Lecture #5 Thin-walled structures. Normal stresses.
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Transcript of Lecture #5 Thin-walled structures. Normal stresses.
Lecture #5Thin-walled structures.Normal stresses
FOREWORD
2
Modern aircraft structures are usually thin-walled beams (shell beams).
“Thin-walled” means that one of dimensions (thickness) is much smaller than others. Thus, the middle surface could be specified.
Shells could be stiffened and not stiffened.
Stiffeners are used to:a) support the skin from buckling;b) optimize the stress state.
General shell Membrane shell
The stress state is formed by membrane and bending
stresses
Stresses are uniformly distributed along the
thickness (only membrane stresses)
Less effective Most effective
General caseHard to realize in practice, but typical for thin shells
3
TYPES OF SHELL
TYPES OF SHELL
Vertical displacement plot
4
Stiffened shell
Not stiffened shell
TYPES OF SHELL
Bending stress plot
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Stiffened shell
Not stiffened shell
TRUSS STIFFENING OF THE SKIN
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Junkers F.13,Germany, 1920
GEODESIC STIFFENING OF THE SKIN AT FUSELAGE
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Vickers Wellington, Great Britain, 1938
THIN-WALLED STRUCTURES (modern design)
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THIN-WALLED STRUCTURES (modern design)
9
Longitudinal Lateral
WingSpar caps, stringers
and skin (panel)Ribs
FuselageStringers and skin
(panel), beamsFrames
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STRUCTURAL MEMBERS
HISTORICAL PROGRESS OF AIRCRAFT STRUCTURES
1903-1920. Truss structures, unstressed skin
11
The skin is not much stressed
HISTORICAL PROGRESS OF AIRCRAFT STRUCTURES
1920-1930. Monoplanes and corrugated skin introduced
Tupolev TB-3, Soviet Union, 1932Take-off mass 19 500 kg, wingspan 39.5 m
12
The skin carries only shear stresses
HISTORICAL PROGRESS OF AIRCRAFT STRUCTURES
1930-1940. Aluminium extensively used, stressed skin.
Messerschmitt Bf.109, Germany, 1935Take-off mass 3 375 kg,max. speed 720 km/h
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The skin carries both normal and shear stresses
NORMAL STRESSES IN THIN-WALLED BEAMS
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The distribution of normal stresses obeys the hypothesis of planar cross sections:
,w x y a b x c y
For the case of uniform linear material, it comes to be:
, yz xz
y x
MN Mx y x y
A I I
CROSS SECTION DISCRETIZATION
15
The discretization of real cross section is usually used to possess the calculations of moments of inertia and other geometrical properties:
- small but complex elements like stringers are substituted by point areas;
- skins are substituted by center lines;
- complex center line is substituted by polygonal curve.
CROSS SECTION DISCRETIZATION
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The problem is to find the moment of inertia.Dimensions:a = 60 mm; h = 22 mm; 1 = 4 mm; 2 = 6 mm;H = 120 mm.
CROSS SECTION DISCRETIZATION
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One option is to substitute the real cross section by center lines with appropriate thicknesses.
Result:1000 cm4
(exact value:975 cm4;2.5% error).
CROSS SECTION DISCRETIZATION
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Another option is to use concentrated areas instead of stiffeners and webs.
Result:997 cm4
(exact value:975 cm4;2.5% error).
WHERE TO FIND MORE INFORMATION?
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Megson. An Introduction to Aircraft Structural Analysis. 2010Chapter 15
… Internet is boundless …
TOPIC OF THE NEXT LECTURE
20
Normal stresses.Method of reduction coefficients
All materials of our course are availableat department website k102.khai.edu
1. Go to the page “Библиотека”2. Press “Structural Mechanics (lecturer Vakulenko S.V.)”