistance to buckling in its highly loaded sides. The aerodynamic shape is completed by additional elements called formers and stringers. This technique is most widely used in early aircrafts. In modern aeronautical engineering, this technique is used in lightweight aircrafts.

4. Geodetic construction: In this type of construction multiple flat strip stringers are wound about the formers in opposite spiral directions, forming a basket like appearance.This proved to be light, strong and rigid. This technique was widely used in British warplanes in the World War II. The study of pressure distribution inside a cylinder is not only useful in the field of aircraft fuselage construction, but also in other industrial applications such as the construction of aquatic sportscraft, gun barrals, submarines and pipes carrying fluid at high pressure.

2. OBJECTIVES

• To understand the stress and strain development in a fuselage-like cylindrical structure.


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• To identify the different designs of the fuselage of an aircraft.

• To discuss the effect of the presence of geometrical discontinuities on the stress field.

• To identify the stress field in two-dimensional space and to calculate the stresses in a thin walled cylindrical vessel using simple equilibrium equations.

• To familiarize with functions and practical use of strain gauges in determining the unknown stresses at prescribed conditions in an instrumented thin walled pressure vessel, accounting for both open and closed end conditions.

• To relate the results to the proper design of a fuselage of an aircraft.

3. THEORY OF THIN WALL CYLINDER The stress state in the wall is essentially triaxial and consists of 3 principal components namely:

• Axial stress (longitudinal stress) ��

• Tangential stress (hoop stress) �� • Radial stress ��

http://www.mech.uwa.edu.au/DANotes/cylinders/thin/thin.html

Axial stress

Cylinders are classed as being either :

o open - no axial component of wall stress, or

o closed - an axial stress must be equal to the fluid pressure.

http://www.mech.uwa.edu.au/DANotes/cylinders/thin/thin.html


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A fluid container sealed by a piston (a) is open. For equilibrium of the overall piston-

and-cylinder assembly, external axial force Fa must be equal to the force exerted by the

fluid. Therefore Fa = pi Ai,where Ai is the internal circular area. Hence there is no need

for axial wall stresses to equilibrate the fluid pressure.

Regardless of the Di/t ratio of the cylinder, if an axial stress exist then it is uniform across the cylinder wall. From equilibrium of forces in the axial direction, axial stress can be calculated. Considering the free body diagram of one end of an internally pressurised closed cylinder (b),it is found that the resultant fluid force pi Ai is equal to the wall stress resultant σa Aa ; where the annular wall area is Aa = Ao - Ai in which Ao is the outside circular area. In the more general case where an external fluid pressure also exists:

( i) σa = ( pi Ai - po Ao ) / Aa

σa = ∆p Di / 4 t (CLOSED) or σa = 0 (OPEN)

The axial stress is either zero in the case of open thin cylinders or half the tangential

stress in closed thin cylinders.

Thin cylinders

As the table below show, thin cylinder is defined as cylinder with inner diameter, Di to thickness, t, ratio of more than 20. In thin cylinders, hoop and longitudinal stress are uniform while radial stress is negligible and thus assumed to be zero. The cylinder is hence assumed to be a thin-walled pressure cylinder in our case.

Thin Thick

Limiting proportions

Di/t > 20 Di/t < 20

Analytical treatment

simple approximation

accurate

Stress state membrane – i.e. biaxial

triaxial

Radial Stress zero varies with radius

Tangential Stress uniform varies with radius

Axial Stress uniform uniform


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Consider a cylindrical vessel of inside radius r and wall thickness t containing a fluid under pressure. No shearing stresses are exerted on the element due to the axial symmetry of the vessel and its contents.

http://www.efunda.com/formulae/solid_mechanics/mat_mechanics/pressure_vessel.cfm

For a short section of the cylinder, dx, hoop stress can be calculated as follow:

where,

p is the internal pressure,

r is the inner radius of the cylinder, and

t is the wall thickness of the cylinder.


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http://www.efunda.com/formulae/solid_mechanics/mat_mechanics/pressure_vessel.cfm

For a short section of the cylinder, dx, longitudinal stress can be calculated as follow:

4. EXPERIMENTAL WORK There are various methods to analyze strains and stresses at a point in a member or a structure. Since small stress is hard to measure in this experiment, we measure strain and thereafter calculate the stress. Strain gauge methods use either electrical or mechanical means to measure strains. In these types of strain gauges, electrical resistance strain gauges are the most accurate ones. In our current experiment, electrical strain gauges will be used to determine the inside pressure of a fuselage or a pressure vessel, the principle stresses at a given point on the pressure vessel and the Poisson’s ratio of the vessel material.

where,

p is the internal pressure,

r is the inner radius of the cylinder, and

t is the wall thickness of the cylinder.


