1. Thin-walled structures. Normal stresses
Lecture #5
Thin-walled structures.
Normal stresses

2. FOREWORD
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. 2

3. TYPES OF SHELL 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 case
Hard to realize in practice, but typical for thin shells 3

4. Vertical displacement plot
TYPES OF SHELL
Vertical displacement plot
Not stiffened shell
Stiffened shell 4

5. TYPES OF SHELL Bending stress plot Not stiffened shell Stiffened shell5

6. TRUSS STIFFENING OF THE SKIN
Junkers F.13,
Germany, 1920 6

7. GEODESIC STIFFENING OF THE SKIN AT FUSELAGE
Vickers Wellington, Great Britain, 1938 7

8. THIN-WALLED STRUCTURES (modern design)8

9. THIN-WALLED STRUCTURES (modern design)9

10. STRUCTURAL MEMBERS Longitudinal Lateral Wing
Spar caps, stringers and skin (panel)
Ribs
Fuselage
Stringers and skin (panel), beams
Frames 10

11. HISTORICAL PROGRESS OF AIRCRAFT STRUCTURES
Truss structures, unstressed skin
The skin is not much stressed 11

12. HISTORICAL PROGRESS OF AIRCRAFT STRUCTURES
Monoplanes and corrugated skin introduced
The skin carries only shear stresses
Tupolev TB-3, Soviet Union, 1932
Take-off mass kg, wingspan 39.5 m 12

13. HISTORICAL PROGRESS OF AIRCRAFT STRUCTURES
Aluminium extensively used, stressed skin.
The skin carries both normal and shear stresses
Messerschmitt Bf.109, Germany, 1935
Take-off mass kg,
max. speed 720 km/h 13

14. NORMAL STRESSES IN THIN-WALLED BEAMS
The distribution of normal stresses obeys the hypothesis of planar cross sections:
For the case of uniform linear material, it comes to be: 14

15. CROSS SECTION DISCRETIZATION
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. 15

16. CROSS SECTION DISCRETIZATION
The problem is to find the moment of inertia.
Dimensions:
a = 60 mm; h = 22 mm; d1 = 4 mm; d2 = 6 mm;
H = 120 mm. 16

17. CROSS SECTION DISCRETIZATION
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). 17

18. CROSS SECTION DISCRETIZATION
Another option is to use concentrated areas instead of stiffeners and webs.
Result:
997 cm4
(exact value:
975 cm4;
2.5% error). 18

19. … Internet is boundless …
WHERE TO FIND MORE INFORMATION?
Megson. An Introduction to Aircraft Structural Analysis. 2010
Chapter 15
… Internet is boundless … 19

20. Method of reduction coefficients
TOPIC OF THE NEXT LECTURE
Normal stresses.
Method of reduction coefficients
All materials of our course are available
at department website k102.khai.edu
1. Go to the page “Библиотека”
2. Press “Structural Mechanics (lecturer Vakulenko S.V.)” 20