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� � ��

where R : the resistance of the wire � : the resistivity of wire material l : the length of wire A: the cross-sectional area of wire As the object expands, the length l of the wire in the foil increases. Since l is proportional to R, hence resistance R increases. The converse holds true.

5. EXPERIMENTAL PROCEDURE Hydraulics 1. Switch the pressure vessel unit on. 2.Start the SM1007 software on the PC and leave for 5 minutes to allow the gauges to stabilize. 3. Check the hydraulics and open the release valve on the pump (anticlockwise) 4. Wind the handwheel in fully. 5. Fully close the release valve on pump. 6. Operate the pump steadily observing the pressure on the gauge. Stop the pressure at 3 MN/m2. Software 1. Select options from the menu. 2. Set the Gauge Factor to the given on the SM1007 front panel. 3. Press Test SM1007 to ensure that the SM1007 is communicating with the PC. 4. Set the type of setting, ie, closed tube/open tube. 5. Reset the gauge by zeroing it. 6. Proceed with the experiment as provided in the manual using Main Page, Menu Bar, and Tool Bar.


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6. GEOMETRY AND MATERIAL DATA

External diameter do = 86m Internal diameter di = 80 mm Aluminium with Modulus of Elasticity E= 69 GPa Poisson’s ratio υ = 0. 7. RESULTS AND DISCUSSIONS

Determine Poisson’s ratio of the cylindrical material.

Reading gauge 1 gauge 6 gauge 2 1 89.4 93 -29.2 2 174 179.2 -59.2 3 266.4 165.8 -91 4 359.2 358 -123.2 5 446.2 447.6 -153 6 538 538 -184.6

Reading 1 Poisson’s ratio = 29.2 / ½ (89.4+93) = 0.320

Reading 2 Poisson’s ratio = 59.2 / ½ (174+179.2) = 0.347

Reading 3 Poisson’s ratio = 91 / ½ (266.4+165.8) = 0.421


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Reading 4 Poisson’s ratio = 123.2 / ½ (359.2+358) = 0.344

Reading 5 Poisson’s ratio = 153 / ½ (446.2+447.6) = 0.342

Reading 6 Poisson’s ratio = 184.6 / ½ (538+538) = 0.343

Ave Poisson’s ratio = 0.320 + 0.347 + 0.421 + 0.344 + 0.342 + 0.343 6 = 0.358 Determine the inner pressure from the known geometry and strains.

tH

Pr=σ

σ = E ε = t

Pr

t = ½ ( do – di) = ½ (86-80) = 3mm r = ½ di = ½ x 80 = 40mm When gauge pressure = 1 MN/m2, ε = 59.2 mm

69 x 109 ( 59.2 x 10-3 ) = p ( 40 x 10-3) / 3 x 10-3

p = 306 MN/m2 Hence, Inner pressure = 305 MN/m2

Relate data to the design of airplane fuselage.

Reading Pressure (MN/m²)

Hoop Stress (MN/m²)

Gauge 1 (10^-6)

Gauge 6 (10^-6)

Avg. Hoop Strain(10^-6)

Calculated Hoop Stress (MN/m²)

Calculated Pressure (MN/m²)

1 0.00 0.00 0.4 0.4 - - -

2 0.49 6.53 89.4 93.0 91.2 6.293 0.472

3 0.95 12.67 174.0 179.2 176.6 12.185 0.914

4 1.47 19.60 266.4 265.8 266.1 18.361 1.377

5 1.98 26.40 359.2 358.0 358.6 24.743 1.856

6 2.46 32.80 446.2 447.6 446.9 30.836 2.313

7 2.96 39.47 538.0 538.0 538.0 37.122 2.784


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0.00

5.00

10.00

15.00

20.00

25.00

30.00

35.00

40.00

45.00

0.49 0.95 1.47 1.98 2.46 2.96

Str

ess

(M

N/m

²)

Pressure (MN/m²)

Open Ends Hoop Stress

Experimental

Theorectical

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

2 3 4 5 6 7

Pre

ssu

re (

MN

/m²)

Reading Number

Open Ends Pressure

Experimental

Theorectical

Reading

Pressure (MN/m²)


Long Stress (MN/m²)

Gauge 1

Gauge 2

Gauge 3

Gauge 4

Gauge 5

Gauge 6

1 0.00 0.00 0.00 0.0 0.0 0.0 0.0 0.0 0.0

2 0.49 6.53 3.27 77.8 10.8 26.2 47.8 68.6 87.2

3 0.97 12.93 6.47 150.0 26.2 57.0 93.6 126.4 158.6

4 1.54 20.53 10.27 232.2 41.8 86.6 135.4 183.2 230.0

5 2.03 27.07 13.53 310.2 57.4 116.8 180.0 243.6 305.0

6 2.54 33.87 16.93 383.8 72.2 146.0 223.4 302.0 378.0

7 3.03 40.40 20.20 458.4 87.4 177.0 269.0 364.0 455.0


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0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

2 3 4 5 6 7

Pre

ssu

re (

MN

/m²)

Reading Number

Closed Ends Pressure

Experimental

Theorectical

0.00

5.00

10.00

15.00

20.00

25.00

30.00

35.00

40.00

45.00

0.49 0.97 1.54 2.03 2.54 3.03

Ho

op

Str

ess

(M

N/m

²)

Pressure (MN/m²)

Closed Ends Hoop Stress

Experime

ntal

Reading

Pressure (MN/m²)


Long Stress (MN/m²)

Gauge 1 (10^-6)

Gauge 6 (10^-6)


Calculated Hoop Stress (MN/m²)

Calculated Pressure (MN/m²)

Calculated Long Stress (MN/m²)

1 0.00 0.00 0.00 0.0 0.0 - - - -

2 0.49 6.53 3.27 77.8 87.2 82.5 5.693 0.427 2.846

3 0.97 12.93 6.47 150.0 158.6 154.3 10.647 0.799 5.323

4 1.54 20.53 10.27 232.2 230.0 231.1 15.946 1.196 7.973 5 2.03 27.07 13.53 310.2 305.0 307.6 21.224 1.592 10.612

6 2.54 33.87 16.93 383.8 378.0 380.9 26.282 1.971 13.141

7 3.03 40.40 20.20 458.4 455.0 456.7 31.512 2.363 15.756


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Reading Pressure (MN/m²)

Gauge 1 (10^-6)

Gauge 6 (10^-6)


Gauge 2 (10^-6)

Poisson's Ratio

1 0.00 0.0 0.0 - - -

2 0.49 77.8 87.2 82.5 10.8 -0.131

3 0.97 150.0 158.6 154.3 26.2 -0.170

4 1.54 232.2 230.0 231.1 41.8 -0.181

5 2.03 310.2 305.0 307.6 57.4 -0.187

6 2.54 383.8 378.0 380.9 72.2 -0.190

7 3.03 458.4 455.0 456.7 87.4 -0.191

Explain the effect of the presence of geometrical discontinuities on the resulting stress

field.

Before we analyse the effect of geometrical discontinuities on a stress field, a stress field can be

viewed using an experimental method called photoelasticity. Photoelasticity is a visual method

for viewing the full field stress distribution in a photoelastic material. When a photoelastic

material is strained and viewed with a polariscope, distinctive coloured fringe patterns are seen.

Interpretation and analysis of the pattern reveals the overall strain distribution. Alternatively,

stress field can also be analysed with the use of electrical strain-gauges. Discontinuity in

geometry has a significant effect on the stress distribution around it. Geometric stress

concentration factors can be used to estimate the stress amplification in the vicinity of a

geometric discontinuity.

When a material is subject to bending or torsion loads, almost all of the stress occurs at the

surface. A hollow tube is nearly as strong as a solid rod of similar size, but the hollow tube is

much lighter in weight. Many aircraft parts are hollow rather than solid in order to save weight.

However, the main disadvantage of a hollow part is that it tends to fail much more suddenly and

catastrophically than a solid part if stressed beyond its elastic limit. This is worsened when there

is presence of geometrical discontinuity in the material such as thin shell, where fatigue cracks

begin and lead to fracture.


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Discontinuities are called stress raisers and areas

where they occur are called stress concentration.

A stress concentration is a location in an object

where stress is concentrated, where the part is

most likely to crack or fracture. An object is

strongest when force is evenly distributed over its

area, so geometric discontinuities results in a

localized increase in the intensity of a stress field.

Examples of geometric discontinuities are: cracks,

sharp corners, holes, threads, scratches, nicks,

pits, notches and, changes in the cross-sectional

area of the object. High local stresses can cause

the object to fail more quickly. Thus a material fails, via a propagating crack, when a

concentrated stress exceeds the material's theoretical cohesive strength. The real fracture

strength of a material is always lower than the theoretical value because most materials contain

small cracks that concentrate stress. Fatigue cracks always start at stress raisers, so removing

such defects increases the fatigue strength. Maximum stress is several times greater than

where there is no geometrical discontinuity.

The presence of notches can display very well the effect of geometrical discontinuity on the

resulting stress field. Considering a piece of bar with uniform diameter, the stress is uniform

throughout the bar when it is under tension. However, if a notch is present in the bar, the cross-

sectional area of the bar is reduce at the site of the notch, thus the stress at the notch will be

higher than the stress experienced in the other parts of the bar. Notch sensitivity of a material is

a measure of how sensitive a material is to notches or geometric discontinuities.

Geometrical discontinuities can lead to

serious or even fatal accidents. Cut-outs in

skins (such as windows), sharp bends and

weld joints are common sites of stress

concentration in a stress field due to

geometrical discontinuity. One such example

is the de Havilland Comet. For the de

Havilland Comet I, the fatigue cracks

propagated from the window corners and the

stress concentration is high due to the

square-like shape, subsequent models of

Comet changed to oval-shaped windows to

reduce the stress concentration near the

window and planes nowadays have windows

with rounded corners. Components that that are formed by stretching, bending and welding

would have high chances with cracks being formed. There will be uneven stress concentration

at the bend as well. Thus, such components are likely to fail along the bend or at the welded

site. The effect of such situation is made detrimental when the components are made to operate

at low temperate where there is a possibility that ductile-brittle transition will occur.


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Most of the time, highly stressed parts are processed to have a smooth surface. This is

because a small and unobvious nick, scratch or pit may act as a stress riser that concentrates

the surface stress enough to cause the part to crack and fracture eventually. Roughness may

be enough to weaken a part significantly. For metals, corrosion can cause a smooth surface to

become rough and cause fatigue crack. This can lead to a detrimental phenomenon called

explosive decompression in many fatal aircraft accidents, due to improper repair of cracks or

failure of adhesive used to bond sheets of metal together in a fuselage.

In an elliptical crack of length 2a, width 2b and radius of curvature ρ of the crack tip, under an

applied external stress σ, the stress at the ends of the major axes is given by:

One method to measure or estimate the degree of adverseness of geometrical discontinuity on

the resulting stress field in a material is to calculate the stress concentration factor. Stress

concentration factor is the ratio of the highest stress to a reference stress of the gross cross-

section. As the radius of curvature approaches zero, the maximum stress approaches infinity.

The stress concentration factor is a function of the geometry of a crack (radius of curvature),

and not of its size. They can be sited in engineering reference materials to predict the stresses

that could not be analyzed using strength of materials approaches.

Thus, a counter method of reducing one of the worst types of stress concentrations, such as a

crack, is to drill a large hole at the end of the crack. The drilled hole, with has a relatively large

diameter, causes a smaller stress concentration than the sharp end of a crack. As the drilled

hole will have a larger radius of curvature than a sharp end, the stress concentration factor will

be lower. However, this is only a temporary solution and must be corrected promptly.

There are two ways to calculate stress concentration factor. One of them is to use finite element

method and the other is theoretical value which can be calculated from the equation above.

There can be a difference with both calculated value. While using a FEM program, the obtained

value is more accurate. This difference may result from the reason that the program is more

sensitive in division of elements. In other words, the difference is probably due to the ability of

element analysis of program.

Through this discussion and experiment, we can also note the importance of stress

consideration in the design of the fuselage. It is also important to systematically check for

possible stress concentrations caused by cracks -- there is a critical crack length for which,

when this value is exceeded, the crack proceeds to definite catastrophic failure. This ultimate

failure is definite since the crack will propagate on its own once the length is greater than the

critical crack length. (There is no additional energy required to increase the crack length so the

crack will continue to enlarge until the material fails.) The origins of the critical crack value can

be understood through Griffith's theory of brittle fracture. Specifically, from this experiment, hoop


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stress is dominant in the fuselage during flight and if a longitudinal crack is ignored, it can cause

the fuselage to crack up during flight.

8. References

1. Aircraft Accident Reconstruction and Litigation (3rd Edition) -- By Barnes Warnock

McCormick, M. P. Papadaki, Published by Lawyers & Judges Publishing Company 2003

2. Behaviour of Skin Fatigue Cracks at the Corners of Windows in a Comet I Fuselage -- By R. J. ATKINSON, W. J. WINKWORTH and G. M. NORRIS, Published by Ministry Of Aviation Aeronautical Research Council Reports and Memoranda

3. http://upload.wikimedia.org/wikipedia/commons/4/4a/Aircraft_fuselage_schematic.JPG 4. http://en.wikipedia.org/wiki/Monocoque 5. http://en.wikipedia.org/wiki/Fuselage 6. http://www.efunda.com/formulae/solid_mechanics/mat_mechanics/pressure_vessel.cfm 7. http://www.mech.uwa.edu.au/DANotes/cylinders/thin/thin.html 8. http://www.avweb.com/news/maint/184271-1.html

9. http://www.tech.plym.ac.uk/sme/interactive_resources/tutorials/FailureCases/images/CM

8ALYU2.jpg

10. http://www3.ntu.edu.sg/mae/Research/programmes/Sensors/sensors/photoelasticity/ 11. Laboratory Manual for Experiment A1.4, School of Mechanical And Aerospace

Engineering , Nanyang Technological University 12. S A Meguid, Fact Sheet on Strain Gauges, 2005. 13. Understanding Aircraft Structures, John Cutler, Collins, 1991.

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